Re: Antonelli’s Logicism

[Noah Schweber]

>Is choice really necessary? Suppose I make A and B disjoint by tagging
their elements to get A’ and >B’, and define C = anything that is A’ or B’,
and say H(A,B) iff neither “most C are A’ “ nor “most C >are B’ “ ?

>Why doesn’t that get the Hartig quantifier?

Without choice we might not be able to compare the sizes of the sets
involved: if neither A nor B admits an injection into the other, then "most
C are A' " and "most C are B' " will both read as false.

Of course if we replace "<" ("there is an injection one way but not the
other way") in the Reschler quantifier with "<=" ("there is an injection
one way") then everything works nicely even without choice.




 - Noah
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