To my mind, it demands a reason from each philosophy. But each of them pretty much has one, because this astonishing power was noticed long before now. Alongside the early philosophers in Greece were the Pythagoreans, who worshipped that power as a god.

If you admit any kind of idealism you end up assuming mathematics has transcendental roots, in a Platonic sense. So of course, mathematics describes reality because reality is built upon the mind of God, or whatever your essentialist replacement is, and so are we.

And if you assume total naturalism, but take a view of mathematics that makes abstract objects mental constructions, then mathematics describes reality because we are evolved to deal with reality, and mathematics is built upon our natural intuitions, which are honed over hundreds of thousands of years of adaptation.

Every discipline relies upon some evolved experience and intuition. But our logical and spatial intuitions apply to pretty much every action we take, and therefore have a lot more opportunities to fail us, and get improved. In doing math, we are merely extracting the combinatorial power bred into us.

An exception would be philosophies of science that try not to consider mathematics and the other exact sciences as a special case. If you try to adopt a philosophy of mathematics as an abstract version of an experimental science, rather than as an internal exploration of human psychology or mental structure in general, you can have a very hard time with this question.

Various utilitarians and pragmatists have proposed such an approach, but they then focus elsewhere and fail to address this question.

None of our other experimental sciences have failed to go through what Kuhn identifies as a 'revolution', where some underlying model is completely replaced by a different one -- we moved from Alchemy's four elements to Chemistry's limitless number, from Substance Theory to Atomism, from Aristotelian notions requiring direct contact to transmit effects and presuming inherent rest to Newton's laws, from Ptolemaic geocentrism to Copernicanism. In each case, we lost a little ground to the new insights. (e.g. Alchemy had reasons why liquids puddle and water expands -- Chemistry didn't, for quite some time. Ptolemy's math was way better than heliocentric models until Kepler realised orbits are elliptical.)

So if mathematics is based on experience, like other scientific endeavors, we should see the same thing happen there, and we don't. No element of mathematics has undergone such an upset. Even ideas that struck people as insane when they arose, like irrational measures, or multiple infinities, have been grafted into mathematics leaving the rest whole.

To my mind, it demands a reason from each philosophy. But each of them pretty much has one, because this astonishing power was noticed long before now. Alongside the early philosophers in Greece were the Pythagoreans, who worshipped that power as a god.

If you admit any kind of idealism you end up assuming mathematics has transcendental roots, in a Platonic sense. So of course, mathematics describes reality because reality is built upon the mind of God, or whatever your essentialist replacement is, and so are we.

And if you assume total naturalism, but take a view of mathematics that makes abstract objects mental constructions, then mathematics describes reality because we are evolved to deal with reality, and mathematics is built upon our natural intuitions, which are honed over hundreds of thousands of years of adaptation.

Every discipline relies upon some evolved experience and intuition. But our logical and spatial intuitions apply to pretty much every action we take, and therefore have a lot more opportunities to fail us, and get improved. In doing math, we are merely extracting the combinatorial power bred into us.

An exception would be philosophies of science that try not to consider mathematics and the other exact sciences as a special case. If you try to adopt a philosophy of mathematics as an abstract version of an experimental science, rather than as an internal exploration of human psychology or mental structure in general, you can have a very hard time with this question.

Various utilitarians and pragmatists (including, to some degree Karl Popper) have proposed such an approach, but they then focus elsewhere and fail to address this question.

None of our other experimental sciences have failed to go through what Kuhn identifies as a 'revolution', where some underlying model is completely replaced by a different one -- we moved from Alchemy's four elements to Chemistry's limitless number, from Substance Theory to Atomism, from Aristotelian notions requiring direct contact to transmit effects and presuming inherent rest to Newton's laws, from Ptolemaic geocentrism to Copernicanism. In each case, we lost a little ground to the new insights. (e.g. Alchemy had reasons why liquids puddle and freezing water expands -- Chemistry didn't, for quite some time. Ptolemy's math was way better than heliocentric models until Kepler realised orbits are elliptical.)

