# Tentative Solution to the Problem of Induction

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Wed 21 Apr, 2010 10:26 am
Alright, so I've been studying Hume a lot recently with my "Philosophical Topics" class, and have been working on poking some holes in the Problem of Induction. This solution seems (to me) to work, but I figure it can't possibly be that easy, so I want you guys try and pull it apart if you're interested.

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First, I'll summarize the Problem of Induction, so somebody can correct me if I'm understanding it wrong or incompletely:

All inductive reasoning (cause and effect, scientific inquiry, etc) is based on our knowledge of past experience. We trust that fire will always burn us, and water will always suffocate us, because they have always done so in the past. This trust in past knowledge, however, is based upon the fact that past knowledge has been reliable in the past (Uniformity of Nature). This justification is circular and therefore unacceptable, so we have no logical basis to trust inductive reasoning.

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Now, here's my rebuttal as it appeared in my recent paper on EHU:

I am willing to admit that there is no saving induction if we're going to play by Hume's rules. Here is the problem of induction as stated in formal logical structure:

If an argument has no support aside from itself, then it is a circular argument.
If an argument is circular, then it has no logical justification.
Past experience has no support aside from itself.
Therefore, past experience is a circular argument.
Therefore, past experience has no logical justification.

As far as deductive reasoning goes, this is pretty much bulletproof. If a, then b, etcetera. It's constructed of basic syllogisms. The premises are all true by definition, so there's no attacking those either. All that leaves us is the deductive terms themselves: "if - then" and "therefore", in this case. Should we somehow discredit deductive reasoning as a whole, the problem of induction falls apart as well.

Hume states that "all the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas and Matters of Fact." (Sec. 4 Part 1 - para. 1) Deductive reasoning is based on Relations of Ideas upon which may be derived by mere operation of thought bereft of any real world experience. Matters of Fact, on the other hand, must be observed in and learned from the real world. It is these which we base inductive reasoning upon. I must object, however, that "were we brought on a sudden into this world" with no prior experience of anything, including examples of equality and causation, it would be quite impossible indeed to understand concepts such as "therefore" and "if - then". Both imply that one thing has caused another, and it would be necessary to observe examples of cause and effect to comprehend this operation of logic.

One can easily argue, as such, that "therefore" and "if - then" are Matters of Fact, not Relations of Ideas. This argument can be applied to any knowledge usually considered "a priori". Triangles for example, are merely "three sided figures". How could one possibly comprehend such a thing were they not already familiar with the real world concepts of "three", "side", and "figure"? My proposition is this: There is no a priori knowledge. It simply does not exist, and all things considered Relations of Ideas are actually Matters of Fact.

Given the above assertion, we must conclude that deductive reasoning is actually based entirely on Matters of Fact. The problem of induction discredits inductive reasoning by means of the accusation that Matters of Fact cannot be held as reliable or consistent, because there is no logical justification for the uniformity of nature. Given that the problem is constructed by deductive reasoning, now based in Matters of Fact, we observe a troublesome paradox:

Deductive reasoning either discredits Matters of Fact or it does not.
Deductive reasoning is based upon Matters of Fact.

If deductive reasoning discredits Matters of Fact, it discredits itself.

If deductive reasoning discredits itself, it cannot discredit Matters of Fact.

Therefore, deductive reasoning cannot discredit Matters of Fact.

By the above logic, deductive logic cannot safely attack Matters of Fact, or by extension inductive reasoning itself.

The ramifications of this are incredible: suddenly science works again, and many of Hume's more interesting points cease to hold water; because if the problem of induction is inherently faulty, we may return to our trust of scientific knowledge and the uniformity of nature as is the natural course of common sense. To challenge induction again, one would either have to make an argument based on some system other than deductive and inductive reasoning, or prove the existence of knowledge inherent in the human mind, returning deductive reasoning to the realm of a priori.

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So anyway, what do you guys think?
Any constructive criticism would be much appreciated.

Bill Maxwell

Tue 11 May, 2010 11:36 pm
@DaMunky89,
DaMunky89;154887 wrote:
Alright, so I've been studying Hume a lot recently with my "Philosophical Topics" class, and have been working on poking some holes in the Problem of Induction. This solution seems (to me) to work, but I figure it can't possibly be that easy, so I want you guys try and pull it apart if you're interested.

---
First, I'll summarize the Problem of Induction, so somebody can correct me if I'm understanding it wrong or incompletely:

All inductive reasoning (cause and effect, scientific inquiry, etc) is based on our knowledge of past experience. We trust that fire will always burn us, and water will always suffocate us, because they have always done so in the past. This trust in past knowledge, however, is based upon the fact that past knowledge has been reliable in the past (Uniformity of Nature). This justification is circular and therefore unacceptable, so we have no logical basis to trust inductive reasoning.

