Is Justification Closed Under Simplification?
- Posted by Andrew Bailey on Monday, March 26, 2007 at 6:45 PM
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7 Comments |
In a word, no. Epistemologists typically distinguish between doxastic and propositional justification. The former is belief entailing; the latter is not. In this post, I shall argue that neither condition is closed under simplification.
Let 'J(s, t, p)' abbreviate 'S at t is justified in believing that p.' We may ask whether the following principle is true on either reading of 'is justified:'
Closure: Necessarily, (J(s, t, p&q) only if J(s, t, p) & J(s, t, q))
Closure has some degree of initial plausibility. In most cases, at least, where we believe conjunctions, we believe the conjuncts too. And it seems that whatever justification we might have for the conjunction would apply to the conjuncts too.
But this is a snare and a delusion. The principle as stated is false.
On the doxastic reading of J, J(s, t, p) is true only if S at t believes that p. But it’s possible to believe a conjunction without believing both conjuncts. Take the busy Jones, who simply hasn’t got the time to perform simplification. Jones is justified in believing some conjunction (he came to believe the conjunction on hearing it asserted by some reliable source, say); but Jones has never reflected on his belief in the conjunction and realized that he could infer either conjunct from it. Jones is justified in believing a conjunction at a time then, even though he does not believe one of the conjuncts at that time (and hence does not believe with justification one of the conjuncts at that time).
Consider now the propositional reading of J, according to which a subject may have justification for p even if that subject doesn’t in fact believe that p. On this reading too, Closure is false, and not because of a failure to believe. Sally has recently taken a course in logic, where she was taught that simplification is invalid. Sally believes that p does not follow from statements of the form p&q. Sally is mistaken, but she has very good reasons to believe this (her teacher is quite well-respected in the field, she hears). Suppose now that Sally has a good argument for the thesis that p&q. Sally has no argument for the thesis that p, however, since she doesn’t think simplification is a valid maneuver. In fact, it seems to Sally that to infer p from the premises before her is a decidedly unjustified move. It’s plausible in this case to think two things. First, Sally has propositional justification for p&q. Second, Sally does not have propositional justification for p (were she to form the belief that p, say, she’d be believing contrary to her epistemic duties). If this is right, Closure fails on the propositional reading of J too.
7 Comments:
alex at 9:42 PM said... I'm not so sure about the argument against PJ-Closure. Depending on what kind of justification you have in mind, your counterexample might not work.
Say the concept of justification you have in mind is necessary for warrant. One might plausibly think that despite the fact that she believes that simplification is false, she can still be warrant-PJ-justified in inferring p from p&q, since her deduction process is properly functioning.
Then there is a wrinkle in your example: suppose that Sally's teacher is unjustified in believing that simplification is false; or suppose that he is lying. Can we say that Sally's belief that simplification is invalid be justified? And can it serve as a defeater for the inference from p&q to p? These are dark matters...
Even if what I say is wrong, you need to be clearer about what kind of justification your interested in. It might turn out that some kinds of justification are closed under simplification, and others aren't. If we've learned anything from Alston's work, it's that we can't be too careful in talking about the properties of different kinds of justification. The different kinds of justification might do crazy things...
Andrew Bailey at 4:35 PM said... Alex: you're right, I should have been more clear. I have in mind what you might call "Classical Justification:" that concept involving fulfilling one's epistemic duties, being within one's epistemic rights, and the like.
This is what drives the intuition that Sally isn't justified in performing simplification; doing so is a breach of subjective epistemic duty, and hence a breach of epistemic duty full stop.
I do not take Classical Justification to be a necessary condition of warrant, incidentally (here I follow Audi and perhaps Plantinga).
Noumena at 6:12 PM said... Why is a breach of subjective duty a breach of duty full stop?
My reaction to the Sally case (including when you presented it last week in Al's seminar) was initially and continues to be `No, Sally has justification. She's just wrong in thinking that she doesn't.' Similarly, the rigourist Kantian who thinks duty requires him to lie when the SS come to take away his Jewish friend hiding in the basement is simply wrong about what duty requires of him.
bradley james at 12:09 PM said... I agree with Dan in thinking that Sally has justification without awareness. Otherwise, you can run that counterexample against any rule of inference in propositional logic.
