Adapted for the Internet from:

Why God Doesn't Exist


    Frege and Wittgenstein reduced the notion of object to anything they could identify with a variable.

    “ The expression ‘ƒ(x)’ denotes the object to which the function ƒ maps the
       object x.”  [1]

    “ the variable name ‘x’ is the proper sign of the pseudo-concept object. Wherever
       the word ‘object’ (‘thing’, ‘entity’, etc.) is rightly used, it is expressed in logical
       symbolism by the variable name…So one cannot, e.g., say ‘There are objects’ as
       one says ‘There are books’…”  [2]

    Hence, whether we talk about a chair or a table, we can simply call it x and then deal with the variable.
    However, their argument has to do with the name we assign an object and not with the object itself. The ‘variable’ they
    are referring to is a noun or a term (i.e., to anything that can be used as the subject of a sentence) and not strictly a
    corporeal body. They confirm that this is the meaning and context of their version of the word object when they apply
    it to specific examples:

    “ Frege called the object x the ‘argument’ of the function ƒ and called ƒ(x) the
       ‘value’ of the function. Since Frege also recognized two special objects he
       called truth-values (The True and The False), he defined a concept to be any
       function that always maps its arguments to truth-values. For example, whereas
       ‘x2 +3’ and ‘father-of(x)’ denote ordinary functions, the expressions ‘Happy(x)’
       and ‘x > 5’ denote concepts. The former denotes a concept which maps any
       object that is happy to The True and all other objects to The False; the latter
       denotes a concept that maps any object that is greater than 5 to The True and
       all other objects to The False. Given that concepts like being happy and being
       greater than 5 map their arguments to truth values, the atomic sentences of
       Frege's language, such as ‘Happy(b)’ and ‘4 > 5’, become names of truth-values.”  [3]

    “ The same holds of the words "Complex", "Fact", "Function", "Number", etc…
       They all signify formal concepts and are presented in logical symbolism by
       variables”  [4]

    Therefore, the arguments against this notion of object are the same I raised earlier. Wittgenstein concluded that for the
    purposes of grammar and logic, there is no difference between a noun and an object. I reply that for the purposes of
    Physics and Science, it does.
Frege says that a
variable is an object
Look, Red! All other matters aside, if you
can't tell the difference between your
grandma and a wolf, you've got more
than just a problem with your eyesight.


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