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

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.