On Apr 29, 1:30 pm, fom <fomJ...@nyms.net> wrote: > On 4/28/2013 9:36 PM, Graham Cooper wrote: > > > > > the problem with mereology is it uses ALL(S) quantifier > > and C (subset) to co-define each other.. > > That is a nice observation Herc. > > The only problem is that the foundational > investigations for mathematics have a historical > context. > > What is correct about mereology is that it is > consistent with Leibniz. In analyzing the notion > of class, Lesniewski concluded that the existential > import of a class and its constituents is > simultaneous. In describing the difference, he > explained the notion as intensional and contrasted > it with the extensional logic of a Fregean or a > Russellian approach. > > In like fashion, Leibniz contrasted his notion > of logic with the extensional Scholastic logic. > In this respect Leibniz' logic is also intensional > for a different reason. In Leibniz' case, the sense > of the syllogistic hierarchy had been characterized > by informational complexity. In other words, a genus > is part of a species because more information is needed > to specify a species than that of the genus with which > it is associated. > > It is an unfortunate fact that most of modern > foundational mathematics is overly influenced by > Russell without questioning Russell's philosophy. > > For what this is worth, Cantor rejected the "extension > of a concept" formulation used by Frege and Russell. > In fact, Cantor's notion of sets involves a "theory > of ones" approach which suggests a Leibnizian view > of individuation. > > I would argue that the problem with the received > paradigm is that the sign of equality is improperly > characterized. Leibniz' original introduction of > the principle of identity of indiscernibles involves > geometric intuitions not represented in the logicist > framework of Frege and Russell. > > Your criticism of mereology will be believed by those > who have not pursued what the original sources have > written. And, it will be respected by me because of > its insight. It is, however, a statement that does > not question the alternative which is equally nonsensical. > > Analytical philosophy is based on one thing -- avoid epistemology > at all costs. When one denies that position, there are > not many choices, > > http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma >
Ponytail stunt ends in death A daredevil stuntman has died while attempting to cross a river using just his ponytail.