By Professor William Demopoulos

The concept arithmetic is reducible to common sense has a protracted historical past, however it was once Frege who gave logicism an articulation and safeguard that reworked it right into a special philosophical thesis with a profound impression at the improvement of philosophy within the 20th century. This quantity of vintage, revised and newly written essays by means of William Demopoulos examines logicism's central legacy for philosophy: its elaboration of notions of research and reconstruction. The essays examine the deployment of those rules through the vital figures within the historical past of the topic - Frege, Russell, Ramsey and Carnap - and in doing so light up present issues in regards to the nature of mathematical and theoretical wisdom. concerns addressed contain the character of arithmetical wisdom within the mild of Frege's theorem; the prestige of realism concerning the theoretical entities of physics; and the right kind interpretation of empirical theories that postulate summary structural constraints

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An inertial frame associates a spatial coordinate system, and therefore a notion of distance, with a free motion. But the relevant notion of distance is evidently one that relates distances at a time; it therefore presupposes the concept of simultaneity. While it might seem natural to make the “absolutist” assumption that all inertial frames employ the same relation of simultaneity, the very fact that we can question this assumption shows that it is not something that should be pre-judged, as it would be if the assumption of the absoluteness of simultaneity were built into the notion of an inertial frame, as it is in classical mechanics.

198). 36 Logicism and its Philosophical Legacy for drawing the factual–nonfactual distinction on the basis of whether the vocabulary of a theory is descriptive or logical runs the risk of reducing the distinction to one of conventional choice rather than methodological principle. In order to address these issues it is necessary to look in greater detail at how Einstein illuminated our understanding of the application of a geometrical theory. We can then turn to the application of arithmetic and the consideration of how it differs from geometry.

But according to the Tractatus a proposition is informative only to the extent that it makes such a partition. The fact that logical propositions fail to be informative in this sense is what underlies the Tractarian idea that they are without factual content: failing to partition states of affairs, they assert no facts. Carnap was well aware that Wittgenstein’s analysis of logical truth in terms of tautologousness is severely limited and that it needs to be supplemented if it is to cover interesting cases that arise in “higher logic” and mathematics.

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