Hume's non-problem of Induction?

[Obw]

Is Hume's problem of induction really a problem at all? What assumptions does the problem rest on and what is their nature?

To my mind there are two, and I've given this alot of thought and it's preoccupied me for a few months now both with reading and thinking. (Yes Tab, books!).

(1) A metaphysical assumption that the only necessity to exist is a logical one.

(2) A more epistemological assumption that it is irrational to think there is any other necessity simultaneous to logical necessity.

If a good argument can be found as to either of these, then I want to hear it. We can debate whether or not they really are determining assumptions, but I don't want this to be just about that. I'd rather have someone show me that an argument can be found to support one or the other, because to my mind they are the determining assumptions of Hume's induction and they are the cause of alot of nonsense.

I've got to the point now where I am starting to think, unbelievably, that Hume's problem of induction, that many good philosophers have failed to deal with, might not actually be a problem at all. There was Ayer, who noted that it musn't be a real problem because he couldn't find a way to solve it. I think the above reasoning is a little better than that though.

[Impenitent]

not a problem at all?

I frankly don't understand your points...

(1) A metaphysical assumption that the only necessity to exist is a logical one.

A metaphysical assumption about existence? where? hume is an empiricist... nothing metaphysical about it... it exists. period. only then can anything be said about it. ball b moving after ball a strikes it is our expectation of the unseen event... there is no logical connection between events. the metaphysical assumption is made by those that claim that they "know" that ball b will move when all they are basing that movement upon is an error in reasoning, begging the question. for hume it exists when it exists, the moment, nothing more.

(2) A more epistemological assumption that it is irrational to think there is any other necessity simultaneous to logical necessity.

what exactly do you mean? are you under the impression that synthetic a priori judgments are rational?

-Imp

[Obw]

Sorry Imp - my bad. I've not made myself clear. I'll clarify later on.

[Obw]

Ok, work with me on this one.

Most of the attempts to refute Hume on this have accepted these two assumptions. So when I read about this it started me thinking and compared other attempts to see if indeed they had let Hume decide the 'rules' of what was being argued.

These are the rules as best as I can see them, that define the debate over induction. If we take induction to mean an argument using inference to suggest that we can infer:

m/min of all A are B

from

From m/min of all observed (cases of) A(s) are B

then it's generally said that Hume shows us there is no guarantee that this sort of inference is truth preserving.

BUT it's been suggested that Hume has only provided the argument for why this is true logically and that he has not considered other constraints, other than logic, that may be involved. For example, there are sometimes physical constraints that surpass logical constraints (i.e. logic allows for something to be possible which is not actually possible - logic 101).

More later, today is a nightmare.

[Impenitent]

BUT it's been suggested that Hume has only provided the argument for why this is true logically and that he has not considered other constraints, other than logic, that may be involved. For example, there are sometimes physical constraints that surpass logical constraints (i.e. logic allows for something to be possible which is not actually possible - logic 101).

no, you've got it backwards...

hume demands empirical evidence, not logical possibility...

the "logical possibility" route is a kantian synthetic a priori judgment

a causes b... no

a happens.

b happens.

there is no logical connection between the two.

-Imp

[Obw]

Not really. Hume's argument is that no finte set of observations can logically entail the corresponding universal statement - so that it's possible to accept the propositions behind the premises of an inductive argument while disagreeing with the conclusion without contradicting oneself. i.e. the conclusions are not adequately determined by the premises. Thats basically the difference, and the problem.

He then says because there is no guarantee available for induction, it's irrational to rely on it. Hume's pointing out it is always logically possible for the conclusion of an inductive argument to be false while its premises remain true. What he does not do, is show that it would be physically impossible for that conclusion to be true, in this or any imagined worlds.

Let me know if you get me, or if anyone gets me, before I go on.

[Impenitent]

Not really. Hume's argument is that no finte set of observations can logically entail the corresponding universal statement -

true... instance a, instance b, instance c and so on and so on is only a sequence of instances, not a universal demand that the future must resemble the past... to claim the future will resemble the past because of the past begs the question and is fallacious.

so that it's possible to accept the propositions behind the premises of an inductive argument while disagreeing with the conclusion without contradicting oneself. i.e. the conclusions are not adequately determined by the premises.

you will have to show an inductive argument in which the premises are acceptable and do not beg the question.

