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Single Idea 9926

[filed under theme 5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic ]

Full Idea

While in general a relation is taken to be a set of ordered pairs <u, v> = {{u}, {u, v}}, and hence a set of sets of sets, in special cases a relation can be represented by a set of sets.

Gist of Idea

A relation is either a set of sets of sets, or a set of sets

Source

JP Burgess / G Rosen (A Subject with No Object [1997], II.C.1.a)

Book Ref

Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.150

A Reaction

[See book for their examples, which are <, symmetric, and arbitrary] The fact that a relation (or anything else) can be represented in a certain way should never ever be taken to mean that you now know what the thing IS.

The 15 ideas from 'A Subject with No Object'

9918 Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen]
9919 The old debate classified representations as abstract, not entities [Burgess/Rosen]
9921 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen]
9922 If space is really just a force-field, then it is a physical entity [Burgess/Rosen]
9923 We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
9924 Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
9925 Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
9926 A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
9928 Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen]
9927 Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen]
9929 Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen]
9930 Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen]
9933 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
9932 The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
9934 Number words became nouns around the time of Plato [Burgess/Rosen]