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Gray_Area comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: Gray_Area 29 September 2007 09:25:35AM 7 points [-]

Perhaps 'a priori' and 'a posteriori' are too loaded with historic context. Eliezer seems to associate a priori with dualism, an association which I don't think is necessary. The important distinction is the process by which you arrive at claims. Scientists use two such processes: induction and deduction.

Deduction is reasoning from premises using 'agreed upon' rules of inference such as modus ponens. We call (conditional) claims which are arrived at via deduction 'a priori.'

Induction is updating beliefs from evidence using rules of probability (Bayes theorem, etc). We call (conditional) claims which are arrived at via induction 'a posteriori.'

Note: both the rules of inference used in deduction and rules of evidence aggregation used in induction are agreed upon as an empirical matter because it has been observed that we get useful results using these particular rules and not others.

Furthermore: both deduction and induction happen only (as far as we know) in the physical world.

Furthermore: deductive claims by themselves are 'sterile,' and making them useful immediately entails coating them with a posteriori claims.

Nevertheless, there is a clear algorithmic distinction between deduction and induction, a distinction which is mirrored in the claims obtained from these two processes.