PHIL 6510 Semantics

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8 Terms

1
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|= P

  • truth-functionally true

  • iff a sentence P is true on every TVA

2
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P |=

  • truth-functionally false

  • iff a sentence P is false on every TVA

3
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truth-functionally indeterminant

iff a sentence P has been true and false on some TVAs

4
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P =||= Q

  • truth-functionally equivalent

  • iff sentences P and Q have the same truth value on every TVA

5
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Γ |≠

  • truth-functionally consistent

  • iff there is a TVA where all members of the set of sentences Γ are true

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Γ |=

  • truth-functionally inconsistent

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Γ |= P

  • truth-functionally entails

  • iff there’s no TVA on which every member of Γ is true and P is false

8
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truth-functionally valid

an argument of SL iff there’s no TVA on which all its premises are true and the conclusion is false