Indirect Proof: Definition and Examples

Indirect Proof

Philosophy deals with many puzzling arguments and terms that may be difficult to comprehend. One of such terms is called indirect proof. Also referred to as reductio ad absurdum, this term means the argument that has been pushed to absurd extremes by using a logical sequence of ideas (Forman & Rash, 2015). This concept is interesting since it is based on the logic – the basis of reasoning and the main tool of discovering the truth. In this case, however, logic is tricky. A person using this approach begins with suggesting some hypothetical situations and then continues to remove uncertainties in each of these situations to force an inescapable conclusion (Reba & Shier, 2014). In this short essay, the author attempts to explain how this principle works and provides some examples to help readers understand the complex concept.

Indirect Proof Definition and History of the Term

Indirect proof is a unique mode of argument. It aims to demonstrate that something is right by showing that denying this truth would lead to absurdity. At the same time, it can be used for proving that a contention is incorrect by demonstrating that it inevitably leads to a ridiculous conclusion (Sedley, 2006). Indirect proof has three main steps. First, there is a statement that is assumed to be true. Second, there is a statement used to show a contradiction. Third, a negating statement is provided.

The term has a long history. It is believed that this approach was first applied by Greek philosophers, who are famous for their brilliant logical reasoning and argumentation. For instance, one of the ancient Greek thinkers applied reductio ad absurdum in his poem to demonstrate that attributing human characteristics to gods is incorrect. He proved it as follows. According to the philosopher, if animals could draw and had imagination, they would definitely draw gods with animal attributes. However, gods cannot possess both forms. Therefore, the belief that they have human features is also wrong (Osborne, 2004). It is one of the first indirect proof example logic.

Indirect Proof Practice

If one enters the “indirect proof khan academy” phrase in Google research, one may find many examples of reductio ad absurdum used in different spheres of knowledge. Let us look at some of them. For example, one may assume that sleeping is the best way of achieving the perfect health. However, it is definitely not true. If a person has a sleeping problem and sleeps days and nights for many months, he (she) is certainly not healthy. Therefore, the first statement is false. Consider another example: if you were scared to death, then you would probably be dead by now. Given the fact that you are alive, you cannot be that scared. One may make up hundreds of similar statements.

The reductio ad absurdum approach is so useful that it has been extensively used in many spheres of knowledge, from mathematics and logic to literature. It is used by mathematicians to prove mathematical theorems. It has been used by such writers as Jonathan Swift, Samuel Beckett, Plato, and others as a vivid literary tool to emphasize some statements. Indirect reasoning is also used in courts to prove that something is true or false. Briefly speaking, it may be useful in any logical reasoning. As seen, indirect proof is a universal tool that can be used both in science and everyday life to convince people. Try this approach next time you want to beat someone in an argument.


This is a sample of a philosophy essay that can be used as a reference only. If you need philosophy essay writing help, you can use our online writing services. Contact us as say “I need you to write my philosophy essay,” and we will do our best to create an excellent paper within the deadline.

Forman, S., & Rash, A. M. (2015). The whole truth about whole numbers: An elementary introduction to number theory. New York, NY: Springer.
Osborne, C. (2004). Presocratic philosophy: A very short introduction. Oxford: OUP Oxford.
Reba, M. A., & Shier, D. R. (2014). Puzzles, paradoxes, and problem solving: An introduction to mathematical thinking. Boca Raton, FL: CRC Press.
Sedley, D. (2006). Oxford studies in ancient philosophy XXXI: Winter 2006. Oxford: OUP Oxford.

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