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"Understanding" needs awareness. Machines are not aware. So machines cannot understand. But many senses of "awareness". MU"understands" maths and the CMS has limited awareness. |
Penrose believes that it is not possible for a computer program to fully understand mathematics. He argues that "genuine understanding" requires awareness, and since machines cannot be aware, they cannot understand. There are several senses of the word "awareness" used by Penrose in this argument, not all of them consistent. I would argue that a machine that understands mathematics does need to have some form of awareness, eg of the underlying goals and subgoals, of the perceptual features, heuristics, etc. But it is not clear that the machine needs to be aware of the temperature of the room, what the weather is like, etc. To some extent, the Contextual Memory System shows some awareness by using features to represent its state of attention. The Mathematics Understander does show some limited understanding of mathematics, and is therefore an existence proof that Penrose is wrong. |
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