Is there some more fundamental math theory than logic?

Asked Apr 07 '18 at 15:57

Active Apr 07 '18 at 15:57

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As I know logic is mathematical theory which studies mathematical theories themselves, but is there some mathematical theory which is more fundamental ? By more fundamental I mean that this theory maybe studies logic itself or studies structures as logic. My question can also be interpreted as:"Is there some theory which is "lower" in chain of deducing whole mathematics ?".

asked Apr 07 '18 at 15:57

Юрій Ярош

2,086

no idea, i would imagine it would be something axiomatic, then again the most basic arguement is the basal axioms so....yeah logic from there – Vaas Apr 07 '18 at 15:58
@Vaas So there is no such theory ? – Юрій Ярош Apr 07 '18 at 16:10
1

Mathematics as a whole is absorbent in an odd sense. In particular, any "theory" which might have the ability to properly formalize mathematics is already formalizable within mathematics (I'm being intentionally vauge.) – Not Mike Apr 07 '18 at 16:30
My answer to How do I convince someone that $1+1=2$ may not necessarily be true? might be of interest. – Dave L. Renfro Apr 07 '18 at 16:37
@NotMike So is mathematical logic this theory ? – Юрій Ярош Apr 07 '18 at 17:02
well lets consider it logically yes? first things first. do you agree to the 3 basal axioms? ie...the universe exists, and we all occupy the same universe.
Events happen in the universe which are observable.

from these observations we can learn something

(been a while but i think these were the basal axioms)
– Vaas Apr 07 '18 at 18:55
You might be interested to study philosophy (of mathematics, logic and/or language). Also this might interest you: https://math.stanford.edu/~feferman/papers/whatrests.pdf – Ettore Sep 08 '20 at 17:30

Is there some more fundamental math theory than logic?

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