Er,, of course there are many, right? With two finite sets of size N there are N! 1-1, onto unique mappings, I believe.
But relax. I went off the deep end with examples of things like decidability. All I'm curious about is whether or not it is possible to somehow make philosophy, or simply intellectual conversation a bit more concrete. Wouldn't you think computation and algorithms could express at least an interesting subset of intellectual discourse? I remember being driven to watching Michael Sandel's great "What Is The Right Thing To Do" Harvard Justice lectures by Nick's vocabulary and style. I found it a thrilling series and am glad its now part of a MOOC. I'll probably watch more of similar a nature. Exciting! Unfortunately, some of the philosophic conversations I hear are poorly motivated and lack MS's great skill at driving people towards wanting understanding. -- Owen On Wed, Apr 17, 2013 at 2:09 PM, glen <g...@ropella.name> wrote: > > Well said, Steve! Mostly, what's kept me from commenting on the > "isomorphism" thread is ... well, the word "isomorphism". [grin] > > I spend _all_ my time... seriously ... arguing against the "Grand > Unified Model" (GUM). For some reason, everyone seems so certain, > convicted, that there exists the One True Truth (and they usually think > Cthulu whispers in their ear about it). Even those of us who admit that > it may not exist, claim it's a Worthy Goal and we should all tow the line. > > I do not believe there exists a single isomorphism between computing and > philosophy. If _any_ exist at all, there are many. [*] And if I believe > that, then I have to consider the efficacy of my spending time figuring > out a single isomorphism. Yes, to show that one exists would be > interesting. But all it would achieve is continual and annoying > [mis]citation of that one demonstration, giving ammo to the GUM crowd. > > Not only is that not in my ideological best interests, it's not even in > my practical best interests. It would be a result analogous to Goedel's > Incompleteness Theorems, where everyone from postmodern Eddington > typewriters to serious people would jump in and muddy the waters. > Practically, all I want to do is find ways to get my work done and > finding/demonstrating a single isomorphism won't help me do that ... > > UNLESS we could demonstrate there are _multiple_ isomorphisms. Or > better yet, draw up a rough characterization of the distribution of all > morphisms, including multiple iso-s. > > In the interests of problem solving, perhaps we could break down the > task and, rather than searching for an isomorphism, we could just lay > out one example morphism in some practical detail? I think we could > mine the IACAP crowd for examples: http://www.iacap.org/ I had a lot of > fun at the one meeting of theirs I managed to attend. > > [*] I'll leave the parentheticals alone and avoid trying to explain how > there can be multiple isomorphisms between any 2 particular things. ;-) > > Steve Smith wrote at 04/17/2013 12:18 PM: > > The stew is getting nicely rich here. While I wanted to ignore Owen's > > original question regarding isomorphisms between computing > > (language/concepts/models?) and philosophy as being naive, I know it > > isn't totally and the somewhat parallel conversation that has been > > continuing that started with circular reasoning has brought this out > > nicely (IMO). > > > > -- > =><= glen e. p. ropella > And I know I ain't digging on your lies > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >
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