On August 2, Mr Harvie of the Mathematics department, addressed the Philosophical Society on the relationship between logic and mathematics.

In order to provoke discussion Mr Harvie maintained a viewpoint he did not completely hold. Mr Harvie maintained that although mathematics is logical in form it does not have its roots in logic.

Over the past hundred years the characteristic method has been the axiomatic one. In this method you postulate axioms and then argue from I hem. But do these axioms refer to anything: are there any entities to which the axioms refer. This led to the idea that mathematics should be expressed in logical terms.

However during the last 50 years working mathematicians have ignored this. They know little of the logical foundations of the subject. A mathematician has experience of a thing and he puts down axioms to make the idea precise. This is to him a satisfactory basis for asserting the axioms. Mathematics has no need for the calculations logicians are trying to force upon them. The clearest example of this is in the work of the "Bourbaki." They believe mathematics is a set of unconnected systems.

In other words logicians have made their own subject and can solve their own problems. The results do not affect mathematicians.

Mr Harvie went on to discuss various specific points arising from logic and mathematics.