Friday, March 02, 2007

Sextus Empiricus', I mean Hume's, Problem

Okay so I apologize for the epistemology, but here comes some. Recall Hume's problem of induction: Either principles of induction are justified inductively or deductively. Principles of induction (like x% of observed As are Bs so x% of unobserved As are Bs) are not necessary truths, so they are not justified deductively. But justifying them inductively is viciously circular; so they are not so justified.

One can extend this argument as follows: If inductive principles are not justified, then nothing is justified inductively. But deduction is justified either inductively or deductively. And it's not justified deductively since that would be circular. So deduction is not justified.

Rich considers the former, but not the latter, argument in his book. His take on it is that inductive principles like the above are not justified inductively or deductively. But there are necessary a priori truths like 'knowing that x% of observed As are Bs gives one a reason to believe that x% of unobserved As are Bs' that justify inductive inferences. One can then block the extended argument by denying that nothing is justified inductively.

I am attracted to the claim that there are a priori truths that justify inductive inferences. What worries me is that it is not very plausible to suppose that deduction is justified inductively. So it seems that, ultimately, pressure must be put on the 'that's circular' part of the argument. But circular reasoning is bad, right?

It strikes me that there are a couple of options here: distinguish good and bad circularity and say why the justification of deduction involves the former, hold that any justified deductive principle stands in an infinitely long chain of reasons, or hold that there are justified basic beliefs that justify deductive principles (maybe those principles themselves are such beliefs). But these are exactly the options at play in the familiar infinite regress argument concerning the structure of justified beliefs--the only difference is that the familiar arguments focus on empirical beliefs.

I think foundationalism is just as plausible in the a priori case as in any other. But I won't plump for that here. I am more interested in whether the following are correct:

(A) Coherentism is an attempt to distinguish good and bad circularity for empirical beliefs. But coherentism seems especially implausible when brought to bear on a priori beliefs about principles of induction and deduction. This is because conditions on coherence typically include things like a requirement that the relevant propositions "jointly probabilify" each other and that they are logically consistent.

More interestingly:

(B) At bottom, Hume's problem of induction does not raise any problem not solved by a sufficiently adequate response to the infinite regress problem. It's really just a special case of that problem--not a fundamentally different one, as has been traditionally supposed.



Blogger Joshua said...

I am a little bit confused by the post. What is being referred to by 'induction' and 'deduction'? Are these inference forms or psycological processes or something else entirely? If they are inference froms, then I am not exactly sure how they are connected to the issues in epistemology.

Moreover, surely we can have arguments that fit those inference forms and have the conclusions that those inference forms are good. Also, my guess is that in most situations, if we read and understand those arguments and justifiably believe all the premises, then we are reasonable in believing the conclusion. I believe this is the case regardless of whether the inference from that the argument fits is an inductive inference form or a deductive inference from and also regardless of whether the conclusion is about induction or deduction.

Maybe the claim is that there are certain physchological processes that we engage in, some of which are inductive processes and some of which are deductive processes. And we need to have good reason to engage in those processes. Notice that this is an issue of practical reasoning rather than an issue of epistemology. Because it is an issue about what we are rational in doing not what we are rational in believing. We might connect it to epistemology if we think that we have good reason to engage in those processes only if we have decent reason to believe that those processes have some good making feature. But, I see no reason to believe that if we are engaging in one of those processes (either one) while coming to believe that one of those processes (either one again) is good, then we are not justified in our belief.

Finally, I am not sure how all this connects up to the foundationalist coherentist debate. One thing that is interestingis that bonjour has given an argument against foundationalism that seems strikingly similar to the problem of induction. Perhaps the claim is that the problem of induction is simply a special case of this problem that BonJour presents.

In any case, I guess I am not sure what to say in response to your post because I am not sure I understand the various points yet. can you tell me a little more.

8:55 AM  
Blogger rock* said...

What Joshua said.

1:17 PM  
Blogger Chris Tillman said...

Consider any proposition P you are justified in believing. You are either justified in believing P on the basis of your being justified in believing other propositions that entail P ('deduction') or by being justified in believing other propositions that make P probable but don't entail P ('induction').

