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I am reading a book called 'A book of Set Theory by Charles C.Pinter'.

There is a sentence which I find confusing. It goes like this.

" We will use letters P,Q,R,S to denote sentences(a sentence is a statement which is unambiguously true or false); used in this sense, P, for instance, is to be understood as asserting that "P is true." "

Does this mean that we always assume that P is true or does this mean that we argue that P is true and we will show that such argument(that P is true) is true or false?

Andrés E. Caicedo
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Jin
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1 Answers1

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This sentence simply says that whenever we say "P", then it is a shorthand for saying that P is true.

For example: if we have the statement "exists a white sheep", then whenever we say "exists a white sheep" we actually mean "the statement that says that 'exists a white sheep' is true".

This is actually how we use statements when talking: we don't say, "the statement that 'most cows have four legs' is true", we say "most cows have four legs". In set theory, this is not how sentences are necessarily used, so the author just pointed out that that is how he will use sentences in this case.

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