The Posts on Aristotle’s defense of the Principle of Contradiction and the play of the Self-Negating Expression go back over 2,000 years. I’d like to set forth a more recent example, one less than a century old, just to convince you that things haven’t changed much.
‘Logic is to Philosophy what Mathematics is to Nature’. So goes the line. For me the distinction has always been fuzzy. But I will use both headings.
The problem-zone is the point of intersection between Mathematics and Philosophy. Or more precisely, the Mathematician’s application of philosophical notions, the noble intent to come to terms with issues better dealt with if the researcher was familiar with the evolution of philosophical presumptions over the millennia.
First, the Mathematician’s interpretation of the idea of ‘Unity’ and secondly, his application of the idea of ‘Truth’.
There are others: the notion of Finiteness, for example, a central theme of the Hilbert Program; the notion of the Observer: the emergence of Metamathematics and its arrangement of hierarchical statements; the blithe takes on the notion of ‘Isness’ or Ontological Presence: ‘There is an X such that…’