Two challenges to inductivism

Inductivism is the conjoint thesis that there are genuine inductive inferences and that successful inductive inferences provide inductive knowledge. This paper presents two challenges to inductivism. The first is explaining how many observations are required for inductive inferences in a precise and non-arbitrary way. This is the threshold problem. The second is providing an account of how inductive knowledge can be a qualitative change from a mere quantity of observations. This is the qualitative leap problem. I anticipate and criticize some attempts to solve these problems. One strategy is based on the idea that inferences are justification attempts and that different inference types require different theories of justification. Thus successful inductions can receive an externalist interpretation as reliable processes in which the evidential threshold isn't reflectively accessible. I object that this solution generates new versions of the threshold problem and doesn't address the qualitative leap problem. I also argue that any attempt to solve the two problems will be unsuccessful, since an evidential threshold for inductive inferences is implausible in principle. The conclusion is that inductive skepticism is justified.