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?