Charles, I fully understand your response --- it is typical when people interpret NARS according to their ideas about how a formal logic should be understood.
But NARS is VERY different. Especially, it uses a special semantics, which defines "truth" and "meaning" in a way that is fundamentally different from model-theoretic semantics (which is implicitly assumed in your comments everywhere), and I believe is closer to how "truth" and "meaning" are treated in natural languages (so you may end up like it). As Mark suggested, you may want to do some reading first (such as http://nars.wang.googlepages.com/wang.semantics.pdf), and after that the discussion will be much more fruitful and efficient. I'm sorry that I don't have a shorter explanation to the related issues. Pei On 10/8/07, Charles D Hixson <[EMAIL PROTECTED]> wrote: > Pei Wang wrote: > > Charles, > > > > What you said is correct for most formal logics formulating binary > > deduction, using model-theoretic semantics. However, Edward was > > talking about the categorical logic of NARS, though he put the > > statements in English, and omitted the truth values, which may caused > > some misunderstanding. > > > > Pei > > > > On 10/7/07, Charles D Hixson <[EMAIL PROTECTED]> wrote: > > > >> Edward W. Porter wrote: > >> > >>> So is the following understanding correct? > >>> > >>> If you have two statements > >>> > >>> Fred is a human > >>> Fred is an animal > >>> > >>> And assuming you know nothing more about any of the three > >>> terms in both these statements, then each of the following > >>> would be an appropriate induction > >>> > >>> A human is an animal > >>> An animal is a human > >>> A human and an animal are similar > >>> > >>> It would only then be from further information that you > >>> would find the first of these two inductions has a larger > >>> truth value than the second and that the third probably > >>> has a larger truth value than the second.. > >>> > >>> Edward W. Porter > >>> Porter & Associates > >>> 24 String Bridge S12 > >>> Exeter, NH 03833 > >>> (617) 494-1722 > >>> Fax (617) 494-1822 > >>> [EMAIL PROTECTED] > >>> > >>> > >> Actually, you know less than you have implied. > >> You know that there exists an entity referred to as Fred, and that this > >> entity is a member of both the set human and the set animal. You aren't > >> justified in concluding that any other member of the set human is also a > >> member of the set animal. And conversely. And the only argument for > >> similarity is that the intersection isn't empty. > >> > >> E.g.: > >> Fred is a possessor of purple hair. (He dyed his hair) > >> Fred is a possessor of jellyfish DNA. (He was a subject in a molecular > >> biology experiment. His skin would glow green under proper stimulation.) > >> > >> Now admittedly these sentences would usually be said in a different form > >> (i.e., "Fred has green hair"), but they are reasonable translations of > >> an equivalent sentence ("Fred is a member of the set of people with > >> green hair"). > >> > >> You REALLY can't do good reasoning using formal logic in natural > >> language...at least in English. That's why the invention of symbolic > >> logic was so important. > >> > >> If you want to use the old form of syllogism, then at least one of the > >> sentences needs to have either an existential or universal quantifier. > >> Otherwise it isn't a syllogism, but just a pair of statements. And all > >> that you can conclude from them is that they have been asserted. (If > >> they're directly contradictory, then you may question the reliability of > >> the asserter...but that's tricky, as often things that appear to be > >> contradictions actually aren't.) > >> > >> Of course, what this really means is that logic is unsuited for > >> conversation... but it also implies that you shouldn't program your > >> rule-sets in natural language. You'll almost certainly either get them > >> wrong or be ambiguous. (Ambiguity is more common, but it's not > >> exclusive of wrong.) > >> > Well, truth values would allow one to assign probabilities to the > various statements (i.e., the proffered values plus some uncertainty), > but he specifically said we didn't know anything else about the terms, > so I don't see how one can go any further. If you don't know what a > human is, then knowing that Fred is one doesn't tell you anything about > his other characteristics. > > So when you have two statements about Fred, you "know" the two > statements, but you don't know anything about the relationship between > them except that their intersection is non-empty. Since it was > specified that we didn't know anything about them, Fred could be a line, > and human could be vertical lines and animal could be named entities. > > For fancier forms of logic (induction, deduction, etc.) you need to have > more information. Most forms require that there be at least a partial > ordering available, if not several. Many modes of reasoning require > that a complete ordering be available. (It doesn't need to be an > ordering that guarantees that every iteration will end up with a member > of the set...consider the problem of stepping through a hash table...you > can do it, but you'll get lots of empty cells, and you can't predict the > order. What you can predict is complete coverage. This is an > importantly useful characteristic. It lets you check "for all" assertions. > > I'll admit I haven't read your papers on NARS, but I don't see how that > could obviate these "primitive" characteristics. You can't do induction > without an ordering. Deduction doesn't require an ordering, but it > requires rules of inference. Simple assertions don't require rules of > inference, but do require assertion...which generally means a verb > (possibly understood). This is why "if x then y" is often translated > into English as "x implies y", but a better translation might be "x > implies y, but I'm not asserting x". > > I.e., two children of the same parent can be expected to have similarities. > P.S.: > > ABDUCTION INFERENCE RULE: > Given S --> M and P --> M, this implies S --> P to some degree > I.e., two children of the same parent can be expected to have > similarities (in the context of inheritance...they will at least be > similar to the extent that they inherited the same characteristics). > > INDUCTION INFERENCE RULE: > Given M --> S and M --> P, this implies S --> P to some degree > I.e., two parents of the same child can be expected to have similarities > (in the context of inheritance). This one seems dubious, but to the > extent that it's true then one should also expect "P-->S to some degree". > If I look a parents and their children, this seems reasonable...though > the "to some degree" is quite unpredictable. OTOH, if I look at object > classes, it seems to fail completely. It's quite surprising to find > induction appear to be less certain than abduction. Either I'm not > properly understanding what is meant (Well, I did mention that I hadn't > read the original papers), or perhaps this needs a bit more thought. It > seems very sensitive to context. I also note that I can't relate this > definition easily to the meaning of induction used in the phrase in > "mathematical induction". Or to electrical induction. > > OTOH, it's certainly true that if two parents are related through a > child, one can expect, at minimum, for them to be members of closely > related species. ... I feel uncomfortable with calling that piece of > reasoning induction, however. Model-consistency seems a better phrase. > (I.e., I have a model of the world, and in that model only closely > related species can engender offspring. N.B.: I am aware of model > violations, where, e.g., microbes can cause insects or mammals to > engender offspring...so I have a more detailed model to account for > that.) This is clearly a much more complex process than your proposed > simple rule...but I'm not certain that "induction" is an appropriate > term. I have a model for how other forms of induction work, and this > doesn't appear to fit into it. (OTOH, it's a rather loose model, and if > this usage became well-established, it would probably adjust. But the > adjustment would, for at least a while, feel unnatural.) > > Still, utility rules. If this rule is useful, then it's a valid rule. > I may be unhappy with the name that it was given, and may feel that it > appears unduly context sensitive, but I'm trying to apply it in the more > general space of reasoning, rather than within the context of your > proposed system. And it's quite plausible that as program objects > become more complex, then it will be more difficult to perform multiple > inheritance between distantly related objects. (One might consider why > so many computer languages have opted for single inheritance with > interfaces. It might be a consequence of this rule [which I still don't > want to call induction].) > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?&; > ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=51231788-117b62
