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Are contradictions possible?


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43 minutes ago, Farid said:

Hi everyone,

I just have a question about contradictions. Is there any proof that contradictions are not possible? 

Can define what you mean by "contradiction"? And in what field: math, physics, chemistry, engineering, art, sociology ...

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27 minutes ago, Sensei said:

...OP wrote in General Philosophy section of this forum..



I think that Wikipedia page, in its entirety, provides a comprehensive answer to the question. Unless the OP has an example that isn't covered there?


And is perfectly summarised by this:

39 minutes ago, michel123456 said:

Yes & no.


1 hour ago, Farid said:

Is there any proof that contradictions are not possible?

In formal logic, the law of excluded middle ([math]A\vee\neg A[/math]) is an axiom and so does not require proof. I don't think the concept of formal proof is relevant in other areas.


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4 hours ago, Farid said:

Is there any proof that contradictions are not possible? 

A contradiction is when you propose that a sentence is true, but a sentence that says the opposite is true too. Now there are all kind of situations, especially when vague concepts are used, where this is not quite unproblematic. But if you take the concepts precise, then two such sentences cannot be true.

Now imagine that the sentence says something about empirical reality, e.g. 'that car is black'. Then it is impossible that the sentence 'that car is not black' is true at the same time. (The vague concepts here could be 'oh well, it is nearly black'.) Simply because the car cannot have 2 colours at the same time (no, no, that the lights are red does not count.)

Now say we have a theory, from which it follows that that car is black and is not black. What can you conclude about the real colour of the car? Exactly nothing: such a theory is worthless. As a principle: if we can deduce from a set of supposed truths a proposition, and also exactly the opposite of that proposition, then at least one of our supposed truths is obviously no truth at all. So we can use the principle of contradiction (or better, non-contradiction) to see if:

  • at least one of our propositions was wrong
  • or I made an error in my logical  argumentation

So you can use the principle of contradiction to prove if some set of propositions can be true together or not. But then, how could you prove if the principle of non-contradiction is correct? Formally, I think you can't. But practically it is impossible to see how it could be invalid.

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