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Mathematics without Infinity

Kirby Urner
5 min readMay 18, 2018

The circle of folks willing to philosophize out loud, about matters mathematical (hello Gilbert & Sullivan), is usually quite small, as the risk of making a fool of oneself are high, whereas pure boredom seems likewise a “hard place” to get unstuck from.

A mathematics without infinity, of which we could have a great many, at least in theory, might seem like double trouble insofar as “infinity” is usually seen as a draw.

People flock to the carnival to be amused by the vertigo. There’s nothing like “infinite recursion” to give a stomach butterflies, and isn’t that what they pay for?

My sparring partner, likewise a good friend, blames Wittgenstein’s influence for my pronounced case of Finitism. I’ll gladly concur.

What a lot of people miss about Ludwig’s critique of the “private ostensive definition” is that “infinity” is often on the other end of that private pointing stick.

In other words, to assure one’s self that “infinity” has meaning, a solipsist might “look within” and concentrate really hard, on “that which is infinite” (privately shown).

One needs only a moment, the thinking goes, to reassure one’s self: it’s still there, that treasure box experience that is “the meaning” of infinity.