```To infer means there is "a process" which permits to infer.. if there
is none... then you can't simply infer something.```
```
2008/11/9 Brent Meeker <[EMAIL PROTECTED]>:
>
> Quentin Anciaux wrote:
>> 2008/11/9 Brent Meeker <[EMAIL PROTECTED]>:
>>> A. Wolf wrote:
>>>>> I can if there's no rule of inference.  Perhaps that's crux.  You are
>>>>> requiring
>>>>> that a "mathematical structure" be a set of axioms *plus* the usual rules
>>>>> of
>>>>> inference for "and", "or", "every", "any",...and maybe the axiom of
>>>>> choice too.
>>>> Rules of inference can be derived from the axioms...it sounds circular
>>>> but in ZFC all you need are nine axioms and two undefinables (which
>>>> are set, and the binary relation of membership).  You write the axioms
>>>> using the language of predicate calculus, but that's just a
>>>> convenience to be able to refer to them.
>>>>
>>>>> Well not  entirely by itself - one still needs the rules of inference to
>>>>> get to
>>>> Not true!  The paradox arises from the axioms alone (and it isn't a
>>>> true paradox, either, in that it doesn't cause a contradiction among
>>>> the axioms...it simply reveals that certain sets do not exist).  The
>>>> set of all sets cannot exist because it would contradict the Axiom of
>>>> Extensionality, which says that each set is determined by its elements
>>>> (something can't both be in a set and not in the same set, in other
>>>> words).
>>> I thought you were citing it as an example of a contradiction - but we
>>> digress.
>>>
>>> What is your objection to the existence of list-universes?  Are they not
>>> internally consistent "mathematical" structures?  Are you claiming that
>>> whatever
>>> the list is, rules of inference can be derived (using what process?) and
>>> thence
>>> they will be found to be inconsistent?
>>>
>>> Brent
>>
>> Well I reverse the question... Do you think you can still be
>> consistent without being consistent ?
>>
>> If there is no rules of inference or in other words, no rules that
>> ties states... How do you define consistency ?
>
> A set of propositions is consistent if it is impossible to infer
>
> Brent
>
> >
>

--
All those moments will be lost in time, like tears in rain.

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