How to Test Validity using Reductio ad Absurdum

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SUMMARY

The discussion focuses on the method of Reductio ad Absurdum for testing validity in propositional logic. The process involves assuming a proposition is true and demonstrating that this leads to a contradiction, thereby proving the proposition must be false. An example provided is the proof that √2 is irrational, illustrating the method's application in logical reasoning. Participants seek resources, particularly from academic sources, to better understand this technique.

PREREQUISITES
  • Understanding of propositional logic
  • Familiarity with logical contradictions
  • Basic knowledge of mathematical proofs
  • Ability to interpret academic resources
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  • Research academic papers on Reductio ad Absurdum from university philosophy departments
  • Study examples of logical proofs involving irrational numbers
  • Explore advanced topics in propositional logic, such as modal logic
  • Learn about other proof techniques, such as direct proof and proof by contradiction
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Students of philosophy, mathematicians, and anyone interested in enhancing their understanding of logical reasoning and proof techniques.

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.
 
a very elementary example could be proving that √2 is irrational
 

Thread 'My basic understanding of set theory'

If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those...
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