When I was younger...

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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. Systems that take seriously the idea that confirmation of truth is easy falls under the banner of "geometric logic", whose algebraic model are  frames, and topologies are just frames of subsets. So I see the relation between "facts" and "concepts" a little bit like the relation between "points" and "open sets", but more in a "internal language of a topos" or "pointless topology" fashion: we don't have access to points per se, only to open sets, and we imagine that points are infinite chains of ever precise open sets


It also happens to me when I got to solve a problem that many have and realize in retrospetct that it was a combination of luck, knowing the right people and skills that you don't know how to transfer, possibly because they are genetic traits. It must be frustrating to hear, after a question like "how have you conquered your social anxiety?", the condensed answer "mostly luck"


On the other hand, it makes you think when you realized how much these kinds of social status booster have permeated every step of the hierarchical ladder of any large organization... and yet, somehow, things still  work out


There is, at least at a mathematical / type theoretic level.

In intuitionistic logic,  is translated to , which is the type of processes that turn an element of  into an element of , but since  is empty, the whole  is absurd as long as  is istantiated (if not, then the only member is the empty identity). This is also why constructively  but not 

Closely related to constructive logic is topology, and indeed if concepts are open set, the logical complement is not a concept. Topology is also nice because it formalizes the concept of edge case


One thing to remember when talking  about distinction/defusion is that it's not a free operation: if you distinguish two things that you previously considered the same, you need to store at least a bit of information more than before. That is something that demands effort and energy. Sometimes, you need to store a lot more bits. You cannot simply become superintelligent by defusing everything in sight.

Sometimes, making a distinction is important, but some other times, erasing distinctions is more important. Rationality is about creating and erasing distinctions to achieve a more truthful or more useful model.

This is also why I vowed to never object that something is "more complicated" if I cannot offer a better model, because it's always very easy to inject distinctions, the harder part is to make those distinctions matter.


Well, I share the majority of your points. I think that in 30 years millions of people will try to relocate in more fertile areas. And I think that not even the firing of the clathrate gun will force humans to coordinate globally. Although I am a bit more optimist about technology, the actual status quo is broken beyond repair

Answer by MrMind90

The fact is surprising when coupled with the fact that particles do not have a definite spin direction before you measure it. The anti-correlation is maintained non-locally, but the directions are decided by the experiment.

A better example is: take two spheres, send them far away, then make one sphere spin in any orientation that you want. How much would you be surprised to learn that the other sphere spins with the same axis in the opposite directions?


How probable is that someone knows their internal belief structure? How probable is that someone who knows their internal belief structure tells you that truthfully instead of using a self-serving lie?


The causation order in the scenario is important. If the mother is instantly killed by the truck, then she cannot feel any sense of pleasure after the fact. But if you want to say that the mother feels the pleasure during the attempt or before, then I would say that the word "pleasure" here is assuming the meaning of "motivation", and the points raised by Viliam in another comment are valid, it becomes just a play on words, devoid of intrinsic content.

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