To: |
Ontolog <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
Jon Awbrey <jawbrey@xxxxxxx> |

Date: |
Tue, 07 Aug 2007 23:00:03 -0400 |

Message-id: |
<46B931B3.54B4FB46@xxxxxxx> |

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (01) JA = Jon Awbrey JFS = John F. Sowa (02) JFS: Yes, Peirce gave very general foundations for much, much, more than classical FOL. (03) JA: I'm sure you must know, if you think about it, that many of the statements that you make below are not exactly so. Peirce's interpretation of basic logical symbols was far more abstract, formal, or general than our conventional readings of boolean syntax, as evidenced among many other facts by the deep duality between the entitative interpretation and the existential interpretation of logical graphs. (04) JFS: The fact that Peirce did much more than classical FOL does not contradict the fact that the FOL subset of his 1885 paper on the Algebra of Logic is exactly compatible with the FOL subset of his existential graphs of 1906 and exactly compatible with the FOL subset of Frege's publications. (05) "Compatible" is a word that bears further examination, but I do not think I could bear to begin that interrogation this late in the day. (06) The desire to assimilate the general conception of logic that courses through the tradition of Aristotle, Leibniz, Kant, Boole, and Peirce to the line that was founded on Russell's Frege and Tarski's Hilbert appears to be far stronger than I ever would have guessed a few years ago, even though I had long been aware of the general run of its ilk. (07) There is a natural tendency of mind to synthesize and unify, and that is a bent that I understand, sympathize with, and share. But the wish to assimilate even at the expense of a reductive synthesis goes farther than I would like to see. (08) JFS: That is a truly remarkable point that is *not* true of *any* programming language or system that has been defined by purely behavioral methods. It's importance cannot be overstated. (09) There may be a particular misunderstanding on his point. Yes, I could hear the echoes in recent exchanges of all those old wrangles between declarative stylists and procedural stylists in programming languages, but that is not what I personally am talking about when I refer to the pragmatic aspects of logic. I am referring to the conception of logic as a normative science, which is part of what Peirce meant by defining logic as formal semiotic. This footing for logic is not a thing that can be shoehorned into more reductive forms, not without sacrificing a few of its toes. (010) JA: It is also evident in the fact that Peirce gave axioms for boolean algebra in dual symmetric form, even writing them in the fashion that was customary to present dual axiomsets for projective geometry. This leads to a very distinctive way of regarding the interpretation of logical calculi, where symbols that we once regarded as "logical constants" take on variable meanings. (011) JFS: Indeed, Peirce had profound insights into logic that are worth much more study than most logicians have bothered to give them. (012) JFS: But it is also true that the ISO standard for classical FOL with the extensions in the CL standard is already far beyond what most people are using today. (013) JFS: Let's take it one step at a time. (014) Let's just be sure they are forward steps. Life is short, the art is long, indeed, but what I have seen in my time so far has mostly been a lot of bak.peddling. (015) Jon Awbrey (016) o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ ¢iare: http://www.centiare.com/Directory:Jon_Awbrey getwiki: http://www.getwiki.net/-UserTalk:Jon_Awbrey zhongwen wp: http://zh.wikipedia.org/wiki/User:Jon_Awbrey http://www.altheim.com/ceryle/wiki/Wiki.jsp?page=JonAwbrey wp review: http://wikipediareview.com/index.php?showuser=398 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (017) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (018) |

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