## ABSTRACT

The first problem to consider is how does one study the philosophy of mathematics. Is it necessary to be a professional mathematician to make a contribution or to understand what its philosophy is all about? The great names in the history of the subject, such as Husserl, Frege, Cantor, Peano, Hilbert, Whitehead and Russell, and in more modern times Gödel and Dummett, were all trained as mathematicians. The subject is usually called mathematical logic: therefore a general theory of logic is required, which is a fundamental part of the general subject of philosophy also. I think that a technical knowledge of mathematics is not essential for the philosophy of mathematics. All mathematical concepts can be expressed in language; thus, if a new concept is developed, a new language can be found to express it. A new word must be found for the new concept, usually from the Greek or Latin language. Therefore the study of the philosophy of mathematics can be an exercise in linguistic analysis. The fact that there are three schools of thought – the logicist, the formalist and the intuitionist – is sufficient evidence that the foundations of mathematics are not universally agreed. There is an interesting way of looking at the foundations of mathematics and comparing it with architecture. In constructing a building the foundations are laid first and the building is raised on top of that, reaching completion with the roof. In mathematics the procedure appears to be the reverse. There is an immense structure of mathematics built up over the centuries, but the very foundations of mathematics – what it really means – have not yet been provided.