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Induction on Identity

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Induction on Identity (1991 – Objectivity V1N2, V1N3)

“Existence is Identity, Consciousness is Identification. . . . Logic is the art of non-contradictory identification” (Rand 1957, 1016). I think this view is correct, fresh, and important.

“He whose subject is existing things qua existing must be able to state the most certain principle of all things. This is the philosopher, and the most certain principle of all is that regarding which it is impossible to be mistaken. . . . Which principle this is, let us proceed to say. It is that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect” (Metaph. 1005b8–20) There are no contradictions in reality.* [1] Contradiction is the fundamental indicator of discordance with reality.[2] Contradiction is the fundamental fallacy of deductive inference.

Non-contradiction is the fundamental rule of valid deductive inference because identity is the fundamental law of reality.[3] The law of identity is commonly stated as “A is A” or “a thing is itself.”* An existent is itself and not something else. Then an inference that something both is a certain thing and not a certain thing is faulty. A thing cannot both be and not be a certain thing. The ground of non-contradiction, the ground of validity in deductive inference, is the law of identity.

In moving from identity to non-contradiction, we move from “a thing is itself” to “a thing is itself and not something else.” This maneuver draws to the fore our knowledge that any thing is a certain, specific thing. A thing is something. A thing is what it is. “To exist is to be something. . . . It is to be an entity of a specific nature made of specific attributes” (Rand 1957, 1016). This is the law of identity come of age.

Gottfried Wilhelm von Leibniz was cognizant of the intimate connection between the principle of (non-)contradiction and the principle of identity. (Nicolaus of Autrecourt cognized much of the connection already in the fourteenth century; see Weinberg 1969, 9–30.) “The first of the truths of reason is the principle of contradiction or, what comes to the same thing, that of identity” (Leibniz 1969, 385). By truths of reason he meant necessary propositions, and by necessary propositions he meant propositions whose contradictories cannot be true. By truth he meant correspondence of a proposition with reality, possible or actual (Leibniz 1981; see also Rescher 1979, 130–34).

Primitive truths of reason, Leibniz called identicals. Among affirmative identicals are “the equilateral rectangle is a rectangle” and “A is A” and “each thing is what it is” and “at any given time a thing is as it is.” As negative identicals, we have “what is A cannot be non-A.” There are also negative identicals that are called disparates. An example would be “warmth is not the same thing as color” (Leibniz 1981, 4.2.361–63; 1966, 306).

The principle of non-contradiction (or identity), according to Leibniz, tells us only what is possible, not what is actual. Its truth is founded in the essence of things. It is an innate truth, and it applies to ideas that are innate (such as geometrical ideas), which is to say, ideas not derived from the senses, but ideas found ready in the mind. The principle of non-contradiction also applies to sensible truths, as when we say “sweet is not bitter.” The actual is among the possible, and Leibniz might admit that the principle of non-contradiction has application to sensible truths without going on to sink the principle into the bedrock of the actual.

As Leibniz saw it, truths of reason and their necessities do come from outside us “since all that we do consists in recognizing them, in spite of ourselves and in a constant manner.” To demonstrate the existence of these necessities,

I have taken for granted that we thing and that we have sensations. So there are two absolute general truths: truths that is, which tell of the actual existence of things. One is that we think; the other, that there is a great variety in our thoughts. From the former it follows that we are; from the latter, that there is something other than us, that is to say, something other than that which thinks, which is the cause of the great variety of our experiences. Now the one of these is just as incontestable and as independent as the other . . . . (1966, 307)

In contrast to truths of reason, in Leibniz’s analysis, are truths of fact. Truths of fact are known by observation and induction, not by deduction. Their truth “is founded not in the essence (of things) but in their existence; and they are true as though by chance” (Leibniz 1963, 274). Truths of existence are contingent. Truths of existence are true. They have hypothetical and physical necessity, if not absolute and logical necessity (Mates 1986, 116–19; Ishiguro 1982; Wilson 1976). But denial of existential truths does not result in contradiction, at least not in the finite mind of man. Really?

Existence is Identity. I think—and have thought since discovering Rand’s thought—that the law of identity is the ground of inductive inference as well as deductive inference. Here, then, is induction grounded on identity.

Continued below—

Varieties of Induction

Ockham – Contingency

Nicolaus – Experience of Substance

Nicolaus – Reasoning to Substance

Hume – Experience of Cause and Effect

Hume – Reasoning to Cause or Effect

Hume – Necessity

Hume – Uniformity

Existence is Identity

References

Aristotle 1941 [c. 348–322 B.C.]. The Basic Works of Aristotle. R. McKeon, editor. New York: Random House.

Ishiguro, H. 1982. Leibniz on Hypothetical Truths. In Leibniz: Critical and Interpretive Essays, M. Hooker, editor. Minneapolis: University of Minnesota Press.

Leibniz, G. W. 1963 [1666]. Dissertation on the Art of Combinations. Quoted in Copleston, F. 1963. A History of Philosophy, volume 4. Garden City, NY: Image Books.

——. 1966 [1675]. Letter to Simon Foucher. In The Philosophy of the 16th and 17th Centuries, R. H. Popkind,s editor. New York: The Free Press.

——. 1969 [1692]. Critical Thoughts on the General Part of the Principles of Descartes. In G. W. Leibniz: Philosophical Papers and Letters, 2nd ed., L.E. Loemker, translator. Dordrecht: Kluwer Academic Publishers.

——.1981 [1704]. New Essays on Human Understanding. P. Remnant and J. Bennett, translators. Cambridge: Cambridge University Press.

Mates, B. 1986. The Philosophy of Leibniz: Metaphysics and Language. New York: Oxford University Press.

Rand, A. 1957. Atlas Shrugged. New York: Random House.

Rescher, N. 1979. Leibniz: An Introduction to His Philosophy. Totowa, NJ: Rowman and Littlefield.

Weinberg, J. R. 1969 [1948]. Nicolaus of Autrecourt. New York: Greenwood Press.

Wilson, M. D. 1976 [1972]. On Leibniz’s Explication of “Necessary Truth.” Reprinted in Leibniz: A Collection of Critical Essays, H. G. Frankfurt, editor. South Bend: University of Notre Dame Press.

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This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.

~~~~~~~~~~~~~~~~

Notes

1. “Logic rests on the axiom that existence exists” (Rand 1957, 1016).

2. The definite article may be inappropriate. It remains an open question whether Rand’s exclusions by non-contradiction (a, b, c) rely just as well on alternative denial as on non-contradiction. Both are norms from the fact of identity (and the need of consciousness for reality).

3. See also Peikoff 1991, 118–19.

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Predications are conceptual identifications. Edward Zalta takes the discipline of logic to be “the study of the forms and consequences of predication” (2004, ch. 23). That conception of logic fits well with Rand’s conception of logic as “the art of non-contradictory identification.”

The final section of my 1991 essay outlined a theory of predication based on the fundamental proposition Existence is Identity. This essay was written before I came to my “With Measurement” Program.* One of my waiting tasks is to provide the measurement rendition of predication theory (a, b) under Rand’s metaphysics and theory of concepts and under my extensions of both by contemporary measurement theory.* I plan to fulfill that task later on in this thread. (I would again like to thank Michael and Kat for making this forum and my Corner possible.)

In the course of my further developments of the original essay “Induction on Identity,” I will, in this thread, discuss and incorporate the recent work on induction by David Harriman and Leonard Peikoff (a, b, c, d; Peikoff 1985 [V59N2]).

Edited by Stephen Boydstun

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Stephen,

Thanks for posting this. I was reminded how exact and how spare Rand's metaphysics is. Identity is the cornerstone of metaphysics. Rand's use of the word art when talking about logic struck me as interesting, suggesting a wide flexibility in method as long as identification and noncontradiction are part of the process. I read your other essay and was particularly struck by the Aristotelian conception of causality. The inclusion of attributes and relations as well as entities and actions was a reminder to me that relations among attributes, entities and actions fills out a broader conception of causality than I had remembered.

I look forward to your thoughts on Harriman's book.

Jim

Edited by James Heaps-Nelson

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Thanks for the encouragement, Jim.

~~~~~~~~~~~~~~~~

—Varieties of Induction

In valid deductions, premises provide absolutely conclusive reasons for conclusions drawn from them. Conclusions deduced validly are contained implicitly in the premises. To suppose premises true and a conclusion validly deduced from them false would itself entangle one in a contradiction. The necessity with which the valid deduction follows is just the force of the impossibility of contradictions in reality.

In the Topics, Aristotle speaks of induction as “a passage from individuals to universals” (TP 105a12). Such an induction proceeds “from the known to the unknown” (156a5). Such an induction “extends our knowledge beyond information contained in the premises” (Kelley 1988, 167). Induction in this sense is traditionally called incomplete or problematic induction. It is better called ampliative induction, to signify simply that the conclusions go beyond the premises (Wright 1979, 8–9).

In the Posterior Analytics, Aristotle speaks of induction as “exhibiting the universal as implicit in the clearly known particular” (APo 71a8). In this sense, induction is termed abstractive or intuitive. The abstractive is surely close to the sense of induction to which Rand refers in saying that “the process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction” (1990, 28). I have only a little to say distinctively about this type of induction, so I shall say it right now and shall not again take up abstractive induction in later sections.

Our concepts are abstracted from the experiences we have had and the concepts we have previously formed. One desideratum for our concepts is that they effect economies in our ways of thinking about past experience and the nature of the world. That is why concepts have intensions and why they are organized hierarchically. Another desideratum is that the concepts we form be ones productive of good ampliative inductions in the future.

But in what sense is the process of abstraction itself an induction? Looking at abstraction rather formally, there is induction in moving from “this item is an x and that item is an x” to “all such items are x’s.” The reliance here on identity is obvious: “such items” are identical items within the bounds of what it takes to be an x. From this formal perspective, abstractive induction seems akin to recursive, or mathematical, induction (which will be discussed later in this essay).

In actual abstractions, of course, the x gets filled in with something definite: “This is hue, that is hue, . . . all such qualities are hue. This is an inertial force, . . . all such forces are inertial. This is a billiard ball, . . . all such things are billiard balls.” Where “all such” is purely hypothetical, we have still only the recursive induction we had when x was left unspecified. Where the “all such” is meant to say “all such (and there have been, are, or will be specific such that we have not examined),” then it seems we are back to ampliative induction. In judging that two items are of a single kind, we may also rely on induction where we have not examined all characteristics relevant to the classification. This, too, is ampliative induction. I am inclined to think that induction commonly denominated abstractive is an amalgam of straight ampliative inductions and a recursive induction akin to mathematical induction.

Ampliative inductions are not absolutely conclusive.[4] By this common saying, we mean not that they are always rationally uncertain, but that taking the starting points of these inductions to be true and the inductions false would not itself entangle one in a contradiction.

We typically think, with Aristotle, that ampliative induction carries one from a certain number of examined cases to an indefinitely large number of unexamined cases. That is, we typically think of ampliative inductions as establishing generalizations, whether from everyday experience for practical conduct or from systematic observation and controlled experimentation for scientific theory. Ampliative induction, however, may instead carry us from a certain number of examined cases to the next case which turns up. This is commonly termed eduction. It is inductive inference from particulars to particulars. Like generalizing induction, eduction proceeds from the known to the unknown.

We routinely make inferences from particulars to particulars, without explicit generalization. Such inferences are also made by animals incapable of generalization. “Animals have, on the one hand, certain congenital propensities, and on the other hand, an aptitude for the acquisition of habits. Both of these, in a species which succeeds in surviving, must have a certain conformity with the facts of the environment” (Russell 1948, 429). Even if an animal cannot generalize explicitly, we might think of its behavior as guided by implicit generalizations, such as fire burns. The child, too, “knows from memory that he has been burnt, and on this evidence believes, when he sees a candle, that if he puts his finger into the flame of it, he will be burnt again. He believes this in every case which happens to arise; but without looking, in each instance, beyond the preset case. He is not generalizing; he is inferring a particular from particulars” (Mill 1973, 2.3.3).

Eduction goes far back with us; not only to the toddler stage, but to infancy. Jean Piaget (1954) concluded from his investigations that infants first acquire a notion of enduring objects at nine months of age. Until then, if a toy attractive to the infant were covered with a cloth, the infant would make no attempt to lift the cloth and grasp the toy, even though she were capable (after the fifth month) of performing each of these actions. Piaget concluded that, until the ninth month, the infant does not regard the toy as an enduring entity that continues to exist while not in view; only after the ninth month does the infant begin to infer the continued existence of objects.

Piaget’s conclusion was consistent with his view, and that of traditional empiricists (e.g. Helmholtz 1885), that comprehension of a world extending beyond immediate sensory experience is the product of a long process of visual and manual exploration. From the fifth month to sometime in the second year, the infant attempts to manipulate what she sees and to see what she manipulates. These explorations were thought to lead to elementary comprehension of an objective enduring world.

Piaget’s observations have been reconfirmed many times, but Piaget’s interpretation is now widely questioned. Infants younger than nine months may fail to lift the cover and grasp the toy not because by lack a notion of enduring objects, but because they are not yet able to coordinate such a means-ends sequence (Baillargéon 1986, 38–39). It is likely that this inability is due to immaturity of the frontal cortex (Diamond 1989). Recent experiments, not demanding coordination of means-ends-sequences, indicate that infants as young as six months (Baillargéon 1986), even four months (Baillargéon 1987), understand not only that objects continue to exist when not seen, but that moving objects continue along trajectories when not seen and that those trajectories could not be through other solid objects. Perhaps this is the most primitive form in which we grasp the principle of non-contradiction (see also Peikoff 1985).

Infants four months old can determine whether two objects (rings) are connected by a solid (but occluded) link through bimanual grasping and displacement of the two objects They can discriminate visually (without touching) which of two assemblies, linked rigidly or elastically, they previously explored haptically. Object perception, even in the earliest phases of our development, seems to be mediated by relatively central mechanisms; haptic and visual discriminations are coordinated even before the onset of active manual-visual explorations (Streri and Spelke 1988; Spelke 1989). Notice, “counter to the views of Quine (1960) and others, that the organization of the world into objects precedes the development of language and thus does not depend upon it. I suspect, moreover, that language plays no important role in the spontaneous elaboration of physical knowledge” (Spelke 1989, 181).

We come to language and explicit generalization (Macnamara 1986, 114–17, 163–70). John Stuart Mill argues persuasively that general propositions such as all men are mortal are a record of our past inferences from particulars to particulars.

All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more: The major premise of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premise, being the particular facts from which the general proposition was collected by induction. (Mill 1973, 2.3.4; cf. Russell 1948, 431–32)

This does not mean that generalizations and syllogistic reasoning are useless. With registration of experience in the form of general propositions,

the particulars of our experiments may then be dismissed from the memory, in which it would be impossible to retain so great a multitude of details; while the knowledge which those details afforded for future use, and which would otherwise be lost as soon as the observations were forgotten, or as their record became too bulky for reference, is retained in a commodious and immediately available shape by means of general language. (Mill 1973, 2.3.5)

Another reason Mill gives for generalizing rather than inferring directly from particulars is subjection of our near-term expectations, hopes, and fears to objectivity. Rather than simply pronouncing on the next case, we should try to generalize; reluctance to do so indicates infirmity in the grounds of our eduction. This seems a valid psychological point, but Mill goes too far, saying, “whenever, from a set of particular cases, we can legitimately draw any inference, we may legitimately make our inference a general one” (ibid.). Such a principle is not applicable to time-dependent processes. Most of us are justified in believing we shall be alive a month from now, but none of us would be justified in believing we shall be alive always. Again, we are justified in believing the earth will orbit the sun once more, but not justified in believing this will continue forever.

Ampliative induction of the generalizing sort has received the most attention from philosophers, and it will be receiving most of our attention in this essay. The ways in which this sort of induction is grounded on identity will be our chief concern. We shall be aiming at the fully human modes of induction.

Man’s knowledge differs from that of the beasts: beasts are sheer empirics and are guided entirely by instances. . . . Beasts, so far as one can judge, never manage to form necessary propositions, since the faculty by which they make sequences is something lower than the reason which is in man. The sequences of beasts are just like those of simple empirics who maintain that what has happened once will happen again in a case which is similar in the respects that they are impressed by, although that does not enable them to judge whether the same reasons are at work. That is what makes it so easy for men to ensnare beasts, and so easy for empirics to make mistakes. (Leibniz 1981, 4.1.50)

I shall also be proposing a distinct ground, again on identity, for mathematical induction. Recall the principle of mathematical induction (Cuillari 1989, 41–45; Hamilton and Landin 1961, 78–99, 115–16). A statement, P(n), to be proved for integers n > t, where t is a fixed positive integer, is true, provided:

(i) P(t) is true, and

(ii) If P(t), P(t+1), . . . P(n) are true, then P(n+1) is true.

First verify (i), that P(n) is true for n = t. Then try to show that assuming the antecedent of (ii) to be true implies that the consequent of (ii) is also true.

Unlike ampliative induction, mathematical induction is absolutely conclusive. The conclusion of an argument by way of mathematical induction is implicitly contained in the premises. Mathematical induction is, overall, a deductive argument. The inductive character of (ii) is a peculiarity of the serial order property of the infinite set of natural numbers.

The challenge to ground mathematical induction is the challenge to ground, in the world or perhaps in the operation of the mind, denumerable infinite sets (on Gottlob Frege and Richard Dedekind, see Kneale and Kneale 1984, 467–71, 492–93; see also Poincaré 1983, 398–402; Hilbert 1983, 191–94; and Gödel 1983, 463,–64). One of Frege’s objections to Mill’s proposal to ground arithmetic in empirical reality was that this would jeopardize the existence of the infinite set of natural numbers, to which there might be no corresponding empirical collection. (Saying that the set of naturals is just counting “1,2,3, and so forth forever” will not do. Where in empirical reality is the basis for such infinite counts?) [5]

It might be thought that the ground of such sets and mathematical induction would be at hand once we have firm ground for abstractive induction, particularly in its recursive aspect. In other words, it might be thought we have the objective basis of denumerable infinite sets once we have a theory of universals that bases them in objective reality. Let us sort this out in some detail.

There are overlaps, but also disjunctions between the problem of grounding (denumerable) infinities and the traditional problem of universals. Recall the latter problem: the world is made up of only particular, individual things. (This idea won overwhelming acceptance among the philosophically minded, which it enjoys to this day, between the times of Abelard [1079–1142] and Ockham [1290–1349].) Yet thoughts about the world are largely in terms of universal ideas, or concepts. The challenge, then, is to discover how we form our universal ideas from experience of only particulars and, so, to spell out the relationship of concepts to the particulars belonging under them. In taking on this challenge, philosophers really are taking on not much less than the issue of the relationship between thought and reality.

It will be useful to make the common distinction between the extension and the intension of a concept. The extension consists of just those individuals the concept refers to, and the intension is a criterion, possibly complex, by which just those individuals might be grouped together.

