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[the divide] separates two kinds of mathematical statements: “finitistic” ones, which can be proved without invoking the concept of infinity, and “infinitistic”
by gfody 9y ago
[the divide] separates two kinds of mathematical statements: “finitistic” ones, which can be proved without invoking the concept of infinity, and “infinitistic” ones, which rest on the assumption — not evident in nature — that infinite objects exist.
- johncolanduoni 9y agoThe article stated this in a very silly way. Infinite objects existing in nature has nothing to do with whether reasoning about certain infinite objects (e.g. The real numbers) is sound, any more than thinking about counterfactuals is impossible because they differ from the real world.
- gfody 9y agofurther in she cites Aristotle potential vs. actual which I guess is more philosophy than math but it covers the point you're making now.