Thats basically the difference, and the problem.

He then says because there is no guarantee available for induction, it's irrational to rely on it. Hume's pointing out it is always logically possible for the conclusion of an inductive argument to be false while its premises remain true.

no, because the premises beg the question and they are not logically true... they are at best assumptions...

What he does not do, is show that it would be physically impossible for that conclusion to be true, in this or any imagined worlds.

he doesn't have to show anything except that the premises are flawed. once the premises are shown to be false, nothing follows...

Let me know if you get me, or if anyone gets me, before I go on.

I get you, but you have hume's argument backwards...

he isn't worried about conclusions, he is concerned with premises that beg the question...

-Imp

[Obw]

Well we have to sort this out before I continue.

Hume's pointing out it is always logically possible for the conclusion of an inductive argument to be false while its premises remain true.

no, because the premises beg the question and they are not logically true... they are at best assumptions..

I'm confused as to what is making you think I have it backwards. So far, all I've done is explain what induction is to Hume. It doesn't matter if he cares more about premises or conclusions, the fact remains his problem of induction states that it's logically possible for premises to be true where conclusion is false (who could argue with this?) - i.e. the inference is not truth preserving and therefore - the problem of induction and science is unreliable and insanity is sanity [russell] etc etc.

he doesn't have to show anything except that the premises are flawed. once the premises are shown to be false, nothing follows...

Quite true but irrelevant to breaking down the problem of induction.

Induction involves the conclusion necessarily and so I am involving it necessarily in my thinking.

I hope we can agree on what the problem of induction is (even if you don't think it to be a problem, which is great, because I don't either..!).

[Impenitent]

Well we have to sort this out before I continue.

Hume's pointing out it is always logically possible for the conclusion of an inductive argument to be false while its premises remain true.

no, because the premises beg the question and they are not logically true... they are at best assumptions..

I'm confused as to what is making you think I have it backwards. So far, all I've done is explain what induction is to Hume. It doesn't matter if he cares more about premises or conclusions, the fact remains his problem of induction states that it's logically possible for premises to be true where conclusion is false (who could argue with this?) - i.e. the inference is not truth preserving and therefore - the problem of induction and science is unreliable and insanity is sanity [russell] etc etc.

no, the premises beg the question and are false.

http://www.princeton.edu/~grosen/puc/ph ... ction.html

"(DATA) In my experience, all Fs are Gs
(THEORY) Therefore, in general all Fs are Gs, (or at least, the next F I examine will be G).
is not deductively valid. It is logically possible for the conclusion to be false when the premise is true. So a skeptic might say: In so-called inductive reasoning, human beings commit a fallacy. They accept a general proposition on the basis of an invalid argument. And this means that their acceptance of that general proposition is unjustified.

Now this is not exactly Hume's way of raising skeptical worries. Hume rather takes the invalidity of the inference from DATA to THEORY as evidence that we have failed to make our method fully explicit. That we unheasitatingly pass from DATA to THEORY shows that we accept a principle connecting the two, a principle that normally passes unnoticed because we take it so completely for granted, but which figures implicitly in every instance of inductive reasoning.

Hume formulates this missing premise as the claim that the future will resemble the past. But for our purposes it will be useful to work with a somewhat more precise formulation. What we need to make the inverence from DATA to THEORY valid is a premise of the form:

(UN) For the most part, if a regularity R (e.g., All Fs are Gs) holds in my experience, then it holds in nature generally, or at least in the next instance.
"UN" stands for the "Uniformity of Nature". This is a traditional (post-Humean) label for the missing premise, though in fact it is misleading. For UN is not simply the claim that nature exhibits regularities. It is the claim that the regularities that have emerged in my experience are among the regularities that hold throughout nature. It might better be called a principle or representativeness, for its central message is that my experience, though limited in time and space to a tiny fraction of the universe, is nonetheless a representative sample of the universe.

The inference from DATA + UN to THEORY is valid. Moreover, there is no question for now about our right to accept the DATA. So if we want to know whether we ever have a right to accept a generalization like THEORY, we must ask whether we have reason to believe UN.

