Interactions: Mathematics, physics and philosophy, 1860-1930 by Vincent F. Hendricks

By Vincent F. Hendricks

The major subject matter of this anthology is the original interplay among arithmetic, physics and philosophy in the course of the starting of the 20 th century. during this ebook, ten popular philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics. the result's a various but thematically concentrated compilation of firstclass papers on arithmetic, physics and philosophy, and a source-book at the interplay among them.

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In so doing, Kant lays the ground for the claim that forces cannot have absolute directions. Indeed this phoronomic analysis is intended to feed directly into the definition of force that Kant provides in the next section of the MFNS, the “Dynamics”. 26 Kant introduces a law of equal action and reaction, which in turn permits us to transform the kinematic definition of the composition of motions into a dynamical one (in Kant’s terminology, a phoronomic into a mechanical one). According to this a priori “Law of Mechanics”, the dynamical interaction of two bodies entails the motion of both of these with respect to that reference frame in which momentum is conserved, namely that determined by the centre of mass of the bodies.

This concept of “same relative position”, “has not been applied by all mechanists who have made use of this principle [the conservation of energy], but it is obviously necessary to its physical application”. ”32 To assume positional dependence is to assume the possibility of establishing congruence relations, so that our implication from above can be rewritten as: (principle of decomposition & determinability of congruence relations) ⇒ (constant vis viva ⇒ postulate of central forces) Unfortunately, Helmholtz continues to assume, as did Kant before him, that the conditions on the positional determination of two points remain the same in more complex systems.

In their illegitimate, non-regulative employment, such transcendental ideas correspond to rules which are not “strictly speaking” true. Treating them as if they were true leads us into the various “antinomies” of reason, for instance into asserting both that the world must have a first cause, and that there can be no first cause. Taken regulatively, however, they perform a valuable role, for they direct the understanding to systematise its rules hierarchically, and thus to construct a unified totality of natural laws.

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