[FOM] Origins of the double turnstile

Guillermo Badia guillebadia89 at gmail.com
Fri Jan 6 16:41:46 EST 2017

According to Hodges (Model Theory, p. 83), the notation goes back to the
foreword of "The theory of models" edited  by Henkin and Tarski in 1965.
Hope this is useful :-).


On Fri, Jan 6, 2017 at 6:47 PM, 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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