Paradox or Simply Unassertable...

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Paradox or Simply Unassertable...

Post  John on Wed Oct 31, 2012 7:35 pm

So, there was this guy once, G.E. Moore, who thought it was funny to 'take the piss' out of people (he was British, hence the slang). He once said something along the lines of "Albany is the capital of New York, but I don't believe it," which literally blew Wittgenstein's mind. All kidding aside, take some proposition P, and take some unary operator Be() which indicates belief, then we can write this as (P and ~Be(P)), that is, we can assert P, but also assert that we do not believe P. This is obviously odd, as it is difficult to see how we can assert P without believing P, though the fact that it is placed within a functional operator might make this tractable (I admit though, I have not figured out how yet). When considering "Albany is the capital of New York, but I don't believe it," the assertion does, to be sure, seem somewhat...unbelievable. Consider the following however, "With proper boundaries, [url=[url=Laplace's Equation]http://www.maths.qmul.ac.uk/~wjs/MTH5102/laplace.pdf[/url]]Laplace's Equation[/url] has a unique solution, but I don't believe it." I have had this thought before! When learning how to derive Laplace's Equation for electric fields, I simply could not come to terms with this actually being true, but it is true nonetheless.

The problem stems from the oddity of the situation, but there seem to be occasions where it is not that odd (as indicated above). Has the paradox been solved, or was it never really that paradoxical?
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