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The groups you've mentioned set forth their axioms and accepted logic and construct their math accordingly. There's no disagreement here, as there's no "disagre
by avip 8y ago
The groups you've mentioned set forth their axioms and accepted logic and construct their math accordingly. There's no disagreement here, as there's no "disagreement" between Euclid and Lobachevsky.
- foldr 8y agoThere is disagreement about what constitutes an acceptable mathematical proof. E.g., is proof by contradiction a proof?
- theamk 8y agoYes, it is certainly a proof (in a most commonly-used logic systems) There may be some logic systems where proof by contradiction is not a proof. The existence of such logic systems does not mean there is any disagreement between mathematicians.
- foldr 8y agoNo, it doesn't, but as a matter of fact there has been disagreement among mathematicians on those issues. See e.g. https://en.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_controversy https://en.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_contro....