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Indeterminate Properties?
But why can't an object have indeterminate properties? One answer is as follows. What
would it be for something to have an indeterminate property? What would it be, for example, for
something to be green, but not any particular shade of green? One explanation is this. X is
green, but no particular shade of green, if and only if the following is the case:
(1) Either X is green 0 or X is green 1 or X is green 2 or .
.. or X is green n
 where green 0, green 1, green 2, .
.. green n represent all possible determinate shades of green
(2) None of the following statements are true: "X is green 0"; "X is green 1"; "X is green
2"; . . . "X is green n1"; "X is green n".
But this situation is logically impossible, for a disjunctive statement cannot be true unless at
least one of its disjuncts is true  given the way that the logical connective "or" is defined in
terms of truthtables.
The upshot is that unless there is some other way of explaining what it is to have an
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 Fall '09
 JorgeRigol

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