SCORECARD! Can't tell the players without a scorecard!

[Michael Stuart Kelly]

Induction is not a valid form of deduction, and deduction is not a valid form of induction. Duh. Hearing is not a valid form of seeing, and seeing is not a valid form of hearing. This is not useful or illuminating.

Roger,

I have come across this problem ever since the beginning of my discussions on epistemology and it took a while before I could believe that something this simple was the problem. But it is.

Michael

[Daniel Barnes]

Roger, you say now:

To say that induction is not a form of deduction is ~not~ to say that it is "deductively invalid."

But you said at #100:

Huh? Are you simply saying that induction is not deduction, and that induction is not deductively valid?If so, Peikoff agrees with this...(DB emphasis)

I want to focus on this for a moment, because you go on to attack me in this new post for putting words in your mouth "again." Yet here it is - that Peikoff regards induction as deductively invalid - in your own words, provided with context (your post no., and quoted a greater length in my previous post).

If you (and Peikoff) don't in fact agree that induction is deductively invalid, and your first claim was in error, fine. But please now withdraw the charge that I have "put words in your mouth" here, as this is plainly not the case.

Now, as to this case:

I wrote:

So can we just clarify: Does Peikoff consider induction to be deductively invalid? (with "induction" referring to the standard version of the problem, eg: x number of birds fly=all birds fly, and "valid" meaning according with standard logical deductive procedures)

Roger replied:

There you go again! (With the putting-words-in-mouth again. You did this in a previous post, too.) I said ~nothing~ about birds in general flying. I was talking about swans, who do fly, having two basically different kinds of attributes: color, which all entities have, and wings, which birds have.

Well, here's the passage I was referring to, your #154:

Roger:

There is a world of difference between saying: All swans are winged and All swans are white

It takes very little experience, at least on the adult level, to realize that its particular means of locomotion is an essential characteristic of any animal, while its particular color is not, and that the non-essential characteristics are subject to variation while the essentials are not, and that predictions about non-essentials are so iffy, while predictions about essentials are trustworthy.

Now here I admit I assumed you thought flight was "essential" to birds when you said its particular means of locomotion was an "essential characteristic of any animal."

But this is because you did not actually state why flight is "essential" to swans, and not colour. I apologise for this assumption.

So can you explain exactly why it is, in fact, impossible for a flightless swan to one day be found?

Of course, it goes without saying, you can achieve this by merely playing with the definitions; by simply choosing to nominate "flight" as an essential characteristic of swans. But in reply, obviously one could equally do the same with a particular colour too, such as "whiteness." This would therefore be a simply an arbitrary or ad hoc decision - which you are welcome to make of course, but this would hardly demonstrate your contention that it is somehow "essential." Alternatively you might try to provide grounds that flight is "essential" to swans, because swans are birds and it is "the means of locomotion" of some birds. But of course this would be logically invalid.

Roger:

Induction is NOT enumeration. You can validly induce from one or two examples, if you have observed accurately, grasped the causal connections involved, and integrated your observations to other observations and conclusions.

Ok. Can you give a concrete example of what you consider a "valid" induction from one or two examples?

Roger:

And I disagree with your implication that enumerative "induction" is "the usual sense of the word 'induction'". Induction ~integrates~ observations; it does not merely amass them and assume that they belong together because of the sheer numbers.

Here are the two definitions from the wikipedia entry on the problem of induction

"1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class of objects (for example, "All swans we have seen are white, and therefore all swans are white", Hume's Problem of Induction, 18th century, before the discovery of Cygnus atratus in Australia); or

2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, the attractive force described by Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity)."

Both of these are clearly enumerative i.e. generalising based on "some number of observations" or a "sequence of events."

This is what induction is generally taken to be, Roger. This is what Hume is talking about being invalid.

(I'll turn to your question of whether deductive logic is deductively valid in a moment,)

Roger:

Still waiting. :-)

It's no great mystery, but I will explain more fully a bit later. Suffice to say for now it is the methodological rule that here can be no possible counter examples that validates deductive logic.

If you want to dispense with such a rule, or declare it insufficient for true deductive soundness, let's hear why and what you propose to replace it with.

Further, I hold that there is no such rigorous principle to similarly validate induction. If you know one, please state it.

Edited September 17, 2007 by Daniel Barnes

[Roger Bissell]

(I'll turn to your question of whether deductive logic is deductively valid in a moment,)

Roger:

Still waiting. :-)

It's no great mystery, but I will explain more fully a bit later. Suffice to say for now it is the methodological rule that here can be no possible counter examples that validates deductive logic.

If you want to dispense with such a rule, or declare it insufficient for true deductive soundness, let's hear why and what you propose to replace it with.

Further, I hold that there is no such rigorous principle to similarly validate induction. If you know one, please state it.

No counter examples to deductive conclusions? You must be kidding.

reb

[Michael Stuart Kelly]

Continuing on my earlier thought, if one claims that induction does not exist and defining terms leads to infinite regress, all one has left is deduction from propositions and isolated observation of concretes. That's why induction (and everything else in epistemology) is criticized for not being a valid form of deduction. Deduction from propositions is all that's left for critical thinking and logic.

