Reductio Ad Absurdum: Understanding Contradictions

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In summary, the conversation discusses the use of contradictions in proving a statement. The question is raised about how to determine if a contradiction is sufficient evidence to prove a statement is incorrect. It is explained that in mathematics, even one contradiction can cause the entire system to fall apart. However, it is also noted that a contradiction may simply be the result of a mistake, such as an incorrect initial assumption. Correcting these mistakes is necessary to ensure the validity of the proof.
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Hi, I have a little question concerning contradictions :

If I have a statement "A" that I want to prove, and only have the possibility for it to be True or False.

After some manipulations, I arrive at some contradiction. (Here's where my question begins.)

How can we know that a contradiction is enough to be sure at 100 % that a statement is not correct?

Is it because in Mathematics, for a thing to be True or False, it must always be ALWAYS "working" without arriving at some contradiction ? (Mathematical ideas must always work, and not sometimes yes, sometimes no.)

I just want to be sure of thinking of it in the right way, corrections would be greatly appreciated ! Thank you !
 
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How can you know that a contradiction is enough? After you've checked to make sure you didn't make a mistake.

Mathematics cannot tolerate even one contradiction. With one single contradiction (X and both not X are true), *all* of mathematics falls apart. It's called the principle of explosion. Wikipedia article: http://en.wikipedia.org/wiki/Principle_of_explosion.

That said, there is no contradiction if you've just made a mistake somewhere. You've made a mistake, that's all. Suppose that you find a contradiction as a consequence of some initial assumption and verify that every step after making some initial assumption is solid. That doesn't mean you didn't make a mistake. You did. The mistake was making that initial assumption! The initial assumption has to be incorrect. By assuming something and then showing that this leads to a contradiction, you have but no choice but to reject that initial assumption.
 
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AHhhhh! This is clear now ! It make sense lol

Thank you !
 

What is Reductio Ad Absurdum?

Reductio Ad Absurdum is a logical argument where a contradiction is used to disprove a statement or argument.

How is Reductio Ad Absurdum used in science?

In science, Reductio Ad Absurdum is often used to test the validity of a hypothesis or theory by showing that if the hypothesis is true, it would lead to absurd or contradictory results.

What is the process of using Reductio Ad Absurdum?

The process of using Reductio Ad Absurdum involves assuming the opposite of the statement or argument being made and then showing that it leads to a contradiction. This contradiction then proves that the original statement or argument is false.

What are the limitations of Reductio Ad Absurdum?

One limitation of Reductio Ad Absurdum is that it can only disprove a statement or argument, it cannot prove it to be true. Additionally, it relies on logical reasoning, which can sometimes be subjective.

Can Reductio Ad Absurdum be used in everyday life?

Yes, Reductio Ad Absurdum can be used in everyday life to test the validity of arguments or beliefs. It can also be used to identify flaws in reasoning and to make more informed decisions.

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