## Comment: Maths and foundations of reasoning (Score 0) 131

`Physics is built upon mathematical structures which have their origin in the 19th century. Both Set Theory and Peano Arithmetic effectively grant you the assumption that there is no limit on how high you can effectively count. This leads to models of these theories essentially asserting that there are countable numbers which are greater than the number of particles in the observable universe. I fear this is leading to a hidden paradox in the reasoning process that physicists are using, albeit one that is hard to see and communicate.`

Consider this assumption as follows:

(you can count) (higher than) (you can count)

and compare this with the statement 'X > X'. There must be a practical physical limit on counting, and by assuming this limit away, you are rendering the resulting reasoning system physically implausible. An effect known in classical logic is that from a single contradiction, using the rules of logic, you can logically derive any statement at all. The problem with the foundations of mathematics as they are is that they are incompatible with physical plausibility, and to naively shoehorrn in physical plausibility leads to logical inconsistency and 'weird stuff' appearing. I fear that this is the beast that theoretical physicists are actually wrestling with, albeit unknowingly.

Consider this assumption as follows:

(you can count) (higher than) (you can count)

and compare this with the statement 'X > X'. There must be a practical physical limit on counting, and by assuming this limit away, you are rendering the resulting reasoning system physically implausible. An effect known in classical logic is that from a single contradiction, using the rules of logic, you can logically derive any statement at all. The problem with the foundations of mathematics as they are is that they are incompatible with physical plausibility, and to naively shoehorrn in physical plausibility leads to logical inconsistency and 'weird stuff' appearing. I fear that this is the beast that theoretical physicists are actually wrestling with, albeit unknowingly.