On Thu, Aug 14, 2008 at 12:59 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > A more worrisome problem is that B may be contradictory in and of > itself. If (1) I can as a human meaningfully explain logical system X, > and (2) logical system X can meaningfully explain anything that humans > can, then (3) system X can meaningfully explain itself. Tarski's > Indefineability Theorem shows that any such system (under some > seemingly reasonable assumptions) can express the concept "This > concept is false", and is therefore (again under some seemingly > reasonable assumptions) contradictory. So, if we accept those > "seemingly reasonable assumptions", no logic satisfying B exists. > > But, this implies that AI is impossible.
At risk of being really annoying I have to say: it does not imply anything of the sort! How could it imply some idea if it can't even represent it? It implies impossibility to you because you are capable of dealing with fictions of boundaries as if they were real until you either conflate two or more bounded concepts, or simply transcend them by virtue of the extent of your everyday experience. In order to deal with logic you have to be taught how to consider such a thing to be bounded from the rest of reality. That is not difficult because that is a requirement of all thought and it is a fundamental necessity of dealing with the real universe. To study anything you have to limit your attention to the subject. I believe we can use logic in AI to detect possible errors and boundary issues. But then we have to build up a system of knowledge from experience which seems to transcend the usual boundaries when that kind of transcendent insight becomes useful. After a while transcendent insight is itself recognized to be bounded and so it becomes part of the mundane. Think of this way, boundaries are primarily dependent on limitations. Jim Bromer On Thu, Aug 14, 2008 at 12:59 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > This looks like it could be an interesting thread. > > However, I disagree with your distinction between ad hoc and post hoc. > The programmer may see things from the high-level "maze" view, but the > program itself typically deals with the "mess". So, I don't think > there is a real distinction to be made between post-hoc AI systems and > ad-hoc ones. > > When we decide on the knowledge representation, we predefine the space > of solutions that the AI can find. This cannot be avoided. The space > can be made wider by restricting the knowledge representation less > (for example, allowing the AI to create arbitrary assembly-language > programs is less of a restriction than requiring it to learn > production-rule programs that get executed by some implementation of > the rete algorithm). But obviously we run into hardware restrictions. > The broadest space to search is the space of all possible > configurations of 1s and 0s inside the computer we're using. An AI > method called "Godel Machines" is supposed to do that. William Pearson > is also interested in this. > > Since we're doing philosophy here, I'll take a philosophical stance. > Here are my assumptions. > > 0. I assume that there is some proper logic. > > 1. I assume probability theory and utility theory, acting upon > statements in this logic, are good descriptions of the ideal > decision-making process (if we do not need to worry about > computational resources). > > 2. I assume that there is some reasonable bayesian prior over the > logic, and therefore (given #1) that bayesian updating is the ideal > learning method (again given infinite computation). > > This philosophy is not exactly the one you outlined as the AI/AGI > standard: there is no searching. #2 should ideally be carried out by > computing the probability of *all* models. With finite computational > resources, this is typically approximated by searching for > high-probability models, which works well because the low-probability > models contribute little to the decision-making process in most cases. > > Now, to do some philosophy on my assumptions :). > > Consideration of #0: > > This is my chief concern. We must find the proper logic. This is very > close to your concern, because the search space is determined by the > logic we choose (given the above-mentioned approximation to #2). If > you think the search space is too restricted, then essentially you are > saying we need a broader logic. My requirements for the logic are: > A. The logic should be grounded > B. The logic should be able to say any meaningful thing a human can say > The two requirements are not jointly satisfied by any existing logic > (using my personal definition of grounded, at least). Set theory is > the broadest logic typically considered, so it comes closest to B, but > it (and most other logics considered strong enough to serve as a > foundation of mathematics) do not pass the test of A because the > manipulation rules do not match up to their