Thoughts on my view of induction and deduction?

[LauricAcid]

I don't follow your train of thought, since I don't know what not proving the premises of an argument to be true has to do with question begging about the validity of argument forms, and there are deductive arguments that prove that certain deductive forms are truth preserving. But it does seem to me that some arguments in support of deduction may also be question begging, though I also tend to view that the most basic view of deduction is not an argument in support of it but rather to take it as axiomatic, even axiomatic in the sense that to deny deduction entails self-contradiction.

Edited September 23, 2005 by LauricAcid

[DavidOdden]

I don't follow your train of thought, since I don't know what not proving the premises of an argument to be true has to do with question begging about the validity of argument forms, and there are deductive arguments that prove that certain deductive forms are truth preserving.

These arguments are question-begging, since they depend on the validity of some forms of deductive inference. If you do not stipulate that a particular rule is universally T-preserving, then you cannot deductively prove that there is some deduction that is universally T-preserving. (BTW, you should more carefully distinguish "true" and "T". "T" is a formal property without any metaphysical commitments -- it's a pure-consciousness entity; "true", on the other hand, describes a relation grounded on one end to existence).

[Felix]

This refers to Doug Clayton. I wrote this so damn slow that Lauric Acid and David Odden could lead a discussion while I was writing.

Therefore:

Edited for clarity.

Wow. Very interesting. This makes me wish even stronger for Peikoffs book on induction to appear. (Yeah, I know it won't help. Primacy of existence. But I still wait for it desperately.)

Induction is finding out the causal link by finding out the identity of things. This is great.

But I wonder, how do we know the identity of things? And how do we know we have it?

If we have it, then the induction is true. O.K.

But when do we have it?

Finding that identity (and its properties) brings me back to the ravens (or swans) immediately.

When do I know that I learned something about the identity of something?

I can say, it's a raven. Therefore it is black.

How's this different from: Every raven that has a certain gene is black.

I know it must derive from facts known about genetics. But everytime I try to elaborate this, I have a short circuit in my brain. (In addition to that, I hardly know anything about genetics.)

I admit to be a newbie to this, I just started out reading OPAR.

Perhaps someone can give me a better example. (Something that keeps my brain intact, please. )

Edited September 23, 2005 by Felix

[dougclayton]

The question is not of induction being true or false, but rather of it being valid or invalid, reliable or unreliable, correct or not correct. Who are the professors who say that all inductive arguments are false? What would it even mean to say that all inductive arguments are false? On the other hand, if one claims that induction is valid, then the burden is to justify that claim. Nor could I evaluate your claim that to argue against induction is to infer from the falsity (whatever that means pertaining to argument forms) of some inductions to the falsity of all of them, unless you pointed to such anti-induction arguments that have been made and what else goes into them. Meanwhile, most basically, the famous argument, whatever its merits, against arguments for induction is that arguments for induction are question begging, since the most basic argument in support of inductive reasoning is itself inductive.

Fair enough: induction itself is not true or false, but valid or invalid, etc (it is the conclusions arrived at through induction that are true or false). I was being sloppy in my choice of words. As for your other points, I will have to think about them and get back to you.

I do have one question, though: you say arguments supporting inductive reasoning rely on induction, and fall to question-begging. However, arguments against induction also rely on induction, and thus fall to self-refutation. So clearly one of these points is wrong, or there is no way to know anything about the validity of induction at all.

[LauricAcid]

These arguments are question-begging, since they depend on the validity of some forms of deductive inference.

Arguments for deduction do seem to be question begging if they use deduction (or, to avoid question begging, one might draw the line by saying that deduction is axiomatic). But, at least offhand, I don't see how that is related to the question of determining the truth of premises in deductive arguments.

If you do not stipulate that a particular rule is universally T-preserving, then you cannot deductively prove that there is some deduction that is universally T-preserving.

If you mean that one has to use deduction to prove the soundness of a deductive system, then I don't see a way to disagree, since I don't know of any other way to prove soundness.

BTW, you should more carefully distinguish "true" and "T". "T" is a formal property without any metaphysical commitments -- it's a pure-consciousness entity; "true", on the other hand, describes a relation grounded on one end to existence).

If you mean 'T' or '0' as used in mathematical logic, then I don't deny that this does not necessarily refer to what people in general, or Objectivists specifically, mean with the word 'truth'.

you say arguments supporting inductive reasoning rely on induction, and fall to question-begging. However, arguments against induction also rely on induction, and thus fall to self-refutation.

