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Understood. But, the point that I raised is not merely syntactic. On a fundamental level, a description of the territory is a map, so when you attempt to contrast correcting a map vs rejecting a description of a territory, you are really talking about correcting vs. rejecting a map.
Yes, in the case of number 1 you have proved via contradiction that there is no red cube, and in #2 you have concluded that one or more of your assumptions is incorrect (i.e. that your map is incorrect). However, this is not a map vs. territory distinction; in both cases you are really dealing with a map. To make this clear, I would restate as:
So, I guess I don't really have anything additional to add about intuitionistic logic - my point is that when you talk about a description of the territory vs. a map, you are really talking about the same thing.
Thanks. The next thing I was going to say is that the intuitionistic strategy of neutrality with regard to affirming or negating propositions in worlds until proof comes along roughly (i.e. in a sense to be argued for later) differentiates the classical and intuitionistic approaches like so:
The classical approach is good for having one "world" description that is almost certainly inaccurate. This can be gradually updated, making it represent one map.
The intuitionistic approach is good for having multiple world descriptions that are almost certain... (read more)