Our ability to think about abstractions and extrapolations off of abstractions comes because we are able to create game boundaries around the systems that we think about. So yes you can talk about infinite resources and compare it to the domain of the lambda calculus, but this kind of thinking is possible only because we are able to abstract ideas by creating rules and barriers for the games. People don't always think of these as games because they can be so effective at producing material change that they seem and can be as practical as truck, or as armies of trucks.
> It is possible that your logic, fleshed out, could circumnavigate the > issue. Perhaps you can provide some intuition about how such a logic > should deal with the following line of argument (most will have seen > it, but I repeat it for concreteness): > > "Consider the sentence "This sentence is false". It is either true or > false. If it is true, then it is false. If it is false, then it is > true. In either case, it is both true and false. Therefore, it is both > true and false." Why? I mean that my imagined program is a little like a method actor (like Marlon Brando). What is its motivation? Is it a children's game? A little like listening to ghost stories? Or watching movies about the undead? The sentence, 'this sentence is false,' obviously relates to a boundary around the sentence. However, that insight wasn't obvious to me every time I came across the sentence. Why not? I don't know, but I think that when statements like that are unfamiliar, you put them into their own abstracted place and wait to see how it they are going to be used relative to other information. Let's go with your statement and suppose that the argument is unfamiliar. Basically, the first step would be to interpret the elementary partial meanings of the sentences without necessarily integrating them. Each sentence is put into a temporary boundary. 'It is either true or false.' Ok got it, but since this kind of argument is unfamiliar to my imaginary program, it does not immediately realize that the second sentence is referring to the first. Why not? Because the first sentence creates an aura of reference, and if the self-reference that was intended is appreciated, then the sense that second sentence is going to refer to the first sentence will - in some cases - be made less likely. In other cases, the awareness that the first sentence is self referential might make it more likely that the next sentence will also be interpreted as referring to it. The practical problems of understanding the elementary relations of communication are so complicated, that the problem of dealing with a paradox is not as severe as you might think. We are able to abstract and use those abstractions in processes that can be likened to extrapolation because we have to be able to do that. I don't think the problems of a self-referential paradox is significantly more difficult than the problems of general reference. Not only are there implicit boundaries, some of which have to be changed in an instant as the conversation develops, there are also multiple levels of generalization in conversation. These multiple levels of generalization are not simple or even reliably constructive (reinforcing). They are complex and typically contradictory. In my opinion they can be understood because we are somehow able access different kinds of relevant information necessary to decode them. This is one reason why I think that the Relevancy Problem of the Frame Problem is the primary problem of contemporary AI. We need to be able to access relevant information even though the appropriate information may change dramatically in response to the most minror variations in the comprehension of a sentence or of a situation. I didn't write much about the self-referential paradox because I think it is somewhat trivial. Although an AI program will be 'logical' in the sense of the logic of computing machinery, that does not mean that a computer program has to be strictly logical. This means that thinking can contain errors, but that is not front page news. Man bites dog! Now that's news. Jim Bromer ------------------------------------------- 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
