Equinumerous

In the first example, we have two concepts that are equinumerous: ❋ Zalta, Edward N. (2009)

The number of Fs is identical to the number of Gs if and only if F and G are equinumerous. ❋ Zalta, Edward N. (2009)

Instead numbers were to be defined as classes of equinumerous classes. ❋ Linsky, Bernard (2009)

Examples he cited were the Frege/Russell definition of numbers as classes of equinumerous classes, the theory of definite descriptions, the construction of matter from sense data, and several others. ❋ Linsky, Bernard (2009)

For Bolzano, equipollence and “having exactly the same kind of construction” (die ganz gleiche Entstehungsart haben) are taken together as a sufficient condition for infinite sets being equinumerous or having the same cardinal number. ❋ Gerard Varni (2009)

Crispin Wright's ˜neo-Fregean™ programme shows how Peano's postulates can be derived within the framework of second-order logic from nothing except the Humean principle that the same number attaches to equinumerous concepts. ❋ Papineau, David (2007)

This brings him close to Frege's idea that the number of a given class is the class of all classes equinumerous to that given class. ❋ Wilson, Fred (2007)

In this problem, which has historically been presented as concerning "marriage", there are two disjoint equinumerous sets, which we may call "men" and "women". ❋ Unknown (2009)

Oresme's proof is somewhat reminiscent of Georg Cantor's (1845 “ 1918) demonstration that certain infinite sets are equinumerous. ❋ Kirschner, Stefan (2009)

If numbers are supposed to be identical if and only if the concepts they are numbers of are equinumerous, what guarantee do we have that every concept has a number? p253) ❋ Rey, Georges (2008)

(Compare the way that in set theory ˜equinumerous™ is antecedent to ❋ Smart, J. J. C. (2007)