That is an enormous stumbling block for discussing ideas.

Michael

[Ellen Stuttle]

I don't think that Rand would agree with you about the animal part being "essential," Merlin, given that she says this (and similar wording other places) about her meaning of "essential":

ITOE, pg. 68

[my emphasis added]

Objectivism holds that the essence of a concept [elsewhere called the "essential characteristic"] is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of a man's knowledge.

She goes on, btw, to say that the essence "may be altered with the growth of man's knowledge."

I don't think she'd have considered animality to distinguish humans from "all other existents within the field of a man's knowledge."

(I don't agree with her theory of a concept having an "essential" characteristic -- or with quite a bit else in her theory of concept formation. I'm here just pointing out that I think, on her own terms, she wouldn't have considered "animal" "essential" in her meaning to the concept "man" (human).)

Ellen

Why don't you think she'd have considered animality to distinguish humans from non-animals such as plants and non-living things?

I did only a brief search and did not find her explicitly endorsing the species-genus model of definition, but think she endorsed it implicitly. So I agree with MSK's last point in #219. Distinguishing is evident on two levels in the genus-species model. The genus distinguishes the members (animals in the case of 'man') from non-members in general. The species (rationality in the case of 'man') distinguishes the members from non-members within the genus.

P.S. Rand explicitly uses the genus-differentia model of definition on p. 41 of ITOE (2nd ed.). I take it as equivalent to the genus-species model.

I think she would (I'd add, of course) have considered animality to distinguish humans from non-animals and non-living things. But notice, she didn't say, "distinguishes these units from SOME other existents" but instead from ALL other existents.

She definitely used the genus-differentia model of definition. But judging from what she wrote about "essential characteristic," I think she thought of that as being the characteristic(s) named by the differentia; the genus she thought of as connecting the differentiated category to a wider category.

Here's a series of quotes which I think makes clear how she viewed the issue of "essence."

An objective definition, valid for all men, is one that designates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept--according to all the relevant knowledge available at that stage of mankind's development. [iTOE, 61 original; 46 expanded]

[Notice she says two parts there: the essential characteristic AND the genus; thus she isn't considering the genus to be the essential distinguishing characteristic.]

The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated--by means of a distinguishing charactersitic(s)--from other existents possessing a commensurable characteristic, a "Conceptual Common Denominator." A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.

The distinguishing characteristic(s) of the units becomes the differentia of the concept's definition; the existents possessing a "Conceptual Common Denominator" become the genus.

[....] The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.

[in later quotes she says the essential characteristic differentiates from ALL other existents; obviously the genus doesn't do that but instead, as she says, connects to a wider group.]

[....] In the definition of man ("A rational animal"), "rational" is the differentia, "animal" is the genus. [iTOE 53 original, 41-42 expanded]

When [the maturing person (she says at about the time of adolescence)] grasps that man's distinctive characteristic is his type of consciousness--a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason--he reaches the one and only valid definition of man, within the context of his knowledge and of all mankind's knowledge to date: "A rational animal."

[....]

Now observe, on the above example [that of the stages she describes in defining "man"], the process of determining an essential characteristic: the rule of fundamentality. When a given group of existents has more than one characteristic distinguishing it from other existents, man must observe the relationships among these various characteristics and discover the one on which all the others (or the greatest number of others) depend, i.e., the fundamental characteristic without which the others would not be possible. This fundamental characteristic is the essential distinguishing characteristic of the existents involved, and the proper defining characteristic of the concept.

Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others.

For instance, one could observe that man is the only animal who speaks English, wears wristwatches, flies airplanes, manufactures lipstick, studies geometry, reads newspapers, writes poems, darns socks, etc. None of these is an essential characteristic: none of them explains the others; none of them applies to all men; omit any or all of them, assume a man who has never done any of these things, and he will still be a man. But observe that all these activities (and innumerable others) require a conceptual grasp of reality, that an animal would not be able to understand them, that they are the expressions and consequences of man's rational faculty, that an organism without that faculty would [not be a man--and you will know why man's rational faculty is his essential distinguishing and defining charactersitic.

If definitions are contextual, how does one determine an objective definition valid for all men? It is determined according to the widest context of knowledge available to man on the subjects relevant to the units of a given concept.

[....]

An objective definition, valid for all men, is one that disignates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept--according to all the relevant knowledge available at that stage of mankind's development.

[....]

This does not mean that every man has to be a universal scholar and that every discovery of science affects the definitions of concepts: when science discovers some previously unknown aspects of reality, it forms new concepts to identify them (e.g., "electron"); but insofar as science is concerned with the intensive study of previously known and conceptualized existents, its discoveries are identified by means of conceptual sub-categories. For instance, man is classified biologically in several sub-categories of "animal," such as "mammal," etc. But this does not alter the fact that rationality is his essential distinguishing and defining characteristic, and that "animal" is the wider genus to which he belongs.

[iTOE, ?-59 original, 44-47 expanded]

Let us note, at this point, the radical difference between Aristotle's view of concepts and the Objectivist view, particularly in regard to the issue of essential characteristics.

