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Single Idea 12227
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional.
Gist of Idea
Abstractionism needs existential commitment and uniform truth-conditions
Source
B Hale / C Wright (The Metaontology of Abstraction [2009], §5)
Book Ref
'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.188
A Reaction
They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent.
The
23 ideas
from B Hale / C Wright
10622
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The neo-Fregean is more optimistic than Frege about contextual definitions of numbers
[Hale/Wright]
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10624
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The incompletability of formal arithmetic reveals that logic also cannot be completely characterized
[Hale/Wright]
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10626
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Objects just are what singular terms refer to
[Hale/Wright]
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10630
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Abstracted objects are not mental creations, but depend on equivalence between given entities
[Hale/Wright]
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10631
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If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological
[Hale/Wright]
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10627
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Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
[Hale/Wright]
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10629
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If structures are relative, this undermines truth-value and objectivity
[Hale/Wright]
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10628
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The structural view of numbers doesn't fit their usage outside arithmetical contexts
[Hale/Wright]
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8784
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Neo-logicism founds arithmetic on Hume's Principle along with second-order logic
[Hale/Wright]
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8786
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One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines
[Hale/Wright]
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8783
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach
[Hale/Wright]
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8787
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The Julius Caesar problem asks for a criterion for the concept of a 'number'
[Hale/Wright]
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8788
|
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
[Hale/Wright]
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12223
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It is a fallacy to explain the obscure with the even more obscure
[Hale/Wright]
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12224
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Are neo-Fregeans 'maximalists' - that everything which can exist does exist?
[Hale/Wright]
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12225
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Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
[Hale/Wright]
|
12226
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The identity of Pegasus with Pegasus may be true, despite the non-existence
[Hale/Wright]
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12227
|
Abstractionism needs existential commitment and uniform truth-conditions
[Hale/Wright]
|
12228
|
Equivalence abstraction refers to objects otherwise beyond our grasp
[Hale/Wright]
|
12231
|
Reference needs truth as well as sense
[Hale/Wright]
|
12229
|
Maybe we have abundant properties for semantics, and sparse properties for ontology
[Hale/Wright]
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18443
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A successful predicate guarantees the existence of a property - the way of being it expresses
[Hale/Wright]
|
12230
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Singular terms refer if they make certain atomic statements true
[Hale/Wright]
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