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Single Idea 10111
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
]
Full Idea
A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true.
Gist of Idea
Asserting Excluded Middle is a hallmark of realism about the natural world
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.91
A Reaction
Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism?
Related Idea
Idea 9024
Excluded middle has three different definitions [Quine]
The
28 ideas
with the same theme
[propositions must be either true or false]:
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1312
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If everything is and isn't then everything is true, and a midway between true and false makes everything false
[Aristotle on Heraclitus]
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1701
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A prayer is a sentence which is neither true nor false
[Aristotle]
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12363
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Everything is either asserted or denied truly
[Aristotle]
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21668
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Epicurus rejected excluded middle, because accepting it for events is fatalistic
[Epicurus, by Cicero]
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6023
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Every proposition is either true or false
[Chrysippus, by Cicero]
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2669
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Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem
[Cicero]
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21595
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Excluded middle is the maxim of definite understanding, but just produces contradictions
[Hegel]
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18844
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You would cripple mathematics if you denied Excluded Middle
[Hilbert]
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2947
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Questions wouldn't lead anywhere without the law of excluded middle
[Russell]
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21539
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Excluded middle can be stated psychologically, as denial of p implies assertion of not-p
[Russell]
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18944
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Russell's theories aim to preserve excluded middle (saying all sentences are T or F)
[Sawyer on Russell]
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15941
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For intuitionists excluded middle is an outdated historical convention
[Brouwer]
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9357
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Excluded middle is just our preference for a simplified dichotomy in experience
[Lewis,CI]
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19192
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The truth definition proves semantic contradiction and excluded middle laws (not the logic laws)
[Tarski]
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9024
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Excluded middle has three different definitions
[Quine]
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9195
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Intuitionists reject excluded middle, not for a third value, but for possibility of proof
[Dummett]
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8179
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The law of excluded middle is the logical reflection of the principle of bivalence
[Dummett]
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7334
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Anti-realism needs an intuitionist logic with no law of excluded middle
[Dummett, by Miller,A]
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17587
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The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false
[Inwagen]
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9775
|
Excluded Middle, and classical logic, may fail for vague predicates
[Fine,K]
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10251
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The law of excluded middle might be seen as a principle of omniscience
[Shapiro]
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8729
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects
[Shapiro]
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9605
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If a proposition is false, then its negation is true
[Brown,JR]
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21605
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Excluded Middle is 'A or not A' in the object language
[Williamson]
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10111
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Asserting Excluded Middle is a hallmark of realism about the natural world
[George/Velleman]
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15934
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Mathematical proof by contradiction needs the law of excluded middle
[Lavine]
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8709
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The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false
[Friend]
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17924
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Excluded middle says P or not-P; bivalence says P is either true or false
[Colyvan]
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