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On Fri, 8 Aug 2003, And Rosta wrote: > John: > > And Rosta scripsit: > > > > > Likewise, I accept that people are countable, but dispute that xod is, > > > > Why? Once we have singularized xod, surely his cardinality is 1. > > The reasons I've given in other messages: since a contrast between one xod > and two xods is impossible, I have no criteria for counting him. Certainly > xod is a single person, I have no doubt about that. But I can't find > grounds for thinking he can be counted as a single xod. Likewise, oxygen > is one element, but I don't think it is one oxygen. I think it is > uncountable, qua oxygen. I am beginning to understand what you mean. But I don't see why you don't simply say that, distinct from the fact that any other cardinality is unthinkable, the number is countably one. How do we define countable? As 1:1 mapping to the whole numbers. And I can map the number of Oxygens just as I can map the number of noses on your face. That the existence of a second copy be inconceivable is NOT a requirement for counting. An example might be the number of sides of a coin. A three-sided coin is not a coin; neither can a coin have only one side; let's assume then that it's impossible to imagine a coin with any but 2 sides. But that's 2, not tu'o. I can't see this situation as any different than the number of Oxygens, xods, or Misters. The reason I gave tu'o as the cardinality of substance chunks is because of the plastic nature of the boundaries between chunks. Pour a glass of water into another glass and you have one glass; 1 + 1 = 1. That's a situation where cardinality of pieces is meaningless and useless, and as we all know, the useful way to deal with substances is using mass or volume quantities. This doesn't damage the fact that the cardinality of all the water in the universe is 1. -- The Pentagon group believed it had a visionary strategy that would transform Iraq into an ally of Israel, remove a potential threat to the Persian Gulf oil trade and encircle Iran with U.S. friends and allies...