semantics. I explain this > at some length here: > > http://groups.google.com/group/opencog/browse_thread/thread/28755f668e2d4267/10245c1d4b3984ca?lnk=gst&q=abramdemski#10245c1d4b3984ca > > A more worrisome problem is that B may be contradictory in and of > itself. If (1) I can as a human meaningfully explain logical system X, > and (2) logical system X can meaningfully explain anything that humans > can, then (3) system X can meaningfully explain itself. Tarski's > Indefineability Theorem shows that any such system (under some > seemingly reasonable assumptions) can express the concept "This > concept is false", and is therefore (again under some seemingly > reasonable assumptions) contradictory. So, if we accept those > "seemingly reasonable assumptions", no logic satisfying B exists. > > But, this implies that AI is impossible. So, some of the seemingly > reasonable assumptions need to be dismissed. (But I don't know which > ones.) > > Consideration of #2: > > Assumption 3 is that there exists some reasonable prior probability > distribution that we can use for learning. A now-common way of > choosing this prior is the minimum description length principle, which > tells us that shorter theories are more probable. > > The following argument was sent to me by private email by Wei Dai, and > I think it is very revealing: > > "I did suggest a prior based on set theory, but then I realized that > it doesn't really solve the entire problem. The real problem seems to > be that if we formalize induction as Bayesian sequence prediction with > a well-defined prior, we can immediately produce a sequence that an > ideal predictor should be able to predict, but this one doesn't, no > matter what the prior is. Specifically, the sequence is the "least > expected" sequence of the predictor. We generate each symbol in this > sequence by feeding the previous symbols to the predictor and then > pick the next symbol as the one that it predicts with the smallest > probability. (Pick the lexicographically first symbol if more than one > has the smallest probability.) > > This least expected sequence has a simple description, and therefore > should not be the least expected, right? Why should it not be more > expected than a completely random sequence, for example? > > Do you think your approach can avoid this problem?" > > Again, if the argument is right, then AI is impossible (or, as Wei Dai > put it, induction cannot be formalized). So, I again conclude that > some assumption needs to be dismissed. In this case the most obvious > assumption is that the prior should be based on minimum description > length. I thought at the time that that was the wrong one, but I am > not sure at the moment. > > So, any ideas how to resolve these two problems? > > --Abram > > > > PS-- I don't want to leave the quote from Wei Dai completely out of > context, so here is Wei Dai's full argument: > > http://groups.google.com/group/everything-list/browse_frm/thread/c7442c13ff1396ec/804e134c70d4a203 > > > On Wed, Aug 13, 2008 at 10:15 AM, Mike Tintner <[EMAIL PROTECTED]> wrote: >> THE POINT OF PHILOSOPHY: There seemed to be some confusion re this - the >> main point of philosophy is that it makes us aware of the frameworks that >> are brought to bear on any subject, from sci to tech to business to arts - >> and therefore the limitations of those frameworks. Crudely, it says: hey >> you're looking in 2D, you could be loooking in 3D or nD. >> >> Classic example: Kuhn. Hey, he said, we've thought science discovers bodies >> feature-by-feature, with a steady-accumulation-of-facts. Actually those >> studies are largely governed by paradigms [or frameworks] of bodies, which >> heavily determine what features we even look for in the first place. A >> beatiful piece of philosophical analysis. >> >> AGI: PROBLEM-SOLVING VS LEARNING. >> >> I have difficulties with AGI-ers, because my philosophical approach to AGI >> is - start with the end-problems that an AGI must solve, and how they >> differ from AI. No one though is interested in discussing them - to a great >> extent, perhaps, because the general discussion of such problem distinctions >> throughout AI's history (and through psychology's and philosophy's history) >> has been pretty poor. >> >> AGI-ers, it seems to me, focus on learning - on how AGI's must *learn* to >> solve problems. The attitude is : if we can just develop a good way for >> AGI's to learn here, then they can learn to solve any problem, and gradually >> their intelligence will just take off, (hence superAGI). And there is a >> great deal of learning theory in AI, and detailed analysis of different >> modes of learning, that is logic- and maths-based. So AGI-ers are more >> comfortable with this approach. >> >> PHILOSOPHY OF LEARNING >> >> However there is relatively little broad-based philosophy of learning. Let's >> do some. >> >> V. broadly, the basic framework, it seems to me, that AGI imposes on >> learning to solve