On Fri, Oct 10, 2008 at 8:56 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>> Well, it depends on the semantics. According to model-theoretic >> semantics, if a term has no reference, it has no meaning. According to >> experience-grounded semantics, every term in experience have meaning >> --- by the role it plays. > > That's why I said "almost-meaningless" ... if those are the only > relationships > known to the system, then the terms in those relationships play almost > no roles, hence have almost no meanings... Since each inference rule usually only considers two premises, whether the meaning of the involved concepts are rich or poor (i.e., whether they are also involved in other statements not considered by the rule) shouldn't matter in THAT STEP, right? >> Further questions: >> >> (1) Don't you intuitively feel that the evidence provided by >> non-swimming birds says more about "Birds are swimmers" than >> "Swimmers are birds"? > > Yes, but only because I know intuitively that swimmers are more common > in my everyday world than birds. Please note that this issue is different from our previous debate. "Node probability" have nothing to do with the asymmetry in induction/abduction. For example, "non-swimmer birds" is negative evidence for "Birds are swimmers" but irrelevant to "Swimmers are birds", while "non-bird swimmers" is negative evidence for "Swimmers are birds" but irrelevant to "Birds are swimmers". No matter which of the two nodes is more common, you cannot have both case right. >> (2) If your answer for (1) is "yes", then think about "Adults are >> alcohol-drinkers" and "Alcohol-drinkers are adults" --- do they have >> the same set of counter examples, intuitively speaking? > > Again, our intuitions for this are colored by the knowledge that there > are more adults than alcohol-drinkers. As above, the two sets of counter examples are "non-alcohol-drinking adult" and "non-adult alcohol-drinker", respectively. The fact that these two statements have different negative evidence have nothing to do with the size of the related sets (node probability). > Consider high school, which has 4 years: freshman, sophomore, > junior, senior. > > Then think about "Juniors & seniors are women" and "women > are juniors & seniors" > > It seems quite intuitive to me that, in this case, the same pieces of > evidence support the truth values of these two hypotheses. > > This is because the term probabilities of "juniors and seniors" > and "women" are intuitively known to be about equal. Instead of "supporting evidence", you should address "refuting evidence" (because that is where the issue is). For "Juniors & seniors are women", it is "juniors & seniors man", and for "women are juniors & seniors", it is "freshman & sophomore women". What I argued is: the counter evidence of statement "A is B" is not counter evidence of the converse statement "B is A", and vice versa. You cannot explain this in both directions by node probability. >> (3) According to your previous explanation, will PLN also take a red >> apple as negative evidence for "Birds are swimmers" and "Swimmers are >> birds", because it reduces the "candidate pool" by one? Of course, the >> probability adjustment may be very small, but qualitatively, isn't it >> the same as a non-swimming bird? If not, then what the system will do >> about it? > > Yes, in principle, PLN will behave in "Hempel's confirmation paradox" in > a similar way to other Bayesian systems. > > I do find this counterintuitive, personally, and I spent a while trying to > work > around it ... but finally I decided that my intuition is the faulty thing. > As you note, > it's a very small probability adjustment in these cases, so it's not > surprising > if human intuition is not tuned to make such small probability adjustments > in a correct or useful way... Well, actually your previous explanation is exactly the opposite of the standard Bayesian answer --- see http://en.wikipedia.org/wiki/Raven_paradox Now we have three different opinions on the relationship between statement "Birds are swimmers" and the evidence provided by a red apple: (1) NARS: it is irrelevant (neither positive nor negative) (2) PLN: it is negative evidence (though very small) (3) Bayesian: it is positive evidence (though very small) Everyone agrees that (2) and (3) are counterintuitive, but most people trust probability theory more than their own intuition --- after all, nobody is perfect ... :-( To me, "small probability adjustments" is a bad excuse. No matter how small the adjustment is, as far as it is not infinitely small, it cannot be always ignored, since it will accumulate. If all non-bird objects are taken as (either positive or negative) evidence for "Birds are swimmers", then the huge number of them cannot be ignored. It is always possible to save a theory (probability theory, in this situation) if you are willing to pay the price. The problem is whether the price is too high. Pei ------------------------------------------- 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=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
