That’s how we ended up with things like maths and logic. They are not just descriptions of human thought, they are norms in their own right: when an individual departs from the norm, we conclude that the individual is wrong, not that the description of human intuition has been falsified.
But this then sounds like that math or logic is a “thing”, and then I must ask where that does thing reside? Either in physical reality out there, or in people’s minds.
If you simply define math as a symbol manipulation game, still the expected outcome is that not playing any game by the accepted norms is wrong, not that the game is wrong. Why this “game” then predicts reality surprisingly well, part of the answer is that only subsets of it do, as math as practiced by mathemathicians is far above and beyond what is usable for it by physics, and part of the answer is that because we simply like to study the kinds of things math happens to be useful for. If basic algebra is a formalization of the rules of a certain set of human intuitions and then every higher math is simply whatever is generated by those rules, this predicts precisely that it will be useful for some of the things we like to study, without it really being a “thing”.
But this then sounds like that math or logic is a “thing”, and then I must ask where that does thing reside? Either in physical reality out there, or in people’s minds.
It doesn’t have to be either or. You can learn maths from books, .ir record your knowledge in them.
Consider Vaniver on Harari on cultural artefacts:-
There are no gods in the universe, no nations, no money, no human rights, no laws, and no justice outside the common imagination of human beings.People easily understand that ‘primitives’ cement their social order by believing in ghosts and spirits, and gathering each full moon to dance together around the campfire.
What we fail to appreciate is that our modern institutions function on exactly the same basis.But, of course, those modern institutions (as well as the ‘primitive’ ones) function. One division Harari discusses that I found useful was objective, subjective, and inter-subjective:
An objective phenomenon exists independently of human consciousness and human beliefs. … [Radioactivity is his example.]The subjective is something that exists depending on the consciousness and beliefs of a single individual. … [A child’s imaginary friend is his example.]The inter-subjective is something that exists within the communication network linking the subjective consciousness of many individuals. If a single individual changes his or her beliefs, or even dies, it is of little importance. However, if most individuals in the network die or change their beliefs, the inter-subjective phenomenon will mutate or disappear. …Many of history’s most important drivers are inter-subjective: law, money, gods, nations.
But this then sounds like that math or logic is a “thing”, and then I must ask where that does thing reside? Either in physical reality out there, or in people’s minds.
If you simply define math as a symbol manipulation game, still the expected outcome is that not playing any game by the accepted norms is wrong, not that the game is wrong. Why this “game” then predicts reality surprisingly well, part of the answer is that only subsets of it do, as math as practiced by mathemathicians is far above and beyond what is usable for it by physics, and part of the answer is that because we simply like to study the kinds of things math happens to be useful for. If basic algebra is a formalization of the rules of a certain set of human intuitions and then every higher math is simply whatever is generated by those rules, this predicts precisely that it will be useful for some of the things we like to study, without it really being a “thing”.
It doesn’t have to be either or. You can learn maths from books, .ir record your knowledge in them.
Consider Vaniver on Harari on cultural artefacts:-