I have some questions related to multivalued logic. I am new to this forum, (I study mathematics) so I would be grateful to any useful advice. I am doubtful on even posting this question on Philosophy SE.

Can 3 valued logic (True, False, Indeterminate) be the basis of mathematics? If accepted so, can normal mathematics like proofs, relations, sets, function, calculus, analysis and algebra be developed? Much of modern math is based on the bivalence principle and the law of the excluded middle??

Also, what if fuzzy logic (developed by Zadeh) and set theory and fuzzy arithmetic are used as the foundations of mathematics? What would be the demerits to this approach? And can it be applied fields of study like physics? And probably new fields like QM and GR?

I have some questions related to multivalued logic. I am new to this forum, (I study mathematics) so I would be grateful to any useful advice. I am doubtful on even posting this question on Philosophy SE.

Can 3 valued logic (True, False, Indeterminate) be the basis of mathematics? If accepted so, can normal mathematics like proofs, relations, sets, function, calculus, analysis and algebra be developed? Much of modern math is based on the bivalence principle and the law of the excluded middle??

Also, what if fuzzy logic (developed by Zadeh) and set theory and fuzzy arithmetic are used as the foundations of mathematics? What would be the demerits to this approach? And can it be applied fields of study like physics? And probably new fields like QM and GR?

Apart from other questions, my questions is can we develop normal mathematics from this framework??