[Popper of course, had he known of Rand's theories, wouldn't have considered this a "radical difference"; both Aristotle and Rand propose the idea of "essences."]

It is Aristotle who first formulated the principles of correct definition. It is Aristotle who identified the fact that only concretes exist. But Aristotle held that definitions refer to metaphysical essences, which exist in concretes as a special element or formative power, and he held that the process of concept-formation depends on a kind of direct intuition by which man's mind grasps these essences and forms concepts accordingly.

Aristotle regarded "essence" as metaphysical; Objectivism regards it as epistemological.

Objectivism holds that the essence of a concept is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of man's knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man's knowledge. The metaphysical referent of man's concepts is not a special, separate metaphysical essence, but the total of the facts of reality he has observed, and this total determines which characteristics of a given group of existents he designates as essential. An essential characteristic is factual, in the sense that it does exist, does determine other characteristics and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of "essential characteristic" is a device of man's method of cognition--a means of classifying, condensing and integrating an ever-growing body of knowledge. [iTOE, 68 original, 52 expanded]

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Edited September 23, 2007 by Ellen Stuttle

[Ellen Stuttle]

Continuing on my earlier thought, if one claims that induction does not exist and defining terms leads to infinite regress, all one has left is deduction from propositions and isolated observation of concretes. That's why induction (and everything else in epistemology) is criticized for not being a valid form of deduction. Deduction from propositions is all that's left for critical thinking and logic.

No, one isn't left with "deduction from propositions and isolated observation of concretes"; one has conjectures and refutations, which is how science actually operates and is how Popper believed (and I'm thinking he was right about this) so does the very process of perception and all of animal learning. (Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist; instead that it doesn't give you certainty about what's true. But one hardly needs certainty in order to manage one's practical and cognitive activities.)

Ellen

___

[Michael Stuart Kelly]

Ellen,

Essential to the essential characteristic for determining the differentia is the standard of measurement. Without a defined unit of measurement, there can be no measurement-omission. The standard of measurement is given in the genus. (Measurement can be cardinal or ordinal.) Without perceptual awareness, there is no conceptual awareness. Thus the standard of measurement is cognitive awareness in "animal" (the genus). There are other characteristics (all of them, in fact), but that is the standard of measurement. That standard of measurement is essential. That standard applied to the genus is one of the major components of how "fundamentality" is determined. Without it there is no differentia.

Play the words and split the hairs any way you want, agree or disagree, but that's Objectivist concept formation.

Michael

[Michael Stuart Kelly]

(Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist; instead that it doesn't give you certainty about what's true. But one hardly needs certainty in order to manage one's practical and cognitive activities.)

Ellen,

Rather than argue, Google this:

Popper "induction does not exist"

Then read the first 50 or so entries to get an idea of where this notion came from.

Michael

[Ellen Stuttle]

(Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist; instead that it doesn't give you certainty about what's true. But one hardly needs certainty in order to manage one's practical and cognitive activities.)

Ellen,

Rather than argue, Google this:

Popper "induction does not exist"

Then read the first 50 or so entries to get an idea of where this notion came from.

Michael

Well, I looked through the first several which came up. They all do include the words "induction does not exist," but I don't think what's being meant in the articles is what I understood you to mean. I understood you to be saying that the claim had been made that no one ever does form a general belief on the basis of a sample of observations. I think that people do form such beliefs -- the way things have always been is the way they'll always be. Daniel can correct me if I'm wrong, but I don't think Popper said that no one ever does thus generalize. The point, though, is that such generalizations aren't valid; additionally Popper argued that they aren't how science is done and, more widely, they aren't how we ever learn.

The selections I looked through so far (some of them are quite long and I only read a section) I think are saying the same.

Here is a sample about scientific method written by working scientists. This says just what I was saying, that science doesn't in fact use induction but instead something which looks like it:

Banegas JR, Rodríguez Artalejo F, del Rey Calero J.

Departamento de Medicina Preventiva y Salud Pública, Facultad de Medicina, Universidad Autónoma de Madrid. joseramon.banegas@uam.es

We are focusing mainly on the so-called problem of induction. We sustain, in line with Popper, that the scientific method does not use inductive reasoning, but rather hypothetical-deductive reasoning. Although the movement from the data evaluating a hypothesis to a conclusion on the latter goes from the specific to the general, that is, in an inductive direction, the induction does not exist as a reasoning process or inference. That is, there is no method that enables us to infer or to verify hypotheses or theories (we cannot explore all of the possible situations to see whether the theory stands up), or even to render them very probable. Besides, scientists look for highly informative theories, not highly probable ones. What we actually do is to propose a hypothesis as a tentative solution to a problem, to confront the prediction deduced from the hypothesis with actual experience, and evaluate whether the hypothesis is rejected or not by the facts. As theories cannot be verified, we can only accept them if they withstand an attempt to reject them. Consequently, the test of a theory consists of criticism or a serious attempt at falsification, that is, the elimination of error within a theory, in order to reject it if it is false. The objective is, thus, the search for true theories. For this purpose, the scientific method uses a systematic set of methodological (not logical) rules, that is, decisions.

