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.
Gist of Idea
In science one observation can create high probability, while a thousand might prove nothing
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §10)
Book Reference
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.16
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.
Related Idea
Idea 2798 Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]