Thoughts on my view of induction and deduction?

[LauricAcid]

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.

Correct. But if one used an argument form to derive a contradiction, then either the premises used to derive the contradiction are self-contradictory or the argument form itself is invalid. So if no self-contradictory premises were used, then the argument form itself is invalid. So if one showed that the argument form of induction used with premises that are not sefl-contradictory leads to some contradiction, then the argument form of induction is proven invalid. In that way, one would have used induction to prove the invalidity of induction.

[DavidOdden]

How weren't the examples proper induction?

They don't derive universal statements from specific ones, so I don't see how they have any bearing on the question.

[LauricAcid]

Whereas most logicians would say they're not inductive because the conclusions follow necessarily from the premises.

If an inductive argument is a generalization from specific to universal, then what is this argument:

So far, everytime I push the elevator button, the elevator stops on my floor; therefore, if I push the elevator button right now, the elevator will stop on my floor.

[AisA]

Correct. But if one used an argument form to derive a contradiction, then either the premises used to derive the contradiction are self-contradictory or the argument form itself is invalid. So if no self-contradictory premises were used, then the argument form itself is invalid. So if one showed that the argument form of induction used with premises that are not sefl-contradictory leads to some contradiction, then the argument form of induction is proven invalid. In that way, one would have used induction to prove the invalidity of induction.

No, you have not. If you reach a false generalization, you have merely proven that there is an error in your thinking. You have not discredited induction; you have merely demonstrated your lack of omniscience (or worse).

If an inductive argument is a generalization from specific to universal, then what is this argument:

So far, everytime I push the elevator button, the elevator stops on my floor; therefore, if I push the elevator button right now, the elevator will stop on my floor.

If the full extent of your knowledge in this context is the mere observation of the correlation of the elevator stopping at your floor after you push the button -- with no knowledge of the causal connections involved -- then you have made an unwarranted generalization.

[LauricAcid]

Of course, if the method of inference were incorrectly applied, then the method is not thereby discredited. But, if we assume that the method were correctly applied, and all that went into the argument were non-contradictory premises and a method of inference, but a contradictory conclusion were derived, then wouldn't the error have to be in the method of inference?

As to the elevator button, suppose one has knowledge of the causal connection, then is the inference inductive? Also, (1) what is your definition of 'causal connection'? and (2) Would one avoid having made an unwarranted inference just by supposing that there is some causal connection without specifying what it is? E.g., one might not know how the button actually mechanically affects the elevator, but one does suppose that there is a mechanical connection.

Edited September 28, 2005 by LauricAcid

[dougclayton]

If an inductive argument is a generalization from specific to universal, then what is this argument:

So far, everytime I push the elevator button, the elevator stops on my floor; therefore, if I push the elevator button right now, the elevator will stop on my floor.

(First, assume the elevator works, since that's irrelevant to the issues here.)

Your argument as presented is primarily deduction: 1) the elevator stops on my floor when I push the button, and 2) I just pushed the button, therefore 3) the elevator will arrive now. But I think I know what you mean, so let me illustrate where the induction should have happened: knowing that "the elevator stops on my floor when I push the button."

Whether that principle is based on induction depends on what you mean by it. If you mean a scenario equivalent to "all swans are white," then this is not induction as your conclusion does not follow from the causal nature of elevator, but merely repeated observations of correlation. That makes it a generalization, but since you don't know why it arrives, you can never know if it will fail to arrive one day.

On the other hand, if you mean, "I know that the button is wired up to circuitry that identifies this floor and sends a signal to the elevator to move to my floor when I push it," then this is induction, because you know why it arrives, and thus can say it will always arrive.

Contrast this approach with that of astrologers or Pavlov's dogs: they notice something that happens to follow something else, and commit the fallacy of post hoc, ergo propter hoc and conclude that it will always follow.

I see that AisA has summarized it brilliantly while I was composing my post:

If the full extent of your knowledge in this context is the mere observation of the correlation of the elevator stopping at your floor after you push the button -- with no knowledge of the causal connections involved -- then you have made an unwarranted generalization.

[LauricAcid]

dougclayton: I too edited in repsonse to AisA's edit.

[hunterrose]

They don't derive universal statements from specific ones, so I don't see how they have any bearing on the question.

I know I'm probably in for a whale of a speech but...