Here's another:

Popper's Philosophy and Learning

Zenchang Qin

So that Popper argues that pure logical induction does not exist at all! Because mathematical inference or learning are not logical consequence of given conditions.

The English is bad there, but I think what's being said is that there isn't a logical way of doing induction, not that no one ever -- illogically -- jumps from observing some to concluding all.

Ellen

___

[BaalChatzaf]

The English is bad there, but I think what's being said is that there isn't a logical way of doing induction, not that no one ever -- illogically -- jumps from observing some to concluding all.

Ellen

___

I am giving 8 to 5 odds that Mike does not get it.

Objectivists generally do not comprehend the difference between Abduction (or Reduction) which is conjecturing hypothetical causes as opposed to enumerative induction as described by Francis Bacon. The kind of Induction that leads us to hypothesize that all swans are white and all crows are black is not typical of the kind of thinking that physicists do.

Discussing Science with most Objectivists is like discussing the shape of the Earth with Hollow Earth People. It is an exercise in futility. There are a few folks on this board who get it, but not many. Most are still hung up on Aristotle's notion of Cause.

Interactions in the Real World are a -collective- property of the participating entities. They might even be thought of as emergent properties. They are not the properties of entities taken singly or in isolation. Interactions are relational predicates, not singular predicates.

I plan to post a piece on how Aristotelean Causation has been transmogrified in the modern scientific context. That will be posted presently.

Ba'al Chatzaf

Edited September 18, 2007 by BaalChatzaf

[Ellen Stuttle]

Catching up to Michael's post #219 (many posts, many interrelated subjects on this thread):

[....] "Essential characteristic" and "essential part of the definition" are two different things.

A definition without a genus is not a definition in Objectivism [...].

I know that "'essential characteristic' and 'essential part of the definition' are two different things" and that "a definition without a genus is not a definition in Objectivism." The subject which, insofar as I noticed, was being discussed was "essential characteristic." It's Rand's view that there is such a characteristic which needs to be identified in forming a definition of a concept to which Daniel objects in speaking of Rand's "essentialism." Rand was very much in the Aristotelian tradition of definitions which Popper criticized. The difference, in her words, was that:

Aristotle regarded "essence" as metaphysical; Objectivism regards it as epistemological. [iTOE, 68]

Although she characterizes this difference as "radical," it isn't radical at all from a Popperian standpoint. From that standpoint it's the difference between two variants of the same mistake.

Ellen

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Edited September 18, 2007 by Ellen Stuttle

[Daniel Barnes]

Ellen:

Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist...

Popper says that induction doesn't exist for a number of reasons.

Firstly, he's talking about the problem as posed by Hume, and as is usually understood (see the wiki entry above). This is clearly quite different from whatever it is Roger and Mike and Leonard P happen to call "induction" so we'll leave the existence or not of that whatever-it-is to one side for now.

Secondly, he means it does not exist, or is a "myth", because the method of conjecture and refutation explains the phenomena that looks like induction equally well, without recourse to illogic. Hence it is the superior theory. In light of that, induction, like other early explanations of phenomena that were later found to be illogical , can only be now regarded to exist as a myth, or a failed theory.

Thirdly, he means it does not exist for the extremely simple reason that none of its most famous adherents, nor anyone on this forum, are even able to formulate a principle or theory of inductive truth that has anything like the rigour of our theory of transmission of truth in deductive logic.

Before we get into the nuts and bolts of the two, all we need to do is compare a deductive conclusion to an inductive conclusion to see the difference.

P1:All men are mortal P2:Socrates is a man therefore C: Socrates is mortal.

Compare this with:

It rained for the last 3 Tuesdays therefore it will rain next Tuesday.

Absurd as this sounds, this example is in fact exactly what induction suggests is the way to go about establishing true predictions or theories. That is, from some (completed unspecified) number of past observations or events.

Of course, it doesn't even work from a probable point of view, because there is no successful theory of inductive probability either:

Again:

It rained for the last 3 Tuesdays therefore it is X% probable it will rain next Tuesday.

I invite any of our allegedly "inductivist" friends to fill in the X% with the "inductively" correct result, and demonstrate how they arrived at their conclusion.

There simply is no such thing.

Edited September 18, 2007 by Daniel Barnes

[merjet]

She definitely used the genus-differentia model of definition. But judging from what she wrote about "essential characteristic," I think she thought of that as being the characteristic(s) named by the differentia; the genus she thought of as connecting the differentiated category to a wider category.

Here's a series of quotes which I think makes clear how she viewed the issue of "essence."

"An objective definition, valid for all men, is one that designates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept--according to all the relevant knowledge available at that stage of mankind's development" [iTOE, 61].

Notice she says two parts there: the essential characteristic AND the genus; thus she isn't considering the genus to be the essential distinguishing characteristic.

"Man's essential characteristic is his rational faculty" ["What Is Capitalism?" CUI, 16].

