Re: Non unique Universe

2009-07-04 Thread Bruno Marchal
On 03 Jul 2009, at 19:07, Brent Meeker wrote: Right. I have no problem with arithmetical possibilities, provability, etc. But without some defined scope the use of possible makes me uneasy. In modal logic possible and necessary are just operators that must be interpreted in some

Re: The seven step series

2009-07-04 Thread Bruno Marchal
On 04 Jul 2009, at 04:31, m.a. wrote: New comments in italics. For example {1,2} INTERSECTION {2, 7} is equal to some set, actually the set {2}. OK?..No! Why not the sets

Re: The seven step series

2009-07-04 Thread m.a.
Bruno, Can you provide definitions of belongs-to and included-in that distinguish them from union and intersection? Here we met a set of sets. The set of subsets of a set, can only be, of course, a set of sets. The set {2, 21, 14} is a set of numbers. The set { { }, {4,

set incompleteness

2009-07-04 Thread John Mikes
Dear Bruno, I mentioned that I have something more on the 'set' as you (and all since G. Cantor) included it in the formulations. I had a similar notion about my aris-total, the definition of Aristotle that the 'total' is always more than the 'sum' of its components. Of course, at the time when A.

Re: set incompleteness

2009-07-04 Thread Bruno Marchal
John, On 04 Jul 2009, at 18:24, John Mikes wrote: Dear Bruno, I mentioned that I have something more on the 'set' as you (and all since G. Cantor) included it in the formulations. I had a similar notion about my aris-total, the definition of Aristotle that the 'total' is always more

Re: The seven step series

2009-07-04 Thread Bruno Marchal
On 04 Jul 2009, at 15:17, m.a. wrote: Bruno, Can you provide definitions of belongs-to and included-in that distinguish them from union and intersection? Belongs-to and included-in are relations. Their value are true or false. 1) (x belongs-to A) means that the object x

set

2009-07-04 Thread John Mikes
Dear Bruno, thanks for the prompt reply, I wait for your further explanations. You inserted a remark after quoting from my post: * * If you advance in our epistemic cognitive inventory to a bit better level (say: to where we are now?) you will add (consider) relations (unlimited) to the names of