ABSTRACT
5.1. Mathematics and systems of deductions: consistency. The idea of the parts of mathematics as systems of deductions goes back to Euclid’s work in geometry, geometry being the first part of mathematics that was made into a system of this sort. What a system of deductions is has been outlined clearly enough to the reader for us not to have to go into more detail about it at this stage, though more will be said later. What we will have to say something about here is another side or level of a system of deductions, the idea of which has been very important for Mathematical Logic.