---
Now, here's my rebuttal as it appeared in my recent paper on EHU:

I am willing to admit that there is no saving induction if we're going to play by Hume's rules. Here is the problem of induction as stated in formal logical structure:

If an argument has no support aside from itself, then it is a circular argument.
If an argument is circular, then it has no logical justification.
Past experience has no support aside from itself.
Therefore, past experience is a circular argument.
Therefore, past experience has no logical justification.

As far as deductive reasoning goes, this is pretty much bulletproof. If a, then b, etcetera. It's constructed of basic syllogisms. The premises are all true by definition, so there's no attacking those either. All that leaves us is the deductive terms themselves: "if - then" and "therefore", in this case. Should we somehow discredit deductive reasoning as a whole, the problem of induction falls apart as well.

Hume states that "all the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas and Matters of Fact." (Sec. 4 Part 1 - para. 1) Deductive reasoning is based on Relations of Ideas upon which may be derived by mere operation of thought bereft of any real world experience. Matters of Fact, on the other hand, must be observed in and learned from the real world. It is these which we base inductive reasoning upon. I must object, however, that "were we brought on a sudden into this world" with no prior experience of anything, including examples of equality and causation, it would be quite impossible indeed to understand concepts such as "therefore" and "if - then". Both imply that one thing has caused another, and it would be necessary to observe examples of cause and effect to comprehend this operation of logic.

One can easily argue, as such, that "therefore" and "if - then" are Matters of Fact, not Relations of Ideas. This argument can be applied to any knowledge usually considered "a priori". Triangles for example, are merely "three sided figures". How could one possibly comprehend such a thing were they not already familiar with the real world concepts of "three", "side", and "figure"? My proposition is this: There is no a priori knowledge. It simply does not exist, and all things considered Relations of Ideas are actually Matters of Fact.

Given the above assertion, we must conclude that deductive reasoning is actually based entirely on Matters of Fact. The problem of induction discredits inductive reasoning by means of the accusation that Matters of Fact cannot be held as reliable or consistent, because there is no logical justification for the uniformity of nature. Given that the problem is constructed by deductive reasoning, now based in Matters of Fact, we observe a troublesome paradox:

Deductive reasoning either discredits Matters of Fact or it does not.
Deductive reasoning is based upon Matters of Fact.

If deductive reasoning discredits Matters of Fact, it discredits itself.

If deductive reasoning discredits itself, it cannot discredit Matters of Fact.

Therefore, deductive reasoning cannot discredit Matters of Fact.

By the above logic, deductive logic cannot safely attack Matters of Fact, or by extension inductive reasoning itself.

The ramifications of this are incredible: suddenly science works again, and many of Hume's more interesting points cease to hold water; because if the problem of induction is inherently faulty, we may return to our trust of scientific knowledge and the uniformity of nature as is the natural course of common sense. To challenge induction again, one would either have to make an argument based on some system other than deductive and inductive reasoning, or prove the existence of knowledge inherent in the human mind, returning deductive reasoning to the realm of a priori.

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So anyway, what do you guys think?
Any constructive criticism would be much appreciated.

You may have misunderstood slightly. The problem of induction is better stated here: just because something has happened/been the case however many times in the past, we're not justified that it'll happen again in the future. For example, if every apple you have ever seen has been red, you still can't make the claim 'all apples are red' because one day someone will hand you a green one and your statement falls down.

I'm not sure what you're getting at in the latter stages of your post, but I'll try and reply. Sorry if I get something wrong here. Matters of fact are pieces of knowledge which come from experience. Relations of ideas are those things like mathematics or some definitions.

Relations of ideas are analytic meaning they're true by definition. The empiricists claim that all relations of ideas are analytic and are the only pieces of knowledge you can get a priori. Whereas the foundation for this a priori knowledge may indeed come from experience, you do not need to go off and experience all the triangles in the world before you come to the inductive conclusion that all triangles have three sides. It's in the definition of a triangle. You can get this knowledge of a triangle without ever experiencing every triangle in the world.

Hope I've helped.

DaMunky89

Wed 12 May, 2010 12:59 am
@Bill Maxwell,
Bill Maxwell;163261 wrote:
Whereas the foundation for this a priori knowledge may indeed come from experience, you do not need to go off and experience all the triangles in the world before you come to the inductive conclusion that all triangles have three sides.
Hope I've helped.

