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cousin_it comments on Philosophy: A Diseased Discipline - Less Wrong
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This is why I talked about algorithms. When a human being says "I am a human being", you may quibble about it being "observational" or "apriori" knowledge. But algorithms can actually have apriori knowledge coded in, including knowledge of their own source code. When such an algorithm receives inputs, it can make conclusions that don't rely on "realist" or "idealist" philosophical assumptions in any way, only on coded apriori knowledge and the inputs received. And these conclusions would be correct more or less by definition, because they amount to "if reality contains an instance of algorithm X receiving input Y, then reality contains an instance of algorithm X receiving input Y".
Your second paragraph seems to be unrelated to Kant. You just point out that our reasoning is messy and complex, so it's hard to prove trustworthy from first principles. Well, we can still consider it "probably approximately correct" (to borrow a phrase from Leslie Valiant), as jimrandomh suggested. Or maybe skip the step-by-step justifications and directly check your conclusions against the real world, like evolution does. After all, you may not know everything about the internal workings of a car, but you can still drive one to the supermarket. I can relate to the idea that we're still in the "stupid driver" phase, but this doesn't imply the car itself is broken beyond repair.
I don't think relying on algorithm solves the issue, because you still need someone to implement and interpret the algorithm.
I agree with your second point: you can take a pragmatist approach. Actually, that's a bit how science work. But still you did not prove in anyway that your model is a complete and definitive description of all there is nor that it can be strictly identifiable with "reality", and Kant's argument remains valid. It would be more correct to say that a scientific model is a relational model (it describes the relations between things as they appear to observers and their regularities).
You can be the algorithm. The software running in your brain might be "approximately correct by design", a naturally arising approximation to the kind of algorithms I described in previous comments. I cannot examine its workings in detail, but sometimes it seems to obtain correct results and "move in harmony with Bayes" as Eliezer puts it, so it can't be all wrong.