The extensions of concepts are always denumerable: “Here is one spoon, there is another; here is one lake, there is another; one sister lives here, another lives there; one performance will be this week, another, next.” The extensions of concepts are (aside from concepts of pure numbers detached from particular physical application) indefinitely large but may be finite or infinite. Is the number of spoons that ever will exist finite or infinite? We do not know, and we do not need to know in order to have a perfectly good concept of spoons. It might have seemed at first blush that we use infinite sets whenever we use universals, but that is incorrect (even when individuals in the extension are infinitely decomposable). The problem of universals can be solved without the problem of denumerable infinities being solved therewith. [6]

Let us probe a little further, just to be sure. When using a concept, one treats particular instances as instances of the items falling under the concept. Rand emphasized that in doing this one regards the particular item as a unit among other units (the other items) falling under the concept. This is the same as regarding a member of a set as a member (see further Armstrong 1989, 133–35) except that the criteria by which one selects the members of a set may be purely arbitrary whereas the criteria by which one selects which particulars should be united in a single concept must be natural and useful.

Intensions of concepts and rules specifying the members of sets are both rules of selection. In both cases, listing of included individuals can be supplanted by the selection rule. In both cases, the selection rules unify the individual items and, for large collections, effect economies in thinking. Both in our referring to extensions of concepts by their selection rules and in our referring to memberships of sets by their selection rules, we step back from the itemizing mode of reference and adopt a more global and abstract mode of reference. The selection rules for sets, though, may well be recursively generative of the sets (Hamilton and Landin 1961, 120–28); the sets may be nothing but what (items grouped in thought) would result from repeated application of their definitions (see also Boolos 1983). Such a set could be denumerably infinite. However, in referring to such a set by its definition (or its name) we do not generate the infinite set. The idea of infinite collections cannot receive its grounding simply from the act of abstraction itself, not even from the act of abstraction on a purely generative set.

Before ending this short tour through the garden of induction, we should settle whether abstractive inductions in their recursive mode are absolutely conclusive. In their ampliative mode, of course, they are not.[4] In their recursive mode, they are. If I say “this is a robin, that is a robin, . . . but not all things (just) like these (in the requisite ways) are robins,” then I contradict myself within that very saying. (On perceptual judgments generally, see Kelley 1986, 208–28.)

Continued below—

Ockham – Contingency

Nicolaus – Experience of Substance

Nicolaus – Reasoning to Substance

Hume – Experience of Cause and Effect

Hume – Reasoning to Cause or Effect

Hume – Necessity

Hume – Uniformity

Existence is Identity

References

Aristotle 1960 [c. 348–322 B.C.]. Aristotle Organon. E. S. Forster, translator. The Loeb Classical Library. Cambridge, MA: Harvard University Press.

Armstrong, D. M. 1989. A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press.

Baillargéon, R. 1986. Representing the Existence and the Location of Hidden Objects: Object Permanence in 6- and 8-Month-Old Infants. Cognition 23:21–41.

——. 1987. Object Permanence in 3.5- and 4.5-Month-Old Infants. Developmental Psychology 23:655–64.

Benacerraf, P., and H. Putnam, editors, 1983 [1964]. Philosophy of Mathematics. 2nd ed. Cambridge: Cambridge University Press.

Boolos, G. 1983 [1971]. The Iterative Conception of Set. Reprinted in Benacerraf and Putnam 1983.

Cupillari, A. 1989. The Nuts and Bolts of Proofs. Belmont, CA: Wadsworth Publishing.

Diamond, A. 1989. Differences Between Adult and Infant Cognition: Is the Crucial Variable Presence or Absence of Language? In Weiskrantz 1989.

Gödel, K. 1983 [1944]. Russell’s Mathematical Logic. Reprinted in Benacerraf and Putnam 1983.

Hamilton, H., and J. Landin 1961. Set Theory and the Structure of Arithmetic. Boston: Allyn and Bacon.

Helmholtz, H. 1962 [1885]. Treatise on Physiological Optics. J. Southall, translator. New York: Dover Publications.

Hilbert, D. 1983 [1925]. On the Infinite. Reprinted in Benacerraf and Putnam 1983.

Kelley, D. 1986. The Evidence of the Senses. Baton Rouge: Louisiana State University Press.

——. 1988. The Art of Reasoning. New York: W. W. Norton.

Kneale, W., and M. Kneale 1984 [1962]. The Development of Logic. Oxford: Clarendon Press.

Macnamara, J. 1986. A Border Dispute. Cambridge, MA: Cambridge University Press.

Mill, J. S. 1973 [1843]. A System of Logic Ratiocinative and Inductive. Toronto: University of Toronto Press, Routledge & Kegan Paul.

Peikoff, L. 1985. Aristotle’s “Intuitive Induction.” The New Scholasticism 59(2):185–99.

Piaget, J. 1954. The Construction of Reality in the Child. New York: Basic Books.

Poincaré, H. 1983 [1952]. On the Nature of Mathematical Reasoning. Reprinted in Benacerraf and Putnam 1983.

Quine, W. 1960. Word and Object. Cambridge, MA: MIT Press.

Rand, A. 1990 [1966–67]. Introduction to Objectivist Epistemology. 2nd ed. H. Binswanger and L. Peikoff, editors. New York: Meridian, Penguin Books.

Russell, B. 1948. Human Knowledge: Its Scope and Limits. New York: Simon & Schuster.

Spelke, E. S. 1989. The Origins of Physical Knowledge. In Weiskrantz 1989.

Streri, A., and E. S. Spelke 1988. Haptic Perception of Objects in Infancy. Cognitive Psychology 20:1–23.

Weiskrantz, L. editor, 1989. Thought without Language. Oxford: Clarendon Press.

Wright, G. H. 1979 [1941]. The Logical Problem of Induction. 2nd ed. Westport, CT: Greenwood Press.

~~~~~~~~~~~~~~~~

This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.

~~~~~~~~~~~~~~~~

Notes

4. I ended up retracting this generalization in the later section “Nicolaus – Reasoning to Substance.”

5. Mill’s conception of what would be an “empirical grounding” of denumerable infinities is not the only or best such conception. Turn to Kitcher 1984. On empirical grounding of arithmetic, see also Jenkins 2008.

6. No! The concretes falling as instances under a concept are a denumerable collection. That much is fine. However, for the concept of a spoon, it need not be prejudged whether some spoons existed in endless past ages or will occur in endless future ages. The indefinitely large number of actual spoons subsumed under the concept may have no first or last spoon in time, as far as the elementary concept is concerned. This would suggest that, as substitution units* under the concept, possible particular spoons are isomorphic with the set of integers.*

Dimensions on which the concept spoon consists are not basically temporal. They are ranges of shape and strength over minimal durations, all set by functional adequacy. In what era a spoon existed is irrelevant to its membership (its substitution-unit standing) in the concept class. The class is the class, however, when consideration of temporal order is dropped. So it remains that there may be profound logical and epistemological connection between (i) concretes as substitution units under their concepts and (ii) the set of integers.

When we turn to the measure-value of a spoon along a particular qualitative dimension, such as the spoon’s shape (see UM ¶’s 8–9, Notes 8 and 27), by which the concept can be analyzed, there is no reason to prejudge whether the applicable dimension’s linear order is a closed interval, whether it is dense, or additionally, whether it is continuous (LO, CI, D, C). So I should leave open as well the possibility that there is profound logical and epistemological connection between (i) concretes ranged with their concept-class measure values along a dimension and (ii) the numerical orders Q and R.

Our widest analysis of abstractive induction, under Rand’s measurement-omission theory of concepts (as I have amplified it)—in respect of both substitution units and measure values—is not more complete than our widest analysis of mathematical induction, linear orders, and ordered spaces.* The “ground” of abstractive and mathematical induction is the world in its dimensions and magnitude structures when grasped by our conceptual cognitive systems, our measurement-omission systems.

Edited by Stephen Boydstun

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In valid deductions, premises provide absolutely conclusive reasons for conclusions drawn from them.

Is the word "absolutely" necessary here?

Eduction goes far back with us; not only to the toddler stage, but to infancy. Jean Piaget (1954) concluded from his investigations that infants first acquire a notion of enduring objects at nine months of age. Until then, if a toy attractive to the infant were covered with a cloth, the infant would make no attempt to lift the cloth and grasp the toy, even though she were capable (after the fifth month) of performing each of these actions. Piaget concluded that, until the ninth month, the infant does not regard the toy as an enduring entity that continues to exist while not in view; only after the ninth month does the infant begin to infer the continued existence of objects.

Piaget’s conclusion was consistent with his view, and that of traditional empiricists (e.g. Helmholtz 1885), that comprehension of a world extending beyond immediate sensory experience is the product of a long process of visual and manual exploration. From the fifth month to sometime in the second year, the infant attempts to manipulate what she sees and to see what she manipulates. These explorations were thought to lead to elementary comprehension of an objective enduring world.

Piaget’s observations have been reconfirmed many times, but Piaget’s interpretation is now widely questioned. Infants younger than nine months may fail to lift the cover and grasp the toy not because by lack a notion of enduring objects, but because they are not yet able to coordinate such a means-ends sequence (Baillargéon 1986, 38–39). It is likely that this inability is due to immaturity of the frontal cortex (Diamond 1989). Recent experiments, not demanding coordination of means-ends-sequences, indicate that infants as young as six months (Baillargéon 1986), even four months (Baillargéon 1987), understand not only that objects continue to exist when not seen, but that moving objects continue along trajectories when not seen and that those trajectories could not be through other solid objects. Perhaps this is the most primitive form in which we grasp the principle of non-contradiction (see also Peikoff 1985)..

These are quibbles, no? The exact age is unimportant, and a physiological (immature frontal cortex) description hardly contradicts a psychoepistemoloigcal one. The overall developmental trajectory is unquestioned.

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Thanks for the encouragement, Jim.

~~~~~~~~~~~~~~~~

—Varieties of Induction

In valid deductions, premises provide absolutely conclusive reasons for conclusions drawn from them. Conclusions deduced validly are contained implicitly in the premises. To suppose premises true and a conclusion validly deduced from them false would itself entangle one in a contradiction. The necessity with which the valid deduction follows is just the force of the impossibility of contradictions in reality.

Yes indeed. The conclusions of any valid deduction live in the premises BUT they are sometime nearly impossible to detect in the premises. Example: The proof by Feit-Thompson that every group of odd order is solvable required an entire special issue of the Canadian Journal of Mathematics. The proof was over 250 pages long.

Please see:

http://en.wikipedia....hompson_theorem

To say the conclusion is -implicit- in the premise is to mislead one as to the effort sometime required to -get- the conclusion from the premise. It took 340 years to prove Fermat's Last Theorem which was sitting very cozy in the premises of arithmetic. Inplicit indeed!

t is like mining gold. Sure enough, the gold is beneath our feet, but getting it is a bitch (sometimes).

Ba'al Chatzaf

Edited by BaalChatzaf

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Ted,

I agree the qualifier absolutely is redundant. I wrote this essay nineteen years ago. I hate that first sentence because it is ambiguous. It insinuates unintentionally that conclusions of valid deductions are necessarily true, which is false. Conclusions of valid arguments are necessarily true provided the premises are true.

Bob,

Yes. As you know, proof of “Fermat’s Last Theorem” required that whole new areas of mathematics first be invented and developed. The required premises (the required concepts) for the proof did exist at the time the conjecture was posed.* The concepts in the statement of the conjecture are elementary, but enormously more had to be learned about those concepts in their wider mathematical settings, settings not yet discovered when the conjecture was stated, in order to find the required premises for a proof.

~~~~~~~~~~~~~~~~

PS

Ted,

Cross-modal integration and enduring-object representation at 4 months is an enormous shrinkage of the trajectory in developmental time in comparison to Piaget’s scale. It suggests that the process of acquiring key fundamental representations of the world is rigged up significantly differently than in the classical empiricist model which Piaget’s results had seemed to corroborate. (One purpose to which I was putting all such research was to situate philosophers and their disputes in the most realistic history of their own individual development from infancy. That of course is how I have long seen each one of them as they go about arguing positions in epistemology or presenting their case for skepticism. Reading Locke is wonderful, but it is not the way to be fully serious about epistemology. I digress.)

I should add that Piaget did not regard the new ability of the infant at about 8 or 9 months to show she really has object concept. At that stage, she has become able to retrieve a desired object that she has seen hidden under a cover. But Piaget had reason to conclude that at this stage the infant is not yet representing objects as existing spatiotemporally continuously.

He found that not until about 18 months could an infant succeed at the following task: An object is seen to be retrieved from a hiding place. A hand closes around the object, concealing it. The closed hand is seen to move to a new hiding place, where the object is hidden without the object being exposed to the infant. Until about 18 months, the infant will look in the first hiding place, but not proceed to the second. Piaget thought this proved the infant did not have representation of the continuous existence of objects, until 18 months, when the infant will, after not finding the object in the old hiding place, proceed immediately to look at the new place, where the closed hand had finished its motion.

At 18 months, one has reached the single-word level of language, and could well have 50 words in one’s vocabulary. The picture of development by the results of Piaget bolstered the veil-of-language chicanery fashionable with certain philosophers in mid-twentieth century. Research on infant development these last three decades has sobered the party.

On this and other areas of implication from developmental cognitive psychology to traditional questions of epistemology, you might like to check out:

The Origin of Concepts

Susan Carey (Oxford 2009)

Edited by Stephen Boydstun

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Ted,

I agree the qualifier absolutely is redundant. I wrote this essay nineteen years ago. I hate that first sentence because it is ambiguous. It insinuates unintentionally that conclusions of valid deductions are necessarily true, which is false. Conclusions of valid arguments are necessarily true provided the premises are true.

Bob,

Yes. As you know, proof of "Fermat's Last Theorem" required that whole new areas of mathematics first be invented and developed. The required premises (the required concepts) for the proof did exist at the time the conjecture was posed.* The concepts in the statement of the conjecture are elementary, but enormously more had to be learned about those concepts in their wider mathematical settings, settings not yet discovered when the conjecture was stated, in order to find the required premises for a proof.

My point exactly. Saying the conclusions of a deduction are implicit in the premises (no argument there) tells one nothing of the difficulty involved in making the inference.

Ba'al Chatzaf

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Continuing the 1991 essay:

It is well known that David Hume examined induction and found it deficient in rationality. It is less well known, but in the fourteenth century, Nicolaus of Autrecourt had followed roughly the same line of thought. Both of these thinkers concluded that induction is essentially irrational. I never seriously entertain so skeptical a conclusion—but look straightaway for what has gone wrong in the analysis (see Aristotle Ph. 193a3–9 and Armstrong 1991, 52–54). I want to look closely at the analyses of Nicolaus and Hume. In their errors, we should find clues to the true workings of induction.

—Ockham – Contingency

Nicholaus of Autrecourt followed in the intellectual wake of William of Ockham. Nicolaus was inclined, like Ockham (Copleston 1963, 68–71, 92–96; Boehner 1990, 32–37, 43–45, 118–26, 99–100), to nominalism and to clearing away excessive metaphysics.[7] As Nicolaus posed his original ideas concerning induction on a stage set by Ockham, it will be helpful to recount some salient ideas of the latter.

Ockham held that we have immediate apprehensions of individual things as existents, and upon these we are able to form propositions asserting the existence of such things. We apprehend also immediately certain attributes of present things; in addition to existence, we can predicate certain attributes on the basis of immediate apprehension. We apprehend also immediately our own inner acts (ibid, 74–76; 22–24).

In Ockham’s view, it is the individual present thing that causes us to apprehend it as existent. Out of concern for preserving the traditional Christian doctrine of divine omnipotence, Ockham dresses the natural order of things with supernatural possibilities. God indirectly causes our immediate apprehension of existents by those existents. Though God would never pull such a stunt, he could cause directly everything in our apprehension, save only our assent to existence, without the existents. He could not cause as well our assent to existence in such a case because that would result in a contradiction: the complete, actual apprehension of an existent that did not really exist. Contradictions are impossible in reality, and the omnipotence of God does not extend so far as to contravene the law of non-contradiction.

The order of the world, according to Ockham, follows only from divine choice. God chooses that there be the individual entities that there are; between these distinct entities, there are no necessary connections. The order of the world is contingent (ibid., 79–80, 83 –86, 103–7; 94–95, 122–23, 133–35). How, from the divine liberty, does it follow that the order of the world is contingent? After all, you or I might make a certain flower arrangement, and it would not, for the reason of our having chosen to make it, follow that the arrangement thenceforth would be contingent. Ockham would contend that continuance of our arrangement of flowers, indeed continuance of the whole world, requires the constant concurrence of God. For Ockham continuance of the world requires unceasing divine support, much as for Aristotle (but not for Ockham if I interpret him correctly on projectile motion; Boehner 1990, 139–40) all motion requires a continuing mover. Ockham’s idea seems to be that since at any moment God could populate the world with different entities, ordaining at the same moment a new order in the world, the order we actually find in the world is contingent. This strikes me as an utterly empty contingency, since in Ockham’s own view, God will not be exercising his option of remaking the world.

Ockham follows a second, but related, line of reasoning (cf. TP 7.1) to contingency of the world’s order. “Wherever there is any distinction or non-identity, contradictories can be verified” (Weinberg 1965, 45–46; Boehner 1990, 40). If X and Y are distinct, then though X is entirely X, Y is not entirely X. To verify contradictories means that of an X and Y we can predicate something of X but not Y. This we have just done for any X distinct from Y. But contradictories can hold only of things that are really different things. (Refutation: throughout the argument, X and Y are things or they are true characterizations of things, yet the argument relies on our switching from the latter to the former as it unfolds.) Ockham would go on to say that God could separate really different things no matter how tightly and constantly we find them together. Therefore, connections between distinct things are always contingent. I register the same objection as before: how does such divine liberty imply contingency in the actual world order? (see also Weinberg 1965, 52–56).

Thomas Hobbes (1966, 2.11.1) and David Hume (T 18–19, 24–25) later reiterated this second line of reasoning, but without the supposition that all distinct things are separable by God or any other specific power. They simply assert that all distinct things are separable. They slide from separability in thought to separability in reality.

Ockham sees in the purported contingency of the world’s order support for an important thesis he favors, namely, that we cannot discern the order of the world by a priori reasoning, but must examine what the order is in fact (Copleston 1963, 82–83). This applies to causal relations. We can know them, but only by experience. That Y has a cause can be known in advance, but ascertainment that X is the cause of Y, experience. For X to properly be called the cause of Y, X must be a thing different than Y. Then the causal relation between X and Y is contingent (though completely dependable). It would seem of a piece with this outlook to equate efficient causality with regular succession, and some scholars interpret Ockham’s view in this way (ibid., 83–86). Others argue that Ockham never reduced causality to merely regular succession; Ockham retained the notion of causative power (Weinberg 1965, 146–47).

Ockham distinguished real science, concerned with real things, from rational science, concerned with terms that do not stand immediately for real things. Logic is a rational science for it deals with terms of second intention, terms such as species and genus. Logic presupposes real science; terms of second intention presuppose terms of first intention.

Real science is concerned with individual things, but real science, indeed any science, is of propositions. Ockham often appears to take real science to be mostly a laboring over propositions. Although Ockham was concerned to uphold the Aritotelean view that only individuals exist, Ockham clearly affirms also the Aristotelean view that science is of the universal (in a diluted sense). Science is knowledge of universal propositions (Boehner 1990, 9–15).

Ockham followed Aristotle’s thoughts as well on indemonstrable propositions and on demonstration. Indemonstrables are of two kinds: principles necessarily assented to once the mind grasps their terms or principles known only by experience. That flowers or any other things exist is indemonstrable in the second sense. Demonstration for Ockham is only demonstration of attributes, never existence (Copleston 1963, 71–73). Remember this.