The skeptical problem: We have no good reason to accept UN.

This brings us to the heart of the matter. What reason do we have to believe that our experience is a representative sample of nature? What reason is there to believe UN?

Hume argues, in effect, that there can be no good answers to these questions.

(A) UN itself expresses a matter of fact proposition. Its denial is perfectly conceivable. Given any regularity that holds in our experience so far, we can easily conceive that it will be violated tomorrow. So UN is not a priori. If it is known at all, it is known on the basis of experience.

(B) UN is a claim about unobserved matters of fact. It is a claim, in part, about the future. Hence we cannot know it directly on the basis of observation and experience.

(C) But all "knowledge" of unobserved matters of fact is known (if it is known at all) on the basis of an inductive inference. So if there were any reason to believe UN, it would have to take the form of an inductive argument.

(D) But there can be no convincing inductive argument for UN. UN figures as a premise in any inductive argument. An inductive argument for the principle itself would thus be patently circular.

(E) So there can be no non-circular argument for UN.

[b]it makes a huge difference... the premises are flawed... no valid conclusion may be drawn from them.

he doesn't have to show anything except that the premises are flawed. once the premises are shown to be false, nothing follows...

Quite true but irrelevant to breaking down the problem of induction.

Induction involves the conclusion necessarily and so I am involving it necessarily in my thinking.

I hope we can agree on what the problem of induction is (even if you don't think it to be a problem, which is great, because I don't either..!).

the inductive conclusions are drawn from flawed premises and they are not valid.

the scientific method is based on an error in reasoning.

-Imp

[Obw]

Not really. Hume's argument is that no finte set of observations can logically entail the corresponding universal statement -

true... instance a, instance b, instance c and so on and so on is only a sequence of instances, not a universal demand that the future must resemble the past... to claim the future will resemble the past because of the past begs the question and is fallacious.

If you're happy with this bit then I'm happy.

[Obw]

Regardless of a difference in interpreting Hume, let's just say the problem of induction as it is widely accepted, be that from Hume or just because of him, relies on the two sentences I outlined.

As Grice, I think that any theory which posits a more complex view of reality carries with it the onus of justification - that is, we need not do the hardwork for it. It's widely accepted that rejecting the principle of induction is counterintuitive and that it creates many more problems than it solves (which is none, it solves nothing).

The 'burden of proof' lies on proponents of enumerative induction, particularly with regards to (a) and (b) in my opening post.

[Impenitent]

I don't understand where you want to take this now...

and please clairify the two premises...

hume himself admitted that one lives as if the inductive fallacy did not occur...

-Imp

[Twiffy]

Hey guys! Interesting thread. I know it's out of date, but I followed it up from a newer thread that touched more lightly on the same topic.

So Hume's problem of induction is pretty simply stated, I think, and is more or less as Obw stated early on in the thread.

1) Using induction, we take a finite amount of data, and extrapolate from it an estimation of the probability of a similar future event. The sun has risen every day in recorded human history - therefore, it will almost certainly rise tomorrow.

2) While this is a common practice, it is impossible to justify this sort of conclusion using logic alone.

3) Therefore, since logic does not justify induction, induction must somehow be wrong.

This is the problem as Hume saw it, and while it is a problem in some sense, the solution is pretty simple. This universe doesn't work on logic alone. It certainly works according to logic - but it has extra "axioms" thrown in. Logic does not demand the existence of atoms, but our universe has them anyway. Logic is an important cornerstone of our universe, but there is more to our universe than that - which is why there are mathematicians AND physicists - and among the physicists, there are theoretical physicists and applied physicists.

Essentially, induction is one of the extra axioms of our universe. You can't use logic to prove induction - but it works anyway, in our universe (or at least inductively seems to)! You can easily imagine a (very confusing) universe in which, the more something happens, the less likely it is to happen again in a similar circumstance.

That seems all there is to it! Please let me know if you think any part of the problem of induction has been ill-explained or unresolved.

