Dynamic interactions with the philosophy of mathematics. (English) Zbl 1026.00005

Gillies, Donald; Zheng, Yuxin

Theoria, Segunda Epoca 16, No. 42, 437-459 (2001).

Dynamic interaction is regarded as an important concept for explaining the development of ideas and the growth of knowledge. It is said “to occur when significantly different fields A and B come into relation and their interaction is dynamic in the sense that at first the flow of ideas is principally from A to B, but later ideas from B come to influence A” (p.437).
In the first example presented, the interaction between philosophy of mathematics and philosophy of science is considered by analyzing the philosophy of science of the Vienna Circle as being influenced by logicism. However, later developments in the philosophy of science like T.S.Kuhn’s concept of scientific revolution, I.Lakatos’ conception of scientific research programmes and the view of mathematics as quasi-empiricial prove the backward influence.
The second example deals with the interaction between the philosophy of mathematics and computer science. The early influence of the concept of a Turing machine, Church’s \(\lambda\)-calculus, and Russell’s theory of types on the development of computer science is opposed to later influences of automated theorem proving in the reverse direction, having provoked a discussion in the philosophy of mathematics although logicians had been looking for the mechanization of the process of deduction for a long time.

Reviewer: Volker Peckhaus (Erlangen)

MSC:

00A30	Philosophy of mathematics
01A60	History of mathematics in the 20th century
03A05	Philosophical and critical aspects of logic and foundations
68Q05	Models of computation (Turing machines, etc.) (MSC2010)
03D10	Turing machines and related notions

Keywords:

dynamic interaction; relation between philosophy of mathematics and philosophy of science; relation between philosophy of mathematics and computer science; scientific development