- I shall address the title question, and the answer I shall give is: maybe nothing much. Let me first explain how, exactly, the question is to be understood. I shall interpret it to mean: What is wrong with believing some contradictions? I emphasize the 'some'; the question 'What is wrong with believing all contradictions?' is quite different, and, I am sure, has a quite different answer. It would be irrational to believe that I am a fried egg. (Why, we might argue about, but that this is so is not contentious.) A fortiori, it is irrational to believe that I am both a fried egg and not a fried egg. It is important to emphasize this distinction right at the start, since the illicit slide between 'some' and 'all' is endemic in discussions of the question, as we shall see.
- I think that there is nothing wrong with believing some contradictions. I believe, for example, that it is rational (rationally possible indeed, rationally obligatory) to believe that the liar sentence is both true and false. I shall not argue for this directly here, though.
- I have discovered, in advocating views such as this, that audiences suppose them to be a priori unacceptable. When pressed as to why, they come up with a number of arguments. I shall consider five of the most important, and show their lack of substance. They can be summarized as follows:
- Contradictions entail everything.
- Contradictions cannot be true.
- Contradictions cannot be believed rationally.
- If contradictions were acceptable, people could never be rationally criticised.
- If contradictions were acceptable, no one could deny anything.
- I am sure that there must be other possible objections, but the above are the most fundamental that I have encountered. I shall take them in that order. What I have to say about the first objection is the longest, because it lays the basis for all the others.
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