-Tristan

[Impenitent]

welcome to the boards...

the only problem with "You can't use logic to prove induction - but it works anyway, in our universe (or at least inductively seems to)! " is that with this admission, the scientific method becomes an exersize in faith, no more than a religion...

-Imp

[Mucius Scevola]

The problem is quite large, and it would require a clarification of terms first. But here's my pin-pointed view.

Inductive reasoning is hazardous only when concerning empirical data taken alone, as with the example given by Twiffy, with the Sun being likely to rise everyday as it has unmistakenly did until now. Applied to empirical data considered apart, induction tends to reveal its fallacious side.

Induction has substance only with synthetical a priori judgements, though. And I guess it is wise to say that it is a reasonable application of the causality and community categories from Kant's table. The inductive argument holds water only when its conclusions are taken as apodictical. If we consider the sun "as likely to appear tomorrow as it has done today", then my take is that no induction has taken place here. Indeed, we know a certain phenomenon will take place based on certainty given by scientifical proofs. The sun will be tomorrow where it is today because we have observed its mass and physical properties and melded them with the pure branch of conceptual physics. One might say the two methods are basically the same (based on empirical observation) but in reality they are not - synthetical a priori judgements come in. So the real issue would be if these synthetical a priori judgements are possible and real.

[Obw]

(1) A metaphysical assumption that the only necessity to exist is a logical one.

I think this sentence isn't clear - I mean:

"The only necessity that matters, is a logical necessity." I.e. such a position ignores that there are other alternative types of necessity that govern our world.

[detrop]

To say that ball A did not cause ball B to move when they impacted is like saying that event did not cause the proposition "ball A did not cause ball B to move when they impacted."

If the proposition is "true," and propositions are derived from empirical conditions, and empirical conditions are causal, then propositions are causal and the induction fallacy is a chimera.

Let's walk through it.

I say "I cannot prove that the sun will rise tomorrow," and rightly so, but not because it is impossible to predict, but rather because it is impossible to be in the future and the present at the same time. When tomorrow comes and the sun rises, I will be before myself with the recollection of the comment I made yesterday (today), and say that my prediction was an induction fallacy.

Now substitute all the conditions involved in a rising sun (the sun, earth, rotation , axis, space, etc.) as "ball A" and the proposition "I cannot prove that the sun will rise tomorrow" as "ball B."

Here the induction turns on itself. Regardless of the "waiting to verify" the truth later on, what allows for the possibility of the induction, indeed, everything one way or another involves an induction, is the causal necessity of the "empirical" events, those which are the world and the "epiphenomena" of the "mind."

It cannot be said that "causality" exists....

That statement is nonsense....

For the above two quips to be correct or incorrect, there must be something that caused one or the other, for it certainly can't be both and if it is one or the other it is because of an effect.

Causality is happening where it is being argued that causality doesn't exist and a prediction is an induction fallacy.

But remember, we aren't talking about "predictions" anymore because we know we cannot be in the future and the present at the same time. All we are concerned about is the causal nature of experience and the how it happens in time and space...with "things" here and there. If, as the empircists suspect, propositions are results of impressions of physical data, then they would most certainly be quantifiable and causal.

I don't need to know what a electron is made of to know that it bumps into things. There are trajectories and momentums and other causal effects which dictate the movements. If only we knew the grand masta plan, if only we could see the dice, if only we could find a constant, all the little laws we have found would be justified and we would finally see the biggin.

Alright, try this, Imp. Say that the sun doesn't rise tomorrow because the solar system shifts from a force or something, and there is twenty-four seconds where the laws as we knew them are in disorder. Gravity becomes weaker, magnetic fields change, cellular growth rates increase drastically, and the price of a number four at Jersey Mike's Subs drops almost fifty percent.

Everything is screwed and Humeans everywhere are celebrating in a great magnificent non-causal induction fallacy-free orgy, where nobody makes promises and loves Megadeath.

But look closer, Imp. You are standing outside of the solar system in your space ship watching this happen for twenty-four seconds, where the laws as you knew them are in tact. Your ship generates the same gravity fields, the poles have not changed, your cells are aging at the same rate, and your number four is still soggy and extremely over-priced.

Here you notice that the justification for the disruption of the laws on earth are not universal in that they are only local, but also that they had to be caused by something.