You're getting at the part of my argument that I'm not entirely confident in yet, and am working on the wording of.

My logic doesn't require triangles to stop being analytic. It's the fact that their foundation comes from experience which I'm complaining about. I feel it's fair to say concept A is "dependent on concept B", when concept B serves as its necessary foundation.

After all, if the foundation of a tall building suddenly vanished, the building would be unable to stand on its own. The building is dependent on its foundation to continue standing at all.

Humchuckninny

Sat 22 May, 2010 12:30 am
@DaMunky89,
This is a lot longer than I meant it to be, hehe My main points, which this long, long article attempts to explain, are these:

1. Circular arguments, if they are analytic, can justify themselves (depending on what you mean by justification...)
2. Hume's argument is one of infinite regress, not circular reasoning, and cannot be broken down into circular reasoning.
3. Hume is not questioning the validity of science, or the external world at large. Rather, he is questioning the validity of it on the grounds of rationalism (deductive, formal logic). Rather, we come to know the world through inductive reasoning, which can be just as valid, though only contingently true. Contingent does not equal invalid.

I am no expert on Hume, however I do believe I see a couple of misinterpretations that you make from him.

Quote:
If an argument has no support aside from itself, then it is a circular argument.
If an argument is circular, then it has no logical justification.
Past experience has no support aside from itself.
Therefore, past experience is a circular argument.
Therefore, past experience has no logical justification.

First, I do not believe Hume would agree with your second premise here. Instead of "logical" justification, I think it would be more appropriate to use "synthetic" justification. For it is obvious that there are types of circular arguments which can be logically justified: Relations of Ideas are all circular. The logic behind it is that to contradict such a statement is itself a self-contradiction.

Look at the statement: all triangles have three sides.
The contradiction would be: all triangles do not have three sides.

The contradiction here is a self-contradiction. It cannot be true by definition. This is the importance of Hume (and Kant's) distinction of Matters of Fact and Relations of Ideas. It is not whether or not a statement is a syllogism that makes it a Relation of Ideas, but rather the content of the statement, and whether or not the statement can be contradicted without initiating a self-contradiction.

The logic behind this dates back to Aristotle, and is sound (well, until you get Quine, but then you get into linguistics and Logical Positivism, blah blah blah). But ultimately, Hume would disagree that all circular arguments are logically unjustified - that's the purpose of Relations of Ideas!

Now, onto my second objection: If I may restate your third premise: "past experience has no support aside from past experience."

The bulk of Hume's critique of causality is not a circular one but rather one of infinite regress. I think you make a slight equivocation fallacy in the third premise here in your use of the term "past experience." It is too ambiguous, as it is not circular in the sense that Hume means it.

Let me put it out logically. This is Hume's argument, beginning with your third premise (the first two being irrelevant right now):

My experience at time Z has no support other than my experience at time Y.
My experience at time Y has no support other than my experience at time X.
My experience at time X has no support other than...

The equivocation fallacy comes in because you seem to be using "past experience" first to refer to experience Z, then "past experience" to refer to experience Y. The two are different propositions, and therefore are not circular but rather regress infinitely backwards until memory gives out. Continuing Hume's logic...

My experience at time (N) has no support other than a time [(N)+1]
My experience at time (N) has no support other than an infinite regression of time (N)+1
We cannot know the beginning of an infinite regression.
Therefore, we cannot know the support of any experience at time (N).

Or, even if we wanted to put it in the same terms as your final conclusion, "we cannot know if past experience has any deductive justification."

These two change the outcome of your argument as well. Namely, Hume isn't saying we aren't justified in knowing the world - his claim is that our justification is one of induction rather than deduction. Mostly, Hume's purpose is to yell at the continental philosophers who are trying to rationalize God. He just wants them to realize that you can't know the justification of anything from reason - only experience justifies our beliefs.

His entire claim is that our logic from experience IS inductive logic. By definition, inductive logic cannot be deductively justified - otherwise it would no longer be inductive. Hume is arguing that all our knowledge of the world is justified by inductive reasoning.

The last thing I want to point out is mostly about your response to Bill Maxwell. Basically, I think you and Hume are arguing the same point. "It's the fact that their foundation comes from experience which I'm complaining about." This is the same thing Hume is complaining about!!

The fact that everything we know about the world, we know inductively, means that we cannot justify our knowledge of the world by looking towards the formal logic of deduction.

Science for Hume didn't ever "not work." Hume has more faith in natural sciences than philosophy, because natural sciences evaluate the world using inductive reasoning. Hume isn't challenging inductive reasoning per se.

