Problem of induction

The Problem of Induction is the philosophical issue involved in deciding the place of induction in determining empirical truth. Thus, I know from direct sensations (vision, pain, ...) that you dropped a rock on my toe. Is it true, however, that a rock dropped on my tow will always cause pain? You may propose to test this by a series of dropped rocks, to which I will probably object. But even if you carried out your plan, would a series of painful swollen toes demonstrate that dropping rocks on toes always hurts? Such a conclusion is reached by what is called inductive reasoning, but hte problem of induction is whether inductive reason works. That is, what is the justification for either:

1. generalizing about the properties of an entire class of objects based on some number of observations of particular instances of that class of objects (for example, "All ravens we have seen are black, and therefore all ravens black"); or
2. presupposing that a sequence of events in the future will occur as they always have in the past (for example, the attractive force described by Newton's Law of Gravitation, or Einstien's revision in General Relativity) is universal ("All the rocks I have released have landed on your toes, and therefore the next rock I release will also do so.")

However, any series of observations, however large, may be taken to logically imply any particular conclusion about some future event only if 'induction' itself works. And we may conclude that only inductively! So, for instance, from any series of observations that water freezes at 0°C it is valid to infer that the next sample of water will do the same only if induction works. That such a prediction comes true when tried merely adds to the series; it does not extablish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?

David Hume addressed this problem in the 18th century in a particularly influential way, and no analysis since has managed to evade Hume's critique. Prior to Hume, Sir Francis Bacon had made a strong claim that science was based on induction, but whether individual scientists after Bacon actually believed in his analysis or not, Sir Karl Popper bypassed the 'problem' by noting that science actually does not rely on induction, but rather uses it only to establish 'liklihood of reliability' in hypotheseses, and actually tests possible hypotheseses by experiment. Those failing such a test lose liklihood. Popper went further and stated that an hypothesis which does not allow of such experimental text is outside the bounds of science. This was his doctrine of falsifiability.

Nelson Goodman presented a more sophisticated description of the problem of induction in 1966: