By Richard Milton Martin

ISBN-10: 0585077843

ISBN-13: 9780585077840

ISBN-10: 0873953819

ISBN-13: 9780873953818

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Additional info for Semiotics and Linguistic Structure: A Primer of Philosophic Logic

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And similarly, according to TA3, an entity y is a member of {x3~ -x--} if and only if it is not a member of {x --x--}. TA2 and TA3 are Abstractual Principles of Disjunction and Negation respectively. TA4a is an Abstractual Principle of Quantification. It states, in a special case, that an entity z is a member of the virtual class {x3(y)--y--x--} if and only if for all y, z is a member of the virtual-class function {x3--y--x--}. ) TA4a may be generalized as follows. C. Sums, Products, and Negatives A few interesting notions concerned with virtual classes and virtual-class functions may now be introduced.

This much must suffice for our brief sketch of the theory of virtual relations. It is interesting to emphasize again that the entire theory is merely a development of quantification theory with the addition of identity and one-place abstraction. All the foregoing principles are thus provable solely on the basis of R1-R6, Abst, IdR1-IdR2, MP, and Gen. It is perhaps surprising that so much can be gotten out of so little. Also it is of interest to observe that all of the theory has been provided without the use of real classes or relations.

And the third is the Principle of Partial Symmetry for P. The following theorem then immediately obtains. An individual x is said to be a proper part of an individual y if and only if Pxy but not Pyx. Thus Clearly then the following hold. < previous page page_42 If you like this book, buy it! next page > < previous page page_43 next page > Page 43 Note of course that the other combination does not in general obtain. Consider next the notion of a unit or atomic individual. Let According to this definition, an individual x is an atom, or is atomic, if and only if the following two conditions hold: (i) it is not the case that it is a part of every individual, and (ii) given any y that is a part of x but is not a part of every individual, then x is a part of it.

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Semiotics and Linguistic Structure: A Primer of Philosophic Logic by Richard Milton Martin

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