You're never wrong injecting complexity, but rarely you're right
I just want to put this idea in the form of a post, to gather your impressions. I think it's my main rationalist failure mode. Recently in a Facebook group, some poster has proposed this synthesis of Harari's book '21 lessons': > In the 21st century, three narratives were used to explain the past and predict the future: the fascist, the communist and the liberal narrative. During the century, the latter has prevailed, although in recent times it has started to crack, due to events like the election of Trump, the Brexit, and so on. Then, the same user asked: what could be a new narrative that would help us in the future? I was tempted to reply as I always do: criticize the simplification. I was about to write that the concept of narrative itself is a narrative, that Harari is seeing the past with the eyes of the present, but not necessarily this lens will help with navigating the future, that also a better concept would be that of a memeplex, which is less internally coherent than a story, and thus more complex to pinpoint. Then a reflection occured to me: I always end up doing this, in almost all discussions I partecipate. People simplify too much and come to the wrong conclusion, they consider only the extremes of a spectrum, they use words as rigid classifiers and debate endlessly about them, they do not have internally coherent point of views, etc. I almost invariable end up 'winning' (i.e. appear wise) by injecting some complexity: usually in the form of a new parameter that was buried in the presuppositions. Then, I was struck by another insight: it is too easy to win this way. From a mathematical point of view, a system with a bigger state space is more flexible than a smaller system, and so an 'optimization' that increases the space state is always correct. Is that possible? How probable it is that I've discovered a universal optimization of every human debate? I reasoned that it's very low, and indeed I think I've always failed to consider the downside
I should have written "algebraic complement", which becomes logical negation or set-theoretic complement depending on the model of the theory.
Anyway, my intuition on why open sets are an interesting model for concepts is this: "I know when I see it" seems to describe a lot of the way we think about concepts. Often we don't have a precise definition that could argue all the edge case, but we pretty much have a strong intuition when a concept does apply. This is what happens to recursively enumerable sets: if a number belongs to a R.E. set, you will find out, but if it doesn't, you need to wait an infinite amount of time.... (read more)