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From: Lester Zick on 31 Mar 2007 21:38 On Fri, 30 Mar 2007 13:02:44 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Your "not a not b" has an assumed OR in it. >> >> Tony, let me ask you something: without an AND or any other >> conjunction how would you mechanize the OR conjunction you >> claim I assume? And if it's just there as a basic circumstance of >> nature how do you get from there to other conjunctions and logic >> especially when you consider there's no necessity for conjoined >> components to be present together at the same time? >> >> ~v~~ > >Logical Mechanics 101: > >0-place predicates: > >false() 0 >true() 1 > >1-place predicates: > >x 0 1 > >false(x) 0 0 >x 0 1 >not(x) 1 0 >true(x) 1 1 > >2-place predicates: > >xy 00 01 10 11 > >false(x,y) 0 0 0 0 >and(x,y) 0 0 0 1 >not(x->y) 0 0 1 0 >x 0 0 1 1 >not(y->x) 0 1 0 0 >y 0 1 0 1 >xor(x,y) 0 1 1 0 >or(x,y) 0 1 1 1 >not(or(x,y)) 1 0 0 0 >not(xor(x,y)) 1 0 0 1 >not(y) 1 0 1 0 >y->x 1 0 1 1 >not(x) 1 1 0 0 >x->y 1 1 0 1 >not(and(x,y)) 1 1 1 0 >true(x,y) 1 1 1 1 Okay, Tony. I think I see what the problem is here. I say "not not" is false because it is self contradictory and "not" is true of everything because "not" is the tautological alternative to "not not" and those tautological alternatives are exhaustive of truth. You on the other hand say "true is true" and "false is false" because "true" is in truth tables and "false" is not true. Kinda reminisces me of the conversation I had recently with Dirk van der Putz who's quite happy to discuss the significance of time as long as time means whatever he wants it to mean and as long as he could grunt and point to measures of time which turns out he had quite some difficulty keeping running and measuring time. And you wonder why I don't exactly take your arguments on mechanics seriously? ~v~~
From: Virgil on 31 Mar 2007 21:38 In article <460ef25b(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > Every "sequence" must be a totally ordered set which is order isomorphic > > either to the ordered set of naturals, if it has a first element, or to > > the ordered set of integers, if it does not have a first element. > > Okay. How would you boil down that statement, and in which cases would > you say it applies? To all cases in which "sequence" is to be taken in its mathematical sense.
From: Virgil on 31 Mar 2007 21:41 In article <460ef372$1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <460e82b1(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > >> As I said to Brian, it's provably the size of the set of finite natural > >> numbers greater than or equal to 1. No, there is no last finite natural, > >> and no, there is no "size" for N. Aleph_0 is a phantom. > > > > All numbers are equally phantasmal in the physical world and equally > > real in the mental world. > > Virgule, you don't really believe that, do you? You're way too smart for > that... :) While I have seen numerals in the physical world, I have never seen any of the numbers of which they are only representatives. And I suspect that any who claim to have done so have chemically augmented their vision.
From: Virgil on 31 Mar 2007 21:44 In article <460ef5d1(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > Tony rejects all these options, and apparently has some fourth > > Elusive option. > > > > Stephen > > > > Oy. The "elusive" option is that there is no acceptable "size" for N. > That was really hard to figure out after all this time... There is in ZF and in NBG and in NF. In what system does TO not find a "size" that is suitable in that system?
From: Virgil on 31 Mar 2007 21:45
In article <460ef650(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Bob Kolker wrote: > > Tony Orlow wrote:>> > >> > >> Measure makes physics possible. > > > > On compact sets which must have infinite cardinality. > > > > The measure of a dense countable set is zero. > > > > Bob Kolker > > Yes, some finite multiple of an infinitesimal. In any consistent system in which there are infinitesimals, none of those infinitesimals are zero. |