/sci/ - Science & Math

I dunno' what most maths people might say, but I like Whitehead, so
>When Whitehead and Russell logicized the concept of number, their starting point was our intuition of equinumerous classes of individuals—for example, our recognition that the class of dwarfs in the fairy tale of Snow White (Doc, Grumpy, Happy, Sleepy, Bashful, Sneezy, Dopey) and the class of days in a week (from Monday to Sunday) have ‘something’ in common, namely, the something we call ‘seven.’ Then they logically defined (i) classes C and C to be equinumerous when there is a one-to-one relation that correlates each of the members of C with one member of C, and (ii) the number of a class C as the class of all the classes that are equinumerous with C.

>When Whitehead logicized the space of physics, his starting point was our intuition of spatial volumes and of how one volume may contain (or extend over) another, giving rise to the (mereo)logical relation of containment (or extension) in the class of volumes, and to the concept of converging series of volumes—think, for example, of a series of Russian dolls, one contained in the other, but idealized to ever smaller dolls. Whitehead made all this rigorous and then, crudely put, defined the points from which to further construct the geometry of space.