'Existential Import'...does such a 'concept' have such?


John Dailey

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~ I'm a bit surprised that this subject hasn't even been a bit implicitly ref'd in any discussions I've read oriented on O'ist philosophy (OK: I've not read EVERYTHING in the Web.)

~ Supposedly, it's been demonstratively 'argued'/deductively-shown that using the term 'some' automatically (ummm...'logically') implies (A-H-E-M!) that there is at least 1 existent meant by the statement that 'some' is used in; yet, contrary to Aristotelian analysis, using the term 'all' does not imply 'some', but, implies merely a hypothetical 'if'. An example is "All centaurs are blue" merely means that "IF there is a centaur, THEN it's blue" (regardless its T/F aspect.)

~ In short, to use the term 'some' is to mean that 'some' thing exists, whereas to use the term 'all' does not mean such but means merely a shorthand of speaking hypothetically.

LLAP

J:D

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~ Now, there may be a coherent (not that I've found one) 'deductive' argument on this, but, as we all know by now, if it's merely tautological, well, it's merely tautological, right? Strictly speaking, I've only run across innuendoes that it's been 'deductively' established; I'm open to reading coherently presented deductions. :rolleyes: Of course, I may then have 'other' questions about it's own...'existential import.'

~ Re the idea of Aristotle's 'Categoricals' as lacking in such a concern as E-I, merely because some fantasy-categoricals can be hypotheticalized in an apparently 'meaningful' statement, I find a bit lacking, because...considering fantasy considerations as factors for analyzing 'logic' is a bit fantastical on its face. 'Logic' should be the criteria to analyze 'fantasy' concepts; fantasy-concepts should not be the criteria to 'analyze' logic (aka: a la Kant, use logic to invalidate its worth).

LLAP

J:D

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ADDENDUM:

~ Indeed, to 'conclude'/assert that "All categoricals (especially Aristotelian) have no 'existential import'" seems to have an internally inconsistent/contradictory problem in and of itself...if accepted as 'true' (apart from being merely 'tautologically' so.)

LLAP

J:D

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John, I've been studying Existential Import for the past 15 years or so. The only Objectivist who explicitly deals with it is David Kelley, in his logic text, The Art of Reasoning. I don't think he adequately deals with the issue.

I agree with you: if "some" has Existential Import, so does "all." Here is an excerpt from an email I sent to a college prof. friend just last week:

The whole Boolean interpretation has got me really bugged. Especially the bit about universal categorical propositions NOT having Existential Import, while particular categorical propositions DO. I've read all of B. Russell's blathering in MIND c. 1905, as well as several other interesting essays from then and earlier.

One in particular really expressed some of my own jottings from the past week. Check it out: "The Existential Import of Propositions," by W. Blair Neatby, MIND vol. 6, no. 24, Oct. 1897, pp. 542-546.

He basically blasts the whole notion that universal categorical propositions do not have Existential Import by pointing out that a great many of the examples purporting to illustrate it are actually hypothetical propositions expressed as categoricals. E.g., All students arriving late will be penalized. Since there may in fact be no students who arrive late, it is claimed to lack Existential Import. The proposition, however, is more clearly expressed as a hypothesis: if a student arrives late, he will be penalized.

These supposed categorical universal propositions (actually hypotheticals) are alleged to differ fundamentally from categorical particular propositions. Particular categorical propositions, the Boolean interpretation goes, ~do~ have Existential Import. But as Neatby notes, there are just as many problemmatic examples of particular categorical propositions as of universal categorical propositions. For instance, Some students arriving late will be penalized. There may in fact be no students who arrive late, so this particular categorical proposition lacks Existential Import to the same extent as the parallel universal categorical proposition mentioned in the preceding paragraph. It certainly "does not necessarily imply that any [student] ever arrived late. It may only be a partial statement of a regulation that provides for the [penalizing] of any [student] who comes late without an excuse signed by his [parent]."

Here, in my mind, is the clincher from Neatby:

Formal logicians
have possibly the right to frame whatever convention they find best suited to their purpose. But if they claim the sanction of usage, and consider it urgent to keep in harmony with the actual forms of speech, they
are not at liberty to frame a convention that allows a necessary existential import to particular and singular propositions, and denies it to universal propositions
. In all three cases, the (even apparent) exceptions are rare, but they are found in all alike. It is difficult to imagine what consideration would entitle us to neglect them in any, without entitling us to neglect them in all. [emphasis added][Yikes! Well said, Prof. Neatby!]

Neatby also discusses examples involving deliberate irony and explicitly denial of existence, which are also included among the examples allegedly justifying the doctrine of Existential Import (i.e., its denial that universal categorical propositions have it).

So, how did Russell et al gain the ascendancy over strong challenges like this? I'm at a loss.

To that, I will add: why didn't Kelley dig in harder on the subject, instead of caving in to the modern/Boolean interpretation?