Continued below—

Nicolaus – Experience of Substance

Nicolaus – Reasoning to Substance

Hume – Experience of Cause and Effect

Hume – Reasoning to Cause or Effect

Hume – Necessity

Hume – Uniformity

Existence is Identity

References

Aristotle 1984 [c. 348–322 B.C.]. The Complete Works of Aristotle. J. Barnes, editor. Princeton: Princeton University Press.

Armstrong, D. M. 1991 [1983]. What Is a Law of Nature? Cambridge: Cambridge University Press.

Boehner, P., editor and translator, 1990 [1955]. Ockham: Philosophical Writings. Revised by S. F. Brown. Indianapolis: Hackett Publishing.

Copleston, F. 1963 [1953]. A History of Philosophy, V3P1. Garden City, NY: Image Books.

Hobbes, T. 1966 [1839, 1655]. Elements of Philosophy. In volume I of The English Works of Thomas Hobbes. W. Molesworth, editor. Darmstadt: Scientia Verlag Aalen.

Hume, D. 1978 [1888, 1740]. A Treatise of Human Nature. 2nd ed., L. A. Selby-Bigge, editor. Oxford: Clarendon Press.

Weinberg, J. R. 1965. Abstraction, Relation, and Induction. Madison: University of Wisconsin Press.

~~~~~~~~~~~~~~~~

This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.

~~~~~~~~~~~~~~~~

Note

7. For more on Ockham’s theory of universals and concepts, see Jetton 1998, 50–51.*

Edited by Stephen Boydstun

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Stephen, thank you for informing/reminding us of your essay Induction on Identity.

I note your essay has no references to William Whewell's extensive writing on induction and am curious as to why. No offense intended. Many years ago I read John Stuart Mill's A System of Logic, which refers to William Whewell many times, but didn't read anything by him until recently. I believe his concept colligation is important.

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Oh yes, this essay incorporates explicitly a valuable concept from Whewell. But it comes later in the essay. I have just pulled out from the total references the ones that are used in individual sections of the essay as I post it here.

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Oh yes, this essay incorporates explicitly a valuable concept from Whewell. But it comes later in the essay. I have just pulled out from the total references the ones that are used in individual sections of the essay as I post it here.

Thanks. I stand corrected, although I relied mainly on your lists of references at the end. I now see the following in the second part on page 14:

Inference to the existence of atom is a case of induction in the genre of what William Whewell (1794-1866) termed the concilliant induction (Butts 1982 153-55)

Is that the only one? There is no search tool (except eyeball), since Objectivity online is picture files.

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Yes, that is the only one in this essay. And the proper spelling and punctuation would be consilience-induction. Going to the Name Index for Objectivity, I see there is one other reference to Whewell, in another essay, and that was a mention of his Inductive Table of Optics.

I was fortunate that at my undergraduate school, University of Oklahoma, there was a good History of Science division.* However, I first learned of Whewell not from those scholars, but from my geology professor. One day he read to our class an excerpt by some naturalist or geologist from way back when (I can’t remember the scientist’s name), who was giving an argument to the conclusion that rivers form their valleys. It was a beautiful argument, and the professor told us that it was an example of what William Whewell had called the consilience of inductions.

In the sequel of Induction on Identity (1991), it will be seen below that, in addition to its introduction in the quote in #11, consilience of inductions is put to work in two places:

Nicolaus – Reasoning to Substance: “Consilience-inductions pervade the history of science. Newton’s gravitational law was such an induction, analytically, if not genetically.”

Hume – Experience of Cause and Effect: “It is not only the two billiard balls that are subject to the law of identity; it is not only their behavior that must be ‘consistent’. Everything else that there is or has been or will be, everything else along with the two billiard balls, every thing, individually and altogether, is subject to the law of identity. From identity, manifold identity, comes the consilience of inductions.”

Edited by Stephen Boydstun

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—Nicolaus – Experience of Substance

We turn now to Nicolaus of Autrecourt. There is, in Nicolaus’ view, just one fundamental principle, the principle of non-contradiction. Contradictions cannot be true, and all indubitable principles are illustrations of this one. In any necessary proposition, there is an identity in the signification of the subject and predicate; denial of such a proposition is self-contradictory. In any necessary implication, there is at least a partial identity of the antecedent and the consequent; the antecedent joined with negation of the consequent is a contradiction.

We are justifiably certain of propositions resting on the principle of non-contradiction, the ‘first principle’. We are also justifiably certain of immediate apprehensions. The certainty of immediate apprehension rests on the first principle. Though immediate apprehensions are not propositional, their certainty is guaranteed by the law of non-contradiction. An act of true awareness and the objet of that act are not truly distinct; they are identical. In such a non-propositional cognition, we have the certitude of an identity, which is to say, the certitude of the principle of non-contradiction.

Where apprehension is not immediate, where immediacy is lacking, identity is lacking. Then the objective ground for certitude is lacking. Inference from immediate apprehensions to reality beyond them steps beyond the limits of what is secure on objective grounds (Weinberg 1969, 9–30).

As Nicolaus sees it, the existence of something cannot be certainly inferred from the known existence of another thing. In any such inference, the consequent would not be really the same as the antecedent. The consequent (one thing) could be denied and the antecedent (another thing) affirmed without contradiction since contradiction is the affirmation and denial of the selfsame thing.

Nicolaus then argues, anticipating Berkeley and Hume much later, that we have no natural certain knowledge of the existence of material substance. We have no direct apprehension of substances in our pre-discursive cognitions. We cannot infer the existence of substances from the content of our pre-discursive apprehensions because substance is not wholly the same as that content. Then the existence of material substance cannot be truly known.

Today, we should render Nicolaus’ skeptical conclusion as “the existence of the atomic chemical elements cannot truly be known.” We now understand material substance ordinarily as aggregations of atoms. Nicolaus’ argument can be applied against the modern belief in atoms and their electronic constitutions just as it was applied to belief in more primitive notions of material substance. We shall look at inference to the existence of atoms shortly. Right now I want to caution against a hasty assent to Nicolaus’ contention that we have no direct apprehension of substances in our pre-discursive cognitions. As evidence, Nicolaus points to the uneducated. He claims they possess no knowledge of material substance. I have doubts about that. The uneducated might have a rudimentary knowledge of material substance. The educated person’s notion of material substance, in Nicolaus’ century or our own, might be built upon just such a rudimentary starting point (much as the notion was cultured across the centuries; Jammer 1961, 16–89; Benvenuto 1991, 158–232).

Let me elaborate. Objects present may be given as objects in perception. Objects not given in perception must be inferred. As remarked earlier,* infants as young as four months perceive objects, understand that objects endure beyond the times of their perception, and coordinate information from different sensory modalities concerning a given object. For the young infant, as for the adult, the visual perception of an object is the culmination of a rapid process in which perception of properties of the surface layout before her has preceded. The infant does not yet make use of all the perceptual cues used by adults in perceiving partially occluded objects. The infant relies on the facts that bodies are cohesive and bounded, that bodies move as wholes, independently of other bodies. In the static situation, though, the infant does not yet make use of the adult (gestalt) principles of maximal regularity in color, texture, and form to perceive objects. The infant perceives the gestalt properties; they do not lead her to perceive an object (Spelke 1989, 168–74).

At any stage of development of the visual system, whichever cues are being relied upon by the visual system, it does not seem entirely proper to regard projections of occluded portions of objects by the visual system as inductive inferences. I do not mean to disqualify such projections as inductions because they are non-propositional (see Lindsay 1988). Rather, I am inclined to disqualify them because, notwithstanding the likelihood that the development of the logic in the visual system required repeated experience, such projections have become profoundly automated and are not (any longer?) arrived at by deliberation (Edelman 1989, 70–89).

Objects only partially visible, or even objects availing only the barest perceptual cues, may sometimes nonetheless be perceived as objects. Not all of the object is directly perceived, yet the object is directly perceived. In other situations, though, we must go through a certain amount of deliberation to discern the objects before us. This is not purely perception but perceptual judgment as well. What should Nicolaus say of this latter case? He would say that all is reasonably well. Such is not the occasion of inductive inference he calls into question, for in such a case as this, we make only an inference from some of the parts to the whole. We have previous immediate apprehension of the parts presently missing from view and of the whole object in relation to its parts. Our inference from part to whole on a present occasion may be sustained by the present and past immediate apprehensions taken together (Weinberg 1969, 40). Of course the inference here is inductive, not deductive, and so does not, according to Nicolaus, enjoy the certainty of the first principle.

Consider also cases in which an object disappears entirely from view for a time and then reappears. Here the young infant relies on the continuity of trajectories and on solidity (impenetrability) as characteristics of enduring objects. Later she will learn to rely as well on the facts that objects tend to move with fairly constant or gradually changing speeds and are subject to gravity (require support) (Spelke 1989, 175–80). Of judgments concerning the identity of objects disappearing from view for a while, what would Nicolaus say? It seems he would be caught in the middle. To the one side, he would be inclined to say such inferences are justified (though not with the certainty of the first principle) because of our past apprehensions of the relevant parts and wholes. We now may see only parts of the trajectories of moving objects, but on other occasions, we have seen the wholes. To the other side, Nicolaus might be inclined to say that our judgments concerning the identity of objects visible intermittently are unfounded; he contended at one point that things known by us to have a certain duration might have a duration greater than our observation of them but that we could not know whether they do (Weinberg 1969, 107). It may well matter, we should observe, whether one is making interpolations of trajectories or extrapolations of trajectories, whether one is supposing an object’s continued existence and motion (or rest) between two separate observations or supposing continuation beyond the observation set.

In any case, what Nicolaus is really concerned to challenge is not inference to objects on those occasions when they are directly apprehended only in part, but inferences to substances never directly apprehended at all. In Aristotle’s sense, material substance is the invariant substratum of the changes we observe in objects, and it is that which supports the properties of those objects. Today, for material substance, we look to chemical composition of specific objects and to mass-energy of objects in general.

The idea of substance evidently comes to us before we are instructed in Aristotle or in modern science. We have seen that by four months the infant has comprehended that solid objects are impenetrable; two cannot occupy the same space at the same time (Baillergéon 1987, 1986). This is part of what we mean in ordinary parlance by the substantiality of an object. The infant soon has experience of the pliability or rigidity of solid objects. She experiences their inertia and their weight (Mounoud and Bower 1974). These are all aspects of substantiality. Surely the idea of substance has taken root once the infant has apprehended the elementary substantialities of objects.

These substantialities are given directly in perception; for an object at hand, no inference to them is required. For this reason, Nicolaus will want to say that these substantialities are not aspects of material substance itself; properly speaking, substance lies entirely beyond direct experience. This seems artificial. To be sure, educated adults find by inference aspects of substance underlying, so to speak, those aspects directly accessible in experience: underneath impenetrability we infer electronic repulsions, under inertia we infer the constraint of momentum conservation, and under weight we infer the opposition of terra firma to free fall. How artificial it would be to say that electronic repulsions are aspects of material substance but that the impenetrabilities of everyday solid objects are not. Some aspects of material substance are perceived directly.

Mention should be made here of another aspect of material substance that seems to be readily available in perception: materiality. One can perceive and contrast solid objects with non-solid stuff such as clay, sand, or liquids. Evidently, the pre-linguistic child makes a categorical distinction between solid objects and non-solid stuff. These early ontological categories guide the learning, at about two years of age, of count nouns and mass nouns and their appropriate syntax (in a language such as English, which quantifies differently over count nouns, e.g., a table, and mass nouns, e.g., a glass of water). If a speaker seems to be talking about a present solid object, the child concludes that the word refers to individual objects of the type present. If a speaker seems to be talking about some present non-solid stuff, the child concludes that the word refers to portions of stuff of the type present (Soja, Carey, and Spelke 1991).

The child will be about eight years old before she has a secure concept of materiality. Until then the child will tend to interpret “made out of” as “constructed from” and will rely on the perceptual properties of large-scale chunks of a material in judging kind of material. Until then the child will not typically interpret “made out of” as “is a constituent of” and will not reason that materials, such as wood, remain the same kind of stuff even when they are ground up (Smith, Carey, and Wiser 1985).

Nicolaus is smiling now because he notices all the inductive scaffolding required to arrive at an eight-year-old’s concept of material substance. If we want to defend a concept of substance so mature as this, we cannot merely appeal to perception, but must actually defend induction.

Continued below—

Nicolaus – Reasoning to Substance

Hume – Experience of Cause and Effect

Hume – Reasoning to Cause or Effect

Hume – Necessity

Hume – Uniformity

Existence is Identity

References

Baillargéon, R. 1986. Representing the Existence and the Location of Hidden Objects: Object Permanence in 6- and 8-Month-Old Infants. Cognition 23:21–41.

——. 1987. Object Permanence in 3.5- and 4.5-Month-Old Infants. Developmental Psychology 23:655–64.

Benvenuto, E. 1991. An Introduction to the History of Structural Mechanics: Statics and Resistance of Solids. New York: Springer-Verlag.

Edelman, G. M. 1989. The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books.

Jammer, M. 1961. Concepts of Mass. Cambridge, MA: Harvard University Press.

Linsay, R. K. 1988. Images and Inference. Cognition 29:229–50.

Mounoud, P. and T. G. R. Bower 1974. Conservation of Weight in Infants. Cognition 3(1):29–40.

Smith, C., Carey, S., and M. Wiser 1985. On Differentiation: A Case Study of the Development of the Concepts of Size, Weight, and Density. Cognition 21:177–237.

Soja, N. N., Careu. S., and E. S. Spelke 1991. Ontological Categories Guide Young Children’s Inductions of Word Meaning: Object Terms and Substance Terms. Cognition 38:179–211.

Spelke, E. S. 1989. The Origins of Physical Knowledge. In Thought Without Language. L. Weiskrantz, editor. Oxford: Clarendon Press.

Weinberg, J. R. 1969 [1948]. Nicolaus of Autrecourt. New York: Greenwood Press.

Edited by Stephen Boydstun

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It is fairly well know that Aristotle regarded the Law of Contradiction, not the Law of Identity, as fundamental. Thomas Aquinas and subsequent Thomists followed Aristotle in this regard.

What is less well known is that some Thomists have not only attacked the primacy of the Law of Identity but have also criticized its modern interpretation (e.g., a thing is itself) as a distortion of its original meaning. A good example of this can be found in Richard F. Clarke, S.J., Logic (1916).

This book is available online and can be found here.

For Clarke's critique of the modern interpretation, which he blames of William Hamilton, scroll down to the section on "The Principle of Identity," beginning on page 42.

Ghs

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It is fairly well know that Aristotle regarded the Law of Contradiction, not the Law of Identity, as fundamental. Thomas Aquinas and subsequent Thomists followed Aristotle in this regard.

What is less well known is that some Thomists have not only attacked the primacy of the Law of Identity but have also criticized its modern interpretation (e.g., a thing is itself) as a distortion of its original meaning. A good example of this can be found in Richard F. Clarke, S.J., Logic (1916).

This book is available online and can be found here.

For Clarke's critique of the modern interpretation, which he blames of William Hamilton, scroll down to the section on "The Principle of Identity," beginning on page 42.

Ghs

Thank you for posting that.

The Principle of Identity, that Every being is or contains its own nature or essence, has been distorted by some modern logicians, and thrust forward into the first place as the first and ultimate basis of all Truth. It has been clothed in a garb that was not its own. It has been stated in a formula which has the plausible appearance of a guileless simplicity, and it has then (or rather this perversion of it) been put forward as the rival of the Principle of Contradiction for the office of President of the Court of Final Appeal for all Demonstration, and as not only independent of it in its decisions, but its superior and proper lord.

That is an examplar of literary craftsmanship.

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Rand and I, like Clark and his tradition, include relation to other, different things in saying a thing is itself (e.g.). So far as I recall, Rand will not give priority, ontologically or epistemologically, of either sameness over difference or difference over sameness. On that score, she would not agree with Clark and his tradition that the negative principle, the principle of non-contradiction, is more self-evident and manifest than identity (42). She does put non-contradiction into her elementary definition of logic, and she could easily concur with the idea that non-contradiction is the fundamental rule of logic because logic is a normative discipline.

Like Clark and his tradition, she takes the concept being as in contrast with not being. That is, “to exist is to be something, as distinguished from the nothing of non-existence” (AS 1016). Of course, as readers here know, that is not where she ends the sentence. “To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes.”

Thank you, George, for pointing out this book. It is good to add this text to the history of conceptions of logic (add to a, b). I wonder if Rand was familiar with this text. I was not until now.

I see the book was issued in 1889. Hamilton and Mansel are in this text. The greatest developments in logic since Aristotle, which had just seen publication the decade before Clark’s text, are not touched on therein. Copi’s text Symbolic Logic, which was suitable for a second course in logic as of middle Twentieth Century (when I was an undergraduate) shows some of the ways of casting axiomatically our modern propositional logic. Some of those deductive systems include the negation of contradiction among the axioms and derive such rules as “If p then p.” My favorite is the Nicod system (1916) in which the system of propositional logic is derived from a single (rather complex) axiom and a single rule of inference, both composed using a single operation, alternative denial: “Not both p and q.”

These formalizations of logic are like formalized Euclidean geometry in this way: Various sets of axioms have been shown adequate bases for generating the geometry. But we have practical and scientific interests in Euclidean geometry. When it comes to getting up and down the stairs in the home, that the space of the staircase is Euclidean is practically relied on, and it’s reliability is as free of axiom set and deductive structure as it is free of possible choice of coordinate system (rectangular, spherical, etc.). Logic in application can similarly be independent of choice of adequate axiomatic system.

Edited by Stephen Boydstun

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Thank you, George, for pointing out this book. It is good to add this text to the history of conceptions of logic (add to a, b). I wonder if Rand was familiar with this text. I was not until now.

The Clarke book is one of eight in the Stonyhurst Philosophical Series. This series of Thomistic texts was presumably inspired by the revival of Thomistic studies in the late 19th century, which was centered at the University of Louvain. I first became aware of these books in the early 1970s, when Roy Childs sold me several before moving from Hollywood to New York. I have had the entire series for many years now.

All of these books are of limited value, for obvious reasons, but three are especially worthwhile. (The Clarke book has never been one of my favorites.) These are available for free on Google Books, and I have linked them below:

Theories of Knowledge: Absolutism, Pragmatism, Realism, by Leslie J. Walker, S.J.

Psychology: Empirical and Rational , by Michael Maher, S.J. (This contains a lot on what we would call epistemology today. One of the most interesting features of this book is its treatment of volition, which is similar to Rand's.)

The First Principles of Knowledge , by John Rickaby, S.J.

Ghs

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These formalizations of logic are like formalized Euclidean geometry in this way: Various sets of axioms have been shown adequate bases for generating the geometry. But we have practical and scientific interests in Euclidean geometry. When it comes to getting up and down the stairs in the home, that the space of the staircase is Euclidean is practically relied one, and it’s reliability is as free of axiom set and deductive structure as it is free of possible choice of coordinate system (rectangular, spherical, etc.). Logic in application can similarly be independent of choice of adequate axiomatic system.

That is technically correct, but some formulations are easier to use than others. The Nicod formulation is interesting in that it reduces propositional logic to a single axiom scheme BUT is is clumsy to use in generating proofs. For first order logic the easiest system to use is Natural Deduction because it corresponds so closely to the informal logic used by mathematicians in their proofs.

