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Shiavault - a Vault of Shia Islamic Books The Analytic Turn in Early Twentieth-century Philosophy 1- Frege and Russell: Decompositional and Transformative Analysis The papers in Part One explore the work of Frege and Russell, the two main instigators of the analytic turn that gave rise to analytic philosophy.

As indicated above, both Frege and Russell came to philosophy through concern with the foundations of mathematics, and both sought to demonstrate the logicist thesis that arithmetic (and geometry as well, in the case of Russell) could be reduced to logic by offering transformative analyses utilizing the new quantificational logic. It was in their philosophical attempts to justify their logicist projects that analytic philosophy was born.

In ‘Frege-Russell Numbers: Analysis or Explication?’, Erich Reck takes as his starting-point the logicist definition of the natural numbers as equivalence classes of equinumerous classes which both Frege and Russell gave, and considers the status of this definition, focusing primarily on Frege’s views.

Was it intended as an ‘analysis’, in the sense of revealing what the natural numbers ‘really’ are, or as an ‘explication’, in the sense of offering a reconstruction that does essentially the same job but in a more powerful and rigorous theoretical system? The Platonism that many have attributed to Frege would seem to suggest the first, while the second is compatible with a more conventionalist reading that brings Frege closer to Russell and Carnap.

Reck does not attempt the difficult task of deciding the issue on textual grounds, but he does elucidate the conceptions of analysis involved in asking the question and discuss the constraints on such definitions that might narrow down the possibilities. As far as Frege’s Platonism is concerned, Reck argues that this should not be interpreted as invoking a ‘Platonic heaven’ of abstract objects such as numbers, which we apprehend by some quasi-perceptual ‘intuition’.

The most charitable and sophisticated reading, he suggests, is that developed by Tyler Burge,[^12] according to which getting at ‘the facts of the matter’ is taken to involve reasoning and theory construction rather than (quasi-)empiricist observation.