On a tangential note, I was told in 1961 of a project to prove (on a computer) the theorems in Principia Mathematica. It went well through the first section, and then they hit the brick wall when they encountered statements like "there exists" and "for every". When dealing with infinite sets, these can be hard.
On Apr 16, 2013, at 9:12 PM, Owen Densmore <o...@backspaces.net> wrote: > On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson > <nickthomp...@earthlink.net> wrote: > I don’t think I said that math couldn’t be mapped onto things. I only said > that such mappings are not essential to math and, further, that when such > mappings occur, the door is opened for confusion that is opened in any > semantic relation. > > > Could you show me such a thing? I demonstrated that computers for example do > not suffer from this confusion. Computing is a branch of mathematics that > looked inward and found it could provide real world mappings from 5-tuples > defining a computing engine (the FSA) to real computers. Every time you step > on the in/out mat for a door at a store, you are implementing a FSA. (Note I > bow to your "door" above :) > > Call it "Applied Mathematics" if you'd prefer. But it certainly has a very > high reality coefficient. There is no ambiguity and there is semantic > binding. > > (Note: I realize that ABM does deal with this, and we've dealt with it with > your MOTH model, but it is not necessarily general.) > > Let me simplify. Is there a realm in which philosophy can exhibit a bug? And > more specifically by simply "running" the philosophy engine? > > I believe this may be possible, but I'm not sure. Maybe we'd have to create > a new field. Certainly Turing, Church, von Neumann, Shannon, and many other > in the computational world did. They stood on a brink, vital for going > forward. Von Neumann had to argue for a computer to be admitted to the > Institute for Advanced Study in Princeton .. it was considered just a > machine. Church and Turing showed that to be nonsense. Can we do the same > for philosophy? > > NB: I'm not referring to "computational complexity" in which we deal with the > running time issues of an algorithm, but to the semantics of computation > itself. We really do have a strong grasp on what computation is and we do > not quibble about meaning .. at least without heading immediately to > axiomatic solutions. > > -- Owen > ============================================================ > 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
============================================================ 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