I am working on (actually, more like brainstorming, outlining) a paper on this called "The Fallacy of the Existential Fallacy." It's probably several years away from completion, because I have a lot of other planes circling the field right now. :-/

REB

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~ I'm a bit surprised that this subject hasn't even been a bit implicitly ref'd in any discussions I've read oriented on O'ist philosophy (OK: I've not read EVERYTHING in the Web.)

~ Supposedly, it's been demonstratively 'argued'/deductively-shown that using the term 'some' automatically (ummm...'logically') implies (A-H-E-M!) that there is at least 1 existent meant by the statement that 'some' is used in; yet, contrary to Aristotelian analysis, using the term 'all' does not imply 'some', but, implies merely a hypothetical 'if'. An example is "All centaurs are blue" merely means that "IF there is a centaur, THEN it's blue" (regardless its T/F aspect.)

~ In short, to use the term 'some' is to mean that 'some' thing exists, whereas to use the term 'all' does not mean such but means merely a shorthand of speaking hypothetically.

LLAP

J:D

The problem is with material implication. A materially implies B if and only if it is not the case that A is true and B is false. Doing a truth table shows that False materially implies True. The assertion that all centaurs are blue translates to if x is a centaur then x is blue, for any old x. Never mind that there are no centaurs. For those who like existential import they would deny it is the case that all centaurs are blue since there are no centaurs. But if one denies that all centaurs are blue then there must be an x such that x is a centaur AND x is not blue. But if that is true then there must be an x such that x is a centaur which is to say centaurs exists. And we would not want that.

Another gotcha is that the existential quantifier cannot be expressed as a predicate. Suppose existence is a predicate (just like blue, green, square .... etc. are predicates). Let e be that predicate so e(x) would assert x exists. A reasonable postulate connecting the predicate e to the quantifier E would be -Ex-e(x) which is to say there does not exist x such e(x) is false. But this is equivalent to (x)e(x), that is for all x, e(x) which is to say everything exists (in that sense of having the predicate existence). That simply will not do. The only way out is to say Ex[-e(x)] which is to say there exists something that does not exist. That surely will not do. The only way out of that dilemma is to deny that existence is a predicate.

You might want to look at a paper which details the history of existential import and its ultimate denial:

URL http://uk.geocities.com/frege@btinternet.c...or/Eximport.htm

The author traces the denial of existential import all the way back to Frege, Boole and Jevons.

Ba'al Chatzaf

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J

So, how did Russell et al gain the ascendancy over strong challenges like this? I'm at a loss.

To that, I will add: why didn't Kelley dig in harder on the subject, instead of caving in to the modern/Boolean interpretation?

I am working on (actually, more like brainstorming, outlining) a paper on this called "The Fallacy of the Existential Fallacy." It's probably several years away from completion, because I have a lot of other planes circling the field right now. :-/

REB

Kelley did dig in hard enough to present a generalization of the classical syllogisms. It is called term logic. This restores existential import. See -The Art or Reasoning- by David Kelley, pp 425-469. Also see my reply to the Original Poster as to -why- existential import is denied in contexts based on first order predicate logic. It was not an arbitrary decision. There are good reasons and I gave two of them.

A more basic question you might want to ask is why was categorical logic was replaced by first order logic and propositional calculus based on conditional statements, as opposed to categorical syllogisms. There are a number of reasons, including:

1. Flexibility. FOL can handle n-ary relations, categorical logical cannot.

2. Algebraically FOL is consistent or fits in with complete boolean lattices as a proper algebraic model to propositional reasoning. This is a mathematical consideration and need not be taken up in less technical and more philosophical contexts. Mathematicians do have uses for the empty set and they want their set algebra properly closed under set intersection.

It turns out that FOL is not quite sufficient for mathematical use. In order to assert that every bounded set of real numbers has either a least upper bound or a greatest lower bound one needs second order logic which permits impredicatiive definitions. Again, the need for a logic more general than classical categorical logic flowed from the requirements of mathematics.

In the fullness of time mathematics outgrew metaphysics and had requirements of its own. This required a form of logic that could ground mathematical thinking. This version of logic probably does not get along comfortably with the sort of logic bound up in Aristotelean metaphysics. Aristotle formulated his physics, metaphysics and organon (topics and categories) as a single system of thought. He did not separate logic from metaphysics. More recent developments in both mathematics and the natural sciences have required this separation. The critical events in this separation were the extensions of logic by Boole and Frege. Don't blame everything on Russell and Whitehead. A very comprehensive book on the subject of logic including those developments (old and new) that went beyond Aristotle can be found in"

-The Development of Logic- by William and Martha Kneale, Clarendon Press, 1962. It is a thick book, but for scholars, such as yourself, it is a gold mine.

Ba'al Chatzaf

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J

So, how did Russell et al gain the ascendancy over strong challenges like this? I'm at a loss.

To that, I will add: why didn't Kelley dig in harder on the subject, instead of caving in to the modern/Boolean interpretation?

