- From: Henry Story <henry.story@bblfish.net>
- Date: Fri, 15 Apr 2005 10:49:34 +0200
- To: "Bill Kent" <billkent@bkent.net>
- Cc: 'SWIG' <semantic-web@w3.org>
On 14 Apr 2005, at 22:51, Bill Kent wrote: > Hi- > > I don't know if this dialog is still going on, but I never did get any > response to my email of 2/10/05, which is appended at the very end. > > In the meantime, I've run across an interesting passage in an article > by Jim > Holt entitled "Time Bandits", about Einstein and Godel, in the > February 28, > 2005 issue of The New Yorker. On page 83, he writes: > > <beginning of quote> > > It had been an article of faith that, armed with logic, mathematicians > could > in principle resolve any conundrum at all-that in mathematics, as it > had > been famously declared, there was no ignorabimus. Godel's theorems > seemed to > have shattered this ideal of complete knowledge. > > That was not the way Godel saw it. He believed he had shown that > mathematics > has a robust reality that transcends any system of logic. But logic, > he was > convinced, is not the only route to knowledge of this reality; we also > have > something like an extrasensory perception of it, which he called > "mathematical intuition." It is this faculty of intuition that allows > us to > see, for example, that the formula saying "I am not provable" must be > true, > even though it defies proof within the system where it lives. Some > thinkers > (like the physicist Roger Penrose) have taken this theme further, > maintaining that Godel's incompleteness theorems have profound > implications > for the nature of the human mind. Our mental powers, it is argued, must > outstrip those of any computer, since a computer is just a logical > system > running on hardware, and our minds can arrive at truths that are > beyond the > reach of a logical system. > > <end of quote> I can't answer this point in a short time, though it is a very interesting one, and would be more appropriately discussed on a philosophy forum. A more elaborate answer would involve the following points: - restrictions have been placed on more recent formal systems that have taken Gödel's work into account - Even though Logic can't solve all problems, that does not mean that it is not an excellent tool to solve a huge number of them - fuzzy logics and modal logics need not be thought of as different logics but can well be seen as specialization of logics to certain domains of discourse. See David Lewis' "Counterfactuals" where he shows how modal logic can be expressed in simple first order logical terms. You just need to add quantification over possible worlds, introduce the notion of possible world similarity, and cross world identity. He also shows how to deal with problems of fuzziness in language, by defining the notion of a mathematically precise language and then defining natural languages as sets of sets of such languages. You can use that trick to deal with a huge range of fuzziness issues. - logic does not deny intuition in the least. Good logicians/philosophers are constantly calling upon our intuitions on various conceptual issues. Their aim is to help refine our concepts which at a certain level may seem contradictory in order to create more powerful conceptual structures. Not unlike Einstein reworking our notions of space time, thereby opening up worlds of possibilities unimaginable before. - the logic of emotions has been a major preoccupation of analytical philosophers in the 1990ies. You may find it odd that emotions have a structure or logic but think about the following example: you are walking down a dark alley. You hear some footsteps at a certain distance behind you, and you are worried. The steps get faster and you, not being a martial arts expert, feel defenseless and fearful. Suddenly a voice shouts out "coucou" and you realize it is your brother. The fear disappears, and you turn around with a smile. This story illustrates very well how your knowledge about the environment and your skills shape your emotions. A martial arts expert would not have had fear as he would have felt comfortable that even at the last moment he would have been able to turn the situation to his advantage. He may even have been able to hear better the non aggressive nature of the steps. The terms "would" "could" "knowledge" "skill" are all analyzable using modal logic. Understanding the nature of thought, its relation to logic, and intuition are all very important elements in correctly understanding the behavior of people around you. >>>>>> [snip] >>>>>> Just a point of clarification about identity. (I thought the >>>>>> example >>>>>> is fun enough that it may be of interest) >>>>>> >>>>>> As we all know Madonna is a material girl, and she lives in a >>>>>> material [snip] > > My curiosity has been aroused. What came after the [snip]? Please check the semweb archive. [1] I have proposed a simple solution [2] and will provide a N3 formalization when I get time to do so. The trick is simple to read up on mereology [3] and translate the mereological rules into N3. In any case the madonna problem has some very good solutions. > > Thank you all for keeping me in the loop. > > Bill > > > BTW: The Help Wanted notice on my web site is still open. [1] http://lists.w3.org/Archives/Public/semantic-web/2005Feb/0062 [2] http://lists.w3.org/Archives/Public/semantic-web/2005Feb/0073 [3] http://plato.stanford.edu/entries/mereology/
Received on Monday, 18 April 2005 09:00:40 UTC