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Single Idea 11041

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic ]

Full Idea

Of quantities, some are discrete, others continuous. ...Discrete are number and language; continuous are lines, surfaces, bodies, and also, besides these, time and place.

Gist of Idea

Some quantities are discrete, like number, and others continuous, like lines, time and space

Source

Aristotle (Categories [c.331 BCE], 04b20)

Book Ref

Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.12

A Reaction

This distinction seems to me to be extremely illuminating, when comparing natural numbers with real numbers, and it is the foundation of the Greek view of mathematics.

The 41 ideas from 'Categories'

13121 Substance,Quantity,Quality,Relation,Place,Time,Being-in-a-position,Having,Doing,Being affected [Aristotle, by Westerhoff]
11286 Primary being must be more than mere indeterminate ultimate subject of predication [Politis on Aristotle]
3311 The categories (substance, quality, quantity, relation, action, passion, place, time) peter out inconsequentially [Benardete,JA on Aristotle]
16116 Aristotle derived categories as answers to basic questions about nature, size, quality, location etc. [Aristotle, by Gill,ML]
16155 Aristotle promoted the importance of properties and objects (rather than general and particular) [Aristotle, by Frede,M]
16154 Aristotle gave up his earlier notion of individuals, because it relied on universals [Aristotle, by Frede,M]
16091 Is primary substance just an ultimate subject, or some aspect of a complex body? [Aristotle, by Gill,ML]
11280 Primary being is 'that which lies under', or 'particular substance' [Aristotle, by Politis]
16140 Secondary substances do have subjects, so they are not ultimate in the ontology [Aristotle, by Frede,M]
10965 In earlier Aristotle the substances were particulars, not kinds [Aristotle, by Lawson-Tancred]
12361 Primary substances are ontological in 'Categories', and explanatory in 'Metaphysics' [Aristotle, by Wedin]
3315 Aristotle denigrates the category of relation, but for modern absolutists self-relation is basic [Benardete,JA on Aristotle]
12349 Only what can be said of many things is a predicable [Aristotle, by Wedin]
8287 Earlier Aristotle had objects as primary substances, but later he switched to substantial form [Aristotle, by Lowe]
21345 Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil]
11032 Some things said 'of' a subject are not 'in' the subject [Aristotle]
11033 Predications of predicates are predications of their subjects [Aristotle]
11034 The differentiae of genera which are different are themselves different in kind [Aristotle]
11035 There are ten basic categories for thinking about things [Aristotle]
11036 A 'primary' substance is in each subject, with species or genera as 'secondary' substances [Aristotle]
11037 Colour must be in an individual body, or it is not embodied [Aristotle]
11038 We call them secondary 'substances' because they reveal the primary substances [Aristotle]
12351 Genus and species are substances, because only they reveal the primary substance [Aristotle, by Wedin]
12350 Things are called 'substances' because they are subjects for everything else [Aristotle]
11039 A primary substance reveals a 'this', which is an individual unit [Aristotle]
11837 Some predicates signify qualification of a substance, others the substance itself [Aristotle]
1694 Substances have no opposites, and don't come in degrees (including if the substance is a man) [Aristotle]
11040 A single substance can receive contrary properties [Aristotle]
11041 Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle]
11042 Parts of a line join at a point, so it is continuous [Aristotle]
1695 Without extensive examination firm statements are hard, but studying the difficulties is profitable [Aristotle]
11043 It is not possible for fire to be cold or snow black [Aristotle]
1696 Change goes from possession to loss (as in baldness), but not the other way round [Aristotle]
1697 The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle]
1698 Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle]
11044 One is prior to two, because its existence is implied by two [Aristotle]
1699 A thing is prior to another if it implies its existence [Aristotle]
18366 Of interdependent things, the prior one causes the other's existence [Aristotle]
18367 A true existence statement has its truth caused by the existence of the thing [Aristotle]
1700 There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place [Aristotle]
16739 Four species of quality: states, capacities, affects, and forms [Aristotle, by Pasnau]