I am working on (actually, more like brainstorming, outlining) a paper on this called "The Fallacy of the Existential Fallacy." It's probably several years away from completion, because I have a lot of other planes circling the field right now. :-/

REB

Kelley did dig in hard enough to present a generalization of the classical syllogisms. It is called term logic. This restores existential import. See -The Art or Reasoning- by David Kelley, pp 425-469. Also see my reply to the Original Poster as to -why- existential import is denied in contexts based on first order predicate logic. It was not an arbitrary decision. There are good reasons and I gave two of them.

A more basic question you might want to ask is why was categorical logic was replaced by first order logic and propositional calculus based on conditional statements, as opposed to categorical syllogisms. There are a number of reasons, including:

1. Flexibility. FOL can handle n-ary relations, categorical logical cannot.

2. Algebraically FOL is consistent or fits in with complete boolean lattices as a proper algebraic model to propositional reasoning. This is a mathematical consideration and need not be taken up in less technical and more philosophical contexts. Mathematicians do have uses for the empty set and they want their set algebra properly closed under set intersection.

It turns out that FOL is not quite sufficient for mathematical use. In order to assert that every bounded set of real numbers has either a least upper bound or a greatest lower bound one needs second order logic which permits impredicatiive definitions. Again, the need for a logic more general than classical categorical logic flowed from the requirements of mathematics.

In the fullness of time mathematics outgrew metaphysics and had requirements of its own. This required a form of logic that could ground mathematical thinking. This version of logic probably does not get along comfortably with the sort of logic bound up in Aristotelean metaphysics. Aristotle formulated his physics, metaphysics and organon (topics and categories) as a single system of thought. He did not separate logic from metaphysics. More recent developments in both mathematics and the natural sciences have required this separation. The critical events in this separation were the extensions of logic by Boole and Frege. Don't blame everything on Russell and Whitehead. A very comprehensive book on the subject of logic including those developments (old and new) that went beyond Aristotle can be found in"

-The Development of Logic- by William and Martha Kneale, Clarendon Press, 1962. It is a thick book, but for scholars, such as yourself, it is a gold mine.

Ba'al Chatzaf

Hey, Robert, thanks for the book recommendation. It's a bit pricey, but (as you note) quite pagey, too, so I'll probably order it shortly. (When I get back from a little jazz band gig here in Arizona.) But I've already read a lot about this stuff, so I'm not expecting to find much new in it. I'm mainly interested in it as a reference book and an overview. Good things to have.

Let me return the favor: I strongly recommend Henry B. Veatch's two books, Intentional Logic and (especially) Two Logics. The latter is more recent and makes a very good comparison between traditional Aristotelian and modern Boolean (et al) logic, and gives a rather different perspective on why modern logic "replaced" traditional logic. It's out of print, but there are copies available from used book sellers on the net, hopefully for not an arm and a leg.

In re Kelley -- I mean, specifically, his addressing of the issue of Existential Import. He does not adequately address the modern challenges to the way traditional logic handles (or could handle) categorical propositions. Specifically, once modern logic "has its way" with Aristotle's Square of Opposition, the only thing left is an "X" of Opposition; the implicative relations of the sides of the square are discarded. Kelley does not challenge this, at least not to my satisfaction.

The web page you linked for John is one of many that I have perused. The examples used on this and other web pages, and in various logic texts, to allege traditional logic's inadequacy are really not that difficult to "defuse," and doing so will be the easier part of the paper (or book?) I intend to write. I may have some time before long to go through one of these references, taking apart and answering the challenges, in order to illustrate where I am coming from in defending traditional logic.

REB

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In the meantime -- pending my threatened essay and/or your reading of Veatch's Two Logic) -- here are two reviews of the latter from about 35 years ago (!) by Jeff Riggenbach and George H. Smith. (I will make sure they are also posted down in Jeff's and George's folders here on OL.)

Veatch was probably the best traditional logician in the second half of the 20th century, and the ortho's in the Objectivist movement have ignored (or downplayed) his work to their own detriment. (Binswanger is particularly snarky and condescending toward Veatch in one of his taped lectures. I'd like to see ~him~ write a decent book on logic.)

I particularly like George Smith's take on Veatch's book. I have underscored what I think are the main important points in comparison of modern "relating" logic and traditional "what" logic....reb

AA Book News: Fall 1972 no. 9—review of Veatch’s Two Logics: the Conflict between Classical and Neo-Analytic Philosophy by Jeff Riggenbach

Subtitled “The Conflict between Classical and Neo-Analytic Philosophy,” Professor Veatch’s most recent book on logic is an analysis of two distinct
kinds
of knowledge—a knowledge of
what
things are and
why
they behave as they do, and a knowledge of
how
things may be usefully
related
to each other. In pursuit of the first kind of knowledge, which is particularly important in philosophy and in the humanities, man needs what Dr. Veatch calls a “what-logic,” a logic which enables him to talk or think about what something is. In pursuit of the second kind of knowledge, which is particularly important in mathematics and the sciences, man needs a “relating-logic,” a logic which enables him to organize reality into coherent,
non-contradictory
paradigms or models.