Ba'al Chatzaf

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Note on varieties of induction (above) and the uniformity principle (below), abstract of John McCaskey’s second paper* last summer:

“Whence the Uniformity Principle?” – Abstract

Where did we get the idea that every induction includes some uniformity principle as a presumed premise? The idea is not in Socrates, Aristotle, or Cicero; it is not in medieval writings, Arabic or Latin; it is not in the Scholastics or the Renaissance Humanists; it is not in Francis Bacon, Isaac Newton, Thomas Reid, or William Whewell; in fact, it is not even per se in David Hume. It is definitely in John Stuart Mill, but Mill claims to have gotten it from someone else. It turns out we got the idea from Richard Whately (1787-1863), Oxford professor, author of Elements of Logic (1826), and later bishop of Dublin. This paper recounts the relevant background and then how the idea originated, spread, and became in the second half of the nineteenth century a canonical part of our understanding of induction.

The idea of induction, or epagoge, goes back to Aristotle—who said he got it from Socrates. Aristotle said it is a progression from particulars to a universal. But there is an ambiguity here. Did Aristotle mean progression from observation of particular things to cognition of a universal concept (as Posterior Analytics B 19, other passages, and the Socratic reference indicate) or as a progression from particular statements to a universal statement (as Prior Analytics B 23 seems to say). Is induction fundamentally an aspect of concept-formation or fundamentally a kind of propositional inference? The first was assumed through nearly all of antiquity. But the Neoplatonic commentators introduced the second and and bequeathed the idea to both Latin and Arabic medieval traditions.

Accordingly, Scholastics tried to render induction (when valid) as a kind of syllogism by adding a presumed minor premise, a premise about complete enumeration. It became canonical that induction is an enthymeme in Barbara with the minor premise suppressed. Renaissance humanists and then especially Francis Bacon revived the ancient, Socratic view; it became standard again and remained so until the early nineteenth century.

Then, Richard Whately and his Oxford colleagues, unhappy with the dominance of Baconian induction, sought to revive Scholastic induction. They revived the notion that induction is a kind of propositional inference that can, if the inference is sound, be rendered as a syllogism. But, they claimed, the Scholastics had one bit wrong: It was the major not the minor premise that was suppressed. John Stuart Mill adopted this proposal and considered it the very “ground of induction.” Mill said Whately’s suppressed major was “the uniformity of the course of nature.”

Over the next fifty years, we can watch, step by step, the revival of induction as a kind of propositional inference and the replacement of the major for the minor as the supressed premise. Though Alexander Bain still felt the need in 1870 to warn his students against conceiving of induction in the old, Baconian/Socratic way, by the turn of the century, Whately’s proposal was fully canonical, and the uniformity principle invariably attached to our conception of induction. The proposed paper will detail this transition.

Edited by Stephen Boydstun

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McCaskey has the full abstract and a PowerPoint presentation of Whence the Uniformity Principle? on his website here. Note: 'ppsx' is a PowerPoint file extension introduced with Microsoft Office 2007. If you have an older version of PowerPoint, there is a downloadable viewer here.

Edited by Merlin Jetton

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—Nicolaus – Reasoning to Substance

As one would expect, Nicolaus discounted inferences to material causes along with inferences to material substance. Of causes in general, Nicolaus would ask whether the effect is identical to the cause. If they are identical, then they are not truly cause and effect. If they are not identical, then existence of the effect can be denied and existence of the cause affirmed without contradiction. We may believe there are necessary connections between repeatedly conjoined things or events, but if they are truly distinct, then there is no logical necessity in their conjunction. (Al-Ghazali, a philosopher-theologian in the Islamic tradition, came to the same point in the eleventh century; Weinberg 1965, 135, 89–90.) Moreover, we have no direct perception of any necessity between repeatedly conjoined things or events; we do not perceive any agency or patience in things or events observed to be conjoined (Weinberg 1969, 109–11).

This last contention would seem to be an overstatement since we plainly do perceive agency and patience in our own interactions with the world. Perhaps Nicolaus was thinking here only of physical occurrences to which one is not a party, but only an observer.

The contention of Nicolaus, and of Ockham, that an effect cannot be identical to its purported cause would also seem to be an overstatement, though only a mild one. There are cases in which it seems sensible to say that an effect is virtually identical to part of its cause. The image of an object in a mirror is virtually identical with the optical object before the mirror. There are other cases in which it seems sensible to say that a thing bears in itself part of the identity of its cause. Examples would be die-castings, fingerprints, and DNA sequences. Another example would be the causation of thunder by lightning. There are patterns in the lightning that persist in and can be perceived in the complex waveform of the ensuing thunder. A signature of the lightning is borne by the thunder it generates.

There is one sort of case in which it seems sensible to say that an effect is truly identical with its cause (cf. Nozick 1981, 118–21). We say, for instance, that our experience of the impenetrability of solid objects is caused, in part, by the repulsions of electrons bound to separate objects. In some sense, what we experience is just those electronic repulsions, yet we say the electronic repulsions caused the experience of impenetrability. Should we say that impenetrability is a form in which we can experience electronic repulsions? “Whatever is in something is in it according to the mode of that in which it is” (Aquinas 1975, 1.49.3). Very well, but it still seems sensible to say that the electronic repulsions are part of the cause of our form of experiencing them, that is, our experience of impenetrability (see further, Peikoff 1991, 41–48; Kelley 1986, 36–37, 83–95, 105–11; and Heil 1983, 63–69, 81–86).[9]

Lastly, in every case of alteration, it seems we may sensibly say that a necessary part of the cause of the altered thing is that same thing prior to its alteration. An altered thing inherits from its former self. What it was is partial cause of what it becomes.

More fundamentally, Nicolaus was wrong to hold that objective necessity obtains only across transformations that map a thing, or some parts of it, identically. There are necessary connections also between different things; at least there are prima facie necessary connections between different things. Could it be that where there is an ineradicable necessity, there is either a simple identity transformation, as Nicolaus proposed, or there are underlying identity transformations? In the latter case, where an antecedent and a consequent are underlain by an identity transformation, it might well be that denial of the consequent and affirmation of the antecedent does not itself compose a contradiction. Could it be, though, that identity is a more basic principle that non-contradiction, that identity is the deeper principle of reality, that contradictions are local conflicts with the principle of identity, that identity is not only a local but a global condition?

By the time one were four years old (earlier, by Macnamara 1986, 147–49), one had come to rely on underlying identities of the objects of perception. In identifying kinds of objects, especially natural objects, one had begun to rely not only on properties presently apparent in perception but to ask about presently unapparent properties. One had begun to seek the kind of thing a thing is and to use knowledge of kind, of categorical identity, to override obvious characteristics on their misleading occasions (Markman 1989, 95–135; Keil 1989, 195–215, 249–53).

“Children were taught a property of one object and a different property of a second one. They were shown a third object that looked much like one of the first two but was given the same category label as the other. For example, children saw a tropical fish and were told that it was a fish and that it breathes underwater. They saw a dolphin and were told it was a dolphin and that it pops out of the water to breathe. They then had to decide how a second fish, a shark that looks like a dolphin, breathes. Children relied on the shared category to promote inductions even in this stringent case where perceptual similarity would lead to a different conclusion. Moreover, [studies showed that] children’s inferences are based on common category membership and not just on identity of labels.” (Gelman and Markman 1986, 203)

Inference to the existence of the atomic chemical elements of matter is a very important case of reliance on underlying categorical identities. It is an inference to existents never directly perceived at all, just the sort of inference Nicolaus attacks when he attacks inference to material substance. Occasionally one sees in modern science texts or periodicals what appear to be photographs of individual atoms arrayed in some material. These are really not straight photographs. We have not perceived atoms so directly as in straight photographic perception. Objects in straight photographs are susceptible of being seen also directly or through simple optical magnification. Our “perception” of atoms is even now not direct but inferential (Wichramasinghe 1989).[10]

Well before man had such persuasive images of atoms, their existence could not be rationally doubted. By 1908 evidence of their existence was overwhelming. Evidence of their existence is fortified with every passing year in our glorious age, though our usual focus now is on exploring their properties rather than confirming their existence. We can take their existence for granted.

Inference to the existence of atoms is a case of induction in the genre of what William Whewell (1794–1866) termed the consilience-induction (Butts 1982, 153–55). By 1900 atoms and molecules were evidenced by Dalton’s law of multiple proportions, Gay-Lussac’s law pertaining to the volume of gases, Avagadro’s law (which made possible the determination of molecular weights), and the kinetic theory of gases (which could approximately predict molar heat capacities). After 1908, when Jean Baptiste Perrin published his results on the sedimentation distribution of (visible) particles suspended in a still liquid and his measurement of Avogadro’s constant, the existence of atoms could not be reasonably doubted (Wehr and Richards 1967,* 4–26; Nye 1972).[11] These lines of induction, and many others, converged in favor of the atomic hypothesis. The evidence was and is several and joint. In conjunction the strength of the evidence magnifies.

Consilience-inductions pervade the history of science. Newton’s gravitational law was such an induction, analytically, if not genetically. It unified phenomena formerly disparate, most conspicuously, planetary orbits and projectile trajectories on earth. Newton’s law of gravity and his concomitant theory of space have been displaced by Einstein’s general relativity. It seems to me that this can never happen to the atomic hypothesis (nor to the hypothesis that the earth is rotating for that matter). The atoms are here to stay. Our best theory of many of their properties, the theory of quantum mechanics, might someday be superseded, but atoms will remain theoretical entities for us and our descendents. And serious minds with some scientific education will continue to regard them not only as theoretical entities, but as concretely real things (Friedman 1983, 238–50). Neither atoms nor our atomic lasers (Newton-Smith 1981, 196) are going to go away however we may perfect or supersede our theories of matter in the future (see also Putnam 1988, 9–14, 22–26, 30–37).

I pound the atoms constituting these pages to make a philosophic point[12]: There is such a thing as non-deductive demonstration. There is such a thing as demonstrative ampliative induction.

Now I have contradicted myself. I said earlier* that ampliative inductive inferences, unlike deductive inferences, were not absolutely conclusive. In a significant sense, that is false. Usually it is true but not always.

My contention that there are some demonstrative, absolutely conclusive inductions would seem to bring me into opposition with the consensus among authorities on the subject: “Induction is not a demonstrative form of inference like deduction” (Braithwaite 1953, 257). “The distinction between valid deduction and non-demonstrative inference is completely exhaustive. Take any inference whatsoever. It must be deductive or non-demonstrative” (Salmon 1966, 20). I think perhaps we pass too hastily from (1) the thesis that if premises in a valid deduction are true, the conclusion cannot (cannot ever) be false and (2) the thesis that that is not so for inductive inference to (3) the result that inductions cannot be absolutely conclusive, that is, to the result that true premises in an inductive argument can never ensure truth of the conclusion. But as we know, by our knowledge that atoms exist, this last is not strictly true. It is sometimes the case that the truth of the premises in an inductive argument ensure the truth of the conclusion, but unlike any case of valid deduction, we are not informed of this by the principle of non-contradiction. This circumstance is what one might expect of indeed identity is the broader and deeper principle of reality and the mainstay of induction.

We should also underscore an error made by Ockham. He held that we could never demonstrate existence, only attributes. He was mistaken. Atoms exist. This we now know, proof positive. “Thus we understand truth by considering a thing of which we posses truth” (Aquinas 1947, Pt. 1, Q. 84, Art. 7, Reply Obj. 3; see also Goodman 1983, 64).

Continued below—

Hume – Experience of Cause and Effect

Hume – Reasoning to Cause or Effect
Hume – Necessity
Hume – Uniformity
Existence is Identity

References

Aquinas, T. 1947 [c. 1265-73]. Summa Theologica. New York: Beniziger Brothers.

——. 1975 [1259–68]. Summa Contra Gentiles. A. C. Pegis, translator. Notre Dame, IN: Notre Dame University Press.

Braithwaite, R. B. 1953. Scientific Explanation. Cambridge: Cambridge University Press.

Butts, R. E., editor, 1989 [1968]. William Whewell: Theory of Scientific Method. Indianapolis: Hackett Publishing.

Friedman, M. 1983. Foundations of Space-Time Theories. Princeton: Princeton University Press.

Gelman, S. A. and E. M. Markman 1986. Categories and Induction in Young Children. Cognition 23:186–209.

Godman, N. 1983 [1954]. Fact, Fiction, and Forecast. 4th ed. Cambridge, MA: Harvard University Press.

Heil, J. 1983. Perception and Cognition. Berkeley: University of California Press.

Keil, F. C. 1989. Concepts, Kinds, and Cognitive Development. Cambridge, MA: MIT Press.

Kelley, D. 1986. The Evidence of the Senses. Baton Rouge: Louisiana State University Press.

Macnamara, J. 1986. A Border Dispute: The Role of Logic in Psychology. Cambridge, MA: MIT Press.

Markman, E. M. 1989. Categorization and Naming in Children. Cambridge, MA: MIT Press.

Newton-Smith, W. H. 1981. The Rationality of Science. Boston: Routledge & Kegan Paul.

Nozick, R. 1981. Philosophical Explanations. Cambridge, MA: Belknap Press of Harvard University Press.

Nye, M. J. 1972. Molecular Reality: A Perspective on the Scientific Work of Jean Perrin. Canton, MA: Watson Publishing.

Peikoff, L. 1991. Objectivism: The Philosophy of Ayn Rand. New York: Dutton.

Putnam, H. 1988. Representation and Reality. Cambridge, MA: MIT Press.

Salmon, W. C. 1966. The Foundations of Scientific Inference. Pittsburgh: University of Pittsburgh Press.

Wehr, M. R. and J. A. Richards 1967 [1959]. Physics of the Atom. 2nd ed. Reading, MA: Addison-Wesley Publishing.

Weinberg, J. R. 1965. Abstraction, Relation, and Induction. Madison: University of Wisconsin Press.

——. 1969 [1948]. Nicolaus of Autrecourt. New York: Greenwood Press.

Wickramasinghe, H. K. 1989. Scanned-Probe Microscopes. Sci. Amer. (Oct.):98–105.

~~~~~~~~~~~~~~~~

This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.

~~~~~~~~~~~~~~~~

Notes

9. See also a, b.

10. See also a, b, c, d.

11. David Harriman (2008) places the point at which the atomic theory was inductively proven sometime after Maxwell’s kinetic theory of gases (1866) and not later than the confirmation of Mendeleev’s prediction of gallium (1875). His is not a claim about when all knowledgeable scientists accepted the atomic theory, but a claim about when all the elements of a rational proof of the theory were at hand. I hope later in this thread to look into whether the additional evidence and theory to 1908, my point (in the 1991 essay) of definitive proof for the atomic theory, fits naturally and entirely within the criteria Dr. Harriman has proposed for inductive proof of a theory. Meanwhile, note that criteria for rational induction purportedly sufficient to establish scientific theory in chemistry go back to Jakob Friedrich Fries (1801, 1822).

12. Written in 1991, when typewriter keys and printing press struck paper.

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—Hume – Experience of Cause and Effect

We possess only fragments of the writings of Nicolaus of Autrecourt. Ecclasiastical authorities censured his ideas. Nicolaus was ordered to burn his writings publicly and to recant condemned propositions. This he did in Paris in 1347. We possess the writings of David Hume. Of special interest to us are Book I (Of the Understanding) of A Treatise of Human Nature (T), which appeared in 1738–40, and Enquiries Concerning Human Understanding (E), which appeared in 1748.*

“All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstrably certain. . . . Propositions of this kind are discoverable by mere operations of thought, without dependence on what is anywhere existent in the universe” (E 20).[13] Mathematical, demonstrative science is a sort of rationalist’s paradise. “Every proposition, which is not true, is there confused and unintelligible” (E 132).

“Matters of fact . . . are not ascertained in the same manner” (E 21). When it comes to fact or existence, “whatever is may not be” (E 132). Why does Hume think that? Because “no negation of a fact can involve a contradiction” (E 132). Why does Hume think that? Because “whatever is intelligible, and can be distinctly conceived, implies no contradiction” (E 30) and “the non-existence of any being, without exception, is as clear and distinct an idea as its existence. The proposition, which affirms it not to be, however false, is no less conceivable and intelligible, than that which affirms it to be” (E 132).

Hume’s reasoning here is very rationalist and very weak. That one can conceive of the contrary of some matter does not always mean that that contrary is possible nor that it could not eventually be shown to be self-contradictory. One can conceive of the possibility that there is some odd counting number n such that (n2 – 1) is not evenly divisible by 4, but in truth there is no such number n. One’s ability to conceive of the “possibility” of things truly impossible could be due to a liberality or poverty in one’s concepts or due merely to a present unconcern for truth (Kneale 1949, 79–80; Quine 1980, 20–46; Peikoff 1990, 88–121; Rasmussen 1983; Armstrong 1989, 7–13, 45–51, 54–76).

Let us follow Hume’s enquiry into “the nature of that evidence which assures us of any real existence and matters of fact, beyond the present testimony of our senses, or the records of our memory” (E 21). Hume observes:

All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; . . . he would give you a reason; and this reason would be some other fact . . . . A man finding a watch or any other machine in a desert island, would conclude that there had once been men in that island. All our reasonings concerning fact are of the same nature. And here it is constantly supposed that there is a connexion between the present fact and that which is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious. (E 22; see also T I.3.2)

Hume contends that the connection we suppose to bind distinct factual states of affairs is the causal connection. That is the connection on which we rely when inferring one state of affairs from another. If we conceive causality in a very general way—along the lines of Ayn Rand’s conception—as the law of identity applied to action and to becoming, then we can say that Hume is roughly right in this contention. Hume will soon argue, however, that though we suppose these causal connections, we have no rational basis for believing in them.

In saying that distinct states of affairs are bound together by the causal connection, Hume is only roughly right. Where the distinct states of affairs under consideration are just a single, selfsame state of affairs at different times, the more salient connection is temporal, rather than causal. That is, when we are considering simple identity through time, it is more natural to speak of identity through time than of identity applied to action or becoming.[14]

Hume insisted that time is atomic. It comes in indivisible minimal, finite units. In his arguments for this conclusion, Hume reasons not so much about time as about extension and about quantity in general. He clearly intends these reasonings to be carried over to time as well (T I.2.2). In the imagination, Hume observes, we can subdivide an extension only so far; we cannot subdivide an extension into an infinite number of parts. “’Tis the same with the impressions of the senses as with imagination” (T I.2.1). There are thresholds of perception. As an object recedes, it does not become infinitely smaller yet visible; it becomes finitely small and then vanishes. As the impressions of our senses are not infinitely small and as extension is not infinitely divisible in imagination, physical space, and time, are themselves not infinitely divisible. “Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects . . . . Our ideas are adequate representations of the most minute parts of extension” (T I.2.2). However small a part might be, we can imagine it, and if we can imagine it, it will be finite (see also Fogelin 1988).

I think Hume resorted to such rationalism out of desperation. He was desperate to establish that time was not continuous. If time were continuous, his skeptical fun concerning the existence of enduring objects and the reality of causality would be hard getting started.[15] As we shall see, Hume’s programme would be in big trouble at the start anyway, though time were discrete.

