[FOM] Origins of the double turnstile

Christopher Menzel cmenzel at tamu.edu
Fri Jan 6 12:47:18 EST 2017

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?


Chris Menzel

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