Hume seems to think there is a special problem when P is a foundational principle of induction (some proposition describing a rule of inductive inference, say; call it 'I'). The idea is that you can't be justified in believing I since, if you were, it would be on the basis of induction or deduction. Propositions justified by deduction "all the way down" are necessary truths. By "all the way down" I mean if every link in a justificatory chain that is relevant to your being justified in believing P is a deductive link, then P is justified deductively "all the way down".

But you can't be justified in believing I inductively, either. That's because either some link in the chain that supports I must either be I itself or it must "rely" on I. Here we can think about reliance roughly as follows: argument A relies on rule R iff R would appear in a justification of any inference in A. (Think of "justification" here in the proof sense--where we indicate the justification for inferring a particular conclusion in an argument.)

If your justification for believing I relies on I, then your jusification for I is objectionably circular. So you are not justified in believing I.

I think that's one way to understand what Hume is up to. It has nothing to do with psychological anything.

Rich's reply is that the true principles of induction are necessary truths, so they can be supported deductively.

But it seems to me that, insofar as we had a problem for I, we still have a problem on Rich's proposal. So principles of deduction D would be supported in a manner Hume should find objectionable, if they are supported at all, given the remarks about inductive principles. If that's right, Rich is not offering a complete solution.

My proposal was that the options in specifying a justificatory chain for either I- or D- propositions correspond exactly to the options one is faced with in the infinite regress argument. The justification either terminates in a basic justified belief, it does not terminate, it's circular, or it terminates in an unjustified belief. But then the problem raised by Hume is nothing new. It's a special case of the regress problem--any complete solution to the infinite regress problem will be a complete solution to Hume's problem.

11:30 AM  
Blogger Joshua said...

I think I understand the problem now.
I have two worries.

For the first horn. Since any proposition is a deductive consequence of itself, then if you have a contingently true foundational belief and it deductively supports some proposition, P, then although justification is deductive all the way down, it looks like P could be contingent.

For the second horn, I am not sure I understand what it means for a chain of support to rely on a principle. If I do understnad it, then it seems to me that the following claim is false: If the chain of support of I relies on I, then I is not justified.

I'm going to think a bit longer about your overall proposal though and get back to you. For now, I have to take off. Talk to you soon.

11:53 AM  
Blogger Joshua said...

Okay, I've thought about it some more and decided that this problem of induction is not simply a special case of the regress problem. It seems that the regress problem is a problem of the structure of justificatory chains. We want to know whether or our justificatory chains are infinite, circular, terminal with unjustified final links or terminal with justified final links. However, this problem of induction seems to be a problem involving kinds of justificatory chains, ones that are inductive or deductive, rather than justificatory chain structure.

To make this more clear, we might just assume that foundationalism is the correct answer to the regress problem and see whether we can generate this problem of induction under that assumption. It seems that we can. Suppose we want to know wether our inductive principle, I, is justified or not. We know that if it is justified, then it is justified by a chain of reasoning that leads back to a foundational belief (perhaps a one link long chain). But, segments of beliefs in the chain might be linked by induction or by deduction. That is, the belief (or beliefs) at one point in the chain may entail those in the next or they may simply make them probable. It cannot be that the segments of the chain are linked deductively (because putatively chains that are links deductively only contain necessary truths and I is not a necessary truth). Nor can the segments of the chain be linked inductively (because of the reason that I don't understand). So, inductive principle I cannot be justified.

I think this is a statement of the problem that assumes foundationalism yet is just as problematic as the original statement. If so, then this problem is not simply a special case of the regress problem.

Does that sound right to you.

11:11 AM  
Blogger Brad said...

Hi Chris,

I'd be interested in what you think of Goodman's (1955) sketch of a solution to this problem. He makes the analogy with the justification of deduction and suggests that in both cases the best we can do is achieve reflective equilibrium between our judgments of particular cases of valid inference and our formulation of general rules governing those inferences (a brief overview is in Daniels, 2003, 2.1). How does this fit into your classificatory scheme of solutions to the problem? More generally, how should we think about the method of reflective equilibrium in epistemological terms? It seems closest to a form of coherentism, but it's unclear to me that it runs into the problems with coherentism you identify.


Norman Daniels, “Reflective Equilibrium”, in Edward N. Zalta (Ed), Stanford Encyclopedia of Philosophy, Stanford University, Stanford, 2003.

Nelson Goodman, “The New Riddle of Induction”, in Fact, Fiction, and Forecast, Harvard University Press, Cambridge MA, 1955, pp. 59-83.

11:55 AM  

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