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

The first part seems to be specific statements (grouped into one:) if this dog, and that dog, and in fact every dog I've ever known is a fish -> if all (known) dogs are fish

The second parts seems universal to me: then any and every other dog (including ones not known at this moment) I meet will be a fish.

Don't know if it makes a difference, but I didn't mean "all" as in all existent dogs, but all known dogs.

[dougclayton]

As to the elevator button, suppose one has knowledge of the causal connection, then is the inference inductive? Also, (1) what is your definition of 'causal connection'? and (2) Would one avoid having made an unwarranted inference just by supposing that there is some causal connection without specifying what it is? E.g., one might not know how the button actually mechanically affects the elevator, but one does suppose that there is a mechanical connection.

These are good questions, and if I had all the answers I could make a lot more money by writing a book on induction.

0) Yes, with an understanding that the elevator button is wired such that the elevator would arrive, that would be an inductive inference. That lets you validate the principle, "The elevator comes when I push the button," which permits a whole host of deductive conclusions from that.

1) I would say, and here I'm not so sure, that the causal connection would be a demonstration of the nature of the identity, and how that nature leads to a certain action in a given context. (This, by the way, is why you only truly need one instance to validate an inductive conclusion.) I could try to come up with a concrete example if you're interested.

2) One need not know the particular mechanism if one knows that other humans have set up that mechanism. In that case, the conclusion that the elevator will come is based on a deduction of the form: 1) People have the ability to establish "causal connections" that serve some purpose, and 2) a person put this button in for the purpose of making the elevator arrive, therefore 3) this button causes the elevator to arrive. Of course, one would have to inductively validate the premise that "people have the ability to establish causal connections," but this is pretty easily shown (and is independent of elevators).

[DavidOdden]

What do you mean by 'formal T truth'?

Truth is a relation between a proposition and the metaphysical state of affairs that the proposition describes, which is often called "correspondence". If there is no such state of affairs, then the proposition is not true. T on the other hand carries no existential commitments. T-preserving refers to the relations between the letters T and F as embodied in typical truth-tables for logical connective, in systems that use just T and F.

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.

You're just pissed off because you cooked up this lie about induction and question-begging, which to the extent that it has any merit is as true of deduction. You seem to have this crazy idea that only deduction is entitled to self-justify via reference to a meta-systemic proof.

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.

No, that's just baloney. That's a typical deductivist smear of induction, but it isn't how induction is defined. Induction is simply the application of a rule of generalization, which derives a universally quantified statement from a set of singular propositions given a lack of contradictions. And when you get into notions of "necessity", again you either have to circularly define "necessary truth" as the relationship between a conclusion and a set of premises which you believe follow certain symbolic sequencing rules, or you have to appeal to reality. An appeal to reality will run you into the same fallibility problem that induction encounters, so the "necessarily follows" property either isn't necessarily true (i.e. it's a matter of faith), or it's a matter of stipulation that any derivation of a particular type is called "necessarily true".

[dougclayton]

I know I'm probably in for a whale of a speech but...

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

Don't worry, I'll limit my speech to goldfish size. As David said, an inductive conclusion must "derive universal statements from specific ones." In your example, you start with the universal in one form ("all dogs") and apply a form change to reach another universal ("any particular dog"). The conventional form of induction is, "This dog barks. That dog barks. Thus all dogs bark." That goes from specific to universal (although it is actually not a valid inductive conclusion).

[DavidOdden]

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

The first part ("all dogs") is a universal and false statement and the conclusion ("a particular dog") is also a universal and false statement. Your example isn't a good example of any kind of logical inference since it amounts to the trivial deduction "A->A", where you don't get anything at all from the exercise. The expressions "all dogs" and "any particular dog" are semantically equivalent -- I read what you said as "a particular dog", which is the application of a nontrivial deductive rule, universal instantiation. You can symbolize your proposition in the standard ways by saying "(Ax(D(x)->F(x))->Ax(D(x)->F(x)))". The first part of the formula says "all dogs are fish" and the second (identical) part of the formula says "any particular dog is a fish". Those are just two different natural language expressions with the same semantics.

An instance of universal or inductive generalization is deriving "Ax(F(x))" from "F©". There is more to it than that (such as the requirement for non-contradiction in the full set of propositions that define the context), to be sure, but that is at least a start.