Now let me clarify before everyone goes at my throat.

The challenge here is the difference between necessary truth and contingent truth. The definition of necessary truth is this: any proposition p in which to attempt to make the claim that ~p results in a self-contradiction is necessarily true. The definition of contingent truth is anything which is not a necessary truth.

Necessary and Contingent truths correlate with Matters of Fact and Relations of Ideas, as well as the notions of a priori and a posteriori. I don't think I need to give a lecture on these two here. However, suffice it to say that deductive logic gives us necessarily true propositions, while inductive logic gives us contingently true propositions.

Hume's skepticism (especially when applied to science) simply questions the validity of such things as being necessary or logically deduced. This does not imply invalidity through other systems, such as induction. Induction is valid, but not on the same ground that Deduction is valid. That is the whole dilemma - science cannot claim that they investigate the world due to deductive methods, and therefore all of science is only true contingently. However, according to Hume, that's the only possible way to do it.

I hope this helps. I've read Hume's Treatise and Essay a number of times, but I am by no means an expert.

DaMunky89

Sat 22 May, 2010 12:40 am
@Humchuckninny,
From the looks of it, you have a far better understanding of Hume than I've gained in my limited readings of EHU this last semester.

Our philosophy class pretty much taught Hume as saying that reliance on past experience is circular, but from what you're saying it's far more complex than that, and the nuances we missed are very important.

Given the details you point out here, and that I missed, it begins to appear that I never really disagreed with Hume in any significant way in the first place. Which is good, because now I'm more convinced he isn't a hack. (If only his own writings could have convinced me of that without your help.)

Anyway, I'm working on other stuff tonight, but at some point I'll come back here and post a proper response to your above input. Thanks for the well thought out analysis.

Humchuckninny

Sat 22 May, 2010 08:19 am
@DaMunky89,
It is very complex. Also, your philosophy class was not completely off the mark. Hume does question where the justification for induction comes from, but in such a way that he questions whether or not our knowing that induction can be justified, which I think is where you were getting at.

The whole problem is of course that ultimately, we come to know of induction through our experience of casual relations. Or in other words, we can only know of induction through induction. Err, we can only justify induction through induction. This is where Hume says induction begs the question, and you can derive a circular argument for the justification of induction itself.

The difference is that the justification for a system of logic (such as induction) is what can be circular, not the content of that system (i.e., past experiences). That's where I think things got jumbled. In fact, in my readings of Hume, he sounds like he's not so much as critiquing induction as he is asking for someone to do some homework. He says multiple times that he doesn't agree with what he's proposing, but simply that he cannot find any justification for induction itself outside of induction.

You just have to remember the whole "empiricist" deal. Induction > deduction. Also, it's good that you're in EHU - in the Treatise, Hume makes some pretty bold statements. It's neat to read (especially considering Hume was 19 and just about to be kicked out of college), but he takes back a lot of what he says in EHU, particularly concerning what it takes to justify our knowledge of the world. A much more moderate Hume.

kennethamy

Sat 22 May, 2010 08:34 am
@DaMunky89,
The general issue is not specifically about the past and future, but about whether the observed is good evidence for the unobserved (and even, the unobservable). Hume seems to have thought that even if the observed is good evidence for the unobserved, it cannot be good evidence for the unobservable.But that is a (somewhat) different issue.

I think that the reply to Hume should be that if the observed is not (in general- of course, sometimes it is not) good evidence for the unobserved, then what would be good evidence? More generally, why does Hume think that inductive justification requires justification, but that deductive justification does not?

Humchuckninny

Sun 23 May, 2010 08:55 pm
@kennethamy,
Quote:
I think that the reply to Hume should be that if the observed is not (in general- of course, sometimes it is not) good evidence for the unobserved, then what would be good evidence? More generally, why does Hume think that inductive justification requires justification, but that deductive justification does not?
Hume would most likely argue that thereis no good evidence for the unobserved, deductively. In other words, there is no deductive method of justifying induction. In Kantian terms, there are no a priori synthetic propositions. However, there are a priori analytic justifications. This is where deduction would fall.

I would not agree with your statement that Hume believes inductive knowledge requires justification. You have to remember who Hume's audience is: the continental rationalists. The rationalists have spent the last 200-ish years trying to deductively justify knowledge of the external world, and Hume thinks this is ridiculous. So, he shows them that it is impossible to deductively justify knowledge based on induction - and ultimately, all knowledge of the external world is based on induction.

In fact, Hume doesn't believe induction requires a deductive justification - the very fact that induction is inevitable for any experience is justification enough. By your everyday actions, you are justifying induction. It is impossible not to, just as it is impossible to deductively justify inductive knowledge.

