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From: hagman on 16 Jul 2010 09:46
On 16 Jul., 06:17, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
> The epsilon relation symbol ('e') is just a 2-ary predicate relation
> one, such as '<', ... This suggests that it's conceivable to have a
> different semantics for 'e', besides the set-semantics "being a member
> of".
>
> How about this semantics:
>
> x e y means either one of the followings:
>
> - the thought x originates from thought y, or equivalently
> - part of what thought y is about is thought x.
>
> We could replace "thought" by "perception", "concept", etc...
>
> In this semantics, e.g., the empty thought can be still be syntactically
> defined as ExAy[~(y e x)], just as the empty set.
>
> A few questions arise though:
>
> Q1. Would ZFC as a formal system "support" this semantics, in the
> sense that ZFC theorems could be as much about human thoughts,
> thinking, as it is about sets?

It's possible if two thoughts are the same if and only if they are
about exactly the same thoughts.
And for any two thoughts there is a thought that is exactly about
these thoughts.
And for any thought there is another thought that is about the
thoughts the thoughts the first thought is about are about.
And for any thought there is another thought that is about exactly
those thoughts that are only about thoughts the first thought is
about.
And for any thought that is not the empty thought there is another
thought that the first thought is about and that is about no thought
that the first thought is about.
....
Sounds ugly so far and we have not yet formulated the axiom scheme of
replacement or the axiom of choice :)



> Q2. What would "collection" mean in this semantics of "thoughts"?
>
> --
> ---------------------------------------------------
> Time passes, there is no way we can hold it back.
> Why, then, do thoughts linger long after everything
> else is gone?
> Ryokan
> ---------------------------------------------------

From: Nam Nguyen on 16 Jul 2010 09:46
Frederick Williams wrote:
> Nam Nguyen wrote:
>> The epsilon relation symbol ('e') is just a 2-ary predicate relation
>> one, such as '<', ... This suggests that it's conceivable to have a
>> different semantics for 'e', besides the set-semantics "being a member
>> of".
>>
>> How about this semantics:
>>
>> x e y means either one of the followings:
>>
>> - the thought x originates from thought y, or equivalently
>> - part of what thought y is about is thought x.
>
> "Part of" is axiomatized in mereology.

Right. Although I'd think the axioms have to be "tweaked" to make the
theory fit more with the "thought" paradigm.

--
---------------------------------------------------
Time passes, there is no way we can hold it back.
Why, then, do thoughts linger long after everything
else is gone?
Ryokan
---------------------------------------------------
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