[ed: oh, well-- Doug said it..]

Edited September 28, 2005 by DavidOdden

[LauricAcid]

DavidOdden: You're putting words in my mouth:

You seem to have this crazy idea that only deduction is entitled to self-justify via reference to a meta-systemic proof.

I've never posted anything that even implies that. In fact, here's what I posted in this thread:

"[...] 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."

I have not posted that induction may not also be rationally justified by certain means, and the above quote even recognizes that there are question-begging issues with deduction itself.

You're just pissed off because you cooked up this lie about induction and question-begging, which to the extent that it has any merit is as true of deduction.

What lie have I cooked up about induction and question-begging? Please quote me directly rather than just make things up out of thin air. Anyway, the strawman you've introduced here is also a red herring to distract from the correct point I made that your statement about deductive systems is incorrect and ill-informed.

T-preserving refers to the relations between the letters T and F as embodied in typical truth-tables for logical connective, in systems that use just T and F.

Truth tables do not embody relations between T and F as letters. So whatever this 'T-preservation' thingie is that you imagine is a construct of your own.

That's a typical deductivist smear of induction

If it's used as a smear of induction by others, it is not used as a smear of induction by me.

it isn't how induction is defined

It's a common definition of the word 'induction', whether or not it is an Objectivist definition or your defintion.

Induction is simply the application of a rule of generalization, which derives a universally quantified statement from a set of singular propositions given a lack of contradictions.

That's your definition. Fine, you can have the word 'induction' to use only and exactly as you use it. So, whenever I use the word, consider that I've made a typo and should have typed 'schminductive' instead.

And when you get into notions of "necessity", again you either have to circularly define "necessary truth" as the relationship between a conclusion and a set of premises which you believe follow certain symbolic sequencing rules, or you have to appeal to reality.

All you have to do is point to the law of non-contradiction. Moreover, if you dispute the word 'necessary', then you should explicate what Objectivism means when it uses the word.

An appeal to reality will run you into the same fallibility problem that induction encounters, so the "necessarily follows" property either isn't necessarily true (i.e. it's a matter of faith)

Only if holding the law of non-contradiction is a matter of faith. I've showed you how this works, but you still ignore it.

or it's a matter of stipulation that any derivation of a particular type is called "necessarily true".

You keep failing to understand that there is not just a stipulation, but that for certain important systems there is a proof. Edited September 28, 2005 by LauricAcid

[LauricAcid]

dougclayton, thanks for your response.

1) I would say, and here I'm not so sure, that the causal connection would be a demonstration of the nature of the identity, and how that nature leads to a certain action in a given context. (This, by the way, is why you only truly need one instance to validate an inductive conclusion.) I could try to come up with a concrete example if you're interested.

Examples are always helpful, but a principle is not formulated by just giving examples of it. But you have given some terms by which to formulate the principle, though I fear 'nature', 'leads to', and 'given context' are all notions that are no less in need of explication as is what they meant to define here.

One need not know the particular mechanism if one knows that other humans have set up that mechanism.

In certain instances one might not know whether the connections are man made or not. What if one were just to suppose that there is some causal connection, man made or not? For example, if one did not know the principles of astronomy, would one be unwarranted in inferring that the sun will appear on the eastern horizon within the next twenty four hours? For that matter, if causality is explained in terms of the nature of things, which I take to refer to things as they are understood through Objectivist concepts, then this again reverts to the Objectivist concept of essentiality, so that essentiality cannot be explained in terms of causality without an inversion of hierarchy. So if the 'depend' (if I recall, that is a word used) in the Objectivist explanation of essentiality is not that of causality, then what is it?

[DavidOdden]

It's a common definition of the word 'induction', whether or not it is an Objectivist definition or your defintion

Since you're clearly not interested in serious discussion of methods of reasoning, I'll just leave you with this invitation -- please explain what facts of reality could in principle prove that your misrepresentation of induction is "a common definition of the word 'induction'". Try treating some of what you are saying as being based in facts, rather than your personal wishes. How would you go about verifying that this statement of yours is true?

[LauricAcid]

Since you're clearly not interested in serious discussion of methods of reasoning

Are tyring to set a record for the most number of non sequiturs and false statements in this forum?

I'll just leave you with this invitation -- please explain what facts of reality could in principle prove that your misrepresentation of induction is "a common definition of the word 'induction'".