In the wave of Neo-Analytic philosophy which has all but dominated Western thought in this century, the principles of Classical realism, which must underlie any what-logic, seem to have been mislaid. “Has it never struck anyone as passing strange,” Dr. Veatch asks in his first chapter, “that the logic of
Principia Mathematica
, for all of its elaboration, provides no means either for saying or for thinking what anything is?” Rather, he argues, modern symbolic logic treats entities in what might be called a purely contextual way—it deals with them exclusively in terms of the relations in which they can be made to stand to other entities. It is, in short, a relating-logic. Professor Veatch develops this thesis at length, discussing the meaning in modern symbolic logic of such concepts as causality, induction and deduction. He goes on to identify the metaphysical and epistemological assumptions which underlie the logic of
Principia Mathematica
and even to speculate on what the world would have to look like if modern symbolic logic were used to describe it.

Two Logics
is not only a brilliant presentation of a highly original and provocative thesis; it is also a delight to read, a proof in itself that philosophical style may be at once accurate and urbane, technical and witty. Moreover, certain sections of the book transcend the scope of Professor Veatch’s central argument by providing the kind of intellectual ammunition which may be applied to countless other philosophical disputes. Chief among these is the detailed analysis and refutation of the Analytic/Synthetic dichotomy which occupies almost a quarter of the book. But it is the author’s careful defense of logic as an instrument by means of which we are able to think and talk about what things are that is the book’s primary virtue and most important achievement.

Books for Libertarians: April 1973—review of Veatch’s Two Logics by George Smith

If one agrees with John H. Randall, Jr. that “Aristotle is not a system, but a spirit, a method, an intellectual technique,” then Henry Veatch qualifies as an Aristotelian in the best sense of the term. Like Aristotle, Veatch is concerned with describing reality, with making the universe intelligible to man, and he views logic as an instrument to be employed in pursuit of this goal. And it is this confidence in man’s intellectual powers that breathes life into Veatch’s latest book,
Two Logics
.

The title of this book reflects its highly controversial theme. According to Veatch,
there are two distinct kinds of knowledge: a traditional humanistic or philosophical knowledge that seeks to describe what things are and why they function as they do; and a modern, scientific knowledge that is concerned not with describing reality, but with organizing various logical and linguistic devices into consistent patterns
. Furthermore, argues the author, there is “an entirely different logic operative in the enterprise of humanistic learning from what there is in that of science.”
Humanistic knowledge employs Aristotelian logic, while scientific knowledge relies on the newer symbolic logic elaborated in the
Principia Mathematica
by Russell and Whitehead
.

Veatch points out that
Aristotelian logic—and therefore humanistic knowledge—has all but been abandoned by contemporary science and philosophy
, and he views this as a serious blunder. Considered by itself,
modern logic is woefully inadequate, for it “simply does not allow for, or permit of, one’s saying or thinking what anything is.” By spurning the subject-predicate formulation of Aristotelian logic and dealing solely with the relationship among propositions and logical schemata, modern logic has rendered itself incapable of describing reality. It functions instead as a relating-logic, whose elements are “no more than devices or constructs of our own that enable us to get from one point to another in the cognitive process
.”

Aristotelian logic, in contrast, is a what-logic, a logic concerned with predicating the characteristics and “essences” of existing entities. The knowledge gained in this manner, argues Veatch, is more fundamental than that acquired through relating logic. Instead of mere “calculative knowledge,” what-logic provides us with “substantive knowledge” of reality; and to abandon what-logic altogether, as some scientists advocate, would deprive man of his basic means of comprehension and thrust him into an unintelligible universe.

After drawing the distinction between what-logic and relating-logic, Veatch examines the world-view entailed by each kind of logic, and the implications of each approach for inductive and deductive arguments, scientific and historical explanations, definitions, and so forth. It is the undue reliance on relating-logic, he contents, that has led to such unfortunate consequences as the division between necessary truths and factual truths—the analytic-synthetic dichotomy—as well as the supposition that rules of languages are a self-contained “game” and need not be governed by the real world. Within the context of what-logic, many truths are at once necessary and factual, and the propositions of what-logic reflect necessities existing within nature.

In my opinion, Veatch over-emphasizes the difference between Aristotelian and modern logic. He wishes to preserve the former by claiming that it serves an entirely different function than the latter, and provides us with an entirely different kind of knowledge. I think, however, that
these two approaches are capable of integration, and there is no reason to suppose that the knowledge acquired through philosophy is fundamentally different than that acquired through science
.

Despite this objection,
Two Logics
is a magnificent defense of Aristotelian logic, as well as a devastating critique of certain aspects of modern philosophy. The next time that one is told that Aristotle has been killed by modern logic, offer this book as proof of his resurrection.

OK, draw a double line here (============================================)

Now, let me offer a simple example both to contrast modern and traditional logic as "relating" and "what" logics, respectively, and to show how they could be integrated as per Smith's claim. (And no, I am not going to use modern logical notation. I am trying to communicate the ~ideas~ involved, and that notation will simply induce glazed eyes in those not familiar with it, and do nothing to bridge the gap that Smith says is capable of being bridged.)

Consider the proposition "Silver is the color of my car."

