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Single Idea 8788
[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
]
Full Idea
It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other.
Gist of Idea
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
Source
B Hale / C Wright (Logicism in the 21st Century [2007], 8)
Book Ref
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.196
A Reaction
It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading.
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
|
Objects just are what singular terms refer to
[Hale/Wright]
|
10630
|
Abstracted objects are not mental creations, but depend on equivalence between given entities
[Hale/Wright]
|
10631
|
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
|
Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
[Hale/Wright]
|
10629
|
If structures are relative, this undermines truth-value and objectivity
[Hale/Wright]
|
10628
|
The structural view of numbers doesn't fit their usage outside arithmetical contexts
[Hale/Wright]
|
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]
|
8783
|
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
[Hale/Wright]
|
8787
|
The Julius Caesar problem asks for a criterion for the concept of a 'number'
[Hale/Wright]
|
8788
|
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
[Hale/Wright]
|
12223
|
It is a fallacy to explain the obscure with the even more obscure
[Hale/Wright]
|
12224
|
Are neo-Fregeans 'maximalists' - that everything which can exist does exist?
[Hale/Wright]
|
12225
|
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
[Hale/Wright]
|
12226
|
The identity of Pegasus with Pegasus may be true, despite the non-existence
[Hale/Wright]
|
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]
|
18443
|
A successful predicate guarantees the existence of a property - the way of being it expresses
[Hale/Wright]
|
12230
|
Singular terms refer if they make certain atomic statements true
[Hale/Wright]
|