Stanford Abstract Objects
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What is it?
Stanford article on ways in which one might distinguish abstract from concrete objects.
Where can it be found?
Rosen, Gideon, “Abstract Objects”, The Stanford Encyclopedia of Philosophy (Spring 2006 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2006/entries/abstract-objects/>.
How does it fit in?
If I’m going to criticise C re: his mathematical objects possibly not being abstract, then it’d be a good idea to get a better idea of how that distinction can be made
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Summary
Background and History: - no standard account of distinction - states objects of pure mathematics are universally acknowledged to be abstract - uncertain what the phil. significance of distinction is - only really significant since 20th C. - notes that Plato’s forms were never supposed to be causally inert - Locke: abstract formed by omission of distinguishing detail — rejected by Berkeley and Hume - Frege significant in his positing of a “third realm” (outside of those of concrete objects and of ideas in the mind) for mathematical entities and thoughts (i.e. senses) — this third realm has come to be seen as the realm of the abstract Possible Methods of Distinction: - way of negation (following Frege): abstract is lacking certain features possessed of paradigmatic concrete objects — but in what way does Frege want abstract objects to be mind-independent, i.e. independent of the psychological realm? (for e.g. the game of chess is constructed by us (and hence is mind-dependent in some sense) but would seem to be abstract) — also, what about some for of theism? don’t want to rule that out by definition — additionally, Frege’s definition seems to imply that quarks and electrons are abstract, contrary to - non-spatiality: abstract objects are those that exist outside of time and space (or one or the other) — but does it make sense to claim this of something like the game of chess? — possible distinguish instead in terms of manner in which abstract objects occupy space? (e.g. do not seem to be extended) — claims that prob. dist. view of protons under quantum mechanics is a problem for this view — {[green but is it really, can’t one just add the spatial manifestation via probability distribution to the ways of spatial manifestation held to be characteristic of concrete objects? ]} — {[blue Yes. And anyway QM may well be non-probabilistic. ]} — problem re: impure sets as they seem to be extended in virtue of their members (given that they are concrete objects) — {[green are they really though? certainly they exist (using existence without ontological implication here) in space in some sense but are they really extended in any sense beyond that of their members? ]} - causal inefficacy: abstract objects can’t make stuff happen — in some sense thinking about abstract objects does seem to give them a causal role — and given difficulties in giving clear account of causation, hard to characterise distinctive ways in which abstract and concrete objects participate in the causal order - the way of e.g.: list paradigm cases and hope for the best — difficulties then in accounting for why distinction is of interest — especially in light of problems abstract objects pose in epistemology and phil. of language - conflation: actually just another metaphysical distinction that has been “mislabelled” — not widely held - abstraction: akin to Locke - considering several objects and then dropping distinguishing features — but how do we get from ideas to objects? — ~abstract objects as referents of abstract ideas as this is reliant upon an outdated phil. of mind — new Fregean possibility (due to Wright and Hale): - when we have f(a)=f(b) iff aRb, with R an equivalence relation, then f picks out an abstract entity — note: has special semantic status: RHS is semantically (and perhaps epistemologically) prior to the LHS
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What do I think?
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