A traditional logician divides the proposition into subject (silver), predicate (the color of my car), and copula (is).

Silver // is // the color of my car.

A modern logician divides the proposition into two objects (silver & my car) and a relation between them (is the color of).

Silver // is the color of // my car.

Now, note this: each interpretation points to a ~fact~. The traditional interpretation highlights the epistemic fact that the same thing is being referred to by the subject-term, "silver," and the predicate-term, "the color of my car." The modern interpretation highlights the ontological fact of silver's being the color of my car. I think that ~both~ perspectives (recognizing both of these facts) are necessary for a full understand of how propositions work and what they are getting at.

REB

P.S. -- I realize this is not directly pertinent to the topic of Existential Import, but it does address Robert's comments about why modern logic has (unfortunately, by my view) replaced traditional logic.

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From the review:

Veatch points out that Aristotelian logic—and therefore humanistic knowledge—has all but been abandoned by contemporary science and philosophy, and he views this as a serious blunder. Considered by itself, modern logic is woefully inadequate, for it “simply does not allow for, or permit of, one’s saying or thinking what anything is.” By spurning the subject-predicate formulation of Aristotelian logic and dealing solely with the relationship among propositions and logical schemata, modern logic has rendered itself incapable of describing reality. It functions instead as a relating-logic, whose elements are “no more than devices or constructs of our own that enable us to get from one point to another in the cognitive process.”

To which I respond: It is not the job of logic to identify what things are. That is the job of "hard" science (such as physics and chemistry) which has been done superlatively well. Logic is the art or discipline of valid inference. It is a means of getting from premises to conclusions. Aristotle's logic (traditional term logic) has proven woefully inadequate for identifying what things are and how they operate. Which is why we have relied on mathematically based physics to do the job since the time of Newton. In the age of "what logic" technology floundered. Since the age of "hard" science technology has flourished. I would love to see how "what logic" can be used to design the GPS , for example. Categorical syllogisms are totally incapable of grounding mathematics and is incapable of dealing with dynamic systems. Which is why Aristotelean type logic has been discarded by "hard" science. Such logic is unequal to the tasks required.

Ba'al Chatzaf

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~ Boy! Did I start something, or what?

~ Thanx Roger and Ba'al for chiming in. Hope others do also.

~ Had Kneales' book a while. Talk about 'deep.'! Guess I'll have to get back to that bookmark 1/3rd in.

~ To my mind, one can talk about varied esoteric (to a layman) forms/formats/notations/'analyses'/sub-categories/improvements/etc-ad-infinatum re a human being's use of...(drum roll)...LOGIC, but, Aristotle analyzed the basics of where E-V-E-R-Y-O-N-E must start their 'thinking' about the subject, and what supports the advancements that trivialize their starting point has something 'wrong' with it.

~ It's supposedly 'established' (by consensus, I guess) that Propositional (or is it 'Predicate'?) Calculus is the Einsteinian view that 'implies' Aristotelian Logic (as, Newtonianism/Galilism being derived from Relativity.) Depending 'why' one 'starts' where (reality-based concepts, or, 'truth-tables'), I see it as the other way 'round.

LLAP

J:D

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  • 1 month later...
From the review:

Veatch points out that Aristotelian logic—and therefore humanistic knowledge—has all but been abandoned by contemporary science and philosophy, and he views this as a serious blunder. Considered by itself, modern logic is woefully inadequate, for it “simply does not allow for, or permit of, one’s saying or thinking what anything is.” By spurning the subject-predicate formulation of Aristotelian logic and dealing solely with the relationship among propositions and logical schemata, modern logic has rendered itself incapable of describing reality. It functions instead as a relating-logic, whose elements are “no more than devices or constructs of our own that enable us to get from one point to another in the cognitive process.”

To which I respond: It is not the job of logic to identify what things are. That is the job of "hard" science (such as physics and chemistry) which has been done superlatively well. Logic is the art or discipline of valid inference. It is a means of getting from premises to conclusions. Aristotle's logic (traditional term logic) has proven woefully inadequate for identifying what things are and how they operate. Which is why we have relied on mathematically based physics to do the job since the time of Newton. In the age of "what logic" technology floundered. Since the age of "hard" science technology has flourished. I would love to see how "what logic" can be used to design the GPS , for example. Categorical syllogisms are totally incapable of grounding mathematics and is incapable of dealing with dynamic systems. Which is why Aristotelean type logic has been discarded by "hard" science. Such logic is unequal to the tasks required.