“From the succession of ideas and impressions we form the idea of time. . . . Time cannot make its appearance to the mind, either alone, or attended with a steady unchangeable object, but is always disover’d by some perceivable succession of changeable objects” (T I.2.3; see also I.4.2). This is too simple. Were we perceiving a constant scene, we would still sense the passage of time, for we are living beings, and there is activity in us. Indeed, we are a living activity (Whitehead 1967, 143–44; Minsky 1988, 288). We cannot dwell on this defect of Hume’s account of experience here.

Focus instead on the following: “Wherever we have no successive perception, we have no notion of time, even tho’ there be a real succession in the objects” (T I.2.3). This proposition is inimical to the skeptical side of Hume’s project. He really cannot afford to be admitting that there are objective instants shorter than we might sense. If there are such, then when we sense things in an instant, we have really sensed them over an objective succession. (Hume cannot simply renounce objective grounds of succession if he intends to leave memory intact; see Bennett 1990, 222–29, and Harper 1984, 125–32.) As it turns out, this is just the way it woks. An instant of consciousness is of the order of milliseconds (10-3 s) or longer (Macar 1985; Edelman 1989, 127–33). Yet we know that as we observe an object for an instant the atomic constituents of the object are making insensible (and unimaginable) transitions down at 10-18 seconds, and some nuclear transitions are occurring in the object down at 10-23 seconds. In an instant of observation, there is an ocean of objective time. In an instant, we observe an object’s existence through time, but to us it is all at once. Hume does not want to impugn present testimony of the senses (nor memory); he needs present sense impressions (and memory) as the only valid source(s) for factual knowledge; he hopes to show that against present sense, inferential factual knowledge pales into pretension. Hume does want to impugn the selfsame identity of any object we observe through perceptible time. That project can be of no avail if in fact we already observe objects selfsame across objective time in every instant of observation (see Stroud 1988, 96–117).

We return to Hume’s charges against causal connections. First Hume emphasizes, like Locke and Ockham before him, that causes and effects are not discoverable by a priori reasoning but only by experience. That proposition seems true, at least if our conception of what it means is not too narrow. We should leave open the possibility that the human infant may be organically, genetically predestined to learn certain elementary facts about the world on the basis of the slightest personal experience (Minsky 1988, 115). If this be true, we would want to include pertinent learning (evolution) of the biological species in addition to individual learning per se when asserting that causal relations are gathered from experience only. Such a circumstance should worry Hume somewhat (but it does not; E 45). Some principles of demonstrative reasoning, the principle of non-contradiction in particular, as well as some principles of causal reasoning (which Hume takes to be apart from demonstrative reasoning) might be acquired not so much by experience of the individual as by organic development of the brain in infancy and antecedent evolution of the human brain. Then it becomes more difficult than ever to maintain that there really are any propositions “discoverable by mere operations of thought, without dependence on what is anywhere existent in the universe,” and the alternative “discoverable by a priori reasoning or discoverable by experience” becomes less momentous. We should also leave open the possibility that causes and their effects as such are in some cases, to some extent, perceived directly (Leslie and Keeble 1987; Heil 1983, 36–41).[16]

As every student of philosophy knows, Hume wants to establish more than the wholly empirical origins of our knowledge of causal relations. He wants to establish the further, extreme thesis that no object or event logically implies anything about its causes or its effects.
For the effect is totally different from the cause and consequently can never be discovered in it. . . . When, I see, for instance, a Billiard-ball moving in a straight line towards another; even suppose motion in the second should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from that cause? May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? (E 25)[17]

Hume’s answer is the same as Nicolaus’: habit. We are simply accustomed to seeing the second billiard ball recoil in particular ways (E 35–39). On the principles of habit, the child, like the animal, can come to anticipate that fire will burn (E 82–85). Now no one will deny that we retain our animal nature; we have cognitive resources in common with other animals. What will concern us here, though, is what further intellectual resources we have.

Hume asserts that effects are totally different from their causes, and this is somewhat misleading. The second billiard ball is not the first ball; in this sense, they are totally different. But the second billiard ball is very much like the first, and the motion of the second much like the motion of the first. There are symmetries. We earlier adduced cases of causality in which effects bore more conclusive signatures of their causes on their faces, but even in Hume’s example, the effect resembles the cause (cf. APo 2.16–17).

Hume concludes his famous billiards passage with the claim that all our a priori reasonings can never show any foundation for our expectations of what the second billiard ball will do (E 25). The sense of “a priori” here is unclear. If by “a priori reasonings” he means simply reasoning we might engage in just now while the first ball is on its way (very slowly, I hope) to the second, then I contest his claim.

Hume mentions some equally “consistent and conceivable” responses of the second ball to impact by the first. These responses are suspiciously tame; each could be readily engineered in reality. Imagine, instead, the following: upon being struck by the first ball, the diameter of the second is reduced, or the second disappears, or becomes a pulley, a loaf of bread, a live rabbit, a melody, or the letter B. These fanciful outcomes are as “conceivable” as Hume’s, but they are hardly as “consistent.” Why not?

One never observes simply two billiard balls colliding. There is always more than that present. There are accompaniments, usually taken for granted and not brought into focal awareness. We know (here, imagine) not only that before us there is one billiard ball rolling toward another, but that they reside on the table, that the table rests on the floor, that beneath the building is the earth (the same earth one was upon the day before and the day before that), that one has a body, that it has weight, that one is breathing, that the song playing from the jukebox was popular during WWII.

One billiard ball is rolling toward another. Upon collision something will happen. One knows that already. If the target ball has been screwed to the table from underneath, things would be just as they are now? Not quite. The target ball was rolling freely a few moments ago and has been resting quietly since then. We would have noticed someone securing it to the table (contrast with Nozick 1981, 222–23, and Goodman 1983, 72–81; against the latter, see Hesse 1974, 75–88). If the target ball is going to become a rabbit or the letter B, things have to be radically different than they are if the target ball is just going to continue being the same old ball. One knows that already (cf. Armstrong 1991, 46–49; Harper 1984, 119–22; Brittan 1978, 197–205).

It is not only the two billiard balls that are subject to the law of identity; it is not only their behavior that must be “consistent.” Everything else that there is or has been or will be, everything else along with the two billiard balls, every thing, individually and altogether, is subject to the law of identity. From identity, manifold identity, comes consilience-induction. “And all things are ordered together somehow, but not all alike—both fishes and fowls and plants; and the world is not such that one thing has nothing to do with another but they are all connected” (Metaph. 1075a15–17).

Continued below—
Hume – Reasoning to Cause or Effect
Hume – Necessity
Hume – Uniformity
Existence is Identity

References

Aristotle 1984 [c. 348–322 B.C.]. The Complete Works of Aristotle. J. Barnes, editor. Princeton. Princeton University Press.

Armstrong, D. M. 1989. A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press.
——. 1991 [1983]. What Is a Law of Nature? Cambridge: Cambridge University Press.

Bennett, J. 1990 [1966]. Kant’s Analytic. Cambridge: Cambridge University Press.

Brittan, G. G. 1978. Kant’s Theory of Science. Princeton: Princeton University Press.

Edelman, G. M. 1989. The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books.

Fogelin, R. 1988. Hume and Berkeley on the Proofs of Infinite Divisibility. Philosophical Review 97(Jan):47–69.

Goodman, N. 1983 [1954]. Fact, Fiction, and Forecast. 4th ed. Cambridge, MA: Harvard University Press.

Harper, W. L. 1984. Kant’s Empirical Realism and the Distinction between Subjective and Objective Succession. In Kant on Causality, Freedom, and Objectivity. W. L. Harper and R. Meerbote, editors. Minneapolis: University of Minnesota Press.

Heil, J. 1983. Perception and Cognition. Berkeley: University of California Press.

Hesse, M. 1974. The Structure of Scientific Inference. Berkeley: University of California Press.

Hume, D. 1975 [1893, 1748]. Enquiries Concerning Human Understanding. 3rd ed., L A. Selby-Bigge, editor. Oxford: Clarendon Press.
——. 1978 [1888, 1740]. A Treatise of Human Nature. 2nd ed., L. .Selby-Bigge, editor. Oxford: Clarendon Press.

Kneale, W. C. 1949. Probability and Induction. Oxford: Oxford University Press.

Leslie, A. M. and S. Keeble 1987. Do Six-Month-Old Infants Perceive Causality? In Thought without Language. Oxford: Clarendon Press.

Macar, F. 1985. Time Psychophysics and Related Models. In Time, Mind, and Behavior. J. A. Michon and J. L. Jackson, editors. Berlin: Springer-Verlag.

Minsky, M. 1988 [1985]. The Society of Mind. New York: Simon & Schuster.

Nozick, R. 1981. Philosophical Explanations. Cambridge, MA: Belknap Press of Harvard University Press.

Peikoff, L. 1990 [1967]. The Analytic-Synthetic Dichotomy. In Introduction to Objectivist Epistemology. Expanded 2nd ed., H. Binswanger and L. Peikoff, editors. New York: Penguin Books USA, Meridian.

Quine, W. 1980 [1953]. Two Dogmas of Empiricism. Reprinted in From a Logical Point of View. 2nd ed. Cambridge, MA: Harvard University Press.

Rasmussen, D. B. 1983. Logical Necessity: An Aristotelian Essentialist Critique. The Thomist 47:513–40.

Stroud, B. 1988 [1977]. Hume. London: Routledge.

Whitehead, A. N. 1967 [1925]. Science and the Modern World. New York: The Free Press.

~~~~~~~~~~~~~~~~
This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.
~~~~~~~~~~~~~~~~

Notes
13. Correct affirmations discoverable by mere operations of thought are a priori, but in Hume’s account, they are not also analytic. That does not mean they are therefore synthetic. Hume’s category of things known with certainty by intuition or demonstration is a category of things known neither analytically nor synthetically (Allison 2008, 63–64, 76–83). Hume’s partition is not the analytic-synthetic partition, whose necessary and sufficient criterion of analyticity is self-contradiction under denial, every proposition not analytic being classed as synthetic (as with Leibniz’ fundamental division between truths of reason and truths of fact).

Known by mere operations of thought, in Hume’s view: the relation resemblance, the relation contrariety between existence and non-existence, the relation degree in a quality, and the relation proportion in quantity and number. Known only with information from sensory experience are the standing of things in: the relation identity (self-sameness across time), relations spatio-temporal, and relations causal (T I.1.5, I.3.5).

These seven relations are called philosophical relations by Hume. The first four guide thought, reflective imagination, with certainty; the last three guide with probability. Notice that association of ideas is not among these normative relations. Association is not a philosophical relation. It is a natural mental relation influenced by resemblance, contiguity, and cause and effect (T I.1.4; E 19). The sight of a wound leads one to think of the pain (E 19). The relation of cause and effect is both philosophical and mentally natural (T I.1.5). It would seem Hume must also regard resemblance and contiguity as not only philosophical relations, but mentally natural ones. How else can they be sources of the purely natural relation of association?

Hume tries to use the natural relation association to invalidate causality as a philosophical and rational epistemological guide (as conceived by his predecessors). In the Enquiry, Hume omits the list of philosophical relations, as well as the distinction between philosophical and natural relations.

I would say, contrary to Hume, that none of his philosophical relations are known apart from sensory experience of the natural world, however directly or reflectively they are connected to that experience. Furthermore, habit from association is not an adequate substitute for reason animated by what Hume had called the philosophical relation of cause and effect.

14. In the Treatise, Hume distinguishes between causation and simple identity through time (I.1.5). The latter is left out of account in the Enquiry.

In his 1908 book Identity and Reality, Emile Meyerson writes: "The principle of causality is none other than the principle of identity applied to the existence of objects in time" (page 43 in the 1930 English translation*). That leaves simple identity through time as a form of the causal relation, or at least it makes numerical identity through time a more salient part of the causal relation than in Rand’s formula: “The law of causality is the law of identity applied to action. All actions are caused by entities. The nature of an action is caused and determined by the nature of the entities that act; a thing cannot act in contradiction to its nature” (1957, 1037). (See further: a, b.)

Part of Rand’s law of identity is that one thing cannot simply turn into another without there being a distinctive reason. (Mere wishing, magical words, or mystical words are ruled out as not real reasons.) The birth of the infant mind “is the day when he grasps that the streak that keeps flickering past him is his mother and the whirl beyond her is a curtain, that the two are solid entities and neither can turn into the other, that they are what they are, that they exist” (1957, 1041).

15. It is not only for the sake of arguing the invalidity of the philosophical relation cause and effect that Hume maintains the atomicity and perceptual correspondence of time. The atomicity of time and its perfect concordance with moments of perception is an integral part of Hume’s way of judging the validity of empirical ideas: solely by their traceability to the mental particulars that are simple sense impressions (T I.1.1).

16. See also Gopnik and Schulz 2007.

17. I have exhibited the relationship between (i) the principle that every action-bearing entity bears certain kinds of action and not other kinds of action and (ii) the principle of non-contradiction here. Investigation of what are the kinds of action a certain entity bears will have its own distinctive relationships to the principle of non-contradiction, and constantly the investigation will presuppose (i) in its specially intimate relation with (ii). Not all imaginings of what actions a billiard ball might bear are equally consistent in the logical sense.

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—Hume – Reasoning to Cause or Effect

Any and all things are situated. Billiard balls are in situations. The situations are in situations too. The weather is in a situation no less than a billiard ball. The range of situations in which a thing might be is a concomitant of a thing’s identity. The range of situations in which a thing might be is learned from one’s total experience.[18] The task of sorting out what is what and what can become what in what situations is undertaken not only by scientists and philosophers (Armstrong 1991, 137–39), but by everyone, child and adult (Keil 1989, 159–215).

Hume would want to emphasize that learning from experience is a matter of forming habits. He tried to squeeze far too much into that mode of learning. (On Hume’s attempt to explain generalization in terms of habit, see Stroud 1988, 38–41. Habituation accounts of conceptual knowledge have not fared well in recent years; see Rips 1989 and Jackendoff 1987, 143–48.) In his earlier work, the Treatise, Hume seems to be cognizant of complications. He allows that we sometimes reason about causes and their effects not only according to custom arising from similar past conjunctions, but from a principle of identity. He allows that in cases “more rare and unusual,” we may assist elementary custom by conscious reflection on past experience and arrive at “custom [belief] in an oblique and artificial manner.”

I explain myself. ’Tis certain, that not only in philosophy, but even in common life, we attain the knowledge of a particular cause merely by one experiment, provided it be made with judgment, and after a careful removal of all foreign and superfluous circumstances. Now as after one experiment of this kind, the mind, upon the appearance either of the cause or the effect, can draw an inference concerning the existence of its correlative; and as a habit can never be acquir’d merely by one instance; it may be thought, that belief cannot in this case be esteem’d the effect of custom. But this difficulty will vanish, if we consider, that tho’ we are suppos’d to have had only one experiment of a particular effect, yet we have many millions to convince us of this principle; that like objects, plac’d in like circumstances, will always produce like effects; and as this principle has establish’d itself by a sufficient custom, it bestows an evidence and firmness on any opinion, to which it can be apply’d. (T I.3.8)

We might want to qualify and refine the general principle to which Hume appeals, the principle that “like objects, placed in like circumstances, will always produce like effects,” but it is at any rate clear that Hume is here squirming out of his official position that knowledge of fact is simply a matter of custom or habit.[19] Also in the Treatise, when writing on our knowledge of the continued and independent existence of bodies (T I.4.2) and when writing on our understanding of why things, e.g., clocks, may sometimes behave one way and sometimes another (T I.3.7), Hume senses the inadequacies of his habituation account of inductive inference and tries to make accommodations. In his later work, the Enquiries, he deals with these complications either by not bringing them up or by offering only meager “hints “ of their solution (E 47).

Hume’s commonsense principle that same causes yield same effects was endorsed also by Aristotle: “It is a law of nature that the same cause, provided it remain in the same condition, always produces the same effect” (GC 336a27-28). Ockham endorsed the principle in a form close to Hume’s: “Causes of the same kinds are effective of effects of the same kinds” (Weinberg 1965, 142). Ockham took this principle to be necessary and self-evident. As the principle is formulated by Ockham or Hume, it is subject to two interpretations. One, a broad one, I shall endorse in a moment. The other—and this is what both Ockham and Hume (E 64) most likely meant—is just the principle as stated without ambiguity by Aristotle. I think we should be wary of Aristotle’s principle. Hereafter, I shall refer to it as the narrow mode of causality. Although it obtains throughout vast regions of our experience, throughout much of existence, it evidently does not obtain for physical processes in quantum regimes nor in classical chaotic regimes. I suggest we reformulate the principle more broadly, thus: “Identical existents, in given circumstances, will always produce results not wholly identical to results produced by different existents in those same circumstances.” Application of the law of identity to action or becoming would seem to require only this much (contrary to Peikoff 1991, 14–15).[20]

It is not always the case that identical things placed in the same circumstances yield a single (repeated) result. Some existents yield single distinctive results; others yield distributions of distinctive results. Only if one allows for the latter possibility in one’s construction of the principle that “same causes yield same effects” is it universally true. Within the realm of classical mechanics, which covers billiards, Hume is correct in saying that same causes yield same (single) effects.

Out of all the conditions that obtain in a situation, we typically take only one or a few as cause of some distinctive result, only a select portion of the ways in which the law of identity applies to an action or a becoming (Minsky 1988, 129; van Fraassen 1991, 318–27; Gasper 1991, 293–95). We try to discover among antecedent conditions ones that will make a certain result under a wide range of variations in the remaining variable conditions. In a general commonsense way, everyone knows that characteristic of causes. Then they know, though perhaps only dimly, the principles of induction enshrined by John Stuart Mill: the principle of agreement, the principle of difference, and the principle of concomitant variation (Mill 1973, 3.8; Copi 1961, 363-407; Kelley 1988, 276–87). Aristotle knew something of these principles (Phys. 199b15–20; Top. 146a2–12); more so did Robert Grossette, Albert the Great, Duns Scotus, Ockham, and Francis Bacon (Weinberg 1965, 136–45, 153). That these are effective techniques for arriving at causes is knowable from everyday experience and all the more from modern scientific practice.[21] To rely on these techniques is to affirm the principle of identity operative. In reasoning to causes, we follow most conspicuously not habit but identity.

In a primary sense, causes make things happen.[22] We witness one billiard ball setting another in motion. We would usually say that what happened was that one billiard ball struck the other and set it in motion. According to Hume, we have gotten the idea that the first ball made the second move by custom of having seen like conjunctions of billiard balls in the past. Then why could we not as well say that the second billiard ball’s acceleration is what causes the first ball to strike it rather than what we usually say? (In some circumstances, young children do take effects to precede causes; Bullock, Gelman, Baillargéon 1982, 216.) Perhaps we are more often interested in prediction than postdiction; animals are surely more oriented to the future than the past. Nevertheless, when we look only backwards, why can we not believe that the acceleration of the second caused the first to strike it? I suggest it is because we have direct experience of causal powers, contrary to the fabulous sayings of Hume (E 50), and we know where they lie in this situation (Boyd 1991, 355–66). The idea of causality is more than the (tightly fastened) idea of regular conjunction in regular temporal order even for the simple billiards case.

