Regarding mapping versus description: I agree that my motivations were semantic rather than syntactic. I just wanted to know whether the idea I had made sense to others who know something of intuitionistic logic.
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.
Does it make sense to say that 1 is the strategy of correcting a map and 2 is the strategy of rejecting a description as inaccurate without seeking to correct something?
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:
1 is the strategy of correcting the map and 2 is the strategy of rejecting the map as inaccurate without seeking to correct it.
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 certainly incomplete. Their contours are filled in as more information becomes available and rejected as inaccurate when they lead to contradictions, making each one a holistic representation of a possible territory. (Shoehorning the same approach into classical logic is possible, but you have to create a set of conventions to do so. These conventions are not universal, making the approach less natural.)
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 certainly incomplete. Their contours are filled in as more information becomes available and rejected as inaccurate when they lead to contradictions, making each one a holistic representation of a possible territory. (Shoehorning the same approach into classical logic is possible, but you have to create a set of conventions to do so. These conventions are not universal, making the approach less natural.)
Something like that anyway, but Shramko 2012 has put a lot more thought into this than I have: http://kdpu.edu.ua/shramko/files/2012_Logic_and_Logical_Philosophy_What_is_a_Genueny_Intuitionistic_Notion_of_Falsity.pdf I defer to expert opinion here.