This document discusses the British philosophy of mathematics. It contains a quote from A.J. Ayer's "Language, Truth and Logic" that presents empiricists with two options for explaining the necessity of logical and mathematical truths: either they are not truly necessary, requiring an explanation for their universal acceptance as such, or they have no factual content, requiring an explanation for how non-factual propositions can be true, useful, and surprising. The document also lists some key figures in the development of mathematics between 1545-1668.

1. British Philosophy of
Mathematics
Brendan Larvor
30 October 2006

2. “The empiricist must deal with the truths of
logic and mathematics in one of the following
two ways: he must say either that they are not
necessary truths, in which case he must
account for the universal conviction that they
are; or he must say that they have no factual
content, and then he must explain how a
proposition which is empty of all factual content
can be true and useful and surprising.”
(A.J. Ayer, Language, Truth and Logic 72-3)

3. Cardano 1545 Viète 1591

4. Harriot 1631 Pell 1668

5. Torricelli 1641

6. Torricelli 1641