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HoverHell comments on Skepticism about Probability - Less Wrong Discussion
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You don't (or “I don't”, if that's what you meant).
You could say something like that: “if induction is impossible then decision-making and communication are futile”.
However, that by itself does not disprove / dejustify claims that induction is possible but in other ways / with exceptions (on the lines of “the induction is possible unless applied to god^W magic”).
If you have no non-circular basis for believing in induction, surely it is irrational?
So, what are you trying to say?
"Better" isn't a function of the real world anyway- I'm appealing to it because most people here want to be rational, not because it is objectively better.
What do you mean by "rational" is not a binary?
“Better” / “preferable” / “utility” / … is necessary for “usefulness” e.g. “usefulness of this communication” (and also for decision-making).
By “not a binary” I mean the division is not into “rational” / “non-rational”, but into “more rational” / “less rational”; where “rational” is relevant to the aforementioned “better” (with regards to efficiency of optimization and also forms of communication).
… vaguely speaking.
On thought, my response is that no circular argument can possibly be rational so the question of if rationality is binary is irrelevant. You are mostly right, though for some purposes rational/irrational is better considered as a binary.
Any particular examples?