Thanks Steve, Many good things, and clearly this is an area where you have worked much harder and better to understand than I have, so I am happy to follow you.
>> Whether one is to worry about that or not is a matter of what you like to >> worry about, but clearly it is far from the kinds of uses of truth values >> that I mostly worry about in practical work. > Hmm... I felt I was tracking you right up until this one... I do agree with > the spirit of "we worry about what we choose to worry about"... but are you > saying that Godel's incompleteness is sort of a parlor trick or that it just > defers the real question to a higher level of abstraction, not really > settling (or unsettling) anything? (this is my suspicion and I do have some > hope that the line of inquiry/discussion you allude to here might help > sort that a bit?) This was a self-preserving gambit of email, with apologies. I know that any mention of Godel can tend to spin a thread with a _very_ long ring-down time by people who really care about this topic and have put a lot of time into it. Since I haven't done that, and since I am not able even to keep up with such a thread should it start, I wanted to avoid seeming to make any claim about any technical aspect of this question. As an _outsider_ to very heavy formalisms, I have still been bothered by the status of axioms that seem to assign semantic content from syntactic constructions, without doing any actual work of denotation. Not bothered that the axioms exist, but bothered because I don't know how to think about their status. The notion that statements which cannot consistently be called false must thereby be true for a system to be defined is one such. Another (which I will also only claim to be able to parrot as an outsider) is the notion that all well-formed predicates must be regarded as referring to entities, which gets you into set-theoretic paradoxes. It would not be not my intention to assert that there is anything "wrong" with such constructions. Rather, that they require a use of notions of truth or existence that is largely excluded by the activity of constructing denotations for real things. My interest is then to get some window on what else contributes to constructing denotations in a reliable way. (Confessed bias here on various science problems: most notions start out in common language, and are taken as having some meaning -- examples: particle in physics; individual in evolutionary dynamics -- and only on the far side of learning how to do technical calculations for some more mundane reason do we learn that the words may still be usable, but that to be used reliably vis a vis the world, they can require some rather elaborate construction to attach a definition to. So I am interested in that anyway for material things, and it is some extension of that interest to wonder about sources of confidence or content in expr essions.) >> Hintikka's approach was to define "that which is true" by claiming it must >> have a mapping to a strategy that is sure to win in some appropriately >> defined game. "that which is false" is a strategy that can surely be beaten >> by some other strategy. All the other stuff, which can neither surely win >> nor surely be beaten, is the middle, now not excluded. > Smacks of Wolfram's Class I-IV cellular automata. All CA are either A) > uninteresting because they achieve a steady (Class I) or cyclic state (Class > II) in finite time or B) uninteresting because they are chaotic and random > (Class III)... *EXCEPT* those which magically appear to be actually > *interesting* (Class IV), whatever that (actually interesting) means. Let me propose (though this will be the last, because I am now on the border of making things up) that there is a better reading than that. One could view it as something like the effort to make precise the rules of debate, for application to real settings rather than overly simplified trumped-up ones. A debate should be like a game, in that there should be recognized moves and rules for judging how the state of the argument changes as a result of them. That problem is easy for chess; harder for football because of the scope for innovation and the hidden variables of physical athletics, even harder for gymnastics where artistic merit is part of the competitive goal, and very hard for debate. An argument in a debate that can be said to win against any other argument seems a reasonable formalization of the practical notion of truth that we think of as "having the strength of evidence on that argument's side" by whatever rules govern the debate. It is a virtue to recognize that the debate itself is a component of this judgment, meaning that different rules are possible. Hence the problem of arriving at desired truth-values consists both of designing good rules of debate, and then also searching for good arguments within those rules. I wouldn't assert that some provable optimum in that problem is visible from here (or perhaps ever will be), but it does seem to me that thinking about the structure underlying such problems may be clarifying sometimes. >> The pleasing thing about this would be that, for large games, the middle >> will probably grow combinatorially a lot faster than the things that are >> either true or false. So I was hoping that learning something about that in >> the context of designed games might address some subset of the ways in which >> it is possible to generate statements that seem to satisfy various rules of >> syntax, but should not be presumed to have any associated truth values (but >> best to show that if one _can_ give them a proper semantics as strategies, >> in which nonsense has a defined status). > Interesting... when you use the term "designed games" I think of "evolved > design of games". While there is a lot of intentionality in those who seem > to design the games (e.g. social customs, political, religious, legal > systems) we play within, it seems as if the actual "large games" are evolved > with a combination of something like "natural selection" and very "directed > selection" at play. Yes, sorry; arbitrary phrase. Of course I agree with you. Lots of built stuff is organic, and even if it makes use of cognitive intentionality, one would not say its design was contained within any such intention. Indeed, my interest is mostly in systems where we encounter the phenomenon-in-process, and need to determine even what mode of description is admissible for it. My only intention here was to say that one does need to do _some_ work to speak about a definite thing. In principle, any interaction sequence with some regularities might be called a game, but a word so liberally used is an uncarved pig, in which one has not even tried to look for the joints. When I think about "large" games, I implicitly carry the image of the extensive form in mind, rather than just the normal form. The extensive form is not only large, but is also structured, from the sequence and dependencies of moves. Therefore one can do combinatorics on it. One can speak of how rare subsets of leaves on the tree are, and how hard it is to arrive at them reliably, etc. I can show what this looks like for evolutionary games, where it provides a nice way to get at neutrality, but I am sure the same combinatorics can be made useful in many domains. > I like the phrase here "in which nonsense has a defined status". I would > claim that there is a meta-game in play where this is literally and obviously > the truth... it is why we have so many words for "bullshit" to refer to > utterances deliberately crafted to sound meaningful while being meaningless. > I *think* this is the bread and butter of marketing and of politics (which > contemporarily is significantly driven by marketing?) Maybe one can go further though, and recognize that politics and marketing are simply exaptations of what is resident in communication at all levels. This is probably at some level what I am after. Communication is a coordinating activity. That happens at a lot of levels, and it is a science problem (to be contrasted with a theological one, which is my snide way of referring to discussions based on fixed beliefs and adherence to traditional usages which are not subject to conceptual overturning) to say what is being coordinated. Getting clear formalizations of systems and seeing what they leave out can be a good way to look for the other relevant dynamical systems in play. This need not be a matter for cynicism, even if in actual life it is very frustrating. The question of understanding how things work can remain interesting apart from our need to make use of it, which can have emotional valence. > I didn't realize it was considered (by the community?) a spectacular failure: > Although I can believe that the following " Montague held the view that > natural language was a formal language very much in the same sense as > predicate logic was a formal language." has been demonstrated to undervalue > the richness of natural language. Yes, the way you say it is the right one. Here I have a bad habit of speaking. Often I can very much like "failures", which don't do what they were hoped to do, but which are clear enough and solid enough that we learn from them. They may even be so well done that they furnish really interesting and valuable edifices for other things. I don't know how the community regards Montague Grammar, but I would guess it is in some respectful way like the latter sense. > I personally don't believe that natural language can be separated from A) > Culture and B) Embodiment. One can try to be more model specific. I think i have referred to Ray Jackendoff's "three systems" view in threads before, in his lectures Language, Consciousness, Culture, available in book form. It is semi-concrete enough that one could think of making models. Thank you for this conversation. I have to run. I have people on me telling me I am late for stuff I owe them. Eric ============================================================ 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