She says that explicitly elsewhere, too, but I'm not finding the quote at the moment. She also someplace discusses "raltionality" as making possible and explaining the greatest number of other characteristics of man.

"Objectivism holds that the essence of a concept is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of man's knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man's knowledge. The metaphysical referent of man's concepts is not a special, separate metaphysical essence, but the total of the facts of reality he has observed, and this total determines which characteristics of a given group of existents he designates as essential. An essential characteristic is factual, in the sense that it does exist, does determine other characteristics and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of "essential characteristic" is a device of man's method of cognition--a means of classifying, condensing and integrating an ever-growing body of knowledge" [iTOE, 68].

I grant you've supplied some evidence that Rand considered the differentia but not the genus as the essence. However, the last quote says the essence distinguishes these units from all other existents within the field of man's knowledge. I take this to say the essence includes the genus, too.

Was she inconsistent? Arguably so. In any case, I think that the genus is part of the essence, too, and Aristotle would probably have agreed. "For if a definition is an expression signifying the essence of the thing and the predicates contained therein ought also to be the only ones which are predicated of the thing in the category of essence; and genera and differentiae are so predicated in that category: it is obvious that if one were to get an admission that so and so are the only attributes predicated in that category, the expression containing so and so would of necessity be a definition; for it is impossible that anything else should be a definition, seeing that there is not anything else predicated of the thing in the category of essence" (Topics VII, 3).

[Michael Stuart Kelly]

Although she characterizes this difference as "radical," it isn't radical at all from a Popperian standpoint. From that standpoint it's the difference between two variants of the same mistake.

Ellen,

Both Popper and Rand argue against Aristotle's "essentialism," but she called it "moderate realism" (ITOE, 2nd Expanded Edition, p. 1):

2. The "moderate realists," whose ancestor (unfortunately) is Aristotle, who hold that abstractions exist in reality, but they exist only in concretes, in the form of metaphysical essences, and that our concepts refer to these essences.

As to "induction does not exist," you have it from the horse's mouth. (Actually the horse rider's mouth. )

Until you "get" that measurement is an essential part of Objectivist concept formation, you will develop the blind spot Daniel has and keep misrepresenting it, saying that it is an error of essentialism. He no longer says that explicitly, but it is constantly between the lines. Notice when he talks about induction, there is no cognitive priority (ordinal measurement) in his examples. No hierarchy of knowledge. The concretes are random observations tied to equally random speculations about the future.

Michael

[tjohnson]

If I might add more novel approach to the whole 'what science does' argument from Korzybski. What scientists do, in general, is attempt to create verbal "maps" (theories) of natural phenomena. Using the map analogy is very helpful because we all know that maps can start out crude as with explorers and over time become very accurate. In principle there is no limit as to how accurate a map can become - the detail merely increases. Similarly with physics, for example, we each new development the theory gives us more and more detail but it is never "true" - there will always be room for improvement. So the concept of a theory being true or false does not apply in natural language, only mathematics. Popper's main contribution is the notion of falsifiability, which means that unless a theory can be expressed in such a way so that it's predicted results can be compared with some experimental results then it really is a mere intellectual curiosity.

[Roger Bissell]

Ellen:

Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist...

Popper says that induction doesn't exist for a number of reasons.

Firstly, he's talking about the problem as posed by Hume, and as is usually understood (see the wiki entry above). This is clearly quite different from whatever it is Roger and Mike and Leonard P happen to call "induction" so we'll leave the existence or not of that whatever-it-is to one side for now.

Secondly, he means it does not exist, or is a "myth", because the method of conjecture and refutation explains the phenomena that looks like induction equally well, without recourse to illogic. Hence it is the superior theory. In light of that, induction, like other early explanations of phenomena that were later found to be illogical , can only be now regarded to exist as a myth, or a failed theory.

Thirdly, he means it does not exist for the extremely simple reason that none of its most famous adherents, nor anyone on this forum, are even able to formulate a principle or theory of inductive truth that has anything like the rigour of our theory of transmission of truth in deductive logic.

Before we get into the nuts and bolts of the two, all we need to do is compare a deductive conclusion to an inductive conclusion to see the difference.

P1:All men are mortal P2:Socrates is a man therefore C: Socrates is mortal.

Compare this with:

It rained for the last 3 Tuesdays therefore it will rain next Tuesday.

Absurd as this sounds, this example is in fact exactly what induction suggests is the way to go about establishing true predictions or theories. That is, from some (completed unspecified) number of past observations or events.

Of course, it doesn't even work from a probable point of view, because there is no successful theory of inductive probability either:

Again:

It rained for the last 3 Tuesdays therefore it is X% probable it will rain next Tuesday.

I invite any of our allegedly "inductivist" friends to fill in the X% with the "inductively" correct result, and demonstrate how they arrived at their conclusion.

There simply is no such thing.

Nice job of cherry-picking examples for your big deduction vs. induction challenge. Not.

How about (for deduction):

It always rains on Tuesday.

Tomorrow is Tuesday.

Therefore, it will rain tomorrow.

Oh, the first premise is just the statement of a coincidence, and not something causally determined? And thus not a reliably true premise?

