Intuitionism and the Law of Excluded Middle

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Essay Question: Evaluate the intuitionistic/antirealist reasons for rejecting the law of excluded middle.
The law of excluded middle was held by Aristotle and later echoed by Russell as one of three "Laws of Thought":

  1. "The law of Identity: Whatever is, is.
  2. The law of contradiction: Nothing can be and not be.
  3. The law of excluded middle: Everything must either be or not be."

In symbolic notation, the law of exluded middle says that "(P)V(¬P)" is true.

Dummett's Anti-Transcendence and Rejection of LEM


Dummett rejects the law of excluded middle following his anti-realist argument against transcendence and his identification of truth with assertibility.

Transcendence is the view that for some statements S, it is possible that S is true but we are unable to tell that S is true. Dummett proceeds to close the gap between truth and decidability.

    Dummett's argument against Transcendence:
  • Manifestation: For any S that we understand (know the meaning of), we can make manifest what we know to be its meaning.
  • Meaning: The meaning of S is constituted by its truth conditions.
  • :. For any S we understand, we can make manifest the truth conditions of S.
  • Decidability: We can make manifest S's truth conditions only if we could tell that those conditions were fulfilled if they were.
  • :. For any S we understand, if S is true we can tell that it is true. [AT or Anti-transendence]

This now requires a different view of truth, because no platonist view of truth will support anti-transendence.


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