So if mathematics is based on experience, like other scientific endeavors, we should see the same thing happen there, and we don't. No element of mathematics has undergone such an upset. Even ideas that struck people as insane when they arose, like irrational measures, or multiple infinities, have been cleanly folded into mathematics leaving the original model whole.

To my mind, it demands a reason from each philosophy. But each of them pretty much has one, because this astonishing power was noticed long before now.

If you admit any kind of idealism you end up assuming mathematics has transcendental roots, in a Platonic sense. So of course, mathematics describes reality because reality is built upon the mind of God, or whatever your essentialist replacement is, and so are we.

And if you assume total naturalism, but take a view of mathematics that makes abstract objects mental constructions, then mathematics describes reality because we are evolved to deal with reality, and mathematics is built upon our natural intuitions, which are honed over hundreds of thousands of years of adaptation. We are merely extracting the power bred into us.

An exception might be some philosophies of science that try not to consider mathematics and the other exact sciences as a special case. If you try to adopt a philosophy of mathematics as an abstract version of an experimental science, rather than as an internal exploration of human psychology or mental structure in general, you have a very hard time with this question.

Various utilitarians and pragmatists have proposed such an approach, but they then focus elsewhere and fail to address this question.

None of our other experimental sciences have failed to go through what Kuhn identifies as a 'revolution', where some underlying model is completely replaced by a different one -- we moved from Alchemy's four elements to Chemistry's limitless number, from Substance Theory to Atomism, from Aristotelian notions requiring direct contact to transmit effects and presuming inherent rest to Newton's laws, from Ptolemaic geocentrism to Copernicanism. In each case, we lost a little ground to the new insights. (e.g. Alchemy had reasons why liquids puddle and water expands -- Chemistry didn't, for quite some time. Ptolemy's math was way better than heliocentric models until Kepler realised orbits are elliptical.)

So if mathematics is based on experience, like other scientific endeavors, we should see the same thing happen there, and we don't. No element of mathematics has undergone such an upset. Even ideas that struck people as insane when they arose, like irrational measures, or multiple infinities, have been grafted into mathematics leaving the rest whole.

To my mind, it demands a reason from each philosophy. But each of them pretty much has one, because this astonishing power was noticed long before now. Alongside the early philosophers in Greece were the Pythagoreans, who worshipped that power as a god.

If you admit any kind of idealism you end up assuming mathematics has transcendental roots, in a Platonic sense. So of course, mathematics describes reality because reality is built upon the mind of God, or whatever your essentialist replacement is, and so are we.

And if you assume total naturalism, but take a view of mathematics that makes abstract objects mental constructions, then mathematics describes reality because we are evolved to deal with reality, and mathematics is built upon our natural intuitions, which are honed over hundreds of thousands of years of adaptation.

Every discipline relies upon some evolved experience and intuition. But our logical and spatial intuitions apply to pretty much every action we take, and therefore have a lot more opportunities to fail us, and get improved. In doing math, we are merely extracting the combinatorial power bred into us.

An exception would be philosophies of science that try not to consider mathematics and the other exact sciences as a special case. If you try to adopt a philosophy of mathematics as an abstract version of an experimental science, rather than as an internal exploration of human psychology or mental structure in general, you can have a very hard time with this question.

Various utilitarians and pragmatists have proposed such an approach, but they then focus elsewhere and fail to address this question.

None of our other experimental sciences have failed to go through what Kuhn identifies as a 'revolution', where some underlying model is completely replaced by a different one -- we moved from Alchemy's four elements to Chemistry's limitless number, from Substance Theory to Atomism, from Aristotelian notions requiring direct contact to transmit effects and presuming inherent rest to Newton's laws, from Ptolemaic geocentrism to Copernicanism. In each case, we lost a little ground to the new insights. (e.g. Alchemy had reasons why liquids puddle and water expands -- Chemistry didn't, for quite some time. Ptolemy's math was way better than heliocentric models until Kepler realised orbits are elliptical.)

So if mathematics is based on experience, like other scientific endeavors, we should see the same thing happen there, and we don't. No element of mathematics has undergone such an upset. Even ideas that struck people as insane when they arose, like irrational measures, or multiple infinities, have been grafted into mathematics leaving the rest whole.