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3

I would say that the questions that String/M-theory try to answer are the last ones that our current knowledge of reality allows us to ask. One may think they are the last ones because they are already indirect, as no obvious experimental fact contradicts the current theories (General relativity and the Standard model of particle physics). Instead of ...

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Like yuggib, I have decided to expand my comment(s) into an answer. However, I will be taking a less formal approach. From the comments, it seems that the following might be a satisfactory, workable point of view for the (non-rigorous) physicist: Two physical theories of everything $A$ & $B$ clearly must predict the same physics in any physical ...

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I will expand my comment above into an answer: If you search for a TOE that is a mathematical theory, it has to be at least a logic theory, i.e. you need to define the symbols and statements, and the inference rules to write new (true) sentences from the axioms. Obviously you would need to add mathematical structures by means of additional axioms, symbols, ...

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