Math Forum Discussions

fom

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

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

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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.

<snip>