January 07, 2007

Contradictions Rational and Justified? (Frances)

Suppose Jan is taking a philosophy of logic course. She hears from several of her professors that dialetheism is the best theory for dealing with the semantic paradoxes, and most philosophers of logic even think it’s true. This is a world in which dialetheists have had some sociological success in persuading others of their odd theory.

Independently of the testimonial matter, she personally finds the case for dialetheism very convincing.

So, she has very good evidence E1 that there is good evidence E2 for her belief that proposition X (expressed by something like ‘The claim I am making with this very sentence is not true’) is both true and not true. E1 is her knowledge that most excellent philosophers of logic endorse dialetheism after plenty of expert investigation over many years. The alleged E2 is the alleged direct evidence for dialetheism—the actual philosophical arguments for it. I am not yet (see below) saying that E2 exists in this possible world or any other world. At this point I’m just saying that in this world E1 exists.

I wonder: is this a case in which one is RATIONAL in having a belief of the form ‘P and ~P’ (e.g., ‘Proposition X is both true and not true’)? She has made a mistake, we can assume, but making a mistake in the philosophy of logic is hardly grounds for irrationality.

Return to the actual world: some VERY smart people think that X is both true and not true. I find it hard to believe that all of them are irrational. Perhaps they are confused, but not irrational.

So: it appears as though one can have a rational belief of the form ‘P & ~P’. If that’s right, then it’s going to be pretty hard to formulate general principles of rationality of the form ‘It is always irrational to have beliefs of the form blah blah’.

But is Jan’s belief JUSTIFIED? Given the content of the belief, whether it is justified depends on whether she possesses good evidence for her belief. I’m inclined to think that she does have evidence sufficient for justification PROVIDED controversial philosophical views are ever justified by controversial philosophical arguments (that’s a big ‘provided’). I’m no philosopher of logic, but I take it that the argument for dialetheism is of the form, ‘Well, this is the best overall theory of the semantic paradoxes’. I also take it that many people think it’s a good argument. So now at this point I AM assuming, without any argument, that E2 exists.

Is any of this right??

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