Then you add in the Brouwer Hilbert mess that still causes challenges with talking about where the a priori assumption of the law of the excluded middle causes

Then you add in the Brouwer Hilbert mess that still causes challenges with talking about where the a priori assumption of the law of the excluded middle causes real problems with modern computational challenge. https://en.m.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_controversy https://en.m.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_cont... I think using the words 'fragment of' is less likely to cause issues than invoking constructivist mathematics. But if anyone has better ideas how to explain what you lose with negation as failure etc... I am all ears. Most of the popular ML methods require an assumption of IID, and C in ZFC both introduce LEM, which can be problematic for lots of people's ambitions. It is difficult to not hit very passionate beliefs.