This may be a situation where the modern world’s resources start to break down the formerly strong separation between mind and world.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
These modern machines seem to render the statements within axiomatic mathematical systems as testable and falsifiable as any other physical facts.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
This may be a situation where the modern world’s resources start to break down the formerly strong separation between mind and world.
These days, most if not all of the rules of math can be coded into a computer, and new propositions tested or evaluated by those systems. Once I’ve implemented floating point math, I can SHOW STATISTICALLY the commutative law, the associative law, that 2+2 never equals 5, that numbers have additive and multiplicative inverses and on and on and on.
These modern machines seem to render the statements within axiomatic mathematical systems as testable and falsifiable as any other physical facts.
How would you do this for something like the Poincare conjecture or the unaccountability of the reals?
Also how do you show that your implementation does in fact compute addition without using math?
Frankly the argument you’re trying to make is like arguing that we no longer need farms since we can get our food from supermarkets.
Edit: Also the most you can show STATISTICALLY is that the commutative law holds for most (or nearly all) examples of the size you try, whereas mathematical proofs can show that it always holds.