structure for 'Theory of Logic'    |     alphabetical list of themes    |     expand these ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

[propositions must be either true or false]

24 ideas
If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus]
A prayer is a sentence which is neither true nor false [Aristotle]
Everything is either asserted or denied truly [Aristotle]
Every proposition is either true or false [Chrysippus ,by Cicero]
Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero]
You would cripple mathematics if you denied Excluded Middle [Hilbert]
Questions wouldn't lead anywhere without the law of excluded middle [Russell]
For intuitionists excluded middle is an outdated historical convention [Brouwer]
Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI]
The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
Excluded middle has three different definitions [Quine]
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
The law of excluded middle is the logical reflection of the principle of bivalence [Dummett]
Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett ,by Miller,A]
The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen]
Excluded Middle, and classical logic, may fail for vague predicates [Fine,K]
The law of excluded middle might be seen as a principle of omniscience [Shapiro]
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
If a proposition is false, then its negation is true [Brown,JR]
Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
Mathematical proof by contradiction needs the law of excluded middle [Lavine]
The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend]
Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer]
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]