Ba'al Chatzaf

Ba'al, et.al...excellent topic. :)

The reply of Ba'al to the question of veatch's criticism just points out how closely questions of logic are tied to questions of metaphysics, something of which Veatch was well aware. Pointing out that modal logic is closely tied to the understanding of the world in which to know what things are is to tell us what makes technological innovation is to point out the obvious. In the assumption that there are teleological motions present in nature lies the idea of logic as the attempt to discern the essential character that guides such teleological motion. In the glorification of technological innovation and mathematical flexibility, there is implicit the notion of nature as indifferently extended matter with random motion guided by external force. Let's just say this; I'm not convinced...and neither is Veatch (see his Aristotle, a contemporary appreciation)... that Aristotelean physics was ever 'refuted'; it seems rather that it was replaced by an acceptance the very rhetoric of mechanical success that we see present in Ba'al's reply, and to his greater glory, in Descartes' most interesting works, the Passions of the Soul and the Discourse. Aristotle has been refuted, that is, only once we accept a certain notion of what it means to "demonstrate" something- -and this is, of course, a matter of logic. An interesting book making this argument is Michael Davis' "Ancient Tragedy and Origins of Modern Science".

Of course, as Ba'al suggests, this can all be seen as a divergence of opinion on the nature of mathematical reality, as well; I recommend David Lachtermann's "The Ethics of Geometry" and Jakob Klein's "Greek Mathematics and the Origins of Modern Algebra" on these questions.

Norm Fischer

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John, I've been studying Existential Import for the past 15 years or so. The only Objectivist who explicitly deals with it is David Kelley, in his logic text, The Art of Reasoning. I don't think he adequately deals with the issue.

...

...

To that, I will add: why didn't Kelley dig in harder on the subject, instead of caving in to the modern/Boolean interpretation?

I am working on (actually, more like brainstorming, outlining) a paper on this called "The Fallacy of the Existential Fallacy." It's probably several years away from completion, because I have a lot of other planes circling the field right now. :-/

REB

Roger,

I interpret the issue of existential import as a problem of asserting the existence of things. The modern interpretation takes the issue to mean that universal statements assert absence, while particular ones assert presence. It is what is drawn in Venn's diagrams: shadings, for absence; Xes, for presence. It seems to be a pretty good division of labor among propositional forms.

Contrast this with the traditional interpretation of existential import. In my judgment, traditionalists confound concepts with concretes. Because a concrete is taken always to be enveloped in a concept, albeit in a concept of only one referent, assertions about concretes are thus allowed to take universal-statement forms. And from then, the traditional square of opposition allows for the subalternation relationships, which then permits the sideway relations. But then one has to question whether a concept can have but one referent! It seems to me that this is erroneous. The error may have been caused by a traditionalist conception of the division of cognitive labor between the intellect and the rational soul. That is, concepts are exclusively used by the intellect; and concretes, by the senses. Commenting against Aristotle's psychological treatise, Aquinas sided with Augustine to make this interpretation. (ST I Q84 A1)

Ayn Rand's contribution to this issue is to pry apart concepts and concretes while allowing both to be dealt with by man's mind. (ITOE 11a)

(In this context, I disagree with your suggestion to fuse back concepts and concretes.)

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  • 1 month later...
John, I've been studying Existential Import for the past 15 years or so. The only Objectivist who explicitly deals with it is David Kelley, in his logic text, The Art of Reasoning. I don't think he adequately deals with the issue.

...

...

To that, I will add: why didn't Kelley dig in harder on the subject, instead of caving in to the modern/Boolean interpretation?

I am working on (actually, more like brainstorming, outlining) a paper on this called "The Fallacy of the Existential Fallacy." It's probably several years away from completion, because I have a lot of other planes circling the field right now. :-/

REB

Roger,

I interpret the issue of existential import as a problem of asserting the existence of things. The modern interpretation takes the issue to mean that universal statements assert absence, while particular ones assert presence. It is what is drawn in Venn's diagrams: shadings, for absence; Xes, for presence. It seems to be a pretty good division of labor among propositional forms.

Contrast this with the traditional interpretation of existential import. In my judgment, traditionalists confound concepts with concretes. Because a concrete is taken always to be enveloped in a concept, albeit in a concept of only one referent, assertions about concretes are thus allowed to take universal-statement forms. And from then, the traditional square of opposition allows for the subalternation relationships, which then permits the sideway relations. But then one has to question whether a concept can have but one referent! It seems to me that this is erroneous. The error may have been caused by a traditionalist conception of the division of cognitive labor between the intellect and the rational soul. That is, concepts are exclusively used by the intellect; and concretes, by the senses. Commenting against Aristotle's psychological treatise, Aquinas sided with Augustine to make this interpretation. (ST I Q84 A1)

Ayn Rand's contribution to this issue is to pry apart concepts and concretes while allowing both to be dealt with by man's mind. (ITOE 11a)

(In this context, I disagree with your suggestion to fuse back concepts and concretes.)

Thom, some comments:

1. Your defense of the modern interpretation of universal and particular propositions makes no sense to me. Universal propositions "assert absence" while particular ones "assert presence"?? Tilt. Ain't buyin' that, my friend. In my understanding, I am asserting the same thing in each case: either all or some of the instances of a particular thing, ~if~ any exist, have a certain nature. I think that unless you specify otherwise, you are implicitly asserting that such things exist, whether you are referring to some or all of them. They may in fact ~not~ exist. So? The King of France is bald. The King of France is not bald. Since they are (?) contradictories, one must be true, the other false, right? Wrong. They are both meaningless, unless you further specify: the King of France is a real human being who is bald vs. the King of France is a real human being who is NOT bald--which is presumably what the speaker is meaning to say. Aha, now we're getting somewhere. BOTH statements are false, because the King of France is not a real human being, bald or otherwise. Suppose I had said: the King of France is NOT a real human being who is bald vs. the King of France is NOT a real human being who is not bald. Aha, again. BOTH are TRUE.