Hume acknowledges that we think of causes as having some sort of necessary connection with their effects. This sense of necessity he supposes to be a psychological compulsion arising from our past observations of repeated conjunctions between causes and their effects. “We immediately feel a determination of the mind to pass from one object to its usual attendant. . . . Upon the whole, necessity is something, that exists in the mind, not the objects. . . . Necessity is nothing but that determination of the thought to pass from causes to effects and from effects to causes, according to their experienced union” (T I.3.14). As Hume would have it, even the necessities we find in the interactions of our bodies with other objects are merely projections from necessities we find in our mental operations (T I.4.4). This is absurd. (This error has more subtle relatives, e.g., the thesis of Aquinas that necessity in affirmation of existence is gotten from necessity in intelligibility; see Hoenen 1952, 165–67, 179–81.)

By about three years of age, we have grasped the general commonsense adult principles of causality; we understand that occurrences have causes and that these causes come down to specific mechanisms. The striking of one billiard ball by another is perceptually salient. It is a sharp event. We naturally would seek a trigger of such an event, and in this case, what we would seek is readily apparent. All are agreed that the second ball’s being set in motion had a cause, namely, the first ball’s striking it. This is a causal explanation at the level of common sense. Even at this level, though, not all causal relations are so obvious. That the snowman melted because it became too warm or that the living room became filled with smoke because the damper was not open are a little less obvious. Identification of these causal relations requires, in addition to specific experience, a little more causal reasoning. Such reasoning is a major mode of induction.

It is not from more repetitions of experience, but from a more extensive network of experience and from greater skill in reasoning on causal principles, that we become capable of composing commonsense causal explanations (Bullock, Gelman, Baillergéon 1982).[23] Contrary to the implications of Hume’s model, repetition of experience is not the main influence in our identification of causes. Hume recognized the importance, for humans, of causal reasoning, but he managed to not notice that this is at variance with his insistence on the preeminent role of habit (E 84n1).[24]

When one comes to formulate ideas about inanimate motion more generally, things become much less obvious, and customary experience can put one in the wrong frame of mind. It was very difficult for man to get straight which motions needed to be explained, which motions have causes in the primary sense. Today, students of physics learn the answer when they are taught the law of inertia, the law that a body will continue at constant speed and in a straight line (or will remain at rest) unless acted upon by a force. At a more advanced level, students learn that and how the inertia principle has been recast in more general forms: in the Lagrangian mechanics, as an extremal principle which tells how a body will move when or when not subjected to external forces; and in general relativity, as the principle that free bodies travel along geodesics of spacetime whether curved or flat.

It is only the elementary form of the law of inertia that concerns us here. Aristotle and his followers held to principles contrary the inertia principle. Terrestrial bodies, when moving, naturally tend to move towards certain places of repose (Phys. 199b14–19, 208b9–15, 215a1–21, 230a19–231a17). The heavenly spheres, upon which ride the heavenly bodies, naturally and always move in circular ways. Here let us confine attention to terrestrial bodies whose natural direction of motion is towards the earth: the earthly bodies, not water, air, nor fire. Aristotle’s camp took the free fall of earthly bodies as natural and as standing in no need of special explanation; no external force is being applied to keep such bodies falling to the earth. Any other motion of an earthly body, any motion that is not free fall, needs special external explanation. Moreover, any motion at all requires some explanation. “Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else which moves it” (Phys. 241b34–36).

What could be more sensible? In our life experiences here on the surface of the earth, we have countless confirmations of Aristotle’s thesis every day. To get an object moving requires effort, to keep it moving requires effort, and the object will sooner or later return to rest. The strings of the harp will return to silence. For Galileo and his followers to propose that motion, provided it be uniform, required no explanation, no efficient cause, but that non-uniform motion, including coming to rest, did, they had to put on new thinking caps. (Although it does not affect my argument, I should note for historical accuracy that it was not until Descartes that uniform motion was surely taken to be along a straight line; Galileo took it to be along a circle of constant radius, with center at the center of the earth.) These men could not leave the answer to habitual experience (nor to tradition). Formulating physical principles simply according to the most usual observations would not have led men to the law of inertia. Until this law and its conceptual vantage were discovered, the scientific revolution could not happen (Butterfield 1965, 14–28, 67–85; McClosky 1983).[25]

In common sense and in most scientific reasoning, we make the tried and true presumption that occurrences have causes. Hume discussed this principle in the venerated form “whatever begins to exist, must have a cause of existence.” He contended that this principle is not a necessary truth. He may have actually doubted the truth of the principle (T 78–82). We should distinguish two interpretations of the principle. In one we take cause as material cause, and in the other, we take cause as efficient cause. As to material cause, the principle seems to have held up perfectly in the two and a half centuries of science since Hume. It holds for all elementary particles; every particle gets made from some others. As to efficient cause, the principle holds always for cause in the broad mode; each type of elementary particle has its distinctive ways of coming about. (It seems to me that Kant’s defense of the principle as pertaining to efficient causality, in his celebrated Second Analogy, succeeds for the broad mode, but not for the narrow; Kant 1965 A190-211 B233–56; Brittan 1978, 170–71, 181–82.) Again as to efficient cause, the principle evidently does not hold in the narrow mode for elementary particles. There is no narrow cause of a particle decay, so there can be no narrow cause of the decay products. Remember, too, the proverb of particle physicists: “Seek not reasons for decay, but seek the barriers to decay.” At the level of elementary particles, we seek reasons for stability (Frauenfelder and Henley 1974, 83–87; Sachs 1987, 100–103, 175-77; Weinberg 1981).[26]

We have observed that Mill’s methods of induction—agreement, difference, and concomitant variation—are essential to the growth of scientific knowledge and that they are clearly wedded to a fundamental law of all existents, the law of identity. We have observed also that Hume’s proposed basis for induction—habit—makes no suggestion as to why those techniques should be effective, why they should expose new regularities, orders, and unities of nature. Hume’s account also leaves utterly opaque that great engine of scientific discovery, the hypothetico-deductive method (Copi 1961, 433–51; Hempel 1966, 10–28; Kelley 1988, 344–65).[27]

From the statement of a hypothesis (say, Newton’s law of gravitation), together with some established truths (e.g., the orbit of Uranus) and plausible presumptions, we deduce consequences (a planet beyond Uranus). On the character of confirmation, see Mackie 1981; Newton-Smith 1981, 183-97, 226–32; and Armstrong 1991, 41–46. Both the hypothesis and its consequences are claims about the world. Hypotheses are arrived at by some mix of induction and imagination. We really do not know all that much about how hypotheses are formed (Reilly 1970, 36–38; Hempel 1966, 15–18; Drake 1980; Cohen 1981). We really do not know that much either about how one selects relevant established truths. I assume that not all are selected ahead of the grasping of consequences, but my argument does not depend on this. We do know how the consequences are constructed, or at any rate, how they can be reconstructed (Minsky 1988, 186–89). The consequences are deductions from the hypothesis in combination with select established truths. Now consider the case of a hypothesis that has been subsequently well confirmed by observation of predicted, deduced consequences. On Hume’s model of induction and causality, is this not a minor miracle? Why, on Hume’s view, should deduction yield consequences about what is in the world?

On the view that identity is a deep and general law of reality, the success of the hypothetico-deductive method is intelligible. Validity of our deductions assures us in some measure that we are not in opposition to the universal law of identity. Presumably, that is why validity is desirable. From the vantage of Rand’s principle of identity, we have some idea of why the hypothetico-deductive method works. It is marvelous but not miraculous.

In Hume’s view, as in Ockham’s, the existence of one object cannot be inferred from the existence of another (E 132). Hume contends that, excepting mathematical objects, nothing can be demonstrated of any objects of reasoning (E 131). “All belief of matter of fact or real existence is derived merely from some object, present to the memory or senses, and a customary conjunction between that and some other object” (E 38). Yet in reasoning from a hypothesis to an observable, but as yet unobserved consequence, we can hardly be relying merely on custom. Apparently, Hume never squarely confronted the hypothetico-deductive method. He speaks of “hypothetical arguments, or reasoning upon supposition,” but in these he says there is no “belief of a real existence” (T I.3.4; E 37). Insofar as Hume does begin to consider scientific reasoning, he turns from custom to identity. He may boldly proclaim that “all inferences from experience, therefore, are effects of custom, not of reasoning” (E 36), but in a note, he remarks that scientific knowledge cannot be established purely by experience, but requires “some process of thought, and some reflection on what we have observed, in order to distinguish its circumstances and trace its consequences” (E 36n1; see also E 84n1).

Continued below—
Hume – Necessity
Hume – Uniformity
Existence is Identity

References

Aristotle 1984 [c. 348–322 B.C.]. The Complete Works of Aristotle. J. Barnes, editor. Princeton. Princeton University Press.

Armstrong, D. M. 1991 [1983]. What Is a Law of Nature? Cambridge: Cambridge University Press.

Brittan, G. G. 1978. Kant’s Theory of Science. Princeton: Princeton University Press.

Boyd, R. 1991 [1985]. Observations, Explanatory Power, and Simplicity: Toward a Non-Humean Account. In Boyd, Gasper, and Trout 1991.

Boyd, R., Gasper, P., and J. D. Trout, editors, 1991. The Philosophy of Science. Cambridge, MA: MIT Press.

Bullock, M., Gelman, R., and R. Baillargéon 1982. The Development of Causal Reasoning. In The Developmental Psychology of Time. W. J. Friedman, editor. New York: Academic Press.

Butterfield, H. 1965 [1957]. The Origins of Modern Science. Revised ed. New York: Free Press.

Cohen, I. B. 1981. Newton’s Discovery of Gravity. Sci. Amer. (Mar):150–56.

Copi, I. M. 1961 [1953]. Introduction to Logic. 2nd. Ed. New York: Macmillan.

Drake, S. 1980. Newton’s Apple and Galileo’s Dialogue. Sci. Amer. (Aug):150–56.

van Fraassen, B. C. 1991 [1977]. The Pragmatics of Explanation. In Boyd, Gasper, and Trout 1991.

Frauenfelder, H., and E. M. Henley 1974. Subatomic Physics. Englewood Cliffs, NJ: Printice-Hall.

Gasper, P. 1991. Causation and Explanation. In Boyd, Gasper, and Trout 1991.

Hempel, C. G. 1966. Philosophy of Natural Science. Englewood Cliffs, NJ: Prentice-Hall.

Hoenen, P. 1952. Reality and Judgment according to St. Thomas. H. F. Tiblier, translator. Chicago: Henry Regnery.

Hume, D. 1975 [1893, 1748]. Enquiries Concerning Human Understanding. 3rd ed., L A. Selby-Bigge, editor. Oxford: Clarendon Press.
——. 1978 [1888, 1740]. A Treatise of Human Nature. 2nd ed., L. .Selby-Bigge, editor. Oxford: Clarendon Press.

Jackendoff, R. 1987. Consciousness and the Computational Mind. Cambridge, MA: MIT Press.

Kant, I. 1965 [A-1781 B-1787]. Critique of Pure Reason. N. Kemp Smith, translator. New York: St. Martin’s Press.

Keil, F. C. 1989. Concepts, Kinds, and Cognitive Development. Cambridge, MA: MIT Press.

Kelley, D. 1988. The Art of Reasoning. New York: W. W. Norton.

Mackie, J. L. 1981 [1963]. The Paradox of Confirmation. Reprinted in The Philosophy of Science. P. H. Nidditch, editor. New York: Oxford University Press.

McClosky, M. 1983. Intuitive Physics. Sci. Amer. (Apr):122–30.

Mill, J. S. 1973 [1843]. A System of Logic Ratiocinative and Inductive. Toronto: University of Toronto Press, Routledge & Kegan Paul.

Minsky, M. 1988 [1985]. The Society of Mind. New York: Simon & Schuster.

Newton-Smith, W. H. 1981. The Rationality of Science. Boston: Routledge & Kegan Paul.

Peikoff, L. 1991. Objectivism: The Philosophy of Ayn Rand. New York: Dutton.

Reilly, F. E. 1970. Charles Peirce’s Theory of Scientific Method. New York: Fordham University Press.

Rips, L. J. 1989. Similarity, Typicality, and Categorization. In Similarity and Analogical Reasoning. S. Vosniadour and A. Ortony, editors. Cambridge: Cambridge University Press.

Sachs, R. G. 1987. The Physics of Time Reversal. Chicago: University of Chicago Press.

Stroud, B. 1988 [1977]. Hume. London: Routledge.

Weinberg, J. R. 1965. Abstraction, Relation, and Induction. Madison: University of Wisconsin Press.

Weinberg, S. 1981. The Decay of the Proton. Sci. Amer. (Jun):64–75.

~~~~~~~~~~~~~~~~
This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.
~~~~~~~~~~~~~~~~

Notes
18. Learned here means established in one’s conceptual framework, as in Harriman 2010, 31–34. Compare those pages with Critique of Pure Reason, Bxiii–xiv. On Kant’s connection of induction to taxonomic systematization of nature in the organization of experience, see Allison 2008, 140–51. On the connection of induction to conceptualization, in Francis Bacon and in William Whewell, see McCaskey 2004. On abstractive induction, see here.

19. Allison points out that in warranting induction from experience of a single case, Hume is not only relying on his general principle that “like objects, placed in like circumstances, will always produce like effects.” Hume is also relying on his principle that every event has some cause (Allison 2008, 156). On this latter principle, see third paragraph from last in the present section (and Allison 2008, 93–111, 137–38).

Allison observes also that those two conditions are required, in Hume’s account, not only for induction based on a single case, but for virtually all inference from something observed to something unobserved (e.g., T I.3.13). Hume’s text on inductive inference from the single case (T I.3.8), which I quoted in the third paragraph, shows acutely the power of judgment as acting independently of custom concerning the case at hand. Making the right judgment concerning causally relevant factors in this single-case base for inference in subsequent cases is not helped by appeal to the general rule that like objects placed in like circumstances produce like effects. As a matter of fact, Hume’s two general rules are also not helpful in making the required particular judgment where the observed cases are multiple or numerous. Sorting objects and actions into classes according to usual, manifest similarities does not help either (Allison 2008, 159–60; see also here and Harriman 2010, 9, 31–34).

Hume helps himself, in the quoted passage and in others, to the human power of judgment. That is a power Hume is not entitled to invoke, given his model of human cognition. Barry Stroud writes that Hume’s theory of ideas
obstructs proper understanding of the role, or function, or point of various ideas in our thought about the world because in representing “having” an idea as a matter of a certain object’s simply being “in” the mind, it leaves out, or places in a secondary position, the notion of judgment, the putting forth of something that is true or false. For Hume, ideas exist in the mind and have their identity completely independently of any contribution they might make to judgments or statements that have a truth-value. He sees judging as just a special case of an object’s being present to the mind. . . . He does not see that without an account of how ideas combine to make a judgment or a complete thought he can never explain the different roles or functions various fundamental ideas perform in the multifarious judgments we make, or in what might be called the “propositional” thoughts we have. Consequently, he does not arrive at even the beginnings of a realistic description of what “having” the idea of causality actually consists in. (1988, 232)

20. There were two errors in this paragraph. Firstly, unlike quantum regimes, classical chaotic regimes hold no exceptions to Aristotle’s principle (a, b). Secondly, my broader formula intended to be the minimum implied by the law of identity did not quite reach the minimum, which would be: “For some given circumstance or other, identical existents will produce results not wholly identical to results produced by different existents in those same circumstances.”* As is seen in the link, that picayune revision to the broad formula is occasioned by a consideration that applies to all physical regimes, including the classical regular regime.

The gravamen of the broad formula was captured perfectly well in my 1991 statement: “Identical existents, in given circumstances, will always produce results not wholly identical to results produced by different existents in those same circumstances.” In contrast Leonard Peikoff had maintained earlier that year that Rand’s law of identity entails the following: “In any given set of circumstances, there is only one action possible to an entity, the action expressive of its identity” (1991, 14). Dr. Peikoff’s formula can be read as not in contradiction with mine if his phrase only one action possible is taken to mean only one kind and range of action possible. But that is not the plain reading of his text. In his 1976 lectures The Philosophy of Objectivism (Lecture 2), also, he had maintained that Rand’s law of identity applied to action entailed that only a single action was physically possible to a thing in a given circumstance. Rand gave notice that those lectures were an accurate representation of her views, so I expect she shared the erroneous view expressed by Peikoff concerning uniquely determined outcome. (That there is a unique outcome in all cases is not in dispute; the issue is whether in all cases only that unique outcome was physically possible; see my 1997 reply to Rafael Eilon, 159–62.)

So I expect Rand meant “uniquely determined” in her 1973 formula for the law of physical causality: “All the countless forms, motions, combinations, and dissolutions of elements within the universe—from a floating speck of dust to the formation of a galaxy to the emergence of life—are caused and determined by the identities of the elements involved” (MvMM, 25). In any case, the error is easily corrected without major revision to her metaphysics or to its counters to Hume’s account of causation.

21. Cf. Harriman 2010, 67–71, on the first two methods, the third glossed only as a species of the second. Kelley 1988 discusses all three methods, the third on pages 283–85.

22. An ambitious attempt at developing this elementary thesis into a full-blown account of causation and explanation in science is made in Woodward 2003.

23. On the origins and elaboration of causal understanding in development, see also Chapter 6 of Carey 2009 along with Gopnik and Schulz 2007.

24. It was misleading for me to say that Hume “managed to not notice” that the importance of causal reasoning is at variance with his insistence on the preeminent role of habit in causal attributions. What he managed to “not notice” was the ineffectiveness of his gestures at reconciling that variance. That is, the variance remains.

25. Cf. Harriman 2010, 14–15, 44–46, 49–53. See further, Miller 2006.

26. More on the stability of matter: Lipkin 1995 and Lieb 2009.

27. Contrast my representation of the hypothetico-deductive method in science with its representation by Harriman (2010, 145–46). I have not supposed that the method entails that hypotheses are mere guesswork, which is not the way the method has been employed by any research in physical science with which I am familiar. However much later philosophers of science took hypotheses to be guesswork, that was not the view of William Whewell (Snyder 2006).

Rand’s theoretical philosophy and my own understanding of the methods of science are consonant with the following superbly informed view of Ernan McMullin 1992. (See also.)
Let us restrict the term abduction to the process whereby initially plausible and testable causal hypotheses are formulated. This is inference only in the loosest sense, but the extensive discussions of the logic of discovery in the 1970’s showed how far, indeed, it differs from mere guessing. The testing of such hypotheses is of the most varied sort. It does, of course, involve deduction in a central way, as consequences are drawn and tried out. Some of these may be singular, others may be lawlike and hence involve induction. But we shall not restrict induction to the testing of causal hypotheses, as Peirce came to do. (89–90)

[Our concern] is with the process of theoretical explanation generally, the process by which our world has been so vastly expanded. This is the kind of inference that makes science into the powerful instrument of discovery it has become. . . . As a process of inference, it is not rule-governed as deduction is, nor regulated by technique as induction is. Its criteria, like coherence, empirical adequacy, fertility, are of a more oblique sort. They leave room for disagreement, sometimes long-lasting disagreement. Yet they also allow controversies to be adjudicated and eventually resolved.

It is a complex, continuing, sort of inference, involving deduction, induction, and abduction. Abduction is generally prompted by an earlier induction (here we disagree with Peirce). The regularity revealed by the induction may or may not be surprising. Deductions are made in order that consequences may be tested, novel results obtained, consistency affirmed. The process as a whole is the inference by means of which we transcend the limits of the observed, even the instrumentally observed.

