What is the meaning of ⊢ in the context of ⊢(P->Q) versus in the context of (P ⊢ Q)
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$\vdash$ is not a connective. It means taht the formula $(P \to Q)$ is derivable in the propositional calculus. – Mauro ALLEGRANZA Feb 26 '19 at 19:41
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@MauroALLEGRANZA I don't see an answer to this specific question there. Did I miss something? – Bill Dubuque Feb 26 '19 at 20:12
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1Duplicate of Notation Question: What does ⊢ mean in logic? – Mauro ALLEGRANZA Feb 27 '19 at 07:08
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Possible duplicate of Notation Question: What does $\vdash$ mean in logic? – Bill Dubuque Feb 27 '19 at 15:04
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The turnstile $\vdash$ means that what is on the right is provable (in some proof system) from what is on the left. So $\vdash P\rightarrow Q$ means that the conditional proposition $P\rightarrow Q$ is provable from nothing, i.e. is a tautology. On the other hand, $P\vdash Q$ means that $Q$ is provable given $P$ as a premise.
Francis Adams
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