display all the ideas for this combination of texts
2 ideas
| 8624 | Induction is merely psychological, with a principle that it can actually establish laws [Frege] |
| Full Idea: Induction depends on the general proposition that the inductive method can establish the truth of a law, or the probability for it. If we deny this, induction becomes nothing more than a psychological phenomenon. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §03 n) | |
| A reaction: The problem is that we can't seem to 'establish' the requisite proposition, even for probability, since probability is in part subjective. I think induction needs the premiss that nature has underlying uniformity, which we then tease out by observation. |
| 8626 | In science one observation can create high probability, while a thousand might prove nothing [Frege] |
| Full Idea: The procedure of the sciences, with its objective standards, will at times find a high probability established by a single confirmatory instance, while at others it will dismiss a thousand as almost worthless. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §10) | |
| A reaction: This thought is presumably what pushes theorists away from traditional induction and towards Bayes's Theorem (Idea 2798). The remark is a great difficulty for anyone trying to defend traditional induction. |