# Problem of induction

The problem of induction is the philosophical issue involved in deciding the place of induction in determining empirical truth. The problem of induction is whether inductive reason works. That is, what is the justification for either:

1. generalizing about the properties of a 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 are 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 Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity) is universal.

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 that may be concluded 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 establish 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. Hume looked at ways to justify inductive thinking. He pointed out that justifying induction on the grounds that it has worked in the past begs the question. That is, it is using inductive reasoning to justify induction. Circular arguments are valid, but do not provide a satisfactory justification for the supposition they claim to support. One has no rational basis for belief in the Principle of the Uniformity of Nature. Prior to Hume, Francis Bacon had made a strong claim that science ought to be based on induction.

Karl Popper sought to "bypass" the problem in the philosophy of science by arguing that science does not actually rely on induction, but falsification instead. Popper replaced induction with deduction, in effect making modus tollens the centerpiece of his theory. On this account, when assessing a theory, one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it. Popper went further and stated that a hypothesis which does not allow for experimental tests of falsity is outside the bounds of science. However, critics of Popper's approach to solving the problem, such as the famous utilitarian and animal rights advocate Peter Singer, argue that Popper is merely obscuring the role induction plays in science by concealing it in the step of falsification. In that, they mean that the proposition of something having been falsified is in and of itself a scientific theory and can only be assumed to be definitive through induction; no matter how many times something is demonstrated to have been falsified, if one discards inductive reasoning, it cannot be assumed that such a thing will always be falsified whenever the conditions under which it was first falsified are met.

Isaac Newton considered induction the basis of scientific method at least in his "Opticks".

Nelson Goodman presented a different description of the problem of induction in the article "The New Problem of Induction" (1966). Goodman proposed a new colour, "grue". Something is grue if it is green up until some given time, and blue thereafter. The "new" problem of induction is, how can one know that grass is indeed green, and not grue? The standard scientific response is to invoke Occam's Razor.