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I came across the following explanation for the context insensitivity of the language of propositiional logic (PL) on page 34 of The Laws of Truth by Nicholas Smith:

Because glossary entries pair sentence letters of PL with particular propositions, PL is not context sensitive. That is, every token of F (or any other sentence letter) represents the same proposition: the truth with which F is paired in the glossary. (If F was paired with the sentence type "your best friend is my worst enemy," then different tokens of F would, in general, express different propositions.)

  • I'm not sure I see how pairing F with a sentence type would result in different tokens of F expressing different propositions. Could someone please provide an example that illustrates this?

    I wonder if Smith is referring to a scenario in which F represents a sentence type expressing some indexical claim, such as "I am hungry", and we form a compound proposition or argument that contains multiple tokens of F, such as F /∴ F, that are each produced by a different person, and therefore represent different propositions? (E.g. if Bob writes the first token of F and Carol writes the second, then the first token would stand for the claim "Bob is hungry", whereas the second would stand for the claim "Carol is hungry".)

  • The passage implies that if F were paired with a sentence type, then different tokens of F must represent different tokens of the sentence type. But why is this? Why can't the tokens of F simply refer to the sentence type itself?

  • What would happen if F were to be paired with the sentence token "your best friend is my worst enemy"? Would subsequent tokens of F be undefined?

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    Your example sentence in natural language is a sentence type in a usual default context free manner, unless understood to be uttered in a particular context. This is what your highlighted sentence really means. Once you completely understand this then you would understand if F were paired with a sentence type, then different tokens of F may represent different tokens of the said sentence type. And if F were to be paired with the sentence token "your best friend is my worst enemy", all subsequent tokens of F will be all the same proposition... Sep 19, 2023 at 6:03
  • I think the interpretation that the sentence type contains context-sensitive indexicals is correct. But context-sensitive terms do not have to be indexicals, vague terms, like "bright" or "tall" would also have to be specified by context to turn a type into a token. F cannot refer to a sentence type itself because it is a propositional constant, and sentence types do not express propositions, only tokens do. "Your best friend is my worst enemy" cannot be a sentence token for the same reason, it does not express a proposition until the indexicals are filled in.
    – Conifold
    Sep 19, 2023 at 7:15
  • It seems to me only a convoluted way to express the fact that classical propositional logic is truth functional. The examples are clear: the sentence "The earth is round" has a meaning and a truth value that is independent from the person uttering it (the context) while the sentence "My pen is red" is not. Sep 19, 2023 at 9:47
  • This is the gist of "If F was paired with the sentence type "your best friend is my worst enemy," then different tokens of F would, in general, express different propositions.)" It means that different utterances (token) of the same sentence (the type) are "context sensitive" because they depends of the context: my best friend is not your best friend. Sep 19, 2023 at 14:47

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