"The
Problem of Absolute Universality"
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Abstract:
Quantifiers in natural language and in logic may be restricted
or unrestricted. In the latter case, reflection can introduce an
implicit restriction at the metalevel. But it seems that some
generalizations are absolutely unrestricted, their scope is "absolutely
everything".
Whether we can take such generalizations at face value has been a
matter of debate. I argue that it implies metaphysical realism in
Hilary Putnam's sense. I lay out the logical difficulties coming from
familiar paradoxes that the idea of such quantification gives rise to.
I conclude that one should not take absolute quantification as just a
special case of ordinary quantification and attempt to say what sense
generalizations have that seem to require being understood in that way.