I don't say that all arguments or all possible arguments supporting induction are inductive, but only that at least one very famous argument is that at least the primary arguments for induction are inductive. On the other hand, you say that arguments against induction rely on induction. While that is an intriguing proposition, I don't see in front of us, at least not in this thread, a good argument for that proposition.

[DavidOdden]

On the other hand, you say that arguments against induction rely on induction. While that is an intriguing proposition, I don't see in front of us, at least not in this thread, a good argument for that proposition.

Such an argument (against induction) would have to depend on some premises (no deduction or induction creates a conclusion ex nihilo). Those premises would have to either be, or derive from, a concusion whose correctness is proven inductively. Since I'm saying that there are no good arguments against induction and certainly none have been offered in this thread, I will have to wait until someone invents a supposedly good argument against induction to show how it presupposes induction. Note, btw, that the "truth of premises" problem for deduction is separate from the "T-preservingness of deduction" problem, which was the gist of my second sentence.

As for proving the validity of a system of inferential rules (using "validity" in the standard sense of "working properly" and not the specialised "T-preserving" sense), the way to prove the validity of a rule of inference is empirically: to see that it correctly captures the relationships between propositions and facts. Remember that unlike a consciousness-based philosophy, Objectivism has appeal to reality as a means of verifying claims.

[LauricAcid]

I will have to wait until someone invents a supposedly good argument against induction to show how it presupposes induction.

Whether a good argument or not, the most basic retort of question begging is to the supporter of induction who justifies induction on the grounds that we can inductively see that induction works.

Note, btw, that the "truth of premises" problem for deduction is separate from the "T-preservingness of deduction" problem, which was the gist of my second sentence.

I still don't know what your point is about the truth of premises in deduction and how that point relates to what else you were driving at. Oh well. Nevermind, I suppose.

As for proving the validity of a system of inferential rules (using "validity" in the standard sense of "working properly" and not the specialised "T-preserving" sense), the way to prove the validity of a rule of inference is empirically: to see that it correctly captures the relationships between propositions and facts. Remember that unlike a consciousness-based philosophy, Objectivism has appeal to reality as a means of verifying claims.

This is the point you made in the 'Perfecting Logic' thread. In that thread you had no logical rebuttal to the point I made that your view just leads to making deductive forms irrelevant since the only way to empirically check them is to empirically check their conclusions; so we might as well just empirically check the conclusions and not bother with the deductive argument form itself. Morevover, your view just ignores the way in which empirical confirmation of deductive forms is irrelevant since to deny the validity of the deductive forms is to deny the law of non-contradiction. Edited September 24, 2005 by LauricAcid

[jrs]

I do have one question, though: you say arguments supporting inductive reasoning rely on induction, and fall to question-begging.

If you were trying to use deductive reasoning to prove that some version of inductive reasoning was valid AND in the course of doing so you relied upon a premise established only by the very inductive method in question, then you would be begging the question.

However, this merely means that your attempt to establish induction's validity by this method failed. Induction might still be valid anyway.

However, arguments against induction also rely on induction, and thus fall to self-refutation.

If a generalization "proved" by induction was a universal which did not admit of any exceptions AND you discovered an exception, then this would show that this version of induction was invalid. This argument against induction does not rely on induction (although it might use some premises or methods which are normally established by induction), so it is not self-refuting.

But more generally, "self-refuting" arguments are not necessarily invalid. If they amount to an instance of reductio ad absurdum, then they might very well be valid.

Even if an argument against induction is shown to be invalid because it is self-refuting, this does not establish that induction is valid.

So clearly one of these points is wrong, or there is no way to know anything about the validity of induction at all.

If it ever leads to a contradiction, then it is invalid. Otherwise, you are free to presume that it is valid.

[AisA]

But more generally, "self-refuting" arguments are not necessarily invalid. If they amount to an instance of reductio ad absurdum, then they might very well be valid.

You cannot use induction to "prove" that induction is invalid. If induction is invalid, it cannot be used to prove anything.

[DavidOdden]

Morevover, your view just ignores the way in which empirical confirmation of deductive forms is irrelevant since to deny the validity of the deductive forms is to deny the law of non-contradiction.

