Category
Philosophy of mathematics
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The actual infinite is a useful fiction, not something real
Aristotle, in Physics III, allowed only the potential infinite: you can always count one more, but there's never a completed infinite totality. For two thousand years, most mathematicians agreed. Then Cantor, in…
Started by Vikram Sethi5 replies0 views -
Numbers exist independently of us: mathematical platonism is true
I'll defend platonism in its standard form: there are abstract mathematical objects, they don't depend on minds or language, and mathematical statements are true or false because of them. Main argument: indispensability,…
Started by Tomasz Wójcik5 replies0 views -
Gödel’s incompleteness theorems are constantly misused in philosophical arguments
A public service post, since I see this weekly. What the first theorem says, roughly: any consistent, effectively axiomatised formal system that contains enough arithmetic has true sentences in its language that…
Started by Tomasz Wójcik4 replies0 views -
Did Indian mathematicians have a philosophy of zero?
Brahmagupta's Brāhmasphuṭasiddhānta (628 CE) gives rules for arithmetic with zero as a number: adding zero to a number leaves it unchanged, multiplying by zero gives zero, and so on. He also tried…
Started by Vikram Sethi3 replies0 views