The moral of this pedantic flogging of a dead logician's hobby horse is this: to judge truth and falsity validly, you must say what you mean and mean what you say. You can't get away with ambiguity (e.g., the King of France is bald...or not bald). The same reasoning applies to propositions about imaginary beings (e.g., from fairy tales, mythology, fiction).

2. You may be right in your comments about the traditionalist logicians, but I cannot make head nor tails out of your comments.

3. Ditto for your assertion that I am trying to "fuse" concretes and concepts.

REB

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[...]

Thom, some comments:

1. Your defense of the modern interpretation of universal and particular propositions makes no sense to me. Universal propositions "assert absence" while particular ones "assert presence"?? Tilt. Ain't buyin' that, my friend. In my understanding, I am asserting the same thing in each case: either all or some of the instances of a particular thing, ~if~ any exist, have a certain nature. I think that unless you specify otherwise, you are implicitly asserting that such things exist, whether you are referring to some or all of them. They may in fact ~not~ exist. So? The King of France is bald. The King of France is not bald. Since they are (?) contradictories, one must be true, the other false, right? Wrong. They are both meaningless, unless you further specify: the King of France is a real human being who is bald vs. the King of France is a real human being who is NOT bald--which is presumably what the speaker is meaning to say. Aha, now we're getting somewhere. BOTH statements are false, because the King of France is not a real human being, bald or otherwise. Suppose I had said: the King of France is NOT a real human being who is bald vs. the King of France is NOT a real human being who is not bald. Aha, again. BOTH are TRUE.

The moral of this pedantic flogging of a dead logician's hobby horse is this: to judge truth and falsity validly, you must say what you mean and mean what you say. You can't get away with ambiguity (e.g., the King of France is bald...or not bald). The same reasoning applies to propositions about imaginary beings (e.g., from fairy tales, mythology, fiction).

2. You may be right in your comments about the traditionalist logicians, but I cannot make head nor tails out of your comments.

3. Ditto for your assertion that I am trying to "fuse" concretes and concepts.

REB

Roger,

On Point 1, I am taking John Venn's interpretation literally. Check out DK's Venn diagrams for the four classical propositional forms.

As for "The King of France is/isn't bald," we are dealing here not with a class but with a concrete. In this case the subject is a description of a nonexistent concrete.

The central issue in Points 2 and 3 concerns the separation of singular propositions and general propositions (universal and particular). Traditionalists lump singulars together with universal propositions. This package deal is what generates the issue of existential import.

I would suggest that, given the Objectivist epistemology as the base, logical statements should be taught as having six propositional forms (instead of just the classical four). The extra two take concretes for subjects. U: x is P -- Y: x isn't P. U-statements and Y-statements require the existence of x as part of their truth conditions. If x does not exist, then both "x is P" and "x isn't P" are meaningless and are neither true nor false.

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I would suggest that, given the Objectivist epistemology as the base, logical statements should be taught as having six propositional forms (instead of just the classical four). The extra two take concretes for subjects. U: x is P -- Y: x isn't P. U-statements and Y-statements require the existence of x as part of their truth conditions. If x does not exist, then both "x is P" and "x isn't P" are meaningless and are neither true nor false.

You have a problem here. You treat existence as a predicate. Does it make any sense to say x exists, in the total absence of a predicate applicable to x? It does not.

Proof:

Suppose there were a predicate e such that e(x) asserts that x exists. Then one would postulate that -Ex[-e(x)] which uses the quantifier E (as opposed to predicte). This postulate says (in words) there does not exist any x such that x does not have the property or predicate e. (Think about it. It makes sense to assume this as a postulate). But by Demorgans law this would imply (x)[e(x)] which is to say for all x, e(x) or (in words) for all x, x exists or equivalently everything exists. I don't believe that for a second. Do you? On the other hand if you deny this postulate then there exists (in the sense of the quantifier exists) something to which the predicate e does not apply, which is to say there exists something which is non-existent. Do you belive that?

And that is why existence cannot be predicate. Because if it were we would be lead to one of two conclusions: either everything exists or there exists (in the sense of a quantifier) something that does not exist. Either is absurd. Ergo existence is not a predicate.

QED.

Since it is almost axiomatic among Shi'ite Objectivists (such as Imam Peikoff) that formal (or mathematical) logic is Evil Evasion, Blank Out and probably Kantian, the disproof that existence is a predicate simply does not register. Shi'ite Objectivists define logic as consistent or valid identification which it is not. Logic is the science or discipline of valid inference. Logic does not guarantee the existence of anything nor does it prove the factual (as opposed to tautological) truth of anything. All logic tells you is that the conclusion did or did not follow from premises. Fortunately people like me, realize that mathematical logic is not only useful, but necessary to understand valid reasoning and understanding various systems of valid reasoning. Yes, darlings. There exist non Aristotelian logics just as there exist non-Euclidean geometries.

