ABSTRACT
The problem of induction is a complex one, having various aspects and branches. I shall begin by stating the problem of induction by simple enumeration.
The fundamental question, to which others are subsidiary, is this: Given that a number of instances of a class α have all been found to belong to a class β, does this make it probable, (a) that the next instance of α will be a β, or (b) that all α’s are β’s?
If either of these is not true universally, are there dis coverable limitations on α and β which make it true?
If either is true with suitable limitations, is it, when so limited, a law of logic or a law of nature?
Is it derivable from some other principle, such as natural kinds, or Keynes’s limitation of variety, or the reign of law, or the uniformity of nature, or what not?
Should the principle of induction be stated in a different form, viz: Given a hypothesis h which has many known true consequences and no known false ones, does this fact make h probable? And if not generally, does it do so in suitable circumstances?
What is the minimum form of the inductive postulate which will, if true, validate accepted scientific inferences?
Is there any reason, and if so what, to suppose this minimum postulate true? Or, if there is no such reason, is there nevertheless reason to act as if it were true?
