Tuesday, March 28, 2006
Vallicella on whether the laws of logic are empirical
This is a very old (as blog posts go) post from Bill Vallicella against the claim that the laws of logic are empirical generalizations. It seems to me that naturalism leads to the conclusion that the laws of logic are empirical generalizations, so if this argument works, it cuts against naturalism.
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5 comments:
What's the reconciliation between step 6 and the existence of para-consistent logic?
http://plato.stanford.edu/entries/logic-paraconsistent/
The fact that you can create a logical "game" that does not use the principle that everything follows from a contradiction does not mean that a game like that could possibly map on to reality. The absence of contradiction is a necessary condition for intelligibility, whether or not "logics" can be created that deny it.
Surely Bill could have simplified his task of showing that the laws of logic are not empirical generalisations by denying that there are any valid empirical generalisations.
For example, are any of the following valid empirical generalisations?
1) I see a bent stick in the water, so sticks bend in water.
2) My senses tell me it is raining. My senses are reliable, so it is raining.
3) I can think of no reason for some suffering. My cognitive faculties are reliable, so there is unneccesary suffering in the world.
What counts as a valid empirical generalisation? Only those where the premises necessitate the conclusion?
If Bill had taken the route of denying that we can make valid empirical generalisations when, then his argument would be a lot more succinct.
Victor:
But everybody still has to face Goedel's theorem. If the map's consistent, it's not complete. If it's complete, it's not consistent.
If para-consistent logic is intelligible, then the absence of contradiction (as opposed to the circumscription of contradiction, restricting what counts as a dialetheia and what doesn't) is not a necessary condition for intelligibility.
As an aside, even apart from para-consistent logic, the mere presence of deep and distant implied contradictions doesn't make a world-view *unintelligible*, it just makes it logically impossible. I daresay that all of us have deep and distant implied but unrecognized contradictions in the set of our beliefs. (And hopefully we work to resolve them when we find them, though sometimes we just let them be and are not necessarily irrational for doing so, cf. G. Harman, _Change in View_.)
Even granting these claims about paraconsistent logics, I don't see how you get from there to the claim that logical truths are empirical generalizations. As opposed to saying that we were not a sure as we thought we were as to what the fundamental a priori truths are.
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