Footnotes

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However, observing that it doesn't know the telephone number and cannot infer what it is involves getting around Gödel's theorem. Because, if there is any sentence that is not inferrable, a system powerful enough for arithmetic must be consistent. Therefore, it might seem that Gödel's famous theorem that the consistency of a system cannot be shown within the system would preclude inferring non-knowledge except for systems too weak for arithmetic. Gödel's [G\"odel, 1940] idea of relative consistency gets us out of the difficulty.
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One can understand aspects of a human activity better than the people who are good at doing it. Nadia Comenici's gymnastics coach was a large, portly man hard to imagine cavorting on a gymnastics bar. Nevertheless, he understands women's gymnastics well enough to have coached a world champion.
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Too much work concerned with self-knowledge has considered self-referential sentences and getting around their apparent paradoxes. This is mostly a distraction for AI, because human self-consciousness and the self-consciousness we need to build into robots almost never involves self-referential sentences or other self-referential linguistic constructions. A simple reference to oneself is not a self-referential linguistic construction, because it isn't done by a sentence that refers to itself.
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Some other formalisms give up the law of substitution in logic in order to avoid this difficulty. We find the price of having separate terms for concepts worth paying in order to retain all the resources of first order logic and even higher order logic when needed.
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We assume that our axioms are strong enough to do symbolic computation which requires the same strength as arithmetic. I think we won't get much joy from weaker systems.
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A conviction of about what is relevant is responsible for a person's initial reaction to the well-known puzzle of the three activists and the bear. Three Greenpeace activists have just won a battle to protect the bears' prey, the bears being already protected. It was hard work, and they decide to go see the bears whose representatives they consider themselves to have been. They wander about with their cameras, each going his own way.

Meanwhile a bear wakes up from a long sleep very hungry and heads South. After three miles, she comes across one of the activists and eats him. She then goes three miles West, finds another activist and eats her. Three miles North he finds a third activist but is too full to eat. However, annoyed by the incessant blather, she kills the remaining activist and drags him two miles East to her starting point for a nap, certain that she and her cubs can have a snack when she wakes.

What color was the bear?

At first sight it seems that the color of the bear cannot be determined from the information given. While wrong in this case, jumping to such conclusions about what is relevant is more often than not the correct thing to do.
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Our approach is a variant of that used by [Kraus, Perlis and Horty, 1991].
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These conclusions are true in the simplest or most standard or otherwise minimal models of the ideas taken in consciousness. The point about nonmonotonicity is absolutely critical to understanding these ideas about emotion. See, for example, [McCarthy, 1980] and [McCarthy, 1986]
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Admittedly referring to ``reducing the thresholds of synapses'' is speculative. However, it may be possible to test these ideas experimentally. There should be a fixed set of these substances and therefore definite classes of ideas that they bring in.

John McCarthy
Thu May 25 00:33:25 PDT 1995