In more technical terms, whether or not it is the case that a priori analytic justifications (i.e., deductive reasoning) are supported by induction is irrelevant, as they are known ipso facto. The denial of the justification of deductive reasoning is intellectual suicide. Once you go down the route of denying a priori truths such as formal logic, you lose all sense of coherent argumentation.

rhinogrey

Thu 19 Aug, 2010 05:05 pm
@DaMunky89,
The "Problem of Induction" is a common buzzword among students of epistemology but do you know where the problem ACTUALLY originates from?

Hume was a hardcore Empiricist. That is, he claims that all knowledge begins with and generates from experience. In order for a PROPOSITION to be considered KNOWLEDGE, one must start from a valid SENSORY IMPRESSION to create a valid IDEA. For Hume, all IDEAS are representations of SENSORY IMPRESSIONS. The thing that Hume comes to, then, is that it is impossible to use a SENSORY IMPRESSION to demonstrate a NECESSARY CONNECTION between to events/concepts/things. In Hume's days, it was commonly understood that if a proposition is true a priori, it is true NECESSARILY. If a proposition is true a posteriori, it is true based on EXPERIENCE and is therefore not a NECESSARY experience. NECESSITY exists (ignoring Kripke, Kant, et. al for the moment) ONLY in A PRIORI LOGIC. This is where you jump in with your past-future principle and the so-called "problem of induction."

The reason your argument doesn't work is precisely due to its in-media-res status. You jump in without understanding the terms involved. In order to demonstrate an a posteriori necessity, one need rely on past EXPERIENCES to induce the probability of a future experience occurring the same way. There is nothing in the empirical world to which we can point and say, "there is a necessary connection." No where has anyone experienced a necessary-connection-as-such. At least according to Hume. Now, this levels cause-and-effect, and, it's true, casts a skeptical light over inductive logic. Because what is cause-and-effect except a NECESSARY connection between two events/things/concepts? The NECESSARY CONNECTION, i.e., that between a cause and its effect, is an idea WITH NO CORRESPONDING SENSE IMPRESSION. So, it follows that if cause and effect is invalid, then, yes, any conclusions reached by inductive logic are invalid as well.

This problem is, of course, important in the HISTORY of philosophy but is only relevant today IF you take a hardcore empiricist stance re: knowledge. Philosophy has moved beyond the simple rationalist/empiricist debate, though. Hume was merely responding to people like Leibniz who believed all of reality could be captured in a priori LOGICAL NECESSITIES. But this, of course, erases the chaos of probabilities, and this is what Hume was trying to show. His dogmatist empiricism lead him to a vast skepticism, just as dogma leads religion to nihilism and Rationalism to bizarre schemes like Leibniz'.

Therefore, the problem of induction is a problem for dogmatic empiricists and no one else. Science is safe, unless you want to argue from Absolute Empiricist grounds. And I don't know why you'd want to. What Hume and Leibniz did was exhaust their respective positions, as they drew out empiricism and rationalism, respectively, to the edges of their possibilities. Kant, Hegel, Husserl, etc. took over from there, creating new conceptualizations and avenues of knowledge beyond the empiricist/rationalist opposition (BEYOND GOOD AND EVIL). The common understanding during Hume's time was that Man was not an animal. Hume, whether he wanted to or not, sank this notion, and it was later picked up Freud and Nietzsche, who both saw man's separateness from his primordial animality as illusory. This explains why no simple black/white, good/bad, rational/empirical oppositional continuum can fully explain our existence and the reality surrounding it. ORGANICA thwarts theoretical closure.

John Moriarty

Sat 25 Feb, 2012 03:56 am
Thought experiment: As we proceed in speech or writing, we must usually assume our brain and that of the listener will be as regularly functioning while thinking or writing the end of the sentence as it was at the start. Is there no choice but to be inductive towards states of mind and being at the finish of an utterance not yet complete? I think not, therefore I am right. Oops.

Therefore because all communication assumes induction as regards its process, so no content can be properly deduced; they are inseparable.

Therefore no worthwhile distinction can be made by humans, between inductive thought, and other types.

Maybe it would be just as correct and even simpler to state that all thought is inductive inasmuch as we constantly think to the future, which as we all know has no absolutes.

I think it a complete waste to expend a lot of time questioning the regularity of the natural laws for the reason stated. It hardly matters if induction is justified inductively, there cannot be any alternative. We, who exist in time and space, are locked in with no way out.

The statement “we must always be making assumptions” does not contradict itself even as it makes its own assumption.

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