This last point is sheer nonsense, and surprisingly reveals that you are confused about the distinction between deduction as a method, and specific laws of deductive inference. The law of non-contradiction is obviously valid, and is indeed the fundamental law of logic. Any other method of inference -- deductive or inductive -- which allows the derivation of a contradiction is invalid. Why? Because the law of non-contradiction is not an arbitrary statement about consciousness, it is a metaphysically-grounded statement about existence. The merit of certain modes of deductive inference derives from its connection to reality, and not from an arbitrary declaration that such-and-such method is held to be "deductive".

[jrs]

But more generally, "self-refuting" arguments are not necessarily invalid. If they amount to an instance of reductio ad absurdum, then they might very well be valid.

You cannot use induction to "prove" that induction is invalid. If induction is invalid, it cannot be used to prove anything.

If you knew what "reductio ad absurdum" meant, you would not have said this.

[LauricAcid]

you are confused about the distinction between deduction as a method, and specific laws of deductive inference.

That's rich, coming from you. I have no such confusion, while you cannot even make a coherent distinction between deduction and induction, let alone the specifics within them.

The law of non-contradiction is obviously valid, and is indeed the fundamental law of logic. Any other method of inference -- deductive or inductive -- which allows the derivation of a contradiction is invalid. Why? Because the law of non-contradiction is not an arbitrary statement about consciousness, it is a metaphysically-grounded statement about existence. The merit of certain modes of deductive inference derives from its connection to reality, and not from an arbitrary declaration that such-and-such method is held to be "deductive".

I didn't arbitrarily declare a method to be deductive. Rather, I showed you how one particular argument form is deductively valid by showing how denying its deductive validity would be to deny the law of non-contradiction. Apparently, you still don't understand this.

[LauricAcid]

To expand on jrs's last post, as I understand the point he's making, it is that if induction were invalid, then in a reductio ad absurdum, one may use induction to argue for the invalidity of induction. Generally, an argument that assumes a principle in order to deny that principle may refute the principle and not be a self-refuting argument after all. This seems to me to have some merit (though I find it raises some perplexing problems) and is one of the shrewdest original ideas I've ever read on an Internet board.

Edited September 27, 2005 by LauricAcid

[Free Thinker]

Here is an email I sent to my prof. "Point 1" is my answer to how we know what the fundamental characteristics of an existent is, and "Point 2" further elaborates on the nature of concepts; I think completing my theory.

Two points -

1) The way we determine the "essential characteristics" of an existent is sort of a backwards question. "Characteristics" is really a negative concept - it describes what an object IS NOT. It describes the differences between all the finite numbers of object of which we are aware AND their relation to a existent. The more objects/existents we are aware of, the more specific our language is. The Thus, a concept is NECESSARILY defined by its context - context in this respect meaning the sum total of our knowledge [of existents]. A concept is not the existent itself, but our way of representing it.

2) I can anticipate the question already - "That is all fine and good, but that still cannot possibly predict the future. Even if we understand the nature of concepts, and of the "essential characteristics of the sun", what's not the say that tomorrow the sun WOULDN'T rise?" The answer to this question is that we DON'T know that the sun will certainly rise tomorrow. There is a possibility that it won't rise, but one cannot predict the events that may or may not take place tomorrow. What was the point of all that then? Have I conceded my case? No. The key thing here is that a concept is NECESSARILY defined by its context. Our sum body of knowledge that conditions a given context [of a concept] may or may not change, but that doesn't mean that our statement is false.

Let me explain. Suppose the sun didn't rise tomorrow. This is the EFFECT we observe. By it's nature in reality, a cause must exist. Once we figure out this cause, we revise our statement by adding a qualifier. This does not mean we were wrong in saying that "the sun will rise tomorrow"/ or "the sun will always rise"; because implicit in that statement is a reference to context; the body of knowledge that we based that conclusion on. If we learn that the sun didn't rise because (let's say) an alien used a really big oven mitt to hold the sun down, we have added knowledge to our context and our conclusion changes, but NOT our initial conclusions about the nature of the sun.

[DavidOdden]

1) The way we determine the "essential characteristics" of an existent is sort of a backwards question. "Characteristics" is really a negative concept - it describes what an object IS NOT.

This is absolutely the wrong way to think of concepts. The defining characteristics of a concept state what a concept is. If it were otherwise, you would be faced with massive cognitive chaos when you learned of new type of beings. Suppose you learned of a new kind of being, a langur (a kind of monkey). Your definition of "horse" doesn't make any reference to "langur", nor does your definition of "pig" or "fish". That would mean, according to your existing definition of "horse" (under your theory of concepts), langurs are not in the set of things that you know that horses aren't. That means all of the sudden langurs must be pigs, fish and horses (among other things). This just isn't so: concepts operate in terms of positive attributes -- characteristics shared by the entities.

