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The Problem of Dismissing Induction

The problem of induction, pointed out by David Hume, continues to baffle scientists and philosophers. Theo Clark explains why.

Of late I have been working my way through The Logic of Scientific Discovery by Karl Popper. It provided me with a philosophical dilemma that threatened my faith in science; especially physics. After some initial fretting, I decided I needed to try to resolve this dilemma in an attempt to remove it from my mind. In his book, Popper outlines what he calls ‘the problem of induction’. It is a ‘problem’ that was first demonstrated by David Hume (1711-76) and as a piece of logic it is impossible to fault. Induction, in the scientific sense of the word, is the method of generalising a universal law or principle after numerous observations and tests have been carried out. For example, “every single time I have dropped an object it has fallen towards the centre of the Earth. Therefore all dropped objects will always fall towards the centre of the Earth.” What this is saying is that given a large number of observations of X, and if all known Xs are Y, then all unknown Xs are Y as well. Using the term ‘unknown’ says exactly what the problem is – we do not know! An example from everyday life might be, “I have watched a lot of cricket test matches and as such all cricket balls known to me are red. Therefore all cricket balls unknown to me are red as well.” Thus an inductive conclusion is reached; but as soon as I personally witness a one-day match (where the ball is white) I would see this to be false. