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Re: ONT Class


Hello Jon,

Yes, but once more - the 'duality principle' must be taken into
account when we speak about classes.
Moreover the 'dual calculuses' must be defined for the both parts.

Leonid

Tuesday, January 22, 2002, 5:52:43 AM, you wrote:


JA> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

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

JA> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤




Best regards,
 Leonid
mailto:leo@mmk.ru and copy to leo@mgn.ru
=====================================================
Leonid Ototsky,
www.mgn.ru/~ototsky/ototskyhome.html
Chief Specialist of the Computer Center,
Magnitogorsk Iron&Steel Works (MMK)- www.mmk.ru
Russia
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