Multitude

# Multitude

Commens
Digital Companion to C. S. Peirce
Multitude
1897 | Multitude and Number | CP 4.175

I shall use the word multitude to denote that character of a collection by virtue of which it is greater than some collections and less than others, provided the collection is discrete, that is, provided the constituent units of the collection are or may be distinct. But when the units lose their individual identity because the collection exceeds every positive existence of the universe, the word multitude ceases to be applicable. I will take the word multiplicity to mean the greatness of any collection discrete or continuous.

1902 | Multitude (in mathematics) | DPP 2:117; CP 3.626

Multitude (in mathematics) [Lat. multitudo]: Ger. Mächtigkeit, Cardinalzahl; Fr. puissance; Ital. moltitudine. That relative character of a collection which makes it greater than some collections and less than others. A collection, say that of the A’s, is greater than another, say that of the B’s, if, and only if, it is impossible that there should be any relation r, such that every A stands in the relation r to a B to which no other A is in the relation r.

1903 | Lowell Lectures. 1903. Lecture 3 | MS [R] 459:16

I shall always use the word multitude to mean the degree of maniness of a collection.

1903 | Lowell Lectures of 1903. Lecture III. 2nd Draught | MS [R] 463:11

By multitude I mean that quality of a collection by virtue of which it is greater than all those collections than which it is greater.

1903 [c.] | The Theory of Multitude | MS [R] 24:1

Multitude is that character of a collection by virtue of which it is more than another collection and less than a third.