Friday, May 01, 2009

Some Rought Thoughts on Rational Grounds

The following is all very rough. I recently came across a statement of this sort:

"This argument...is clearly valid, and so if there are rational grounds for accepting its premises, to that extent there are rational grounds for accepting the conclusion...." (from here)

This sounds plausible enough, and might be meant in a reasonable sense, but it's worth noting that the inference here is not generally valid. 'Rational grounds' as a modality works like possibility (indeed, it is one possible interpretation of Lozenge in, if I'm not mistaken, D4-type modal systems). For, of course, you can have rational grounds on both sides of a question; and even if you didn't, your rational grounds might be too weak to do anything with it. And quite commonly if the following sort of argument is valid (where T is the truth operator)

Ta
Tb
Therefore Tc


you can't be sure from the form alone that the following argument is also valid (where lozenge is the rational-grounds-for-accepting operator):

◊a
◊b
Therefore ◊c


(Ta with Tb, because they validly yield Tc, by supposition, would also allow a possibility-preserving conclusion, ◊c; but ◊a with ◊b isn't possibility-preserving in every case that Ta with Tb is.) And the logical reason is fairly obvious; ◊ indicates that there is a domain where it is true. But it doesn't guarantee that everything, or, indeed, anything it is applied to in an argument is in the same domain.

So, for instance, if this is valid:

if p, q
p
Therefore q


you can't also assume that the following is valid:

There are rational grounds for believing that if p, q
There are rational grounds for believing that p
Therefore there are rational grounds for believing that q


It might be the case, for all we know, that our evidence leads in inconsistent directions: our rational grounds in the first premise might also be rational grounds for ~p; or our rational grounds in the second premise might also be rational grounds for ~(if p, q). Likewise, the combination of the rational grounds in the first premise with the rational grounds in the second premise might not, in fact, be rational grounds for ((if p,q) & p). For instance, you might have rational grounds for accepting that if Malebranche influenced Hume, Hume was Catholic, based on Malebranche's own, very Catholic, philosophy, and you might have rational grounds for accepting that Malebranche influenced Hume, based on Hume's own statements; but the latter might also completely rule out the possibility that Hume was Catholic. (A more complicated example, possibly: Fogelin's interpretation of Hume on miracles, which seems to trade on this.)

What you actually need is the following first premise:

If there are rational grounds for p, there are rational grounds for q.


And this is a different premise. So what we would really need in this sort of argument is not the rational grounds for thinking that (if p, q) is true -- but we would need to know that rational grounds for thinking that p bring with them, so to speak, the rational grounds for thinking that q, either because our rational grounds are actually rational grounds for accepting p and for accepting q, or, if the grounds are different in the two cases, because the existence of rational grounds for accepting p implies the existence of rational grounds for accepting q (which is different from the truth of p implying the truth of q).

Of course, when you say, "There are rational grounds for accepting that p," you could just be taking that always to mean or imply that we can presume that p is true. But that's not how we usually mean it.

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