the boundaries of language

I was looking to see if the new issue of the British Journal for the Philosophy of Science is online yet, and ended up having a flick through some back issues. I spotted the final version of a review of Kit Fine's The Limits of Abstraction by a couple of friends of mine, Roy Cook and Philip Ebert.

The book's all about the propects, both technical and philosophical, of somehow maintaining that our knowledge of various mathematical theories can be accounted for using our knowledge of some appropriate (higher-order) logic plus abstraction principles; second-order principles of the form:

For all A and all B, (%(A) = %(B) if and only if A//B),

where % is a 'term forming operator applicable to expressions of the type of [A, B] and [//] is an equivalence relation on entities denoted by expressions of that type'. (The quote's from the intro to Hale and Wright's The Reason's Proper Study). Examples are Hume's Principle:

for all A and all B, the number of As = the number of Bs iff the As are 1-1 with the Bs,

and Basic Law V:

for all A and all B, the extension of A = the extension of B iff A is coextensive with B.

(The latter's not a particularly popular abstraction principle, since despite sounding obviously true, it's basically a principle of naive comprehension for sets.)

Interestingly, the keywords for the review include 'Health-related quality of life', 'Mental health', and 'Physical health'. Good to see Roy and Philip showing once again that the common mis-perception that philosophy of mathematics is cut-off from real-world, real-life concerns is bogus.

Labels: Misc