Tuesday, March 29, 2011

Justifying Logic and the Normal Role of Proof in Justification

Some philosophers aim to show how we can be justified in accepting certain basic logical truths by giving "rule circular" proofs of the soundness of these basic logical truths. They admit that most people will never have considered the proofs in question, and they admit that these people still count as justified in using logic. But, they say that they showing that such proofs can in principle be given makes sense of how we can be justified in believing the basic logical claims established by the proofs right now.

That idea seems prima face implausible. In general the fact that someone 100 years later will prove P from premises that I accept (like the ZF axioms) doesn't suffice to show that I am justified in believing that P now. So why should the case be any different for the proofs of logical principles?

[I would rather say that we are prima facie justified in believing these logical principles in a way that has nothing to do with the possibility of giving further argument; coming up with more or less circular ways of proving the soundness of our logical principles is (at best) a way of improving our justification]

1. Interesting post! This seems like it might turn on whether one is and internalist or an externalist about epistemic justification.

The line you're inclined to seems to be a broadly internalist one. This might help:

http://plato.stanford.edu/entries/justep-intext/

2. Hi Tristan!

Welcome to this blog and sorry for the long delay.

My problem isn't with externalism per se, but rather how to make sense of the apparent *asymmetry* between our intuitions about mathematical cases and what the proponent of rule-circular justification wants to say in re: knowledge of basic logical principles.

Are you thinking that proponents of rule-circular justification would bite the bullet re: knowledge of mathematical theorems and say that you *can* know arbitrary mathematical claims just by finding them obvious?

My sense is that most wouldn't - people who invoke rule circular justification often do so because they want to explain why some claims (like basic logical principles) can be known without further argument while others can't (like the four color theorem). So allowing that the mere possibility of a proof of P suffices to give justification to all believers of P would be giving away the game....

3. Provide proof for the following argument
1. ay(~Gy&~By)
2. "y(Gy v By v Ty)
3.
4. ay (ty v y)