Couldn't agree with you more. And that, in mirror image, is what is wrong with your goofy induction example. It's little better (?) than astrology. No causal relationships are appealed to, just Humean "constant conjunction."

What you insist on calling "induction", i.e., enumerative generalization, is the crudest form of generalization, and it is utterly non-conceptual (non-integrative). Filling one's mind with such trash is the best way to dilute and undercut one's valid generalizations, which are formed not by enumeration, but by grasping the causal connection that makes them so.

And without valid inductive generalizations, there is "no such thing" (no useful, truth-preserving thing) as deduction either.

REB

[Daniel Barnes]

>He no longer says that explicitly, but it is constantly between the lines.

No, actually I say it explicitly all the time..!

[Ellen Stuttle]

Ellen:

Btw, I don't think anyone is saying that induction in the sense of going from particulars to beliefs about universals doesn't exist...

Popper says that induction doesn't exist for a number of reasons.

[snip]

Compare this with:

It rained for the last 3 Tuesdays therefore it will rain next Tuesday.

Absurd as this sounds, this example is in fact exactly what induction suggests is the way to go about establishing true predictions or theories. That is, from some (completed unspecified) number of past observations or events.

I'm obviously not making myself clear, though I thought my subsequent post spelled it out better. What I understood Michael to be saying when he wrote "induction doesn't exist" is that no one ever does reason in exactly the way you indicated in the quoted example. I don't think it's true that no one ever does reason that way. That that form of reasoning is invalid, I agree. If the meaning is "induction as a valid method doesn't exist," understood. But did Popper claim that no one ever forms conclusions by the INvalid method of extrapolating from some unspecified number of examples to the belief that the next example will be the same?

Ellen

___

Edited September 18, 2007 by Ellen Stuttle

[Daniel Barnes]

Roger:

> Nice job of cherry-picking examples for your big deduction vs. induction challenge. Not....And that, in mirror image, is what is wrong with your goofy induction example....No causal relationships are appealed to, just Humean "constant conjunction."

Roger, there is nothing "goofy" about my induction example, and neither did I "cherry pick it." It is a simple one, yes, but perfectly consistent with and no less simple than with standard induction examples like "the sun has risen on X days therefore it will rise tomorrow."

Now, there seems to me to be a problem with what you're saying above. For by "appealing to causal relationships" in addition to the standard inductive description, aren't you merely adding pre-existing theories as to the causes of the weather to your observations? But this then begs the question as to how these causal theories were themselves arrived at, which in turn you would claim is via induction. But this would seem to make your argument a circularity.

At any rate, it hardly does much for your case that instead of providing us with a valid example of induction, or answering the problems even in the "crude" basic version I've provided, you have merely provided us with another deduction.

>It's little better (?) than astrology.

You're right. This is exactly what we Critical Rationalists say about induction.

>What you insist on calling "induction", i.e., enumerative generalization, is the crudest form of generalization, and it is utterly non-conceptual (non-integrative).

Actually, Roger, what I "insist on calling induction" is the standard formulation of the problem, and is what Hume and everyone else is talking about. Your denial of this is simply incorrect. Would you like me to cite further textbook sources? If you are not familiar with the problem, I am happy to discuss its history in more detail if that is what it will take for you to accept that this is indeed the case.

Incidentally, it seems rather unfair to accuse me of "cherry picking" when I believe you have answered few if any of the problems put to you in my previous posts. Do you intend to?

Here's a brief summary:

1) Can you outline your actual argument as to why it would be impossible for a flightless swan to exist, ie why "flight" is "essential" to swans, but not "whiteness"?

2) Can you give a concrete example of what you consider a "valid" induction from one or two examples?

3) Can you answer whether you and Peikoff consider the standard, Humean version of induction as defined by the wikipedia et al to be deductively invalid?

(It would be nice, BTW, if you withdrew your remark about me "putting words in your mouth" as to 3) as you clearly, if accidentally, contradicted yourself in the issue. The error was not mine)

>And without valid inductive generalizations, there is "no such thing" (no useful, truth-preserving thing) as deduction either.

Yes, well some came to believe this, but fortunately it is not true.

Edit: I see our posts may have crossed.

Edited September 18, 2007 by Daniel Barnes

[Ellen Stuttle]

[...] one's valid generalizations, which are formed not by enumeration, but by grasping the causal connection that makes them so.

Reasonable generalizations are formed by hypothesizing causal connection, but there's no way to be sure you've hypothesized correctly -- though you can establish that a prediction has failed.

And without valid inductive generalizations, there is "no such thing" (no useful, truth-preserving thing) as deduction either.

Deduction doesn't make the claim that the premises are true, only that IF they are true, the truth is preserved by valid deductive procedure in the conclusions.

Ellen

___

[Michael Stuart Kelly]

Reasonable generalizations are formed by hypothesizing causal connection, but there's no way to be sure you've hypothesized correctly -- though you can establish that a prediction has failed.

Ellen,

That's the Popper line. If you completely ignore all the information your concepts are made of (including hierarchies) and limit yourself to range-of-the moment observations with random hypotheses as your base standard, this observation holds (even applied to itself).

