Well, I think that statement is formally impossible. Since you define symbols before relations betreen symbols. In math you would write X is a symbol, and Y is none, and then you go on and define true statements, thus you precluded "X must have Y porperty" from the set of valid statements. If you allow symbols do be defined at any point, and at that point you find contradictions, you just showed that your system of inference is inconsistent. Which unfortunately means you lost the ability to make valid statements at all.In other words: I agree Bjorn, you can not define away something, and the attempt invalidates the conclusions.Cheers Arend
A better analogy is that until we have agreed on certain aspects of the definition of "cm" -- we don't have to agree about the unit distance it is based on, but we do have to agree that it's a linear measurement -- then we can't solve for x.If "cm" is linear (like centimeters), then x = 5 cm. But if x were a logarithmic scale, like decibels, then the answer would be different. If 1 cm is equivalent to 1 inch, but 2 cm is equivalent to 10 inches, and 3 cm equivalent to 100 inches, then the answer to the question is 4.00216 cm."cm" is pretty well-defined in conventional circles, but "god" is not.
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