Quantity: Difference between revisions
mNo edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
'''Quantity''' is an irreducible attribute of existents, and therefore it admits only an ostensive definition. | '''Quantity''' is an irreducible attribute of existents, and therefore it admits only an ostensive definition. | ||
When one says | 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. | When one talks about ''adding to'' or ''subtracting from'' A, he is talking about a change in the quantity of A. | ||
| Line 9: | Line 9: | ||
Quantity is the most fundamental concept of math. Other concepts almost as fundamental are [[shape]] and [[likelihood]] [TODO really? think about it]. | Quantity is the most fundamental concept of math. Other concepts almost as fundamental are [[shape]] and [[likelihood]] [TODO really? think about it]. | ||
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.<ref>[TODO I got these from Aristotle, ''Metaphysics'', Book V, Ch. 11-14 ]</ref> 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. | 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.<ref>[TODO I got these from Aristotle, ''Metaphysics'', Book V, Ch. 11-14 ]</ref> 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 concept which measures quantity. | Number is the concept which measures quantity. | ||
Discrete quantities are measured by [[natural numbers]]. Continuous quantities are measured by [[Fractions|fractional numbers]]. [ | Discrete quantities are measured by [[natural numbers]]. Continuous quantities are measured by [[Fractions|fractional numbers]]. [TODO that's not exactly right. Like what about like differences, or <math>\sqrt{2}</math>? Don't both of those things also measure quantity?] | ||
== Examples == | == Examples == | ||
Revision as of 00:46, 22 January 2024
[TODO under construction]
Quantity is an irreducible 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 the most fundamental concept of math. Other concepts almost as fundamental are shape and likelihood [TODO really? think about it].
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.[1] 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 concept which measures quantity.
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 ? 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
References
- ↑ [TODO I got these from Aristotle, Metaphysics, Book V, Ch. 11-14 ]