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Single Idea 8466
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
]
Full Idea
Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics.
Gist of Idea
For Quine, intuitionist ontology is inadequate for classical mathematics
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
Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism.
The
29 ideas
from 'works'
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13736
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Quinean metaphysics just lists the beings, which is a domain with no internal structure
[Schaffer,J on Quine]
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3302
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Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic
[Quine, by Benardete,JA]
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10211
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Quine wants V = L for a cleaner theory, despite the scepticism of most theorists
[Quine, by Shapiro]
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3336
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Two things can never entail three things
[Quine, by Benardete,JA]
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8453
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If we had to name objects to make existence claims, we couldn't discuss all the real numbers
[Quine]
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10311
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No sense can be made of quantification into opaque contexts
[Quine, by Hale]
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10538
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Finite quantification can be eliminated in favour of disjunction and conjunction
[Quine, by Dummett]
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10793
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Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal
[Quine, by Marcus (Barcan)]
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8466
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For Quine, intuitionist ontology is inadequate for classical mathematics
[Quine, by Orenstein]
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8467
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Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit'
[Quine, by Orenstein]
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4712
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Quine says there is no matter of fact about reference - it is 'inscrutable'
[Quine, by O'Grady]
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10667
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A logically perfect language could express all truths, so all truths must be logically expressible
[Quine, by Hossack]
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3325
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For Quine everything exists theoretically, as reference, predication and quantification
[Quine, by Benardete,JA]
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16021
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Quine says we can expand predicates easily (ideology), but not names (ontology)
[Quine, by Noonan]
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8534
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Quine says the predicate of a true statement has no ontological implications
[Quine, by Armstrong]
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10295
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Quine suggests that properties can be replaced with extensional entities like sets
[Quine, by Shapiro]
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3322
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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]
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6078
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Quine brought classes into semantics to get rid of properties
[Quine, by McGinn]
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8479
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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
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Universals are acceptable if they are needed to make an accepted theory true
[Quine, by Jacquette]
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15783
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Definite descriptions can't unambiguously pick out an object which doesn't exist
[Lycan on Quine]
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15782
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Quine wants identity and individuation-conditions for possibilia
[Quine, by Lycan]
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2796
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For Quine the only way to know a necessity is empirically
[Quine, by Dancy,J]
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8450
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Quine's empiricism is based on whole theoretical systems, not on single mental events
[Quine, by Orenstein]
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3868
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To proclaim cultural relativism is to thereby rise above it
[Quine, by Newton-Smith]
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4713
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For Quine, theories are instruments used to make predictions about observations
[Quine, by O'Grady]
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7330
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The principle of charity only applies to the logical constants
[Quine, by Miller,A]
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17862
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Essence gives an illusion of understanding
[Quine, by Almog]
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7970
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Quine is committed to sets, but is more a Class Nominalist than a Platonist
[Quine, by Macdonald,C]
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