Mathematics and the Image of Reason

Mathematics and the Image of Reason

Mathematics and the Image of Reason

Mathematics and the Image of Reason

Synopsis

A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.

Excerpt

Post-modernists proclaim the failure of the projects of the Enlightenment - the death of philosophy, epistemology, morality, imagination and reason. Nietzsche announced the death of God and with him died all hope of founding either a secular morality or a secular epistemology. If God is dead, then so too is ‘that of God in every man’, that ‘natural light of reason’ by which the Good and the True stand revealed. Even mathematics suffers a loss of certainty (Kline 1980). Yet in the very culture within which this loss occurs there has a arisen a new faith - the cult of information technology, of the computer, of scientific facts and figures. But how can numerical representation and computation be worshipped in this way after the death of the mathematician-god, architect of the universe, and after the discrediting of the myth of a supersensible mathematical reality? Because, as in all supplanting of one faith by another, there is a supporting mythology of conquering and vanquished heroes. Transcendent reason, on which the Enlightenment pinned its hopes, has been imprisoned in formal, computational chains and it is the celebration of this victory which forms a necessary, legitimating complement to post-modernist claims. Enlightenment is impossible because reason has been rendered practically and theoretically impotent; it is confined to symbol manipulation, infallibly tracing paths through symbol structures, but incapable of showing a way out of these man-made ‘information’-labyrinths, or even of determining the transition from one such labyrinth to another.

A striking feature of mathematics is that it has two distinct faces - its number-crunching, calculatory face, revealed in applications, and its almost number- and calculation-free face, revealed in the pure mathematicians’ study of abstract structures. Somehow these are related; somehow the non-wordly, abstract study where theorems are proved with an exactness and certitude unparalleled in other branches of knowledge yields powerful methods and techniques for dealing with the physical world. Reason delivers, with apparent certainty, knowledge of an abstract, non-empirical realm, knowledge which is nonetheless of immense practical utility in the empirical world. Is it then any wonder that this should be treated as the paradigmatic manifestation of the power of reason? But at the same time this very power presents a puzzle and a philosophical challenge - how is it possible?

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.