Thursday, May 5, 2011

Will the sun rise tomorrow?

Valid deductive reasoning is that in which the premises provide conclusive reasons for the conclusion, and it is impossible for the premises to be true and the conclusion false. A classic example is the statement that “All men are mortal; Socrates is a man; therefore Socrates is mortal”. In contrast, inductive reasoning generally begins with a finite set of observations (or experimental results) and moves to a generalised conclusion. For example, “the sun has always risen in the morning; therefore it will rise tomorrow.” Induction amplifies what we already know. In inductive reasoning, the premises do not entail the conclusion or make it certain, but may make it reasonable. It is always reasonable to accept a deductive conclusion, but it is only arguably reasonable to accept an inductive conclusion, where many variables may affect the reasonableness of the conclusion. This problem has attracted much debate, especially as most of the decisions we make in everyday life are based squarely on inductive reasoning.

Bertrand Russell
Bertrand Russell pointed out the importance to us of relying on inductive reasoning. If we could not rely on such reasoning, he said, “we could never extend our knowledge beyond the sphere of our private experience; and this exceedingly limited.” According to induction, the only reason we have for assuming that the sun will rise tomorrow is that it has always done so in the past, as far as we can judge. Russell queries whether any number of cases of a law being fulfilled in the past will be sufficient evidence for it being fulfilled in the future. “If not, it becomes plain that we have no ground whatever for expecting the sun to rise tomorrow...” The belief that the sun will rise tomorrow might be falsified if a meteor crashed into the earth. A man who has been a source of food every day for a chicken may at last wring its neck instead of bringing food. Russell asks if we can find “more refined views as to the uniformity of nature”. We would like to know if “futures futures” will resemble “past futures”. Russell concludes that the inductive principle must be accepted or we will have to forgo all justification for our expectations of the future.

The reliability of induction has been argued in its defence, but such a defence cannot hold water if past evidence shows that inductions are not in fact reliably true, and there are surely many cases where people making inductions have arrived at false conclusions (like the unfortunate chicken).

Nelson Goodman
In 1955 Goodman raised a problem that seemed to show that induction is, as Papineau puts it, “downright unreliable”, known as the “green/grue” problem. Stated briefly: we reach an inductive conclusion, based on observation of all those we have seen so far, that all emeralds are green. Now suppose that we define the quality “grue” as applying to all objects which are first examined before (say) 2020 AD and found to be green OR which are examined after 2020 AD and are blue. All emeralds examined so far are thus both green and “grue”. But this cannot be true, as to be green is to be green forever; and to be “grue” is to be green now or blue after 2020 AD. We intuitively believe that the hypothesis is wrong, and that emeralds will still be green after 2020 AD; but the point of Goodman’s puzzle is to illustrate that enumerative inductions cannot always supply true conclusions, and thus cannot always be relied upon.

Green or Grue?
Strawson argued that not relying on induction was irrational. For example, if in the past one has always become wet by going out in the rain without an umbrella, it seems irrational to believe that this time one will not get wet in the rain without an umbrella. The degree of irrationality is arguably the same as believing that rain is not wet. Strawson argues that our use of the word “reasonable” includes the idea of conformance with inductive conclusions. So when we say that something (say a scientific theory) is “reasonable” we mean that it draws on an appropriate number of observed instances.

There are several ways of arriving at a decision such as “it is raining, therefore I will get wet”.  One is based on past experience – in the past when it is raining I have gotten wet – this is inductive reasoning. We could also reach the same conclusion based on the knowledge that water is wet, and so on, using deductive reasoning to reach the same conclusion. We do successfully navigate the social world and natural world. We are able to do this because we have this structure of thought; we are able to deduce, and form expectations, on the basis of conditions. Moreover, we are able to rule out defeasors – so called “Ceteris’ paribus” clauses - those independent variables which are not related to the question under decision. On this view, there arguably is no induction – our reasoning is all deduction.

One value of inductive reasoning, which cannot always be supplied by reliable deductive reasoning, is that it expands our possible knowledge base. As Papineau puts it:

The whole point of inferences is to increase our stock of knowledge. Inferences make new knowledge out of old: they take old knowledge as input, and generate new knowledge as output.

Obviously, inductive inferences that produce incorrect conclusions do not assist in furthering this increase in knowledge. Induction frequently produces false conclusions, but is it also the principal basis of our everyday reasoning upon which we rely, and with which we generally navigate the natural and social world.  We look to rely on probabilities and other yardsticks against which we can measure the reliability of our inductive inferences; but in everyday life these inductive inferences are often made intuitively. It is instructive, at least, to understand the basis upon which we make such judgement calls, and the limitations - and benefits – of doing so.

And that's your philosophy for the day. :-)

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