danilobellini comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (381)
Nice, but the difference with this "belief" is that you're talking about sensory "counting" (visual grouping), and I was talking about the numbers themselves, as models for games, other phenomena, etc., and not just as a "counting" tool.
In the 1+1=3 example, to define the cardinality, he/she used the Peano's axioms, didn't he/she?
I don't see the "visual sensory counting" as the only use for "2+2=4", that's why I don't think this experiment would refute such a priori content.
Another idea: let Ann be a girl with hemispatial neglect in a extinction condition. Ann has problems detecting anything on the left, and she can possibly see 2+2=3 as idealized above, due her brain damage. Will she think that 2+2=3? I don't think so...but if she does...will that be a model for all "integer numbers" aplications? I think in "integer" as a framework for several phenomena, other models, other knowledge, not only the counting one.
For the minds that see 2+2=4 as something patently absurd, because 2+2=3 is part of their intuitive arithmetic, these minds probably won't see the 2+2=4 even when brought to a world like ours. After a time in the 2+2=4 world, they probably won't forget that 2+2=3, unless the 2+2=3 wasn't modeling anything else. But the 2+2=3 was modeling something in their past history, at least the counting principle of their world. So they still have the 2+2=3 belief in their lives while they remember their past. If they forget their past, the 2+2=3 belief might became unuseful, but that still don't make the 2+2=3 an absurd or replaced by the 2+2=4: there are 2 number systems here.
For me, 2+2=3 isn't an absurd. That might be seem as a "common sum with a 3/4 multiplier" or a "X + Y = X p Y/X" where "p" is our common sum and "/" is our division, etc.. This way, like the 1+1=3 example above, only overloads the "+" operator. But, again, this "+" isn't the same from the "2+2=4"