In principle and in fact would include looking at dictionaries and texts on the subject, though my useage is not a misrepresenation.

Meanwhile, if you claim that your definition is a common one (I don't know if you do), you could say what you think is in principle and in fact a basis for your claim.

Edited September 28, 2005 by LauricAcid

[dougclayton]

Examples are always helpful, but a principle is not formulated by just giving examples of it. But you have given some terms by which to formulate the principle, though I fear 'nature', 'leads to', and 'given context' are all notions that are no less in need of explication as is what they meant to define here.

Well, that's why I said I wasn't sure. To be sure, the exact nature of "nature" needs to be clarified (and no, that's not circular). I will have to think about this.

In certain instances one might not know whether the connections are man made or not. What if one were just to suppose that there is some causal connection, man made or not? For example, if one did not know the principles of astronomy, would one be unwarranted in inferring that the sun will appear on the eastern horizon within the next twenty four hours?

One would be warranted in expecting the sun to rise, because correlation is a strong predictor of causality. But one could certainly not regard it as required or certain.

For that matter, if causality is explained in terms of the nature of things, which I take to refer to things as they are understood through Objectivist concepts

I am not sure what this means, but as I read it (the "nature" of a thing depends on Objectivist concepts), then this is wrong. The nature of something is independent of us as observers. Perhaps you can clarify this for me.

This again reverts to the Objectivist concept of essentiality, so that essentiality cannot be explained in terms of causality without an inversion of hierarchy. So if the 'depend' (if I recall, that is a word used) in the Objectivist explanation of essentiality is not that of causality, then what is it?

Ah, now we're getting to the interesting part (where "interesting" means "I have more thinking ahead of me"). First, I don't know the relation between "essentiality" and "causality." But regardless, I don't think discovering some aspect of an item's nature implies knowing what the essential aspect of that item is. For instance, I could discover that a pen rolls across a desk because part of its nature is being round, without meaning that roundness is an essential attribute of all pens (on the other hand, it does mean that roundness is essential to rolling). So I'm unclear on what you mean.

[LauricAcid]

On the other hand, if you mean, "I know that the button is wired up to circuitry that identifies this floor and sends a signal to the elevator to move to my floor when I push it," then this is induction, because you know why it arrives, and thus can say it will always arrive.

But the example I gave was not the conclusion that the elevator always arrives, but rather that the elevator will arrive this particular time. That's an inference to a particular, so is it inductive or deductive in your book?

[LauricAcid]

I am not sure what this means, but as I read it (the "nature" of a thing depends on Objectivist concepts), then this is wrong.

No, I meant the reverse of what you thought I meant.

I don't think discovering some aspect of an item's nature implies knowing what the essential aspect of that item is. For instance, I could discover that a pen rolls across a desk because part of its nature is being round, without meaning that roundness is an essential attribute of all pens (on the other hand, it does mean that roundness is essential to rolling).

I think I understand what you're saying. But you suggested (though you did qualify that your answer is tentative) that causality is explained in terms of a nature leading to something. But doesn't Objectivism hold that natures are identified (if that is the correct word here) by concept formation? Entities have natures, and these natures are identified by the mental process of concept formation, right? But concept formation depends on determining essential properties in the final step of concept formation that is definition. So to explain causality in terms of the natures of things involves concepts which involves essential properties. So while the essence of being a pen might not include roundness, we still have your explanation that roundness is essential to rolling. So, I take it, rolling is inferred from roundness. So what is the causal connection between roundness and rolling? If it has to do with the nature of things, then I suppose the causal explanation starts with the nature of things as being round. But round is a concept and thus requires understanding essence. In the case of roundness, this might not be too difficult, since roundness can be edified mathematically (even though physical objects are not perfectly round), but in other instances I imagine that such edifications are vastly more complex. Edited September 28, 2005 by LauricAcid

[dougclayton]

But the example I gave was not the conclusion that the elevator always arrives, but rather that the elevator will arrive this particular time. That's an inference to a particular, so is it inductive or deductive in your book?

Well, let me quote myself:

Your argument as presented is primarily deduction: 1) the elevator stops on my floor when I push the button, and 2) I just pushed the button, therefore 3) the elevator will arrive now.

