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by honoredb
2901 days ago
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Nitpick: "…had 13 not been prime" is not meaningless whimsy--a prime number of images is harder to lay out on the page. Mentioning this in the caption without explaining it is whimsical, but like a lot of GEB I'd argue it's whimsy with a purpose: training the reader to look for applications of abstract concepts. The reader ideally goes "wait, what? There's no connection between those two things! Unless..." |
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> The basic idea behind the alternative analysis was similar to that proposed by Robert Stalnaker (1968). Let's say that an A-world is simply a possible world where A is true. Stalnaker had proposed that p □→ q was true just in case the most similar p-world to the actual world is also a q-world. Lewis offered a nice graphic way of thinking about this. He proposed that we think of similarity between worlds as a kind of metric, with the worlds arranged in some large-dimensional space, and more similar worlds being closer to each other than more dissimilar worlds. Then Stalnaker's idea is that the closest p-world has to be a q-world for p □→ q to be true.
But "13 is prime" is the most central example of a necessary truth; in this example there _are_ no p-worlds. So the fact that this sentence is, in fact, meaningful shows that the way we use language is doing something different from Stalnaker's model.
And of course, the connection between counterfactuals, analogy making, and general intelligence is one of Hofstader's research interests, and he comes back to it in a later chapter. This example of his again kindof makes fun of counterfactual reasoning about mathematical objects:
> Related to this notion of slipping between closely related terms is the notion of seeing a given object as a variation on another object. An excellent example has been mentioned already-that of the "circle with three indentations", where in fact there is no circle at all. One has to be able to bend concepts, when it is appropriate. Nothing should be absolutely rigid.