|Extensionality, philosophy: (also extensionality principle, extensionality thesis) an attempt to make the language distinct by taking complete sets of denoted objects as the meaning of the referring words. See also extensions, intensions, extensional language, ambiguity, propositional attitudes.|
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Extensionality: "Law of extensionality": if the sentences S1 and S2 have the same truth value, then, each composite sentence that differs only in that it has S1 as a subset , where the other has S2 as a subset, also the same truth value - PriorVs: one can count mixed constructions like "__is green and__" also "__believes that__" into the same category as the simple - if law of extensionality is true, then must "grass is pink" and "grass is purple" be the same thought: - solution: "x thinks, grass is pink" is not a compound sentence with "grass is pink" as a component.
Extensionality/Prior: Lesniewski/Lukasiewicz: if one drops the E, one must admit that some propositions are neither true nor false - PriorVsExtensionality: truth value of a statement depends not only on its truth value. (Circular)
Law of extensionality: propositions with the same truth value are identical.
Extensionality/Prior: "cause", "bring about" seems to be the most extensional operator: the one who brings p about, brings everything into existence ipso facto, what is equivalent with p - but it does not bring into existence what it contains (entailment, asymmetric implication ): E.g. someone is caught by the FBI and a communist, but that does not bring about, that he is a communist.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003