Try this: Sally has recently taken a course in logic, where she was taught that modus ponens is invalid. Sally believes that q does not follow from statements of the form p->q .^ p. Sally is mistaken, but she has very good reasons to believe this (her teacher is quite well-respected in the field, she hears). Suppose now that Sally has a good argument for the thesis that p->q, and she knows that p. Sally has no argument for the thesis that q, however, since she doesn’t think modus ponens is a valid maneuver. In fact, it seems to Sally that to infer q from the premises before her is a decidedly unjustified move. It’s plausible in this case to think two things. First, Sally has propositional justification for p and p->q . Second, Sally does not have propositional justification for q (were she to form the belief that q, say, she’d be believing contrary to her epistemic duties). If this is right, modus ponens fails on the propositional reading of J too.
It seems we could do that with just about any valid inference rule, and that seems wrong to me.
Andrew Bailey at 7:48 PM said... Dan: I doubt I can persuade you on this point. But here's one consideration: don't we all have an epistemic duty to refrain from performing inferences that seem to us to be invalid?
Brad: not so fast. First, distinguish the failure of modus ponens from the failure of justification to be closed under modus ponens.
Second, that justification fails to transmit in some cases of entailment doesn't mean the transmission fails in all. It may be very unusual for one to have justification for p&q and not have justification for p; my claim is only that it's possible. I haven't claimed that justification *can't* transfer over entailment, just that it *needn't*.
Finally, see that I haven't denied the most plausible closure principles. For example, what I say is consistent with the following:
Closure Under Known Entailment: If S is in a position to know that p and S is in a position to know that p entails q, then S is in a position to know that q.
Closure Under Known Entailment is not subject to the failure-to-believe case I described, nor is it subject to the counterexample I gave to the propositional reading of Closure. It's true, in fact. Stronger principles like Closure aren't. Or so I say.
Noumena at 7:21 AM said... I think you were misreading bradley's comment. Each thought experiment is supposed to show that, with respect to some mode of inference I, either (a) justification fails to be closed under I in at least one case, or (b) justification fails to be closed under I in all cases.
Now generalize: since the thought experiment can be easily modified for any (valid) mode of inference I, the universally quantified generalization of either (a) or (b) holds. (b) is spectacularly bad, but (a) by itself means our epistemic logic (understood as either canon or organon) is going to be a mess.
And as for your response to my comment, consider the moral counterpart to that principle: we all have a moral duty to refrain from performing any act which (merely!) seems to us to be immoral. Assuming morality is consistent, this comes damn close to collapsing objective duty into subjective duty. I don't see how you'll be able to sustain any mild moral realism (in the sense that we can be wrong about what duty requires and allows).
Back in the epistemic setting, consider the unfortunate who's in every one of the circumstances needed for the universal generalization of (b) -- poor Sally has been through the worst logic class in history. If your hypothetical maxim is correct, then *objective* duty requires Sally to not form any inferential beliefs. And I just can't accept an account of objective duty that pernicious.
Andrew Bailey at 8:24 AM said... The case was designed to show (a). Of course, if it has shown (a), then it has also shown the disjunction of (a) or (b), but nothing I've said implies that (b). That would would be, as you say, spectacularly bad (and more to the point, implausible).
As far as the consequences of (a) for an epistemic logic, you'll have to be more specific. If what I say is right, no epistemic logic should have rules of inference that look like either of these:
1: From "S justifiedly believes that p&q" infer "S justifiedly believes that q"
2: From "S has justification for p&q" infer "S has justification for p"
But this isn't so bad, is it? After all, the formulation of Closure Under Known Entailment offered above might still be true (I hold that it is). Intuitively, one way to "add to our knowledge" is to deduce the consequences of what we already know. Closure Under Known Entailment respects this intuition.
