I have sometimes been critical of logic, that is logical thinking not informed by physical realities, but of this I am certain: lack of logic permeates our culture. Science is infected by lack of logic as well.
Where do we learn logic? How do we best learn to think logically? Not by solving math problems, but by doing mathematical proofs. Schools have more or less abandoned this practice in favor of memorizing formulas and solving math based problems. A mistake.
Only by doing mathematical proofs – and actively looking for hidden assumptions and errors in reasoning- do we train ourselves to think logically, and although empirical science has data to guide its thinking, our inveterate and perverse tendency to filter out data we do not “believe” in renders this tool all but useless in finding truth without rigorous logical thinking as a guide. The world is logical, once we understand and accept what world we are living in (hint – Darwin’s world, not the biblical fantasy). We need this logical thinking and this is the most valuable lesson we learn from math – if we have learned to think logically, we can derive any formulas we need to solve problems, and we are more likely to solve even empirical problems better for having trained our logical faculty.
Typical of our modern mixed up world – Nietzsche making fun of Socrates for his overdeveloped logical faculty. If only Socrates had developed logic further and given us mathematical logic millennia before mathematicians corrected Aristotle’s errors in logic!
Merely memorizing formulas or worse learning only where to find the formulas is not going to cut it – the illogic runs throughout our society, from its religious, economic, sociological, psychological and political madness to the errant science being done and being sworn to every single day.
What a price we have paid already! What a price there is still to pay!