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6 Wittgenstein did not mean to suggest by this that philosophy does not have a crucial role to play vis-à-vis science. 7 But this would seem to limit philosophy to the task of interpreting scientific prose: the ‘history of evolving ideas’, as it were. C of Relativity as their standard-bearer. What’s more, there is a real danger in this thought that the principal role of philosophy is to describe and not explain. For it has a tendency to promote the view that philosophers are armchair critics, akin to theatre critics, both professionally and temperamentally set apart from the scientific writings whose shortcomings it is their chief job to expose.
It was at these later meetings that Hilbert delivered his famous keynote address welcoming the mathematical world to Paris. Conscious of his place in history, Hilbert took the occasion to remind his audience of the challenges facing them as they entered a new century: If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of to-day sets and whose solution we expect from the future.
Hence the date in Quine’s famous aphorism. Subtitled ‘a formula language, modeled upon that of arithmetic, for pure thought’, the Begriffsschrift took as its goal nothing less than a rigorization of proof itself. Said Frege, My intention was not to represent an abstract logic in formulas, but to express a content through written signs in a more precise and clear way than it is possible to do through words. 2 The result was the introduction of a very general symbolic language 13 PHILOSOPHY OF SCIENCE, LOGIC AND MATHEMATICS suitable for expressing the type of formal inferences used in mathematical proofs.