Template:LEM

Include this template at (or near) the bottom of any page in the field of propositional logic which depends, either directly or indirectly, on the Law of the Excluded Middle (LEM).

Usage
This template can be invoked as:



or:



where  is the ProofWiki page name of a proof which itself depends on the LEM.

If you want this to apply to just one of the proofs of a given theorem, then there exists an optional second parameter which is a number (usually 3 or 4) determining the level of heading that the text of this template appears at. The default is 2 (standard heading) when the template itself is used so as to apply to the entire page.

Note: The current implementation is that only level 4 is available in this context.

Inclusion of this template will result in the page being added to the Law of Excluded Middle category, and the following being added to the page:

Law of the Excluded Middle
This theorem depends on the Law of the Excluded Middle, by way of (link to proof name).

This is one of the axioms of logic that was determined by Aristotle, and forms part of the backbone of classical (Aristotelian) logic.

However, the intuitionist school rejects the Law of the Excluded Middle as a valid logical axiom. This in turn invalidates this from the system of intuitionist propositional calculus.

This depends on the Law of the Excluded Middle.

This is one of the axioms of logic that was determined by Aristotle, and forms part of the backbone of classical (Aristotelian) logic.

However, the intuitionist school rejects the Law of the Excluded Middle as a valid logical axiom. This in turn invalidates this from the system of intuitionist propositional calculus.