The ontological commitment of a sentence is whatever must be among the values of bound variables for the sentence to come out as true.

Willard van Orman Quine

I bring up this quotation not to agree or disagree with Quine, but just to point out the connection between everyday language and mathematics. The connection is well-known in some circles — like,  anyone for whom the phrase “possible world semantics” rings fifty different bells.

If you’re not schooled in such stuff, just notice this: Quine is talking about regular declarative sentences in natural languages, yet using the word “variables”.

One reasonable conclusion to draw is that, through the machinations of Analytical-Philosophy-Of-Language, the reach of mathematics can extend very, very far. How useful is stuff, anyhow? What if mathematics appeared in every declarative sentence you wrote or uttered?


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