Lexicon of Arguments

 

X 71
Metalanguage/Set Theory/Quine: in the metalanguage a stronger set theory is possible than in the object language. In the metalanguage a set z is possible so that ERz applies - ((s) A set of that is the satisfaction relation (in the form of a set of ordered pairs) - not in the object language, otherwise >Grelling paradox.
>Set Theory/Quine, >Object Language/Quine.
X 61
Object Language/Metalanguage/Mention/Use/(s): the object language is mentioned (it is spoken about), the metalanguage is used to talk about the object language.
Object Language/Metalanguage/OS/MS/ordered pairs/Quine: if we define ordered pairs ('x,y': the set whose only elements are {{x},1} and {{y},2}.), this does not mean that in the object language the variables could also take sets or ordered pairs as values.
We use the ordered pairs only in metalanguage.
Metalanguage: is the everyday language in which we talk about logic.
For example, if I say that the pair '3.5' fulfills the sentence "x < y" then I temporarily assume that the sentence "x < y" belongs to the object langauge and that the numbers 3 and 5 belong to the subject area of the object language.
But I don't have to assume that the ordered pairs '3,5' belong to the object language. It is enough that it belongs to metalanguage, and it does.
Fulfillment/metalanguage/object language/Quine(s): what fulfills belongs to metalanguage, what is fulfilled to object language