ONT Class
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| Class, or 'set', or 'aggregate',
|
| (in most connections the words are used synonymously) can best
| be described by saying that classes are associated with monadic
| propositional functions (in intension -- i.e., properties) in
| such a way that two propositional functions determine the same
| class if and only if they are formally equivalent.
|
| A class thus differs from a propositional function in extension only in
| that it is not usual to employ the notation of application of function to
| argument in the case of classes (see the article 'Propositional Function').
| Instead, if a class 'a' is determined by a propositional function 'A', we
| say that 'x is a member of a' (in symbols, 'x in a') if and only if 'A(x)'.
|
| Whitehead and Russell, by introducing classes into their system only as
| incomplete symbols, "avoid the assumption that there are such things as
| classes". Their method (roughly) is to reinterpret a proposition about
| a class determined by a propositional function 'A' as being instead an
| existential proposition, about 'some' propositional function formally
| equivalent to 'A'.
|
| Alonzo Church, in Runes, page 56.
|
| Dagobert Runes (ed.), 'Dictionary of Philosophy',
| Littlefield, Adams, & Company, Totowa, NJ, 1972.
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