Is the concept a priori passed its sell by date?
Mike Gabbay made a point which struck me as right. I’m not going to get it quite right, but roughly, “a priori” knowledge is knowledge by inference. If we presuppose a body of knowledge K, then we can deduce a larger body K2 using inference. All the propositions in K2 but not in K will be a priori. There are many techniques and skills that could come under the heading “inference”, and it could be the case that we learn new skills, either collectively, or individually, from experience. What can be deduced a priori will therefore be relative to experience.
For example, if I knew that there were some trees planted in a square that was seven trees long and seven trees wide, I do not yet know how many trees are in the square. If I know about squares and squaring then I can deduce without further observation that there are 49 trees in the square. I will have made this deduction a priori. I could have found out this knowledge by going out and counting each tree. This would have been a posteriori. I may have been told by my line manager that the best way to count the trees is to multiply the length by the breadth on a calculator. Given this information and a calculator, I could discover that there were 49 trees in the square without counting them. Would this be a priori? I guess Professor Williamson’s point is that the concept of a priori has two much philosophical baggage for this to be a useful question. What have we solved by calling this technique for counting trees planted in squares a priori? No part of the process was either necessary, nor innate nor derived purely from reason, nor absolutely certain. Since these are often thought to be properties of the a priori, perhaps we should stop using the term since it just confuses matters.
However I think it highly useful to make a distinction between what we can find out before hand given a body of knowledge K, and what we just have to wait and see. Lets play dice. I’ll throw two dice and I’ll give you £35 if it’s a double six and you give me £1 otherwise. What do we know a priori? We know a priori that there is a 1/36 chance that you will win. We know a priori that the odds are fair. What we don’t know a priori is who will win. We have to actually throw the dice for that. The fact that we know these things a priori is not innate, or intuitive or necessary or any rubbish like that. It has been hard won by the greatest of our species and been passed down through teaching and tested through experience.