Hi all,

Could anyone please explain what an excluded middle from the following derivation is?

Many thanks

ssharish

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- Oct 16th 2011, 12:25 PMssharishExcluded middle
Hi all,

Could anyone please explain what an excluded middle from the following derivation is?

Many thanks

ssharish

- Oct 16th 2011, 12:49 PMemakarovRe: Excluded middle
The excluded middle is an axiom schema $\displaystyle A\lor\neg A$. This means that A can be replaced by any formula to get an axiom. Equivalently, it is an inference rule with no assumptions.

- Oct 17th 2011, 01:18 AMemakarovRe: Excluded middle
I should add that the law of excluded middle is just a name for formulas of the form $\displaystyle A\lor\neg A$. It does not automatically mean that it has to be used as an axiom. In fact, in natural deduction it is usually derivable using the inference rule of double-negation elimination. Pure natural deduction does not have axioms.