Let us agree to call the entire process retroduction. We are “led backwards” from effect to cause, and arrive at an affirmation, not simply a conjecture. Retroduction in this sense is more than abduction. It is not simply the initial plausible guess. It is a continuing process that begins with the first regularity to be explained or anomaly to be explained away. It includes the initial abduction and the implicit estimate of plausibility this requires. It includes the drawing of consequences, and the evaluation of the match between those and the observed data, old or acquired in light of the hypothesis. Tentative in the first abduction, gradually strengthening if consequences are verified, if anomalies are successfully overcome, if hitherto disparate domains are unified, retroduction is the inference that in the strongest sense “makes science.” (92–93)

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—Hume – Necessity

Hume could find no necessary connection between distinct objects or events. “One event follows another, but we never observe any tie between them. They seem conjoined, but never connected” (E 58). Why is Hume seeking ties and connections between events? Because, for one thing, between some events, he and we have direct experience of such. “Draw a bucket of water from the well, Mr. Hume. Between your arms and the rising bucket, there is a tie, the rope. Place your walking cane on top of either foot and bear down. Notice the connection between your exertion and the pressure on your foot.”[28]

It might be reasonably protested that what Hume really seeks and fails to find is any logical necessity linking distinct events rather than any physical necessity linking distinct events. Hume was surely seeking logical necessitation; as between distinct things, he says repeatedly, one may be denied and the other affirmed without contradiction; there is no logical connection between distinct things. But he was just as surely seeking (and avoiding?) physical necessitation; he complains of being unable to observe any tie between distinct events and speaks of what it is possible for a billiard ball to do. He swings freely back and forth between physical and logical necessity.[29]

Hume’s vacillation is perfectly understandable, I think, because logical necessities (or possibilities) and physical necessities (or possibilities) are in fact not worlds apart. They are not even as far apart as next-door neighbors. Here are six reasons for thinking that logical necessity and physical necessity are intimately related:

(1) Yesterday a grey squirrel visited my balcony. I witnessed it from the library. It is true that yesterday that grey squirrel made that visit to my balcony. It is a physical fact. Tomorrow it will be true that two days past that grey squirrel made that visit. That is a physical truth and a logical truth. Everything that has been will have been, and will have been just as it was, for one day more tomorrow. That is so necessarily, both physically and logically.

(2) The principle of non-contradiction, with its necessity, emerges in development. Physical constraints found in experience may well inform that emergence. For the most part, during the first year of life, infants do not have language. The very young child evidently acquires a working principle of non-contradiction spontaneously, before acquiring language. It seems that in order to begin to acquire language, the child must have the notions truth and falsity and a working principle of non-contradiction. Without these he cannot grasp the notion proposition (Macnamara 1986, 33–37, 105–9, 114–17).

I mentioned in an earlier section* experiments by Renée Baillergéon (1986; 1987) which indicate that by four months, infants apprehend that one solid object cannot pass through another. I suggested that this might be the most primitive form in which one grasps the principle of non-contradiction (see further, Leslie 1989, 194–200). During the last half of the first year, apparently on account of maturation of the frontal cortex, the normal human infant becomes capable of inhibiting prepotent responses: Until about nine months, the infant will reach impulsively for all objects, but by the end of the first year, he can be more selective. He can give a NO command to some otherwise interfering habitual responses in order to execute the reach required for a desired object (Diamond 1989; Edelman 1989, 44–50, 57–63, 120–27, 159–62). This would seem to be an important step along the way to attaining a working principle of non-contradiction. It is plausible that the ability to represent negations and employ a principle of non-contradiction arises from the preverbal child’s perceptual and motor experience of the physical world (Dretske 1988, 62–79, 95–107; see also Peikoff 1985).

(3) In formal reasoning, we use physical props (Rumelhart 1989, 306–11).

(4) There are no purely logical necessities; every logical necessity has some physical bases, namely, neuronal processes. In his seminal study of the relationship of logic and psychology, John Macnamara points out that although logicians study ideal reasonings, “inferences carried out by logicians in conformity with the rules of the ideal logic are still actual” (1986, 7).

(5) The difference between logical necessity and physical necessity would seem to be a graded difference. Geometrical necessities holding in the physical world would seem to lie between the poles of logical and physical necessity. Under physically realized geometrical necessities, I mean to include not only spacetime structures, from relativity, but patterns of spacetime occupation, from quantum mechanics.

(6) There are physical necessities nearly as pervasive as logical necessities: All physical things are in spacetime; at all times, there is a population of physical things, and they have some composition (especially important facts for induction; see Williams 1963, 153–56, 138–39, 160–61); any physical thing has mass-energy; any population has entropy. There are, moreover, three physical quantities that are constants, virtually come what may: mass-energy, electrical charge, and angular momentum (Misner, Thorne, and Wheeler 1973, 875–92; Wald 1984, 312–24).

Concerning physical connections, manifest or obscure, between distinct physical events, Hume would surely ask what necessity there is that tomorrow things will work as they have in the past. Everyone agrees that there is no deductive necessity that the drawing of water from the well tomorrow will go as it has in the past. There is no physical necessity either. Water drawing is physically contingent on a great many things; contrast with the mass-energy of the universe, which is evidently not physically contingent on anything, that is, which is evidently ineradicably necessary. We know there is no necessity that water drawing will succeed tomorrow, and that is not all we know about the subject. We know that if our attempt to draw water tomorrow fails, there are reasons for that, reasons growing out of the way things have been. In addition to this general principle, we have some ideas, from our past experience and consequent general understanding of the world, of what could and could not account for a water-drawing failure.

The general principle that the ways things will be grow out of the ways things have been is not a brand new philosophic insight. Immanuel Kant stressed that an effect “not only succeeds upon the cause,” but “is posited through it and arises out of it” (1965 A91 B124). The contemporary philosopher Robert Nozick employs the same idea: “To say that something is a continuer of x is not merely to say its properties are qualitatively the same as x’s, or resemble them. Rather it is to say they grow out of x’s properties, are causally produced by them, are to be explained by x’s earlier having had its properties, and so forth” (1981, 35).

By our general principle, that the ways things will be grow out of the ways things have been, we assert the law of identity in application to action and becoming, and we assert the reality and unity of material substance in all things physical. Our principle actually applies to nominal variations and constancies as well as to physical ones. A term used in an identical sense throughout a discourse is a case of growing out of—in this case, simply remaining the same—previous character. Notice also that conclusions grow out of premises. Of course all nominal items, and their characters, have physical substrata consisting of brain activities. So all propagations of nominal items through time are supported, though not necessarily isomorphically, by physical propagations, Because our primary concern in this essay is with ampliative induction, our focus is on the physical, but our principle that the ways things will be grow out of the ways things have been would seem to pertain to everything. Hereafter I shall refer to this general principle as the principle of substantive propagation.

Even were Hume to agree that our general principle and our particular principles of water drawing are formulated truly and in accord with past experience, he would emphasize that they cannot be established purely deductively (T 86–87). Therefore, belief in these principles cannot be rational. Our belief is instinctual but not rational. Virtually all contemporary philosophers dispute Hume on this point. Hume’s apparent presumption that only the deductively demonstrable is rational is wrong. The conception of rationality in Hume’s era was very restricted. Today inductive reasoning is widely regarded as complementary to deductive reasoning and every bit as rational.[30]

Continued below—
Hume – Uniformity
Existence is Identity

References

Baillargéon, R. 1986. Representing the Existence and the Location of Hidden Objects: Object Permanence in 6- and 8-Month-Old Infants. Cognition 23:21–41.
——. 1987. Object Permanence in 3.5- and 4.5-Month-Old Infants. Developmental Psychology 23:655–64.

Diamond, A. 1989. Differences Between Adult and Infant Cognition: Is the Crucial Variable Presence or Absence of Language? In Weiskrantz 1989.

Dretske, F. 1988. Explaining Behavior: Reasons in a World of Causes. Cambridge, MA: MIT Press.

Edelman, G. M. 1989. The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books.

Hume, D. 1975 [1893, 1748]. Enquiries Concerning Human Understanding. 3rd ed., L A. Selby-Bigge, editor. Oxford: Clarendon Press.
——. 1978 [1888, 1740]. A Treatise of Human Nature. 2nd ed., L. .Selby-Bigge, editor. Oxford: Clarendon Press.

Kant, I. 1965 [A–1781 B–1787]. Critique of Pure Reason. N. Kemp Smith, translator. New York: St. Martin’s Press.

Leslie, A. M. 1989. The Necessity of Illusion: Perception and Thought in Infancy. In Weiskrantz 1989.

Macnamara, J. 1986. A Border Dispute: The Role of Logic in Psychology. Cambridge, MA: MIT Press.

Misner, C. W., Thorne, K. S., and J. A. Wheeler 1973. Gravitation. San Francisco: W. H. Freeman.

Nozick, R. 1981. Philosophical Explanations. Cambridge, MA: Belknap Press of Harvard University Press.

Peikoff, L. 1985. Aristotle’s “Intuitive Induction.” The New Scholasticism 59(2):185–99.

Rumelhart, D. E. 1989. Toward a Microstructural Account of Human Reasoning. In Similarity and Analogical Reasoning. S. Vosniadou and A. Ortony, editors. Cambridge: Cambridge University Press.

Weiskrantz, L. editor, 1989. Thought without Language. Oxford: Clarendon Press.

Wald, R. M. 1984. General Relativity. Chicago: University of Chicago Press.

Williams, D. 1963 [1947]. The Ground of Induction. New York: Russell & Russell.

~~~~~~~~~~~~~~~~
This essay of 1991 had no notes. I will now add a few endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I will also add some hyperlinks within the text.
~~~~~~~~~~~~~~~~

Notes
28. Hume wrote the Treatise during the two years he stayed in La Flèche, France (age 25–26). In the Introduction to that work, he places himself in the empirical tradition of Bacon and Locke. While traveling from La Flèche back to Paris, having just completed the Treatise, Hume wrote a letter to a friend in England urging the following preparatory reading for study of his own book: Malebranche’s Search after Truth, Berkeley’s Principles of Human Knowledge,* portions of Bayle’s Dictionary,* and Descartes’ Meditations* (Mossner 1969, 12–13). Like Berkeley before him, Hume was significantly influenced by Nicolas Malebranche (Luce 1934). Neither Malebranche nor Hume would be turned around by my examples of the rope and the cane.

The psalmist writes of God: “He spake, and it was done” (33:9). For Malebranche the mind of God is the model of effective understanding and causation. “God contains within Himself in an intelligible fashion the perfection of all the beings He has created or can create, and . . . through these intelligible perfections He knows the essence of all things, as through His volitions He knows their existence. Now, these perfections are also the human mind’s immediate object” (ES 10).

Malebranche was an Augustinian. “The Lord Jesus . . . has intimated to us that the human soul and rational mind which is in man, not in the beast, is invigorated, enlightened, and made happy in no other way than by the very substance of God” (Augustine tractate 23.5; S III.ii.6). Malebranche was a Cartesian:

The mind’s pure ideas are clear and distinct. (S V.10)
Everything one clearly conceives is precisely as one conceives it. (S IV.11.2)
We should reason only about things of which we have clear ideas . . . . The state of the question we propose to resolve must be distinctly conceived. (S VI.ii.1)
Real ideas produce real science, but general or logical ideas never produce anything but a science that is vague, superficial, and sterile. We must, then, carefully consider distinct, particular ideas of things in order to discover the properties they contain, and study nature in this way, rather than losing ourselves in chimeras that exist only in certain philosophers’ minds. (S II.ii.8; further, S I.16, III.i.3, VI.ii.6)

Malebranche innovated philosophy extending beyond Augustine and Descartes. (S – The Search after Truth* [1674–75]; ES – Elucidations of the Search after Truth [1678])

The human mind has the idea of the infinite and has it even before the idea of the finite. “For we conceive of infinite being simply because we conceive of being, without thinking whether it is finite or infinite. In order for us to conceive of a finite being, something must necessarily be eliminated from this general notion of being, which consequently must come first” (S III.ii.6). (Like Descartes, Malebranche does not keep firmly distinct the indefinite and the infinite.)

We conceive an infinitely perfect being, and in this idea is included clearly that such a being exists necessarily. The same could not be said of the concept of an infinitely perfect body. For a body is particular and finite being, not infinite being. Being has its existence of itself. It cannot not be. Everything that exists comes from being. Bodies exist by imperfect participation in being. Being would exist were there no bodies (S IV.11.2). God is infinite perfect being. God exists.

One cannot see a body in itself or of itself. One sees a body only through certain perfections of it in God, perfections that represent the body (S VI.11.3). We experience our sensations without anything resembling them outside us; they are modifications of our minds (S III.ii.5). Contrary to what empiricists claim, we are not able to produce ideas of things after the likeness of objects that seem to make sensory impressions on us (S III.ii.2).

Perception consists of sensation and pure idea (S III.ii.6). The presence of the object of its idea is necessary in perception (S III.ii.1), but from this one should not conclude that the object is the true cause of its idea in us (S III.ii.6).

Ideas differ from one another and have real properties. They are real beings. They are spiritual beings, radically different from bodies they may represent. Ideas cannot be made from matter. Men come to think the mind can form its own ideas because men “never fail to judge that a thing is the cause of a given effect when the two are conjoined, given that the true cause of the effect is unknown to them. This is why everyone concludes that a moving ball which strikes another is the true and principal cause of the motion it communicates to the other, and that the soul’s will is the true and principal cause of movement in the arms, and other such prejudices” (S III.ii.3).

One should conclude, rather, “the collision of the two balls is the occasion for the Author of all motion in matter to carry out the decree of His will, which is the universal cause of all things” (S III.ii.3). God wills “that the latter ball should acquire as much motion in the same direction as the former loses, for the motor force of bodies can only be the will of Him who preserves them” (S III.ii.4). (Malebranche, by the way, was skilled in billiards.)

Bodies cannot move themselves. We could conclude that our minds move them were we to see the “necessary connection” between the idea of our finite minds and motions of bodies. We see none. Only in the idea of the infinitely perfect being, the all-powerful being, is there necessary connection between its will and a body’s motion (S VI.ii.3).

That is the verdict of our conceiving things clearly. It is not the verdict of the senses. The latter see a ball communicate its motion to another. We may say a ball is the natural cause of the motion it communicates. “But natural causes are not true causes; they are only occasional causes that act only through the force and efficacy of the will of God” (S VI.ii.3). A true cause “is one such that the mind perceives a necessary connection between it and its effect” (S VI.ii.3).

To my examples of perceiving causal connections—the rope between straining arm and rising bucket, the cane conveying force from hand to foot—Malebranche will say that such connections are natural causal connections, but lack conceptual, logical necessity. Only in an infinitely powerful and absolutely creative being do power and thought coincide. The orderliness we find in everyday experience and in science are from the perpetual wisdom and creative power of that being (S III.ii.6).

Hume helps himself amply to Malebranche’s arguments against logically necessary connections between causes and their effects in nature (T I.3.14; S VI.ii.3). However, as to Malbranche’s doctrine

that the connexion betwixt the idea of an infinitely powerful being, and that of any effect, which he wills, is necessary and unavoidable; I answer, that we have no idea of a being endow’d with any power, much less one endow’d with infinite power. But if we will change expressions, we can only define power by connexion; and then in saying, that the idea of an infinitely powerful being is connected with that of every effect, which he wills, we really do no more than assert, that a being, whose volition is connected with every effect, is connected with every effect; which is an identical proposition, and gives us no insight into the nature of this power or connexion (T I.4.5; see also T I.3.14 and E 55–57).

In moving or straining one’s arm one has no direct experience of causal power in one’s will, according to Hume (E 51–52), following Malebranche (S VI.ii.3; ES 15, 17 [25–26]; see further, Nadler 2000, 121–25, and 2011). For the logical necessity of the causal links to be known the links must be known. But we do not know how we move our arm. We do not know how the mind interacts with matter, specifically how the mind interacts with nerves and muscles. This argument is weak in Hume, as it is weak in Malebranche. Early modern philosophers sleepwalk back and forth between what they know in first-person experience and what they know from third-person scientific physiology. They appeal to the latter to invalidate the former, which is fallacious (cf. Kelley 1986, 36–43). Hume would commit this error again in contending that one does not sense extension and solidity of the cane directly, rather, one senses only sensory impressions (T I.4.4).*

Hume rejected the traditional distinction of types of cause: efficient, formal, material, exemplary, and final. If any such cause is not essentially an efficient cause, the type he had labored so hard to reduce to constant conjunctions, then it is no cause at all. Furthermore, “we must reject the distinction betwixt cause and occasion, when suppos’d to signify any thing essentially different from each other. If constant conjunction be imply’d in what we call occasion, ’tis a real cause” (T I.3.14).

29. Hume formulates two definitions of cause. He maintains that ultimately they are the same. In the first, causal necessity is physical. The second definition is that of which the first is a projection; its necessity is psychological.

In the first, cause is any resembling class of objects (say, flame) that are followed in time by another resembling class of objects (heat) with which they are contiguous. A cause is “an object precedent and contiguous to another, and where all the objects resembling the former are plac’d in like relations of precedency and contiguity of those objects, that resemble the latter” (T I. 3.14; cf. E 60). Necessity between the conjoined classes would have to include the necessity in what we call kinematics in our physics and engineering, the possible motions in a situation, leaving aside forces and energetics. Hume would take kinematical characterization to stand to experience and reason as geometry stands to them (T I.3.1–2; E 20, 27; see further, Allison 2008, 83–87).

That occasions of billiard balls in motion or rest are followed by occasions of billiard balls in motion or rest is not enough for the implication of causation under the scope intended by Hume’s first definition. Dynamics and other physical restrictions must contract the possibilities left open by kinematics. Hume does not allow that there is anything more to our concepts force and energy fundamentally than there is to our concept cause in general (T I.3.14; E 49, 54). Hume’s concept of force in mechanics would be the Newtonian concept: that external influence which produces an acceleration of a body and whose measure is the time rate of change of the momentum of that body. Hume’s concept of energy in mechanics would also be focused on external influence on a body, specifically communication of motion from one body to another.

In reality, there is no part of matter, that does ever, by its sensible qualities, discover [uncover, display] any power or energy, or give us ground to imagine that it could produce any thing, or be followed by any other object, which we could denominate its effect. Solidity, extension, motion; these qualities are all complete in themselves, and never point out any other event which may result from them. The scenes of the universe are continually shifting, and one object follows another in an uninterrupted succession; but the power or force, which actuates the whole machine, is entirely concealed from us, and never discovers itself in any of the sensible qualities of body. (E 50)

We experience that heat is a constant attendant of flame, but to know a putative power or energy of the flame to produce heat is not possible to us. Were we to know such a power, “we could foresee the effect, even without experience; and might, at first, pronounce with certainty concerning it, by mere dint of thought and reasoning” (E 50). That is straight out of Malebranche. Godlike knowledge is the model for human knowledge.

Causal power is something we project onto occasions of cause, cause as under Hume’s first definition, on account of an unavoidable psychological compulsion named in his second definition of cause: “An object precedent and contiguous to another, and so united with it in the imagination, that the idea of the one determines the mind to form the idea of the other, and the impression of the one to form a more lively idea of the other” (T I.3.14; E 60)

30. For example, at a deep level, consider Hintikka’s distinction between the definitory and strategic rules of logic (cf. those types of rule in chess) and his base for both in interrogative logic. See Inquiry as Inquiry: A Logic of Scientific Discovery (1999); also Suppes, 743–45, and Sintonen, chapter 25, in The Philosophy of Jaakko Hintikka (2006). See also Haugeland’s “Truth and Rule-Following” in Having Thought (1998).

