Friday, February 4, 2011

Closure for knowledge

Here is a closure principle I don't know a counterexample to:

If you know that that s is the conclusion of a sound argument and (non-aberrantly) therefore believe that s, then you know that s.


Heath White said...

I think some work is being done by "non-aberrantly".

But here is something to consider. Consider the closely related principle, "If you know conclusive evidence for S and (non-aberrantly) therefore believe that S, then you know that S."

One might challenge this principle by pointing out that your evidence might be conclusive, but undermined by some kind of defeater. Maybe you shouldn't think it's as conclusive as it is, or maybe you shouldn't believe you know it, so that your inference to S is epistemically irresponsible somehow.

We can apply the same general idea to your principle: maybe you shouldn't believe the premises or maybe you shouldn't believe in the soundness of the argument.

I doubt this works, however. Suppose for reductio that the antecedent of the principle holds but believing that S would be epistemically irresponsible. This is either compatible with knowing S, or not. If it is, then no counterexample. If it is not, then seemingly one's belief in the soundness of the argument was also irresponsible, thus not known, and we have a contradiction.

Heath White said...

Also, there is ambiguity in the prinicple. Is the antecedent:

1. You know that: there exists a sound argument whose conclusion is S.

2. You know that: there exists an argument whose conclusion is S, that the premises are true, and that S is a logical consequence of the premises. (I.e. you also know the definition of soundness.)

3. There exists an argument such that: you know the premises [this is stronger than knowing that they are true] and you know that the premises entail S (or that S is a logical consequence of the premises).

4. In addition to 3, you know the meaning of "logical consequence" or "entails".

5. There exists an argument such that: you know the premises, and you can see how/why the conclusion is a logical consequence of the premises. (One worries about the phenomenology of logical consequence, and the security of this insight, especially for complicated proofs.)

I think one could generate worries about any of these steps. Which of them are sufficient for non-aberrantly concluding S?

Alexander R Pruss said...


A lot of work is done by "non-aberrantly".

The second comment worries me a lot. I don't want to require that you know each of the premises of the argument (for one, that's not enough, since you can know conjuncts but not the conjunction in lottery-type cases)--all I want is that you know that there is a sound argument out there. I am worried, however, about the question of the understanding of soundness. I am kind of inclined to the idea that the notion of a sound argument is primitive--it may be extensionally equivalent to being valid and having true premises, but that's not what it means. It's just a basic quality of an argument that we have a grasp of. But I am worried about how good a grasp one needs to have for the principle to apply.

I just tried to construct a counterexample based on this worry, but it failed because of the "non-aberrantly therefore" connector. It may be that that connector is a cheat.

Randy Everist said...

I'm sorry to confess I'm not entirely sure what "non-aberrantly" means with respect to the principle. Could someone help me out here? I sm still learning in the area of philosophy.

David said...

This may be covered by your "non-aberrantly" proviso, but suppose one of the premises of the sound argument that has s as a logical consequence is one that no one who doesn't already accept s has a good reason to adopt, but you aren't aware of this. Here it seems that even if you believe s because of the sound argument, you don't know s.

Alexander R Pruss said...


Here's my best take on your case. I know the argument is sound. In knowing this, I know that premise 1 (say) is true. But the only way I can know premise 1 is by knowing the conclusion. So I do know the conclusion, but not by means of the premises. So it doesn't sound like a case where I believe the conclusion because of the soundness of the argument.


Here's an aberrant case. I want to be irrational, and I falsely believe that believing the conclusions of sound arguments is irrational. I know that argument A is sound, and so I believe C because A is sound, not however in order to gain truth, but in order to be epistemically perverse. That's not knowledge because it's aberrant.

Randy Everist said...

Thanks! I think I understand it now (though I did have to read it three times ha!)