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Single Idea 8918

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

On Frege's suggestion, functional terms that pick out abstract expressions (such as 'direction' or 'equinumeral') have a typical form of f(a) = f(b) iff aRb, where R is an equivalence relation, a relation which is reflexive, symmetric and transitive.

Gist of Idea

Functional terms can pick out abstractions by asserting an equivalence relation

Source

Gideon Rosen (Abstract Objects [2001], 'Way of Abs')

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7

A Reaction

[Wright and Hale are credited with the details] This has become the modern orthodoxy among the logically-minded. Examples of R are 'parallel' or 'just as many as'. It picks out an 'aspect', which isn't far from the old view.

The 29 ideas from Gideon Rosen

8912 Nowadays abstractions are defined as non-spatial, causally inert things [Rosen]
8913 Chess may be abstract, but it has existed in specific space and time [Rosen]
8914 Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen]
8918 Functional terms can pick out abstractions by asserting an equivalence relation [Rosen]
8919 Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen]
8917 The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]
8916 Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
8915 How we refer to abstractions is much less clear than how we refer to other things [Rosen]
18849 Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
18850 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
18852 A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
18851 Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
18853 A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
18854 The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]
18855 Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
18857 Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
18856 Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
18858 Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
14092 Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen]
14093 An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen]
14094 The excellent notion of metaphysical 'necessity' cannot be defined [Rosen]
14095 Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen]
14096 Explanations fail to be monotonic [Rosen]
14097 Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen]
14100 Figuring in the definition of a thing doesn't make it a part of that thing [Rosen]
14098 An acid is just a proton donor [Rosen]
14099 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen]
14101 Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen]