On Wed, Aug 21, 2013 at 4:23 PM, Shane Mage <[email protected]> wrote:
> All your "paradoxes" are exactly that--statements that have no truth value > (ie., cannot be refuted by factual data or *reductio ad absurdam*). > Of course that is exactly what my paradoxes are. And so are your paradoxes and anyone else's paradoxes. By definition, paradoxes are self-contradictory and don't really "exist"; they are just intellectual "optical illusions". The point is that they are very useful and often illuminate some very deep ideas. As the theoretical physicist Niels Bohr is alleged to have said, "How wonderful that *we* have met with a *paradox*. Now *we* have some hope of *making progress."* There is nothing quaint about these paradoxes. You have a choice of either > (a) giving up on "natural language" and restrict yourself to a stunted > formal language in which logic can be used without running into these > paradoxes, or (b) accepting that natural language cannot be completely > formalized and reduced to logic consistently, and you need to be cautious > in making truth-claims in natural language terms. > > > How can you presume to dictate such a choice? Why do you exclude > clarifying the intended meaning of "natural language" statements through > dialogue (language, let me remind you, is a *social* phenomenon) so as to > be "cautious," so as to make sure that the "truth claims" made in a phrase > are indeed such (and therefore refutable) or merely bullshit? > Well, "dialogue" is a pretty broad escape clause. I suppose in principle, we can always negotiate away any contradictions or toss a coin. But then, how do you assure consistency and non-contradiction? Once ypou start putting formal rules on your "dialogue" process, then you end up back on square one. Negotiation is fine for resolving contradictions in politics, but what about mathematics? Are you claiming that there is no such thing as objective mathematical truth, that it is all socially determined? -raghu.
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