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Why Can't We Quantify Wffs

  1. Dec 4, 2011 #1
    Why do we have to quantify over variables only -- why can't we quantify statements as well? Just out of curiosity... Does it lead to paradoxes or anything?
  2. jcsd
  3. Dec 4, 2011 #2
    I suppose you can quantify over statements if you like. Perhaps you are thinking of "second order logic."
  4. Dec 4, 2011 #3

    Stephen Tashi

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    Science Advisor

    If what you say is true than something would prevent us from using a variable that represented a statement and quantifying over that variable. I don't know what system of logic you are talking about. I suppose that systems of logic need some precautions against being "self referential". Is there a specific statement in the material you are studying that restricts what a variable can represent?
  5. Dec 8, 2011 #4
    In Logic, you may apply quantifiers over symbols that refer to other entities: first-order variables refer to individuals within a class; second-order variables (also known as predicate or class variables) refer to classes of individuals, and you may go on from here.

    Now, it is indeed known that unrestricted second-order quantification leads to inconsistencies (the most well-known is Russell's Paradox; look it up), but that is not exactly your problem: if by a statement you mean a closed expression (no free variables), then it is either true or false in any given interpretation; but what does this refer to? To what entities?
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