equinumerous love

# equinumerous

## Etymologies

Sorry, no etymologies found.

## Examples

• In the first example, we have two concepts that are equinumerous:

Frege's Logic, Theorem, and Foundations for Arithmetic

• The number of Fs is identical to the number of Gs if and only if F and G are equinumerous.

Frege's Logic, Theorem, and Foundations for Arithmetic

• Instead numbers were to be defined as classes of equinumerous classes.

Logical Constructions

• 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.

Logical Constructions

• 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.

Slices of Matisse

• 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.

Naturalism

• 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.

John Stuart Mill

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

The Universe of Discourse

• Oresme's proof is somewhat reminiscent of Georg Cantor's (1845 “ 1918) demonstration that certain infinite sets are equinumerous.

Nicole Oresme

• 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)

The Analytic/Synthetic Distinction