Ba'al Chatzaf

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Logic is the science or discipline of valid inference. Logic does not guarantee the existence of anything nor does it prove the factual (as opposed to tautological) truth of anything.

Bob,

I'm quibbling today, but logic does prove the existence of the mind using it. Without the mind, there is no logic.

That is what Rand meant by calling "existence exists" a specific kind of proposition, an axiom. If you accept that logic exists, you have to accept that a mind exists to use it. From Atlas Shrugged, Galt's speech, pp. 933-934:

We, the men of the mind, are now on strike against you in the name of a single axiom, which is the root of our moral code, just as the root of yours is the wish to escape it: the axiom that existence exists.

Existence exists—and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists.

If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms. A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something. If that which you claim to perceive does not exist, what you possess is not consciousness.

Whatever the degree of your knowledge, these two—existence and consciousness—are axioms you cannot escape, these two are the irreducible primaries implied in any action you undertake, in any part of your knowledge and in its sum, from the first ray of light you perceive at the start of your life to the widest erudition you might acquire at its end.

Just to be clear, here is what she called an axiom, and notice that she called an axiom a proposition (AS, Galt's speech, p. 956):

An axiom is a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge, a statement necessarily contained in all others, whether any particular speaker chooses to identify it or not. An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it.

This is the context of the following statement in the Forward to ITOE, p.3:

For the purposes of this series, the validity of the senses must be taken for granted—and one must remember the axiom: Existence exists. (This, incidentally, is a way of translating into the form of a proposition, and thus into the form of an axiom, the primary fact which is existence.)

I think she would have been clearer if she had stated, "This, incidentally, is a way of translating the primary fact which is existence into the form of a proposition, and thus into the form of an axiom." It's embarrassing to say, but fact is fact. Her awkward inversion confused me for years.

Anyway, the point is if there is thought, there has to be a thinker. When you call one form of thought "logic," that does not change the fact that it is thought. So logic itself, by merely existing, guarantees the existence of consciousness.

Michael

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Anyway, the point is if there is thought, there has to be a thinker. When you call one form of thought "logic," that does not change the fact that it is thought. So logic itself, by merely existing, guarantees the existence of consciousness.

Michael

1. I have a computer program that can do logical inference. So much for consciousness. Propositional logic can be done by finite state automata. In propositional logic and first order logic the correctness of inference is based on the form of the statements, not their meaning.

2. Logic does not address the question of factual truth of propositions in the object language of the logic. It can only determine if a proposition follows from other propositions by the specified rules of inference.

3. Rand defined $logic, not logic. If you want to know what logic, is ask a logician or a mathematician. If you want to know what $logic is, read Rand or listen to Imam Peikoff.

Ba'al Chatzaf

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1. I have a computer program that can do logical inference. So much for consciousness.

Your computer program needs a consciousness to make it in the first place.

So much for your argument.

Michael

Ah, the "First Cause" argument. But what caused the programmer?

--Brant

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Brant,

I don't propose a "first cause" for consciousness. I do insist that computers and robots were originated by conscious human beings.

Why are we even arguing something so obvious?

Well... Bob seems to think logic exists totally cut off from all human connection. Unfortunately, he's not alone.

Michael

Regardless, these machines prove theorems in certain classes of formal logic. In general, proof checking is an algorithmic process not requiring consciousness. Adding numbers, similarly is purely algorithmic and does not require consciousness. Anything that can be done by a machine (regardless of how the machine came to be) does not require consciousness.

Ba'al Chatzaf

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Micheal and Baal are indeed talking about two different things. Micheal's (objectivism's?) idea of logic is not the same as Baal's but I think Baal's is the more widely accepted one. The idea of "non-contradictory identification" seems to encompass recognizing objects, if I am not mistaken. This would definitely be outside the realm of traditional logic.

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Micheal and Baal are indeed talking about two different things. Micheal's (objectivism's?) idea of logic is not the same as Baal's but I think Baal's is the more widely accepted one. The idea of "non-contradictory identification" seems to encompass recognizing objects, if I am not mistaken. This would definitely be outside the realm of traditional logic.

Correct. People who have degrees in logic (or mathematics) or do it for a living will tell you logic is the science/art/discipline of valid inference.

If one wants to know what surgery is, he goes and asks a surgeon. If one wants to know what physics is he goes and asks a physicist. If one wants to know what mathematics is, he goes and asks a mathematician. If an Objectivist wants to know what logic is, he goes and reads Ayn Rand works or listens to lectures by Imam Peikoff or he asks Betsy Speicher. What seems to be wrong here?

Ba'al Chatzaf

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You can find creationists in some colleges too. Go figure! :D Who knows, maybe David Kelley is the Einstein of Logic and in the future his work will be taught everywhere. But right now it's a minority position.

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