This is noticed by Makinson (1966a) who argues that what must be done is reinstate substitutivity and revise Carnap's naïve notion of validity (as logical necessity) in favor of a schematic Quinean notion ("A logical truth … is definable as a sentence from which we get only truths when we substitute sentences for its simple sentences" Quine 1970, 50) that will not make sentences like ◊p valid.
That is, it stands for the set of all sentences that are obtained from the above expression by substituting sentences of LT for the Greek letters φ and ψ.
Maybe it is time to substitute the sentence "sequence determines structure" with the sentence "unfolded structure determines folded structure".
The knowability principle, ∀p(p → ◊Kp), apparently allows us to substitute any sentence whatsoever for p. But notice that our quantifier has wide scope relative to ◊.
If, instead of basic SpellCheck or automatic initial caps, Microsoft Word was to substitute whole sentences and proposed conflicts and emotional denouements in your letter to Con Edison demanding that it explain a six-hundred dollar charge, you would cue the music from "2001: A Space Odyssey" and take a machete to your MacBook.
The description of logical constructions as "incomplete symbols" derives from the use of contextual definitions that provide an analysis or substitute for each sentence in which a defined symbol may occur.
That was immediately obvious to anyone who read his March 2014 GQ profile, in which he used "hashtag winning" as the substitute for a sentence and implied to a reporter that he was getting laid so much that one could use the word "Boob-er" to describe his lifestyle.
That was immediately obvious to anyone who read his March 2014 GQ profile, in which he used "hashtag winning" as the substitute for a sentence and implied to a reporter that he was getting laid so much that the company should be called "Boo-ber".
Beliefs and desires are intentional states: they have propositional content (one believes that p, one desires that p, where sentences substitute for "p" ).
Substitute "country" in that sentence, as in America, and it is every bit as true.
