Φιλοσοφική θεώρηση της μαθηματικής επιστήμης ως αποδεικτικής
The theory of science had been initiated by Aristotle in his Posterior Analytics. It might be said in general that Aristotle identifies here this theory with mathematics. The inquiry about his first principles of science, which cannot be known by demonstration (deduction) and which is the basis of the theory of science, had been discussed by Aristotle in a separate book following his Analytics. Of course, this inquiry is a metaphysical one. From Aristotle’s point of view, the faculty of intuitive reason based on experience is that through which one begins to grasp those principles. Aristotle’s underlying theory is to be found on Euclid’s Elements, written a generation later. On the other hand more recent theories of science, such as Descartes’, Leibniz’ and Kant’s, have a great affinity with the ancient theory. It seems therefore that this theory dominated for many centuries scientific as well as philosophical thought. The aim of the present paper is to examine, following a consideration of the earlier aspects, the recent thesis of mathematical theory as deductive science and to investigate how current philosophical development contributed towards this thesis.