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xod: > 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. I can see that the coin has two sides, because I can see what counts as one side, and hence am able to say how many times one side there are. > 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. In the last great debate I argued that the cardinality is "Mr Number" (Mr Positive Integer), because the paradigmatic contrast between 1/2/3/4/... is neutralized. (More specifically, the contrast between 1 and 2 is neutralized, because that contrast is sufficient to generate the rest.) I can understand how you can operate with a notion of Oneness that generalizes over 1-versus-2 and Mr Number. If we could express all three notions (Generalized One, Contrastive One, Mr Number) then we could agree that the cardinalities are Generalized One, we might even agree that they are also Mr Number, and we might disagree on whether there is a metaphysical difference between Contrastive One and Mr Number. --And.