problems is: >> >> 1) define a *set of options* for solving a problem, and attach if you can, >> certain probabilities to them >> >> 2) test those options, and carry the best, if any, forward >> >> 3) find a further set of options from the problem environment, and test >> those, updating your probabilities and also perhaps your basic rules for >> applying them, as you go >> >> And, basically, just keep going like that, grinding your way to a solution, >> and adapting your program. >> >> What separates AI from AGI is that in the former: >> >> * the set of options [or problem space] is well-defined, [as say, for how a >> program can play chess] and the environnment is highly accessible.AGI-ers >> recognize their world is much more complicated and not so clearly defined, >> and full of *uncertainty*. >> >> But the common philosophy of both AI and AGI and programming, period, it >> seems to me, is : test a set of options. >> >> THE $1M QUESTION with both approaches is: *how do you define your set of >> options*? That's the question I'd like you to try and answer. Let's make it >> more concrete. >> >> a) Defining A Set of Actions? Take AGI agents, like Ben's, in virtual >> worlds. Such agents must learn to perform physical actions and move about >> their world. Ben's had to learn how to move to a ball and pick it up. >> >> So how do you define the set of options here - the set of >> actions/trajectories-from-A-to-B that an agent must test? For,say, moving >> to, or picking up/hitting a ball. Ben's tried a load - how were they >> defined? And by whom? The AGI programmer or the agent? >> >> b)Defining A Set of Associations ?Essentially, a great deal of formal >> problem-solving comes down to working out that A is associated with B, (if >> C,D,E, and however many conditions apply) - whether A "means," "causes," >> or "contains" B etc etc . >> >> So basically you go out and test a set of associations, involving A and B >> etc, to solve the problem. If you're translating or defining language, you >> go and test a whole set of statements involving the relevant words, say "He >> jumped over the limit" to know what it means. >> >> So, again, how do you define the set of options here - the set of >> associations to be tested, e.g. the set of texts to be used on Google, say, >> for reference for your translation? >> >> c)What's The Total Possible Set of Options [Actions/Associations] - how can >> you work out the *total* possible set of options to be tested (as opposed to >> the set you initially choose) ? Is there one with any AGI problem? >> >> Can the set of options be definitively defined at all? Is it infinite say >> for that set of trajectories, or somehow limited? (Is there a definitive >> or guaranteed way to learn language?) >> >> d) How Can You Insure the Set of Options is not arbitrary? That you won't >> entirely miss out the crucial options no matter how many more you add? Is >> defining a set of options an art not a science - the art of programming, >> pace Matt? >> >> POST HOC VS AD HOC APPROACHES TO LEARNING: It seems to me there should be a >> further condition to how you define your set of options. >> >> Basically, IMO, AGI learns to solve problems, and AI solves them, *post >> hoc.* AFTER the problem has already been solved/learned. >> >> The perspective of both on developing a program for >> problem-solving/learning is this: >> >> http://www.danradcliffe.com/12days2005/12days2005_maze_solution.jpg >> >> you work from the end, with the luxury of a grand overview, after sets of >> options and solutions have already been arrived at, and develop your >> program from there. >> >> But in real life, general intelligences such as humans and animals have to >> solve most problems and acquire most skills AD HOC, starting from an >> extremely limited view of them : >> >> http://graphics.stanford.edu/~merrie/Europe/photos/inside%20the%20maze%202.jpg >> >> where you DON'T know what you're getting into, and you can't be sure what >> kind of maze this is, or whether it's a proper maze at all. That's how YOU >> learn to do most things in your life. How can you develop a set of options >> from such a position? >> >> MAZES VS MESSES. Another way of phrasing the question of :"how do you define >> the set of options?" is : >> >> is the set of options along with the problem a maze [clearly definable, even >> if only in stages] or a mess: >> >> http://www.leninimports.com/jackson_pollock_gallery_12.jpg >> >> [where not a lot is definable]? >> >> Testing a set of options, it seems to me, is the essence of AI/AGI so far. >> It's worth taking time to think about. Philosophically. >> >> >> >> >> ------------------------------------------- >> agi >> Archives: https://www.listbox.com/member/archive/303/=now >> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >> Modify Your Subscription: >> https://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com >> > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