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—Hume – Uniformity

Hume thought that if we did have a valid rational basis for induction, it would be the principle “that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same” (T I.3.6). Taken superficially, this principle, the ‘uniformity of nature’ principle is false and uninteresting (Mill 1973, 3.2.2). Wells do not always work, let alone work “uniformly,” and the atomic chemical elements did not always exist. I think the principle that Hume was really trying to get at was an identity principle, something like the principle of substantive propagation, something like, “whether things continue the same or change, there will be reasons, growing out of the way things were at earlier times, for the way things are at later times.”

Hume says it is possible the uniformity principle is false since we can conceive of it being false. The principle is false under the superficial reading, quite apart from Hume’s rationalism. Under the identity reading, the principle stands up to all of our experience, provided we construe “growing out of” in the broad causal mode. The principle stands up to much of our experience even where “growing out of” is construed in the narrow mode.[31]

“Very well,” a modern Humean might say, “how do we know that this identity principle, the substantive propagation principle, with the broad mode of cause, will be true in the future?” Well, how do we know there will be a future? Because we know that our being here just now does not make now cosmically special. “Then all collapsed, and the great shroud of the sea rolled on as it rolled five thousand years ago” (Melville). At this stage of modern science [1991], we reasonably ask whether the universe will eventually contract to a singularity, whether such singularity would be final, whether time would stop. But the end of time, if there be such, is very far off and is not predicated on any fantasies one might indulge concerning the world ending tomorrow (Dicus et al. 1983; Gott et al. 1976).

Immediately after setting out the uniformity principle, Hume reformulates it so as to make it atemporal (T I.3.6). This is close to the assumption we make in attempting to select representative samples from a population. Of course our aim is really only that the samples resemble closely enough the remaining population, only in ways pertinent of our inquiry, and it is often not the case that we have no experience of the population not selected in the sample. We often have some experience of the whole population, and this experience should inform our choice of sampling procedures and our statistical analysis. In these circumstances, Hume’s atemporal form of the uniformity principle affords little skeptical fun. Even where we cannot range freely over a population to take samples for closer examination, we may have reasons to expect the inaccessible population to follow the suite in hand (Mill 1973, 3. 3.3). There are pretty strong reasons of consilience to suppose that atomic chemical elements will continue to be found through electromagnetic radiation spectra, in regions of the universe today [1991] beyond our reach and that the redshifts will continue to increase (cf. Davis 1972, 37–45).

Hume can have his most skeptical fun when he casts the uniformity principle as explicitly about predicting how things will be in the future. “If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, experience becomes useless, and can give rise to no inference or conclusion” (E 32).

As I have already remarked, there is no reason to suppose that the present time is cosmically special. Things as they are over a present time span are a sample of things as they are over other such spans. Time itself does not make a physical difference. Things in a recent time span are presumptively more uniform with things in nearby time spans than in farther time spans because the ways things will be grow out of the ways thing have been. Notice the obvious boundary condition: as time spans approach zero, uniformity tends to perfect identity. This boundary condition seems appropriate for fermions, nuclei, atoms, molecules, and the objects they compose; bosons are another story.

Though time itself makes no physical difference, time is physical. Under the supposition that time is homogeneous, we can derive from Hamilton’s principle (the fundamental dynamical principle in the Hamiltonian formulation of classical mechanics, a formulation under which the transition from classical to quantum mechanics can be smoothly accomplished) the principle of the conservation of energy (Marion 1965, 214–51). The conservation of mass-energy is a very robust principle, experimentally and theoretically. Were the universe eventually to come to a final singularity, the conservation of mass-energy would obtain all along the way. The conservation of mass-energy can be derived also as a consequence of Einstein’s field equation and one of the geometrical identities known as Bianchi identities. (Perhaps the reader demonstrated some trigonometric identities in high school; then the reader has demonstrated some geometric identities. Readers with vector calculus should think of Stokes’ theorem.) It is Einstein’s field equation that warrants our contemplation of the possibility of the universe coming to a final singularity. On the left of that equation, we have geometric structure of spacetime; on the right, we have matter (stress-energy tensor), the source of the geometric structure. Bianchi identities on the left correspspond to conservation of mass-energy on the right (Misner, Thorne, and Wheeler 1973, 364–81; Wald 1984, 5973, 285–95, 450–56).

The modern Humean would continue shamelessly: “Yes, Einstein’s field equations, Hamilton’s principle, and the conservation of energy may have all held up until now, but what about tomorrow? We concede that since the beginning of time there has been nothing cosmically special about present times per se, but what about present times per se in the future? And again, what about this principle of substantive propagation, this principle that the ways things will be grow out of the ways things have been? That may have been true yesterday, but what about tomorrow?”

I shall give a negative argument, then a positive argument. If the ground of induction is the law of identity and no principle is entirely independent of this law, then my arguments should be ultimately circular—well, perhaps spiral, perhaps widening for the positive argument and narrowing for the negative. At any rate of curvature, we may count our circularity on this issue benign, even virtuous. This is not meant to shield my arguments from other types of rational criticism.

The negative argument is this: The principle that the way things will be grow out of the ways things have been is not a bald analytic statement. It is not a stupid tautology. One could go ahead and say “perhaps it is not always the case that the way things will be grow out of the ways things have been” without having misunderstood the simple meanings of the terms of the principle. Suppose the principle were false. Would the principle of non-contradiction then be true tomorrow? If the principle of non-contradiction is true tomorrow without having been an identity in time with itself today, then it is a radical, Humean contingent truth. Then, in the Humean mentality, it could be false day after tomorrow. Then was it true today? Suppose the principle of non-contradiction is true for any tomorrow, but only contingently so. Better yet, suppose we just return to reality. There we find all the necessity worth having. There we find the principle of non-contradiction and our principle of substantive propagation always true.

Immanuel Kant has a very strange explanation for that. I will here resist taking up his account.

The positive argument is this: The principle that the ways things will be grow out of the ways things have been comprehends all of its specific occasions. An oak grows from an acorn, a pair of gamma photons is born from the annihilation of an electron with a positron, mammals evolved from reptiles, the view became clear because I washed the window—these are specific occasions of the principle. Why not just stick to the specific occasions of the principle? Why try to summarize them all in a single principle? What work does our substantive propagation principle do? It helps us think and learn.

Our substantive propagation principle is an example of what Marvin Minsky calls a uniframe (1988, 121–23). That is a description constructed to apply to several different things at once. “We know only a very few—and, therefore, very precious—schemes whose unifying power cross many realms” (126). Our principle that the ways things will be grow out of the ways things have been is one of those schemes (218–19). It enables us to move fluidly among multiple descriptions of a particular occasion of change (393–95), in addition to facilitating assimilation of any and all occasions.

Substantive propagation is not the grandest of uniframes. Highest honor belongs to substantive predication (Minsky 1988, 267; Jackendoff 1987, 148–58; Edelman 1989, 147–48).

Our substantive propagation principle is metaphorical, or analogical (cf. Metaph. 1048a35–b9), but “every thought is to some degree a metaphor” (Minsky 1988, 299; see also Rasmussen 1982, 425–26). Understanding requires that new thoughts be grown from old thoughts (Rumelhart 1989; Brown 1989, 369–85, 390–98, 404–7; Vosniadou 1989, 422–28, 432–33; Collins and Burstein 1989).

"Once scientists like Volta and Ampere discovered how to represent electricity in terms of the pressures and flows of fluids, they could transport much of what they already knew about fluids to the domain of electricity. Good metaphors are useful because they transport uniframes intact, from one world into another. Such cross-realm correspondences can enable us to transport entire families of problems into other realms, in which we can apply to them some already well-developed skills" (Minsky 1988, 299).

Transference of our substantive propagation principle from one domain of change to another does not convey so much detail of form as the fluid-electricity analogy conveys. The form conveyed by our principle must be approximately as general as it is to comprehend all the forms of change there are. I say approximately since a detailed consideration of the various specific principles of change might well yield a more refined, tighter statement of our principle.

David Hume is very pleased to have received these insights into how it is useful to suppose always that the ways things will be grow out of the ways things have been. He really would like to see our positive justification for thinking this principle always true.

Our principle provides a unifying explanation of our successes in finding more specific unifying explanations (cf. Nozick 1981, 268–80, and Rescher 1973, 323–31). Our principle has the connective character of justified true belief; it is a belief which tracks truth (Nozick 1981, 169–78). Had the principle been false in our experience, we could have noticed it; some people think they have noticed it; they are mistaken. Were the principle to be false in some corner in the future, we could notice that (assuming that what could be grows out of what could have been in the past, i.e., assuming our principle true in a looser way). The principle grew out of experience; it is a self-subsuming principle; it is an instance of itself. New experience has grown from the principle (Mill 1973, 3.3.1). Our principle has bearings of a fundamental justified justification (Nozick 1981, 137–40, 641–42).

Continued
Existence is Identity

References

Aristotle 1984 [c. 348–322 B.C.]. The Complete Works of Aristotle. J. Barnes, editor. Princeton. Princeton University Press.

Brown, A. L. 1989. Analogical Learning and Transfer: What Develops? In Vosniadou and Ortony 1989.

Collins, A. and M. Burstein 1989. A Framework for a Theory of Comparison and Mapping. In Vosniadou and Ortony 1989.

Davis, W. H. 1972. Peirce’s Epistemology. The Hague: Martinus Nijoff.

Dicus, D. A., Letaw, J. R., Teplitz, D. C., and V. L. Teplitz 1983. The Future of the Universe. Sci. Amer. (Mar):90–101.

Edelman, G. M. 1989. The Remembered Present: A Biological Theory of Consciousness. New York: Basic Books.

Gott, III, J. R. , Gunn, J. E., Schramm, D. N., and B. M. Tinsley 1976. Will the Universe Expand Forever? Sci. Amer. (Mar):62–79.

Hume, D. 1975 [1893, 1748]. Enquiries Concerning Human Understanding. 3rd ed., L A. Selby-Bigge, editor. Oxford: Clarendon Press.
——. 1978 [1888, 1740]. A Treatise of Human Nature. 2nd ed., L. .Selby-Bigge, editor. Oxford: Clarendon Press.

Jackendoff, R. 1987. Consciousness and the Computational Mind. Cambridge, MA: MIT Press.

Marion, J. B. 1965. Classical Dynamics of Particles and Systems. New York: Academic Press.

Mill, J. S. 1973 [1843]. A System of Logic Ratiocinative and Inductive. Toronto: University of Toronto Press, Routledge & Kegan Paul.

Minsky, M. 1988 [1985]. The Society of Mind. New York: Simon & Schuster.

Misner, C. W., Thorne, K. S., and J. A. Wheeler 1973. Gravitation. San Francisco: W. H. Freeman.

Nozick, R. 1981. Philosophical Explanations. Cambridge, MA: Belknap Press of Harvard University Press.

Rasmussen, D. B. 1982. Necessary Truth, the Game Analogy, and the Meaning-is-Use Thesis. The Thomist 46(3):423–40.

Rescher, N. 1973. The Coherence Theory of Truth. Oxford: Clarendon Press.

Rumelhart, D. E. 1989. Toward a Microstructural Account of Human Reasoning. In Vosniadou and Ortony 1989.

Vosniadou, S., and A. Ortony, editors, 1989. Similarity and Analogical Reasoning. Cambridge: Cambridge University Press.

Wald, R. M. 1984. General Relativity. Chicago: University of Chicago Press.

~~~~~~~~~~~~~~~~
This essay of 1991 had no notes. I have now added some endnotes to indicate changes or emendations to the positions I took in this essay nineteen years ago. I have also added some hyperlinks within the text.
~~~~~~~~~~~~~~~~

Notes
31. Broad causal mode: Identical existents, in given circumstances, will always produce results not wholly identical to results produced by different existents in those same circumstances. Narrow causal mode: Identical existents, in given circumstances, will always produce identically same results. See the fifth and sixth paragraphs of “Hume – Reasoning to Cause or Effect.”*

Is there a cognitive concept of the negative of the principle of uniformity transformed into my principle of substantive propagation “Whether things continue the same or change, there will be reasons, growing out of the way things were at earlier times, for the way things are at later times” with “growing out of” understood as requiring only the broad mode of causality? No. Without this principle, no concepts are cognitive. Nothing is known to be same as self and different from other. Possibility is not known to be different from impossibility. Concepts and propositions are not known to be different from their negations; premises are not known to be different from conclusions, truth different from falsity, knowing different from not knowing. Against the “principle of uniformity” pared down to my principle of substantive propagation, Hume’s indirect proof of the indemonstrability of the principle cannot get started (T I.3.6).

Kant would assimilate the preceding counter to Hume’s case against the “principle of uniformity” under his Kant’s own counter by: thinking of my principle of substantive propagation as a condition of the possibility of the use of the understanding, which then is also a condition on the possibility of experience. Such a principle is not a reflection of the human propensity to project past regularities into the future. No, Kant would see such a principle as “a principle of reason (or reflective judgment) that licenses rather than causally determines such a projection” (Allison 2008, 155; see further 133–60). In that Kantian result, I concur, although in my Randian view, the principle of substantive propagation is a matter of human consciousness as identification, which is prescriptive on account of the base circumstance that existence is identity.

The justification of the principle of substantive propagation given in “Induction on Identity” could be profitably compared with my defense of the axiom “Every action-bearing entity bears certain kinds of action and not others.”* The considerations in the second paragraph of the present Note strike me as sufficient to establish the principle of substantive propagation as an axiom rather than designating it a postulate; the principle cannot be denied without self-contradiction. If it were shown, further, that in the case of concrete entities “growing out of” in the principle of substantive propagation logically entails causal determination, then the postulate (Ia) of “Exclusions of Non-Contradiction: Actions,” the postulate which includes the claim “Every concrete entity is capable of acting and being acted upon,” could be shown to be a metaphysical axiom, rather than a postulate. Because kinematics does not entail dynamics (or statics or kinetics), I do not expect it can be shown that the “growing out of” in the principle of substantive propagation logically entails causal determination. Substantive propagation is consistent, of course, with universal causal determination, but it does not entail it. That is, the principle of substantive propagation does not entail the true and important principle that “All the countless forms, motions, combinations and dissolutions of elements within the universe . . . are caused and determined by the identities of the elements involved” (MvMM).

That important principle is Rand’s statement of the law of causality in her metaphysics. Harriman (2010) writes that the essence of the law of causality is that “an entity of a certain kind necessarily acts in a certain way under a given set of circumstances” (21). Does that formulation of the essence of the causal law coincide with causality in the broad mode or with causality in the narrow mode? Harriman’s statement is slightly ambiguous between the two, though it leans towards the latter mode. Indeed, in further elaboration, he states that future actions can be inferred from past actions because the past actions were effects of causes, and because “if the same cause is operative tomorrow, it will result in the same effect” (21). As I argued in the 1991 text above, application of the law of identity to action and becoming entails only the conception of causality in the broad mode, not the narrow, and taking the latter to apply to all existents is an error. See the preceding section “Hume – Necessity” and its Note 20.

We should notice that were the narrow mode true in application to any and all existents, its epistemological status would be postulate, not axiom. For, to my knowledge, no one has demonstrated the principle of narrow-mode causality to be axiomatic in the required way, such as I have done for certain other propositions belonging to the family “Existence is Identity.”

Mr. Harriman appeals to a brother of my principle of substantive propagation in maintaining that the “justification for inferring the future from the actions of the past is the fact that the past actions occurred . . . for a reason, a reason inherent in the nature of the acting entities themselves” (21). Harriman erroneously supposes this principle entails universal causality in the narrow mode. That is, for all the “forms, motions, combinations and dissolutions of elements within the universe” (Rand’s fine phrase), “if the same cause is operative tomorrow, it will result in the same effect” (21).

With regard to generalizations about kinds of joined actions, such as push of a ball and its rolling, Harriman rightly says they are made true by “some form of causal relationship between the two” (21). C. S. Peirce wrote: “General principles are really operative in nature. This is the doctrine of scholastic realism” (1903, 193). Peirce famously was a proponent of scholastic realism in theory of universal concepts. Particularly, his realism was close to the realism of Duns Scotus, as informed by and as informing modern scientific practice. As applied to generalizations, Peirce saw realist concepts at work in the following way. Take any two occasions of releasing a stone from the hand and watching it fall. However much the two occasions are alike, between them there is any number—an infinity, denumerable or higher—of like possible occasions of its release allowing a stone to fall. A real relation of mediation unites the particular occasions, actual and possible, of the generalization “released stones fall.” Behind that uniformity of nature there must be not mere chance, like a run of straight sixes, but “some active general principle” (ibid.) Every sane person must accept that last statement, where it is understood that the principle does not merely accidentally coincide with moments in which one makes predictions based on it (ibid. See also Peirce 1901, chapter 18, and 1902, chapter 15).

Rand’s theory of concepts is not what has traditionally been called realist. Rather, hers is an objectivist theory. Concepts are “produced by man’s consciousness in accordance with the facts of reality . . . [they are] products of a cognitive method of classification whose processes must be performed by man, but whose content is dictated by reality” (ITOE 54). That cognitive method of classification requires the ability to regard items as (at least) substitution units along a real dimension(s) shared by the items. Regarding things as units, whether as substitution units or also as measure-value units along shared dimensions,* is a “method of identification or classification according to the attributes which a consciousness observes in reality. . . . Units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships” (ITOE 6–7).

Rand’s objectivist theory of conceptual identification, set in her metaphysics, as supplemented by the principle of substantive propagation, is a strong competitor to Peirce’s realist way of tying inductive generalization to universal concepts.

By four months of age, an infant expects objects to fall if not supported (¶8). This is an example of what Mill called eduction, inference from particular past cases to the next particular like case, rather than inductive inference from particulars to general (¶9). Animals also have the limited power that is eduction. Harriman writes that animals “cannot project from their percepts what future to expect” (28). While that is a slight overstatement, it is surely correct with respect to all the expectations we have from induction, which requires conceptual generalization.

Harriman inclines to think that higher animals have direct experience of causation (cf. Enright 1991, §II). Like us, they “perceive that various actions they take make certain things happen. But they cannot go on to infer any generalizations from these perceptions” (28). The important thing is that Harriman rightly affirms that the human animal perceives some causal relations directly. (See “Hume – Experience of Cause and Effect” above* and Yale.) From those percepts, general causal principles (from “Pushed balls roll” to “Applied torque causes onset of rolling”) are formed after the general pattern of how universal concepts are formed from percepts. Harriman’s book is an attempt to spell out more specifically the abstraction process from elementary causal principles such as “pushed balls roll” to general scientific principles—the tremendous abstraction process that is ampliative induction—illustrated by episodes in the history of science (join with Note 27).

David Hume was dead set against the idea that we have any direct perception of causal power operating in the world (Note 29). “We never have any impression, that contains any power or efficacy” (T I.3.14). And Hume was dead set against alleged human powers of abstraction (T I.1.7). Moreover, “a general idea being impossible without an individual; where the latter is impossible, ’tis certain the former can never exist” (T I.3.14). “We never therefore have any idea of power” (ibid.).

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