quen_tin comments on Philosophy: A Diseased Discipline - Less Wrong
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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.