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Single Idea 8467
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
]
Full Idea
Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit
Gist of Idea
Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit'
Source
report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3
Book Ref
Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.57
A Reaction
(See Idea 8454 for the categories of numbers). This is a problem for Dummett.
Related Idea
Idea 8454
The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
The
29 ideas
from 'works'
13736
|
Quinean metaphysics just lists the beings, which is a domain with no internal structure
[Schaffer,J on Quine]
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3302
|
Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic
[Quine, by Benardete,JA]
|
10211
|
Quine wants V = L for a cleaner theory, despite the scepticism of most theorists
[Quine, by Shapiro]
|
3336
|
Two things can never entail three things
[Quine, by Benardete,JA]
|
8453
|
If we had to name objects to make existence claims, we couldn't discuss all the real numbers
[Quine]
|
10311
|
No sense can be made of quantification into opaque contexts
[Quine, by Hale]
|
10538
|
Finite quantification can be eliminated in favour of disjunction and conjunction
[Quine, by Dummett]
|
10793
|
Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal
[Quine, by Marcus (Barcan)]
|
8466
|
For Quine, intuitionist ontology is inadequate for classical mathematics
[Quine, by Orenstein]
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8467
|
Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit'
[Quine, by Orenstein]
|
10667
|
A logically perfect language could express all truths, so all truths must be logically expressible
[Quine, by Hossack]
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3325
|
For Quine everything exists theoretically, as reference, predication and quantification
[Quine, by Benardete,JA]
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16021
|
Quine says we can expand predicates easily (ideology), but not names (ontology)
[Quine, by Noonan]
|
8534
|
Quine says the predicate of a true statement has no ontological implications
[Quine, by Armstrong]
|
10295
|
Quine suggests that properties can be replaced with extensional entities like sets
[Quine, by Shapiro]
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3322
|
Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic
[Quine, by Benardete,JA]
|
6078
|
Quine brought classes into semantics to get rid of properties
[Quine, by McGinn]
|
8479
|
Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things'
[Quine, by Orenstein]
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3751
|
Universals are acceptable if they are needed to make an accepted theory true
[Quine, by Jacquette]
|
4712
|
Quine says there is no matter of fact about reference - it is 'inscrutable'
[Quine, by O'Grady]
|
15783
|
Definite descriptions can't unambiguously pick out an object which doesn't exist
[Lycan on Quine]
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4713
|
For Quine, theories are instruments used to make predictions about observations
[Quine, by O'Grady]
|
15782
|
Quine wants identity and individuation-conditions for possibilia
[Quine, by Lycan]
|
2796
|
For Quine the only way to know a necessity is empirically
[Quine, by Dancy,J]
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8450
|
Quine's empiricism is based on whole theoretical systems, not on single mental events
[Quine, by Orenstein]
|
3868
|
To proclaim cultural relativism is to thereby rise above it
[Quine, by Newton-Smith]
|
7330
|
The principle of charity only applies to the logical constants
[Quine, by Miller,A]
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17862
|
Essence gives an illusion of understanding
[Quine, by Almog]
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7970
|
Quine is committed to sets, but is more a Class Nominalist than a Platonist
[Quine, by Macdonald,C]
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