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I'm currently reading Ludwig Wittgenstein's posthumous Remarks on the Foundations of Mathematics, and one example he keeps using is the logical inference of 'fa' from '(x).fx'

What does this inference mean, or rather what does the notation '(x).fx' indicate?

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up vote 4 down vote accepted

You might look here:

"(x). fx = logical product[9] (of all propositions of the form fx) fa.fb.fc…"

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His notation $(x).fx$ would today usually be written $\forall x\colon f(x)$. If something holds for all $x$, then it also holds for a specific object $a$, i.e. we can infer $f(a)$ from $\forall x\colon f(x)$.

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