The problem of induction was introduced by David Hume (1711-1776) and started with the question of whether or not induction is justified. This is a genuine concern since predictions about the unobserved/future that are derived from experience are made through inductive inference, and are not deductively closed arguments (i.e. not a priori knowledge).
To illustrate the problem, let us begin with the following example:
In my experience, all F's are G's, and no cases of F's have been found to not be G's.
I arrive at the general statement that "All F's are G's" through inductive reasoning.
Is this generalization "justified"? It is immediately clear that the generalization does not necessarily follow from the premise, since it is not arrived at deductively (that is, it is not entailed). So it appears that we take a leap from premise to generalization when we reason inductively.
Upon careful examination of the above example, the generalization can be justified by the apparent "Uniformity of Nature", as discussed by Bertrand Russell in The Problems of Philosophy, Chapter VI. "The belief in the uniformity of nature is the belief that everything that has happened or will happen is an instance of some general law to which there are no exceptions." Herein lays the problem: uniformity of nature is a premise that can only be arrived at inductively, so it cannot be used to justify inductive reasoning. It is a circular argument.
P. F. Srawson attacks this problem from a linguistic standpoint, claiming that the question of whether or not induction is justified is nonsensical. He says that it is "the absurd wish that induction should be shown to be some sort of deduction." His argument is illustrated as follows:
To be rational is to use induction and deduction.
Deductive and inductive reasoning are mutually exclusive.
The word "deductive" describes closed arguments that lead to a priori knowledge.
Deductive propositions are therefore either valid, or invalid on the basis of being either justified or not justified.
The word "inductive" describes the reasoning that leads to degrees of belief that are supported by experience.
So, questions such as "Is there reason in believing in deductive arguments?" and "Are inductive arguments justified?" have no meaning for Strawson.
Karl Popper attempts to show that "the belief that we use induction is simply a mistake. [...] The whole apparatus of induction becomes unnecessary once we admit the [...] conjectural character of human knowledge." He discards induction with his notions of the following:
1. Although we cannot employ induction to acquire a necessary truth, we can necessarily conclude the falsity of a generalization with falsifying evidence, and this is purely deductive.
2. Laws arrived at inductively were based on "unconscious, inborn expectations" or "scanty material, i.e. the few observed instances upon which the law may be based."
He proposes that conjectures (hypotheses) are arrived at arbitrarily, either through myths, or inborn expectations, and that testing (trying to find refutations) is how one arrived at conjectures with (degrees of) corroboration, as opposed to inductive inferences with (degrees of) probability. So, he discards induction, but only to appeal to it in different terms.
Neither attack of the problem is satisfying. No one said it better than Russell when he said that "we must either accept the inductive principle on the ground of its intrinsic evidence, or forgo all justification of our expectations about the future." And all the while philosophers who attack this problem tragically become Kierkegaard's Knights of Infinite Resignation: afraid and too calculating to take the leap that they miss the point.
This was my first assignment after returning to school after an extensive hiatus . This means it was written around. It's just a short little ditty, and I stumbled upon it while going through my old class notes. I was awarded a 90%, and a comment regarding my criticism of criticisms on the problem of induction. I don't think the T.A. who marked it appreciated that I called people in his profession Kierkegaard's Knights of Infinite Resignation. I was hoping he'd get a kick out of it.