Popper wants to predict the future by severing the past, then claim that the method is not reliable because he can't do it (and eventually claims that this does not even exist). If you leave out large chucks of valid epistemology like that, you can prove any theory your heart desires.

Michael

[Ellen Stuttle]

Daniel, speaking of the wikipedia entry you referenced in post #227, I wanted to say something about that:

Here are the two definitions from the wikipedia entry on the problem of induction

"1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class of objects (for example, "All swans we have seen are white, and therefore all swans are white", Hume's Problem of Induction, 18th century, before the discovery of Cygnus atratus in Australia); or

2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, the attractive force described by Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity)."

Both of these are clearly enumerative i.e. generalising based on "some number of observations" or a "sequence of events."

This is what induction is generally taken to be, Roger. This is what Hume is talking about being invalid.

The second example I think is really bad in confusing the issue just in the way people so often confuse it.

A good example of "presupposing that a sequence of events in the future will occur as it always has in the past" would be the example of raining on Tuesday you used or the oft-used example of there always in one's experience having been a sunrise each day so there will be sunrises for all subsequent days one experiences. Neither "[t]he attractive force described by Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity," however, is an example of a such a presupposition and neither was arrived at by (standard meaning) induction; both are scientific hypotheses; both were arrived at by theorizing about what could account for phenomena that don't look alike on the surface (objects falling to the earth -- though the apple story is probably appocryphal -- and planetary orbits).

Ellen

PS: Please don't overlook my post #243 in the shuffle. What I'm trying to ascertain, in brief, is if Popper thought that no one ever IS illogical in method of forming generalizations. That (standard meaning) induction is illogical, completely agreed; that it is not the method used in learning, agreed; but that it is never used by anyone at all, period, that I don't think is true.

___

Edited September 18, 2007 by Ellen Stuttle

[BaalChatzaf]

Reasonable generalizations are formed by hypothesizing causal connection, but there's no way to be sure you've hypothesized correctly -- though you can establish that a prediction has failed.

Ellen. That's the Popper line. If you completely ignore all the information your concepts are made of (including hierarchies) and limit yourself to range-of-the moment observations with random hypotheses as your base standard, this observation holds (even applied to itself).

It is not a "Popper Line". It is the way of the physical sciences. Hypotheses are tested and -retested- when new technology of observation becomes available. That is how it was discovered that Newton's Law of Gravitation is not generally true. When telescopes became good enough to resovle very small angular displacements the motion of Mercury could not be accounted for by Newton's Law.

Hypotheses can be falsified by adverse factual observations but no hypothesis can be guaranteed true everywhere and always. There are always new facts being found and there is no assurance whatsoever that some new fact will not confound a heretofore well supported theory. No scientific hypothesis is safe from potential falsification. No scientific hypothesis cames with a forever and always guarantee of correctness. That is what makes science different from religion.

Before Popper and independent of Popper scientists were falsifying theories based on adverse observations. Popper's fight was with the Positivists who believed it was possible to -verify- a scientific theory forever and always with a sufficient number of supporting observations. Popper was fighting the Verificationists who believe it is possible to prove a scientific theory true once and for all. Newton's theory was falsified long before Popper began publishing. The theory of caloric (heat is a fluid) was falsified in the 19th century long before Popper was born. The Aether hypothesis was falsified by Michelson and Morley (although Michelson did not believe so), long before Popper. James Clerk Maxwell who made important contributions to the theory of heat and thermodynamics sounding a warning alarm concerning specific heat in the late 1860's. He was right. Planck undermined theories based on the continuity of radiation. That is how he came to invent the quantum of energy. Equipartition of energy is just plain false, as Planck showed. There were issues in thermodynamics that were not resolved until quantum theory was developed. And all this without Popper.

Ba'al Chatzaf

[BaalChatzaf]

Reasonable generalizations are formed by hypothesizing causal connection, but there's no way to be sure you've hypothesized correctly -- though you can establish that a prediction has failed.

Ellen. That's the Popper line. If you completely ignore all the information your concepts are made of (including hierarchies) and limit yourself to range-of-the moment observations with random hypotheses as your base standard, this observation holds (even applied to itself).

It is not a "Popper Line". It is the way of the physical sciences. Hypotheses are tested and -retested- when new technology of observation becomes available. That is how it was discovered that Newton's Law of Gravitation is not generally true. When telescopes became good enough to resovle very small angular displacements the motion of Mercury could not be accounted for by Newton's Law.

Hypotheses can be falsified by adverse factual observations but no hypothesis can be guaranteed true everywhere and always. There are always new facts being found and there is no assurance whatsoever that some new fact will not confound a heretofore well supported theory. No scientific hypothesis is safe from potential falsification. No scientific hypothesis cames with a forever and always guarantee of correctness. That is what makes science different from religion.