Now let's say that it was a energy flare that happened every few hundred years, and Newton, who just happen to have knowledge of this energy flare, also happened to place a bet with his contemporaries one day that while sitting under a tree an apple that came loose from the branch would not fall on his head, but instead, Newton himself, as well as his contemporaries, would fall upwards themselves.

Newton timed it so he would be under the tree for the twenty-four seconds of disruption.

The question is, was Newtons bet an induction fallacy if he knew in advance an event was determined to happen which would change the laws of physics as he knew them, but nonetheless be part of a larger set of laws, which his contemporaries knew nothing about?

Do you, Imp, standing in your space ship, with the capacity to travel back in time, disguise yourself and join the group with Newton at the tree, and place a bet against him? Probably not, now that you know Newton knows about the disruption.

Dammit! Now my theory won't work. Nevermind.

[Twiffy]

<b>Imp</b>, thanks for the welcome.

You are absolutely correct to say that the Scientific Method is a matter of faith. "No more than religion" isn't quite right, though - religion doesn't accomplish anything tangible (it doesn't make computers or cure diseases), but the scientific method does.

Here's the gist of things. Math, humans, and universes all work in this way: they have fundamental axioms, rules that you assume, or that you begin with, but cannot in any sense prove. Then, there are deductions you make from these rules. "Theorems", conclusions, etc. Essentially, you have to begin with some assumptions that are unprovable - there's no way to truly start from nothing. Induction, in the sense of humans and in the sense of the universe, is one of these assumptions.

<b>Mucius Scevola:</b>
Unfortunately, there <b>is</b> no synthetic a priori component to induction at its most raw level. Any pure branch of conceptual physics, no matter how pure, has purely observational components behind it. Take Special Relativity, although any other area of physics would work just as well. Sure, physics uses pure math, and math is certainly synthetic a priori. But the assumptions of Special Relativity - its axioms, e.g. that light travels at the same speed in all reference frames - are not in the LEAST deducable from pure logic. Rather, Einstein wasn't able to include this as an axiom until after the Michaelson-Morley experiment, which established the absolute-ness of the speed of light via observation and induction. One could easily imagine a universe in which the speed of light were different, or in which there WERE no cosmic speed limit.

I don't think the problem is quite large at all, but I'm willing to be corrected.

[Impenitent]

You are absolutely correct to say that the Scientific Method is a matter of faith. "No more than religion" isn't quite right, though - religion doesn't accomplish anything tangible (it doesn't make computers or cure diseases)

inquisitions and manifest destinies aside, religion accomplishes many things...

, but the scientific method does.

no, the scientific method accomplishes a logical error... events occur and "scientists" erroneously posit a cause where none is logically warranted.

Here's the gist of things. Math, humans, and universes all work in this way: they have fundamental axioms, rules that you assume, or that you begin with, but cannot in any sense prove.

exactly. but then "truth" would be an assumed agreement...

Then, there are deductions you make from these rules. "Theorems", conclusions, etc. Essentially, you have to begin with some assumptions that are unprovable - there's no way to truly start from nothing.

if you assume it is nothing, it is...

Induction, in the sense of humans and in the sense of the universe, is one of these assumptions.

as is existence

-Imp

[Obw]

If a good argument can be found as to either of these, then I want to hear it. We can debate whether or not they really are determining assumptions, but I don't want this to be just about that. I'd rather have someone show me that an argument can be found to support one or the other, because to my mind they are the determining assumptions of Hume's induction and they are the cause of alot of nonsense.

[Twiffy]

(sigh) Hopefully you understand my meaning when I say that religion doesn't accomplish anything tangible. Religion affects human motivation and human perception, but it doesn't yield a new skill; it doesn't have predictive power (despite all those who argue to the contrary), and it doesn't have any scientific explanatory power (although it has plenty of non-scientific explanatory power).

The scientific method is NOT a logical error. Causality is not only something observable, it is something that can be precisely and mathematically (and thus philosophically) defined.

Even if the scientific method IS a logical error - which you will have a very very difficult time arguing - it STILL has given us more results than any other approach to knowledge and truth IN HISTORY. Almost every modern convenience we have now owes its existence in part to the scientific method.

