If the language under discussion (the object language
) is L, then the definition should be given in another language known as the metalanguage, call it M.
For Carnap, a semantical system is "a system of rules, formulated in a metalanguage and referring to an object language
, of such a kind that the rules determine a truth-condition for every sentence of the object language
" (Carnap, 1942: 22).
The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical relations in the object language
, but the stipulation of conceptual possibilities.
Cohen well illustrates the issue of conflation of the categories in the object language
(Akkadian) and the metalanguage (English) in discussing the (seemingly) different shades of iprus vs.
As a matter of logic, the task of explaining such things as physics, the possibility of physics, and the relationship of physics to the physical universe requires a metalanguage of physics, a higher-order language in which the "object language
" of physics can be an object of reference.
Hence, the way out from the Liar paradox originally proposed by Tarski, explained in  (to exclude semantic predicates from the object language
), and refined by Kripke  (to define a nonstrict metalanguage hierarchy that allows nonparadoxical uses of semantic predicates in the object language
) does not work here.
(a) [ [??]"p" is true[??]] must be regarded as misleading and excluded from formulation in "a correct ideography" [the ideal object language
of the Tractatus].
I begin with a theoretical preamble to my discussion: metalanguage is a language used to make statements about statements in another language (object language
To clarify further, we can use the following often-cited example from Alfred Tarski: "The sentence 'snow is white' is true if, and only if, snow is white." (4) The sentence "'snow is white'" is part of what Tarski calls the object language
, whereas "snow is white" is part of the meta-language.
when the term [b.sup.M] [a metalinguistic equivalent of the object language
empty singular term 'b'] fails to refer.
ways to make the metalanguage [language used to describe the lexical items] less rich, rather than as rich as, or richer than, the object language