But they, the maths, are not literally out there though are they, as objective concepts. Only the forces, and the like, and the way they interact, and so on, are. We impose these concepts on to them with our minds but those concepts are only in our minds as ways to relate to what we 'see' for our own understanding. Therefore, maths is contingent on the behaviour and patterns of the universe and how we 'see' things.
Hi Jack Knave,
Thank you for the above. Sorry for delay in responding.
The question is not whether we
"impose" mathematical concepts onto the physical Universe with our minds. That happens from time to time when people try to force a concept to fit a particular situation where it does not fit. Fortunately, peer review protects against this.
So, the question is whether mathematical concepts are solely imaginary (with no more power than Harry Potter's wand); or whether they are true independently of the human mind, with a propensity to interact with the physical Universe. Successes of modern science indicate the latter.
If mathematical concepts were solely imaginary, then they would be the product of random processes in our contingent brains, with no purpose but amusement, and no more relevance to reality than Harry Potter's wand. If just imaginary and random, it would be difficult to
"impose" them on the physical Universe in a coherent way.
Numbers, squares of numbers, square roots, right angles, triangles, second derivatives etc are not visible in the natural world. For thousands of years, maths developed these concepts, aware of their usefulness for man-made things, but unaware of a relevance to the physical Universe.
However, in about AD 1590, Galileo dropped some stones frim the Tower of Pisa, and from then until AD 1905, he, Newton, Maxwell etc made objective measurement, followed by mathematical equations the critical factor in science - i.e. the certainty of science depended upon the certainity of its mathimatical concepts. How could that be if maths was just an imaginary product imposed by contingent brain?
To be coherent, science needs its maths to be as objective (independent of human mind) as the objectivity of its physical elements (e.g. moons around Saturn).
However, from AD 1905, the sequence of physics was turned on its head. Instead of experiment followed by maths, the more fruitful sequence became abstract maths followed by empirical experiment. Mathematical reasoning enabled forecasts of previously unsuspected phenomena to an extraordinary extent. I gave four examples in my previous post. I can give more examples if you wish.
One could
"impose" equations upon a few things which are already known (if you can get around modern peer review and incoherence), but impossible to make your maths forecast new phenomena such as black holes, gravitational waves, Higgs field etc of modern physics unless the mathematical concepts are as objective as the phenomena they forecast.
So, if we accept the reality of the forecasts of modern physics, then we are forced to accept the reality of the abstract concepts used to make the forecasts. In modern physics, the Universe is contingent upon the maths.
God bless
