Indirect Proof/Also defined as

Indirect Proof: Also defined as

In their handing of Indirect Proof, some sources do not spend much time on explaining the differences between what is defined here on $\mathsf{Pr} \infty \mathsf{fWiki}$ as:

Proof by Contradiction: Assume the truth of the proposition, derive a contradiction, and hence deduce that the proposition must be false.

Reductio ad Absurdum: Assume the negation of the proposition, derive a contradiction, and hence deduce that the proposition must have been true after all.

The former is accepted as a valid argument in general universally.

The latter requires the assumption of the Law of Excluded Middle.

The Law of Excluded Middle can be symbolised by the sequent:

$\vdash p \lor \neg p$

Also see

• Definition:Intuitionist School who reject that Law of Excluded Middle: that just because something is not false does not necessarily make it true.