Before Popper and independent of Popper scientists were falsifying theories based on adverse observations. Popper's fight was with the Positivists who believed it was possible to -verify- a scientific theory forever and always with a sufficient number of supporting observations. Popper was fighting the Verificationists who believe it is possible to prove a scientific theory true once and for all. Newton's theory was falsified long before Popper began publishing. The theory of caloric (heat is a fluid) was falsified in the 19th century long before Popper was born. The Aether hypothesis was falsified by Michelson and Morley (although Michelson did not believe so), long before Popper. James Clerk Maxwell who made important contributions to the theory of heat and thermodynamics sounding a warning alarm concerning specific heat in the late 1860's. He was right. Planck undermined theories based on the continuity of radiation. That is how he came to invent the quantum of energy. Equipartition of energy is just plain false, as Planck showed. There were issues in thermodynamics that were not resolved until quantum theory was developed. And all this without Popper.

Ba'al Chatzaf

[Roger Bissell]

Daniel Barnes

...can you explain exactly why it is, in fact, impossible for a flightless swan to one day be found?

Of course, it goes without saying, you can achieve this by merely playing with the definitions; by simply choosing to nominate "flight" as an essential characteristic of swans. But in reply, obviously one could equally do the same with a particular colour too, such as "whiteness." This would therefore be a simply an arbitrary or ad hoc decision - which you are welcome to make of course, but this would hardly demonstrate your contention that it is somehow "essential." Alternatively you might try to provide grounds that flight is "essential" to swans, because swans are birds and it is "the means of locomotion" of some birds. But of course this would be logically invalid.

I would NOT say that it is impossible for a flightless swan to one day be found. If swans some day evolve into wingless, polka-dotted creatures, that will not invalidate my ~contextual~ definition and concept of swans that includes their being winged. I would simply revise my generalization and move on. (Also see my last point below.) I would not denigrate and reject induction because it did not offer me a timeless, static truth.

Daniel Barnes

Roger:

Induction is NOT enumeration. You can validly induce from one or two examples, if you have observed accurately, grasped the causal connections involved, and integrated your observations to other observations and conclusions.

Ok. Can you give a concrete example of what you consider a "valid" induction from one or two examples?

That yellow cat went "meow." That gray cat went "meow." That dog went "arf." That cow went "moo." Cats go "meow." (Cows and dogs are the "control objects." :-) If a child were to conclude this, it would be perfectly valid IMO. And even if he later found a cat that was incapable of meowing and could only hiss, he'd conclude not that "cats don't meow," but that "that cat can't meow" (i.e., "something's wrong with that cat).

And on the flightless swan model, if a breed of meow-less cats were developed or evolved, this would not invalidate the contextual generalization that (healthy) cats meow. It would just call for a revised generalization. (See last point below.)

Daniel Barnes

Roger:

And I disagree with your implication that enumerative "induction" is "the usual sense of the word 'induction'". Induction ~integrates~ observations; it does not merely amass them and assume that they belong together because of the sheer numbers.

Here are the two definitions from the wikipedia entry on the problem of induction

"1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class of objects (for example, "All swans we have seen are white, and therefore all swans are white", Hume's Problem of Induction, 18th century, before the discovery of Cygnus atratus in Australia); or

2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, the attractive force described by Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity)."

Both of these are clearly enumerative i.e. generalising based on "some number of observations" or a "sequence of events."

This is what induction is generally taken to be, Roger. This is what Hume is talking about being invalid.

Daniel, every generalization is reached within a specific cognitive context, and you cannot state the generalization properly without including that context. Naturally, no one likes to verbally stand on his head each time he makes a generalization, but (as Peikoff points out in IPP) you must remember and at least ~implicitly~ be stating as the preamble to your generalization: on the basis of the available evidence, in other words, within the context of the factors so far discovered, the following is the proper conclusion to draw. Once you make that contextually provisional generalization, you are not off the hook. You must continue to observe and identify the facts of reality, and if new information warrants it, you must qualify your generalization accordingly.

The problem about black swans invalidating "all swans are white", as well as the problem about Einstein invalidating Newtonian physics, is due to the same error: over-generalization, i.e., overlooking the fact that one's generalizations are context-bound. Folks in earlier times didn't have data about the fauna of Australia (?). Newton didn't have data about motion at or near the speed of light.

An error due to over-generalization is not evidence that inductive generalization is invalid in principle, just that it is not infallible, and that you can and should correct the generalization and KEEP GOING! Keep conceptualizing, integrating, forming broader and broader abstractions and generalizations. Certainty is contextual and readily available, so long as one does not hold out for the Platonic, incorrigeable variety.

REB

P.S. -- The great Aristotelian logician H.W.B. Joseph had a very good explanation of the basis for induction. What underlies the observed same characteristics in things is the same causal conditions obtaining. When the causal conditions vary -- e.g., environment or nutrition or mutation causing swan feathers to be black rather than white -- the characteristics vary. The ~causal~ context is what one must be very careful to specify, at least implicitly, in one's generalizations. If you overlook a relevant part of that context, and you come up with anomalous observations, you must seek to understand the context on a deeper level and revise your generalization accordingly.

NONE OF THIS MEANS THAT INDUCTION IS INVALID. Instead, it shows how we must proceed to form valid inductions, and to correct errors that occur.