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Single Idea 18392

[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units ]

Full Idea

Classes, because they have a particular cardinality, are essentially a certain number of ones, things that, within the particular class, are each taken as a unit.

Gist of Idea

Classes have cardinalities, so their members must all be treated as units

Source

David M. Armstrong (Truth and Truthmakers [2004], 09.1)

Book Ref

Armstrong,D.M.: 'Truth and Truthmakers' [CUP 2004], p.114

A Reaction

[Singletons are exceptions] So units are basic to set theory, which is the foundations of technical analytic philosophy (as well as, for many, of mathematics). If you can't treat something as a unit, it won't go into set theory. Vagueness...

Related Idea

Idea 18396 The set theory brackets { } assert that the member is a unit [Armstrong]

The 31 ideas from 'Truth and Truthmakers'

18467 Truth-making can't be entailment, because truthmakers are portions of reality [Armstrong]
18468 Armstrong says truthmakers necessitate their truth, where 'necessitate' is a primitive relation [Armstrong, by MacBride]
18368 For all being, there is a potential proposition which expresses its existence and nature [Armstrong]
18370 A realm of abstract propositions is causally inert, so has no explanatory value [Armstrong]
18372 We need properties, as minimal truthmakers for the truths about objects [Armstrong]
18371 The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong]
18373 If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong]
18374 Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong]
18375 General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong]
18377 Negative truths have as truthmakers all states of affairs relevant to the truth [Armstrong]
18378 Length is a 'determinable' property, and one mile is one its 'determinates' [Armstrong]
18379 The determinates of a determinable must be incompatible with each other [Armstrong]
18380 Negative causations supervene on positive causations plus their laws? [Armstrong]
18381 Necessitating general truthmakers must also specify their limits [Armstrong]
18382 The nature of arctic animals is truthmaker for the absence of penguins there [Armstrong]
18384 One truthmaker will do for a contingent truth and for its contradictory [Armstrong]
18385 Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong]
18386 What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong]
18387 The truthmakers for possible unicorns are the elements in their combination [Armstrong]
18388 Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong]
18389 When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong]
18390 All metaphysical discussion should be guided by a quest for truthmakers [Armstrong]
18391 'Naturalism' says only the world of space-time exists [Armstrong]
18393 For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong]
18392 Classes have cardinalities, so their members must all be treated as units [Armstrong]
18394 In mathematics, truthmakers are possible instantiations of structures [Armstrong]
18396 The set theory brackets { } assert that the member is a unit [Armstrong]
18400 Properties are not powers - they just have powers [Armstrong]
18397 Powers must result in some non-powers, or there would only be potential without result [Armstrong]
18399 How does the power of gravity know the distance it acts over? [Armstrong]
18401 The pure present moment is too brief to be experienced [Armstrong]