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fom
Posts:
1,968
Registered:
12/4/12


Re: Background Theory
Posted:
Dec 8, 2012 6:13 AM


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 firstorder satisfaction.
The problem is simply in understanding that parts are prior to individuals.
Nevertheless, the entire ontology of modern firstorder 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.
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