Did that not answer your question? Application of a universal to a particular is deduction. (As far as I know, that is not particularly revolutionary or controversial.) However, since this was a discussion about induction primarily, I thought you mean the inductive inference that leads you to the universal ("how do I know the elevator will arrive just because it has in the past?"), and that was what I subsequently analyzed in that post. But of course your syllogism is deductive.

[LauricAcid]

But you wrote, "Yes, with an understanding that the elevator button is wired such that the elevator would arrive, that would be an inductive inference."

So if one understands the mechanism but only infers to the extent of a particular expected arrival of the elavator, then, as far as I can glean from your view, the inference is deductive for being from general to particular but it is inductive for being based on the causal connection between pressing the button and the arrival of the elevator.

[dougclayton]

No, I meant the reverse of what you thought I meant.

What, exactly, is the reverse?

I think I understand what you're saying. But you suggested (though you did qualify that your answer is tentative) that causality is explained in terms of a nature leading to something. But doesn't Objectivism hold that natures are identified (if that is the correct word here) by concept formation? Entities have natures, and these natures are identified by the mental process of concept formation, right? But concept formation depends on determining essential properties in the final step of concept formation that is definition. So to explain causality in terms of the natures of things involves concepts which involves essential properties. So while the essence of being a pen might not include roundness, we still have your explanation that roundness is essential to rolling. So, I take it, rolling is inferred from roundness. So what is the causal connection between roundness and rolling? If it has to do with the nature of things, then I suppose the causal explanation starts with the nature of things as being round. But round is a concept and thus requires understanding essence. In the case of roundness, this might not be too difficult, since roundness can be edified mathematically (even though physical objects are not perfectly round), but in other instances I imagine that such edifications are vastly more complex.

To some extent, I will have to think on these ideas. But there is one issue that may be confusing things: the difference between identifying the nature of something and forming a concept for it. For instance, one can see that this particular item will roll because (loosely speaking) there are no flat surfaces it would tend to rest on, so there is nothing to stop it from moving. It is that aspect of its nature that causes it to roll when pushed. At this point, one can say this item will roll when pushed even if we don't have a concept for roundness yet. One cannot say, "round things will roll" because one doesn't have the concept of "round things" yet, but one can see why this item will roll. Once one sees that, it is straightforward to generalize to, "anything with the property of not having flat surfaces will roll," and that gives us the essential characteristic for a new concept. Thus in a sense it is the nature of the item (no flat surfaces) and the context (what happens when pushed) that gives us the essential.

I am trying to formulate these ideas as I go, since I have never thought of this problem before. I am sure the above passage has many poorly chosen words and other errors. But would you say I am on the right track, or is this not even addressing your question?

But you wrote, "Yes, with an understanding that the elevator button is wired such that the elevator would arrive, that would be an inductive inference." So if one understands the mechanism but only infers to the extent of a particular expected arrival of the elavator, then, as far as I can glean from your view, the inference is deductive for being from general to particular but it is inductive for being based on the causal connection between pressing the button and the arrival of the elevator.

Ah, I see the confusion now! My claim that an inference was inductive was serving a different purpose than your line of questioning. So let me answer your intent: combining a principle such as "the elevator will arrive whenever I push the button" with "I just pushed the button" to arrive at the conclusion "it will arrive" is entirely deductive, no matter what one knows about the elevator's mechanism.

My answer had to do with whether or not the principle "the elevator will arrive when I push a button" is formed from a valid inductive process or not, since that's what I thought you were asking (and since the purpose of this thread is examining what, if anything, constitutes a valid inductive process).

[LauricAcid]

What, exactly, is the reverse?

I was recognizing that it is the Objectivist view (please correct whatever is not pinpoint accurate) that things have natures and that concepts are formed to recognize these natures, not that concepts give things their natures.

Meanwhile, I'm going to take some time out to digest the rest of your post.

Edited September 28, 2005 by LauricAcid

[dougclayton]

I was recognizing that it is the Objectivist view (please correct whatever is not pinpoint accurate) that things have natures and that concepts are formed to recognize these natures, not that concepts give things their natures.

That sounds about right. Sorry I didn't understand.

Meanwhile, I'm going to take some time out to digest the rest of your post.

OK, I have more digesting to do too. By the way, I'm curious: what made you choose the name "LauricAcid"?

[LauricAcid]

I like the smell of coconut oil.