On 12/8/2012 1:23 AM, Zuhair wrote: > On Dec 7, 7:21 pm, fom <fomJ...@nyms.net> wrote: >> On 12/7/2012 8:46 AM, Zuhair wrote: >> >>> One might wonder if it is easier to see matters in the opposite way >>> round, i.e. interpret the above theory in set theory? the answer is >>> yes it can be done but it is not the easier direction, nor does it >>> have the same natural flavor of the above, >>> it is just a technical formal piece of work having no natural >>> motivation. Thus I can say with confidence that the case is that Set >>> Theory is conceptually reducible to Representation Mereology and not >>> the converse! >> >> I have no doubt that you are correct. In another post >> in your thread I summarized the work of Lesniewski which >> uses the part relation to characterize classes. His >> method was specifically designed to circumvent the >> grammatical form that leads to Russell's paradox. >> > > Yes, this is clearly resolved here. A set would be an element of > itself iff > it represents a collection of atoms having it among them, this is not > that difficult > to ponder about
You would be surprised. I find no problem with using a part relation for first-order satisfaction.
The problem is simply in understanding that parts are prior to individuals.
Nevertheless, the entire ontology of modern first-order logic is based on interpreting the universal quantifier over sets and understanding sets by the framework of Russell's vicious circles and the hierarchical type theory that arose from it.