Quantity

[TODO under construction]

"Quantity" is a concept identifying an irreducible primary attribute of existents, and therefore it admits only an ostensive definition.

When one says that there is more or as much or less of A than there is of B, he is comparing the quantity of A to the quantity of B.

When one talks about adding to or subtracting from A, he is talking about a change in the quantity of A.

Quantity is perhaps the most fundamental concept of math. Other concepts almost as fundamental are shape and likelihood and identity and set.

We observe that quantity comes in two forms: multitudes and magnitudes. A quantity is said to be a multitude, when there is some restriction on how it could be divided into parts. A quantity is said to be a magnitude, when there is no restriction on how it could be divided into parts. In Objective Mathematics, the notion of a "continuous quantity" is used interchangeably with magnitude, and the notion of "discrete quantity" is used interchangeably with multitude.

"Few" and "many" describe multitudes; "less" and "more" describe magnitudes.

Number is the basically the same concept as quantity. There is, however, a difference in emphasis between these two concepts. Quantity emphasizes the existence part, number emphasizes the consciousness part. Animals can perceive quantity, but only humans can perceive number.

Harry's definition of number: "an identification of a quantity by means of a symbol whose position in a fixed sequence of those symbols is the same amount as what you are identifying."

Discrete quantities are measured by natural numbers. Continuous quantities are measured by fractional numbers. [TODO that's not exactly right. Like what about like differences, or ${\sqrt {2}}$? Don't both of those things also measure quantity?]

Examples

Discrete quantities

The number of apples in the grocery store is a discrete quantity. Although...

The number of oxygen atoms in a room

The size, in bits, of some file on some computer

The number of ingredients in a recipe

The price of a washing machine

Continuous quantities

The height of a man

The speed of a car

The volume of a swimming pool

The weight of a bag of rice

The distance to the sun