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Reading some old logic texts (written around 1930) I noticed that these texts make no difference between propositional variables and terms.

They do make difference between identity and truthvalue but for the rest they are just treated the same.

(p = q) -> ( p <-> q) ( if p is identical to p then p and q have the same truthvalue, equivalent) is a wellformed formula.

When did logicians start to differentiate between terms and propositional variables?

and more important why?

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    $\begingroup$ I think with the introductions of computers. Then they started to talk about grammer (for instance BNF), and then you have to be more precise. $\endgroup$ – Lucas K. Dec 30 '13 at 19:18
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    $\begingroup$ I am pretty sure syntax as an object of study came a little earlier than computers... $\endgroup$ – Andrej Bauer Dec 31 '13 at 23:42
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Your question simply concerns the difference between first-order logic (where the distinction is maintained) and second-order logic / higher-order logic, where propositional variables are indeed simply variables, and therefore terms.

Early work (Frege's Begriffschrift, Whitehead and Russell's Principia Mathematica) used stronger logics, while first-order logic was isolated later. FOL is no "better" than those stronger systems, and indeed higher-order logics are generally preferred for interactive theorem proving.

More discussion here.

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