The No-Free-Lunch theorems show that if a uniform distribution is placed over all logically possible sequences of future events, any learning algorithm is expected to have a generalisation error of 1/2.
(Machine learning theory; interpreted as formal versions of Hume's first fork)
Formal theorems establishing that there are a priori possible situations in which any given algorithm does not perform well, implying no algorithm can be demonstratively guaranteed to perform well across all possible situations
uniform distribution(Probability theory applied to message sets)
A probability distribution in which each element x of a set S is selected with equal probability 1/|S|
Premise P3 can perhaps be challenged on the grounds that a priori justifications can also be given for contingent propositions. Even though an inductive inference can fail in some possible situations, it could still be reasonable to form an expectation of reliability if we spread our credence equally over all the possibilities and have reason to think (or at least no reason to doubt) that the cases where inductive inference is unreliable require a ‘very specific arrangement of things’ and thus