In mathematics when you're right you know you're right.

Adam Kirsch reviews Anthony Gottlieb's new book, The Dream of Enlightenment: The Rise of Modern Philosophy, published by Liveright/Norton in 2016 in the 5 September 2016 issue of The New Yorker.

Kirsch says in his review, “Descartes described reality in terms of qualities that can be measured math­ematically. Descartes himself was a towering mathematician, but he was far from the first philosopher to regard mathematics as the gold standard of truth: Pythagoras and Plato had done so two thousand years before. In the dialogue known as the Meno, Plato depicts Socrates teaching a slave boy the Pythagorean theorem—or, rather, leading the boy to figure it out for him­self. The dialogue shows what is so se­ductive about mathematics, that each step follows inevitably from the previ­ous step, in a way that makes it abso­lutely beyond doubt or error. You can get math wrong, but when you're right you know you're right.”

We who study, do, and teach Mathematics like the phrase “when you're right you know you're right” applied to our discipline. Of course "right” is defined by your logic system. However, once inside a reasonable system there is confidence and we can accept truths without having to reprove them to ourselves. Most importantly, we can build upon these assemblages of axioms and theorems and actually apply the mathematics with  confidence, say, with regard to existence, uniqueness, and convergence.

While the broader issues of philosophy involve  how mind and matter interact, why we exist, and Plato’s “sense of wonder,” it is reassuring that  those who care about knowing, namely philosophers, grant us this absolute which is  that, “You can get math wrong, but when you're right you know you're right.”

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