How to Test Validity using Reductio ad Absurdum

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In summary: A and not A) is true. so, √2 must be irrational.In summary, the Reductio ad Absurdum method in propositional logic involves starting with a self-consistent system and assuming the truth of a statement. By showing that this assumption leads to an absurdity, we can conclude that the statement is false. This method is commonly used in logic to prove statements such as the irrationality of √2.
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StevieTNZ
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Hi there,

I'm quite interested in propositional logic. Can anyone point me to a document out there (preferably from a university website, e.g. a lecturer/Professor etc. of Philosophy's personal webpage) that explains, in a clear manner, how to test for validity using the Reductio ad Absurdum method.

Many thanks,
Stevie
 
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StevieTNZ said:
Hi there,

I'm quite interested in propositional logic. Can anyone point me to a document out there (preferably from a university website, e.g. a lecturer/Professor etc. of Philosophy's personal webpage) that explains, in a clear manner, how to test for validity using the Reductio ad Absurdum method.

Many thanks,
Stevie

Start with a self-consistent system. This means that (A and not A) is false for all A.

Let's say that the truth value of X is unknown. Assume X is true. If you can deduce for some A that (A and not A) is true, then you have done the impossible. Since it is not possible to do the impossible, something is wrong. You've reduced the system to an absurdity. The only possible thing that could be wrong is your assumption that X is true. So X must be false.
 
  • #3
a very elementary example could be proving that √2 is irrational
 

1. What is Reductio ad Absurdum and how is it used in testing validity?

Reductio ad Absurdum is a logical method of proving the validity of an argument by showing that its conclusion leads to an absurd or illogical result. In testing validity, this method is used to demonstrate that an argument is invalid by showing that its conclusion leads to a contradictory or impossible outcome.

2. What are the steps involved in using Reductio ad Absurdum to test validity?

The first step is to assume that the argument is valid and work through the premises to reach the conclusion. Next, we must identify any implicit assumptions or hidden premises that may not be explicitly stated. Then, we use the reductio ad absurdum method to show that the conclusion leads to a contradictory or impossible outcome. Finally, we can conclude that the argument is invalid.

3. Can Reductio ad Absurdum be used to test the validity of any argument?

No, Reductio ad Absurdum is only applicable to arguments that have a clear and explicit conclusion. It cannot be used to test the validity of arguments with ambiguous or unclear conclusions.

4. What are the limitations of using Reductio ad Absurdum in testing validity?

One limitation is that it relies on the assumption that the premises are true. If the premises are not true, then the argument may still be invalid even if the conclusion leads to an absurd result. Additionally, it may not be effective in testing the validity of complex arguments with multiple premises and conclusions.

5. Can Reductio ad Absurdum be used to prove the truth of a statement?

No, Reductio ad Absurdum can only be used to show that a statement or argument is invalid. It cannot be used to prove the truth of a statement, as it only deals with the logical structure of an argument and not the truth of its premises.

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