Truth isn't an assumed agreement. It has a precise definition in our universe. There are statements that are true or false independent of the observer. These are the statements that comprise the system of our universe.

"If you assume it is nothing, it is..."

I have no idea what you mean here. You need axioms (initial assumptions) to make any truth system work. If you have no axioms, you can't have any conclusions.

And lastly... existence isn't necessarily one of those assumptions at all. It really depends on what kind of existence you mean. Human existence is a consequence of those axioms, not an axiom itself. We can observe that humans exist, therefore they do. It's more complicated than that, of course, but all you need do is fill in the gaps with the axioms of "Occam's Razor" and "The Axiom of Induction" and so on, and you're set.

[Impenitent]

(sigh) Hopefully you understand my meaning when I say that religion doesn't accomplish anything tangible. Religion affects human motivation and human perception, but it doesn't yield a new skill; it doesn't have predictive power (despite all those who argue to the contrary), and it doesn't have any scientific explanatory power (although it has plenty of non-scientific explanatory power).

your problem is ignoring that one explaination is as good (and sometimes even more appealing) as another...

The scientific method is NOT a logical error. Causality is not only something observable, it is something that can be precisely and mathematically

mathematics are not observed

(and thus philosophically) defined.

definitions and labels in language are not the things in themselves no matter how you try to bracket them

Even if the scientific method IS a logical error - which you will have a very very difficult time arguing -

no, it is a very simple argument actually...
to claim the future will resemble the past because of the past begs the question. that is what the "repeatability" of the scienific method amounts to being

it STILL has given us more results than any other approach to knowledge and truth

knowledge is impossible and truth is an agreement, nothing more

IN HISTORY. Almost every modern convenience we have now owes its existence in part to the scientific method.

that's fine. almost every modern convenience owes its existence to an error in reasoning.

Truth isn't an assumed agreement. It has a precise definition in our universe.

reveal it to us

There are statements that are true or false independent of the observer.

no, there are not

These are the statements that comprise the system of our universe.

no, these statements comprise the system of statements. the universe is something else entirely... even ludwig himself denounced the tractatus

"If you assume it is nothing, it is..."

I have no idea what you mean here.

it is what you assume it to be and nothing besides

You need axioms (initial assumptions) to make any truth system work.

you need assumptions to make truth systems which are not assumed? are you certain? that is what you have said...

If you have no axioms, you can't have any conclusions.

you can have whatever you invent...

And lastly... existence isn't necessarily one of those assumptions at all. It really depends on what kind of existence you mean.

assuming it necessarily does not need an assumption...

Human existence is a consequence of those axioms, not an axiom itself.

the existence of axioms is a consequence of human invention, nothing more... ask protagoras: man is the measure

We can observe that humans exist, therefore they do.

no, the observation exists... nothing more

It's more complicated than that, of course, but all you need do is fill in the gaps with the axioms of "Occam's Razor" and "The Axiom of Induction" and so on, and you're set.

only to be complicated by the axiom of errors...

-Imp

[Obw]

Incase you had not noticed, Imp is a radical skeptic. Although I somehow reckon you don't live your life in tune with your philosophy, Imp.

[Gobbo]

Imp is a radical skeptic. Although I somehow reckon you don't live your life in tune with your philosophy, Imp.

ROFL

I would hope not.


I've been steadily checking this thread btw.. I wish some other people would comment on this topic as, like ob 1 said initially.. Induction is something that seems to hang onto attention and curiosity - a plague of contentment.

Sadly I've given it quite a bit of thought and I'm not analytical enough to dive into this metaphysical whirlpool and come out with anything readible.

So.. yeah, pointless post here by me.

[yuxia]

your initial discussion of premises and conclusion is actually both completely wrong, induction is a form of argumentation its parallel (or some would like it to be) to deduction. its a form of argumentation. Hume's problem is that the form of argumentation maybe flawed that we mistakenly make the move from the paticular to the general, there is no logical necessity flowing from a finite set of observations to a general principle.

Personally I like Goodmans response to this issue, read Fact, Fiction and Forecast if you havn't its short and provides a good insight on the subject.