if you could figure out physical laws from apriori maths, that really would be unreasonably effective. As it is, physicists have to carefully select maths that works physically from the much larger amount that doesn’t. That this is possible is about as surprising as finding a true history in the library of Babel. The unreasonable effectiveness of maths is the reasonable effectiveness of physics.
For formalists (anti Platonists), 1+1=2 is true in all universes, providing you adopt axioms from which it can be derived. It isn’t a truth about the universe, for them, but it is contingent on choice of axioms. This seems to lead to a vision multiple conflicting mathematical truths, which will seem counterintuitive to some. Formlists can buttress their case by by appealing to two ur -axioms: maths is about minimising contradiction whilst maximising richness of structure,; and speculating that these provide considerable constraints to axioms choice.
Starting from the premise that maths talks us about the world, you are faced with a vision number of puzzles; whether maths is as real as the world, whether the world is as abstract as maths, why physicists and mathematicians are different people doing different things, why some maths is incorrect physics…
Starting from the premise that apple’s are oranges, you are likewise faced with puzzles about why they look and taste different…
Physics is the science of explaining the world with maths. That maths can be used to explain the world has the samemcontent as saying that physics works. It is not statement about maths per se. Historians succeed in using words to describe events. That isn’t a fact about lexicography.
if you could figure out physical laws from apriori maths, that really would be unreasonably effective. As it is, physicists have to carefully select maths that works physically from the much larger amount that doesn’t. That this is possible is about as surprising as finding a true history in the library of Babel. The unreasonable effectiveness of maths is the reasonable effectiveness of physics.
For formalists (anti Platonists), 1+1=2 is true in all universes, providing you adopt axioms from which it can be derived. It isn’t a truth about the universe, for them, but it is contingent on choice of axioms. This seems to lead to a vision multiple conflicting mathematical truths, which will seem counterintuitive to some. Formlists can buttress their case by by appealing to two ur -axioms: maths is about minimising contradiction whilst maximising richness of structure,; and speculating that these provide considerable constraints to axioms choice.
Starting from the premise that maths talks us about the world, you are faced with a vision number of puzzles; whether maths is as real as the world, whether the world is as abstract as maths, why physicists and mathematicians are different people doing different things, why some maths is incorrect physics… Starting from the premise that apple’s are oranges, you are likewise faced with puzzles about why they look and taste different… Physics is the science of explaining the world with maths. That maths can be used to explain the world has the samemcontent as saying that physics works. It is not statement about maths per se. Historians succeed in using words to describe events. That isn’t a fact about lexicography.