The more objects/existents we are aware of, the more specific our language is.

This too is seriously mistaken. English (to pick the specific language we're all using here) doesn't become more or less specific as a result of the sum total experience of speakers of English with the things we're talking about. The more you know about particular concepts, the more specific your references might become -- you might learn not just to distinguish langurs from other monkeys like colobuses and vervets, but also to distinguish the 17 species of langur such as the Spectacled Leaf Monkey, the Capped Langur, the Nilgiri Langur and so on. If you've seen one Nilgiri Langur, you've pretty much seen them all -- it's only when you see other members of the concept langur which are clearly distinct and yet share characteristics, that you have to consider conceptual differentiation and therefore a change in language. Simply observing more monkeys does nothing for you, and even seeing that there are differences does not affect the precision of your language -- you have to make a terminological distinction first, to get any more precision out of language.

[Free Thinker]

David Odden -

The only way I could distinguish what fundamental characteristics an existent had was to say "what distinguishes this thing from that thing". How would you go about doing it?

[hunterrose]

I'll reread all this before I reply, but what's been your professor's response?

[Free Thinker]

I'll reread all this before I reply, but what's been your professor's response?

He hasn't responded yet to the last email I sent him, but basically he buys into the argument that because induction can't "predict the future" (which is a claim induciton REALLY doesn't make), induction is a system of probabilities.

Edited September 27, 2005 by ASelameab

[DavidOdden]

The only way I could distinguish what fundamental characteristics an existent had was to say "what distinguishes this thing from that thing". How would you go about doing it?

To paraphrase the song, accent the positive. State what facts are true of the concept. Don't include non-essential truths, for example "two-legged primate" is not essential to the definition of "man", as in fact you know because a person who has lost a leg is no less of a man. Include what is needed to distinguish the concept from other similar concepts (ones which it would be subsumed under anyhow), so not just "animal", since that includes things that aren't "man". I think Rand's discussion of concepts in ITOE is pretty good and clear, so I'd suggest reading through it and then, of course, if there are further questions that need clarifying, bring them up. The point is that you don't need to define concepts in terms of what they aren't, in order to be able to distinguish two concepts. Definition by complement rarely useful.

[hunterrose]

Include what is needed to distinguish the concept from other similar concepts

Which, as far as the topic's title, goes a way toward removing deduction from "handmaiden" status. Induction can't distinguish a concept from similar concepts, whereas that's deduction's bread and butter. I doubt you could come to the essential characteristic of man solely through induction.

I know deduction's been bypassed and induction is your concern, but it should be noted that induction can be stated in the same way as deduction was:

if all dogs are fish, then any particular dog is a fish.

if all dogs need food, then any particular dog needs food.

Not to say that this invalidates induction, of course.

[logicaalroy]

Hi David Odden,

I am just curious what you really mean when you say "arguments for deduction are question begging". True, David, there is no requirement by some authority that demands that the premises of a deduction be true, but that is the responsibility of the user of deductive logic. I might be misinterpretting you; so I ask for clarification to understand better. There is a trend for some people to think that all deductions are based on axioms and thus, deduction is believed to be unreliable. Many who study logic reply to what Aristotle called "Material" part of logic. So, many students use the term "Material logic" (which I am not to fond of) to express when the premises of a deductive argument are in fact empirically true. When you add valid form to "material logic" you have a practical deductive system that does not fit into an axiomatic system or a question begging system. Have you or anyone else heard this form of response? What are your thoughts about it. [Note: I am not expressing my personal beliefs or thoughts, but what I presented are arguments that I have heard and seen in my study of logic].

Edited September 28, 2005 by logicaalroy

[DavidOdden]

I am just curious what you really mean when you say "arguments for deduction are question begging".

Within the system, it is assumed without proof that a (proper) deduction is automatically / universally truth-preserving or T-preserving (more correctly the latter). One of the usual complaints about induction is that it doesn't produce "necessarily T" results, whereas deduction does. But this is simply assumed, not proven; in other words, this fundamental difference between deduction and induction is stipulated in the definitions of terms, meaning that it is question begging.

