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Single Idea 10405

[filed under theme 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets ]

Full Idea

In the iterative conception of sets, they form a natural hierarchy.

Clarification

In 'iteration', each one generates the next one

Gist of Idea

In the iterative conception of sets, they form a natural hierarchy

Source

Chris Swoyer (Properties [2000], 4.1)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.16

The 23 ideas from Chris Swoyer

14592 Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer]
14593 Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer]
14595 Can properties exemplify other properties? [Swoyer]
14594 Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer]
10399 If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer]
10400 Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer]
10401 The F and G of logic cover a huge range of natural language combinations [Swoyer]
10403 If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer]
10402 Various attempts are made to evade universals being wholly present in different places [Swoyer]
10404 Extreme empiricists can hardly explain anything [Swoyer]
10406 One might hope to reduce possible worlds to properties [Swoyer]
10405 In the iterative conception of sets, they form a natural hierarchy [Swoyer]
10407 Logical Form explains differing logical behaviour of similar sentences [Swoyer]
10410 Anti-realists can't explain different methods to measure distance [Swoyer]
10408 Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer]
10409 Research suggests that concepts rely on typical examples [Swoyer]
10412 If laws are mere regularities, they give no grounds for future prediction [Swoyer]
10411 Two properties can have one power, and one property can have two powers [Swoyer]
10413 The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer]
10416 Can properties have parts? [Swoyer]
10417 There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer]
10421 Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer]
10420 Maybe a proposition is just a property with all its places filled [Swoyer]