[FOM] Origins of the double turnstile

WILLIAM TAIT williamtait at mac.com
Sat Jan 7 09:25:13 EST 2017

It is indeed listed in the “forward on terminology” in *Theory of Models: Proceedings of the 1963 InternationalSymposium at Berkeley* (1965) and, as Richard suggested, that seems to indicate a prior usage. But I looked (roughly) through the proceedings of the Summer Institute for Symbolic Logic (Cornell. 1957) and couldn’t find that notation. Feferman used the notation \vdash_{M} A to mean the sentence A is true in the structure M. Roger Lyndon (*Notes on Logic* 1967) used A \v= B with sentences A and B to mean that B is true when A is. 


> On Jan 6, 2017, at 11:47 AM, Christopher Menzel <cmenzel at tamu.edu> wrote:
> FOM folk,
> The turnstile (\vdash) is typically traced back to Frege and was picked up by Whitehead and Russell, who used it more or less to indicate provability, and of course this largely continues to the present day. But whence the double turnstile (\models) to indicate logical consequence? I thought perhaps I'd find it in Carnap or, at least, in Kemeny's famous 1956 JSL articles, but it's not there; they just adopt ordinary language expressions to indicate semantic relations. From the very limited bit of searching I've done, the double turnstile appears to be of fairly recent vintage. Does anyone know its origins or, at least, can anyone point to an earlyish (even pre-1960) use of the notation?
> Thanks.
> Chris Menzel
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