The one real question is whether the rule of inductive generalization should be admitted into a formal system. Because the classical deductivist approach both wants to detach the formal method from the object of study (namely, existence) and because it does not want to put any limits on premises (they are arbitrary collections of strings), it has to reject inductive generalization.

So my objection is the implication that induction, unlike deduction, is question-begging. Even the dichotomy between induction and deduction is a bit of a spurious dichotomy, formally speaking (though formally speaking, you can always dichotomize in any arbitrary way you want). Adding inductive generalization requires a negligible change to a formal system that is otherwise apparently "deductive". Out of curiousity, how would you define "deductive logic", bearing in mind the range of actually known distinct systems of logic that are classed as "deductive"? When you answer that, keep in mind the difference between formal T and real-world truth.

it should be noted that induction can be stated in the same way as deduction was:

if all dogs are fish, then any particular dog is a fish.

if all dogs need food, then any particular dog needs food.

What is your claim? I presume that you're not claiming that this is an example of induction (since it isn't). Whether or not an inductive generalization is formally valid depends on the rules of form, but let's see if you can explain yourself without needing to go too deeply into that. I just can't figure out what you're getting at, so please clarify.

[hunterrose]

What is your claim? I presume that you're not claiming that this is an example of induction (since it isn't). Whether or not an inductive generalization is formally valid depends on the rules of form, but let's see if you can explain yourself without needing to go too deeply into that. I just can't figure out what you're getting at, so please clarify.

The claim was that the Case against Deduction applied equally to induction, though whether the case itself was valid had already been discussed.

How weren't the examples proper induction?

[AisA]

If you knew what "reductio ad absurdum" meant, you would not have said this.

Reductio ad absurdum does not depend on the validity of an argument in an attempt to refute it. It refutes an argument (or a position) by showing that it leads to absurd consequences (or a contradiction). It thus depends on the argument being invalid, otherwise it could not be shown to lead to absurd consequences.

[LauricAcid]

Within the system, it is assumed without proof that a (proper) deduction is automatically / universally truth-preserving or T-preserving (more correctly the latter).

What do you mean by 'T-preserving'? Anyway, within a consistent system one cannot assume soundness, since a consistent system cannot even EXPRESS its own soundness. But some formal systems (most particularly first order logic) are proven to be sound, but this proof is in a meta-system. You are just shooting off about that which you do not know with fatuous statements as quoted above.

One of the usual complaints about induction is that it doesn't produce "necessarily T" results, whereas deduction does. But this is simply assumed, not proven

The usual definitions of 'induction' and 'deduction' (not Objectivist definitions) are that deduction yields conclusions that follow with necessity from the premises whereas induction does not.

in other words, this fundamental difference between deduction and induction is stipulated in the definitions of terms, meaning that it is question begging.

Then any definition of a word (a sound or combination of letters) regarding anything at all is question begging. Moreover, the distinction between deduction and induction here does not depend on the words 'deduction' and 'induction'. If you object to those words being used, then we could use the words 'schduction' and 'schinduction' instead. So a schductive argument is one in which the conclusion follows with necessity from the premises and a schinductive argument is one in which the conclusion follows only with likelihood from the premises.

The one real question is whether the rule of inductive generalization should be admitted into a formal system.

What formal systems?

the classical deductivist [...] does not want to put any limits on premises (they are arbitrary collections of strings), it has to reject inductive generalization.

If I recall correctly, you made this claim before about 'arbitrary collections of strings' and I corrected you before on this point. Moreover, your inference as to the reason deductive systems are not inductive systems is a non sequitur; it's something just pulled out of your own thin air. One who works with deductive systems does not necessarily "reject" induction anymore than an aircraft pilot rejects the methods of a submarine pilot.

Even the dichotomy between induction and deduction is a bit of a spurious dichotomy, formally speaking (though formally speaking, you can always dichotomize in any arbitrary way you want).

Your classifications need not be considered any less arbitrary than those you call 'arbitrary', unless you can show otherwise, which you have not. Just saying the word 'essential' does not provide a clear (let alone scientific, let alone mathematical) means by which to determine an essential property from an accidental one.

Whether or not an inductive generalization is formally valid depends on the rules of form, but let's see if you can explain yourself

Why don't you explain? What do you think are the rules of form of formal validity for inductive generalizations?

keep in mind the difference between formal T and real-world truth.

What do you mean by 'formal T truth'? Edited September 28, 2005 by LauricAcid