By Julia Annas
The culture of old philosophy is an extended, wealthy and sundry one, during which the notes of dialogue and argument consistently resound. This publication introduces historic debates, attractive us with the traditional advancements in their topics. relocating clear of the presentation of old philosophy as a succession of significant thinkers, the booklet provides readers a feeling of the freshness and liveliness of historical philosophy, and of its big range of subject matters and types.
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Additional resources for Ancient Philosophy: A Very Short Introduction (Very Short Introductions)
The two together made it possible for mathematicians to take the decisive modernist step of setting up the new theory in opposition to all previous ones, as the new autonomous domain that includes, in reworked form, all ‘‘that matters’’ of earlier approaches. Unlike the developments in classical mathematics, contemporary changes in logic grew out of a moribund ﬁeld. It is generally agreed that investigations into logic grew quietly to a halt after Leibniz, his followers like Christian Wolff, and ﬁnally Johann Heinrich Lambert at the end of the eighteenth century.
30 MODERNISM AND MATHEMATICS 35 that much good music remains to be written in C major, or the continued production of good novels with a classical structure. 2 Professionalization Rather, what we see in mathematics is a change in attitude of the whole mathematical profession. Most visibly in Berlin, but also in Go¨ttingen and elsewhere, they had their own ethos. This distinct professional position was strongly conducive to the development of an autonomous body of ideas within and about their subject, which, as we have seen, increasingly declined to make outward reference for its basic terms.
These, and other criticisms I shall look at, all cumulatively undermined previous conﬁdence that Euclid’s Elements were indeed the epitome of reasoning. Projective geometry, by any standards the most remarkable success story of nineteenth-century geometry, in both its synthetic and analytic modes deployed points, lines, and ultimately hyperplanes at inﬁnity in a manner unintelligible to classical geometry. Moreover, as the philosopher and historian Ernest Nagel argued many years ago,3 the use of duality in projective geometry plays havoc with intuition and, he argued, opens the door to purely logical reasoning.
Ancient Philosophy: A Very Short Introduction (Very Short Introductions) by Julia Annas