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This issue happens at the edge of every induction. These two rules support their data equally well: data: T T T T T T F rule1: for all i: T rule2: for i < 7:
by usgroup 9mo ago
This issue happens at the edge of every induction. These two rules support their data equally well:
data: T T T T T T F
rule1: for all i: T
rule2: for i < 7: T else F
- p-e-w 9mo agoThat’s where Bayesian reasoning comes into play, where there are prior assumptions (e.g., that engineered reality is strongly biased towards simple patterns) which make one of these hypotheses much more likely than the other.
- usgroup 9mo agoyes, if you decide one of them is much more likely without reference to the data, then it will be much more likely :)
- wasabi991011 9mo agoDeciding that they are both equally likely is also a deciding a prior. Yes, "equally likely" is the minimal information prior which makes it best suited when you have no additional information. But it's not unlikely that have some sort of context you can use to decide on a better prior.
- usgroup 9mo agoWell that would be extra information. Wherever you find the edge of your information, you will find the "problem of induction" as presented above.