The constant “Pi” could be any sign, but Pi does of course denote something objective: the relationship of the ratio of the circumference of circle to its diameter. Is that relationship a priori as well? If it is, it’s not clear that’s what most logicians mean by a priori. It’s objective, and the relationship may hold independently of our minds–but the relationship is really still a part of nature. There may be few perfect circles in nature, but find a circle, measure the circumference of circle, and the diameter, and one would find something close to 3.1416. (assuming western numbering): the pythagoreans or whoever who established Pi did not merely tune into their immortal soul or “synthetic a priori”– It’s a relation which is perceivable at least.

That’s not to say it’s empirical ala Mill (tho Mill not as naive as some think)–but a certain rational constructivst view of mathematical knowledge seems rather feasible, instead of the usual vague platonic (and Kantian) reliance on the a priori. Humans may have the a priori skills to perceive and construct Pi (from experience of some sort), but the relationship itself is not mentally a priori …………

Given more time cognitivists will most likely map out the specific neural pathways of supposed “a priori” mathematical knowledge (they have already begun to do so): Pi will probably be shown to be cortically located on a sort of neurological hard drive–

]]>The second big move at work in Burge is the claim that testimony *and memory* can figure in a priori entitlements because they *preserve* content, as opposed to being the source of new content. (Hence “Content Preservation”.) I have never understood his argument here, and for testimony, at least, we now have the extended debates on the epistemology of testimony to show that Burge’s view is not the only one.

Still, I side with Kenny in finding Burge’s view, especially as developed by Peacocke, very promising for mathematics. Whether it works, even for testimony, is another matter. Perhaps there is more than one way to ground

a priori knowledge?

But that consequent sounds fine! It only sounds dodgy if you mistake it for “we have to say that most mathematics is not in fact knowable a priori”. I can’t see any other reason to worry about it, nor I suspect would most people working on the a priori be worried by it.

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