Jagmeet Sahota

Senior Project Advisor

Christian Lee

Document Type


Publication Date

Spring 2023


Double negation, law of the excluded middle, logic, law of non-contradiction, not not, indeterminacy, vagueness


According to the law of the excluded middle (hereafter ‘LEM’) any sentence of the form ‘p or not p’ is logically true. In other words, no matter how the work is like in itself, any sentence of this form must be true. Yet the truth of this theorem remains highly controversial. For it appears to be subject to counterexamples. On the other hand, according to the law of non-contradiction, no sentence of the form ‘p and not p’ is true. The law of non-contradiction is an uncontroversial theorem in logic. Yet a simple proof allows us to derive the former from the latter using the rule of double negation. According to this rule, we can infer from not not p that p. The result is that the rule of double negation has been rejected in logical systems that reject LEM. Even with these rejections, double negation seems obviously true. In this paper I discuss the concepts of logic, LEM, double negation, and the law of non-contradiction. Following this are a few reasons for rejecting LEM and double negation with discussion of costs associated with rejecting both. The point of this paper is not to convince you of one side over the other, but rather to allow you to make that choice according to the presented material.






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