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from Part I - Let’s Be Independent
Published online by Cambridge University Press: 28 September 2020
In order to formalise mathematical thinking, Euclid℉s books (in the context of geometry) give the process of axiomatisation. This procedure first gives us a list of objects that are not defined but accepted as given. Then we get a list of axioms which are statements about these objects which are all assumed to be true.We assume also that we are endowed with the notion of logical deduction which we are allowed to apply to the axioms and the statements that have already been derived from the axioms using valid deduction. In this way we obtain theorems. The complete list of theorems that can be derived from the axioms is called a theory.
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