- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Brent Meeker <meekerdb.domain.name.hidden>

Date: Sat, 08 Nov 2008 17:39:36 -0800

Quentin Anciaux wrote:

*> 2008/11/9 Brent Meeker <meekerdb.domain.name.hidden>:
*

*>> 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
*

*>>>> Russell's paradox.
*

*>>> 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 contradiction.

Brent

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden

For more options, visit this group at http://groups.google.com/group/everything-list?hl=en

-~----------~----~----~----~------~----~------~--~---

Received on Sat Nov 08 2008 - 20:39:52 PST

Date: Sat, 08 Nov 2008 17:39:36 -0800

Quentin Anciaux wrote:

A set of propositions is consistent if it is impossible to infer contradiction.

Brent

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden

For more options, visit this group at http://groups.google.com/group/everything-list?hl=en

-~----------~----~----~----~------~----~------~--~---

Received on Sat Nov 08 2008 - 20:39:52 PST

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:15 PST
*