By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?

Why is there Philosophy of Mathematics at all? Ian Hacking. in Metascience (2015).

Peter Williams complains that Richard Dawkins wraps his naturalism in ‘a fake finery of counterfeit meaning and purpose’. For his part, Williams has wrapped his complaint in an unoriginal and inapt analogy. The weavers in Hans Christian Andersen's fable announce that the Emperor's clothes are invisible to stupid people; almost the whole population pretends to see them for fear of being thought stupid . Fear of being thought stupid does not seem to trouble Richard Dawkins. Moreover, Williams offers no reason (...) to think that such fear motivates any of Dawkins' readers. Perhaps all we are supposed to take from the fable is that Dawkins' naturalism is obviously lacking in meaning and purpose. If that is the intended reading, then by using this analogy, Williams has given himself an unnecessarily difficult task. Surely, it would be achievement enough for him to show that Dawkins' naturalism lacks meaning and purpose. There is no reason for Williams to make the extra claim that it obviously lacks meaning and purpose. After all, there is an obvious difficulty with arguing over several pages that something is obviously the case. (shrink)

Brendan Larvor finds that the Archbishop of Canterbury's recent arguments about religious education are a curate's egg.

The schism between analytic and continental philosophy resists repair because it is not confined to philosophers. It is a local manifestation of a far more profound and pervasive division. In 1959 C.P. Snow lamented the partition of intellectual life in to `two cultures': that of the scientist and that of the literary intellectual. If we follow the practice of most universities and bundle historical and literary studies together in the faculty of humanities on the one hand, and count pure mathematics (...) among the sciences on the other, then it is fair to say that the mutual ignorance and occasional hostility between scientists and humanists decried by Snow is still with us. And it runs through the middle of philosophy. Philosophy aspires to say something about everything, so it is unsurprising that philosophers have reproduced in miniature the division between the arts and the sciences. What is worrying is that we have failed to overcome it. (shrink)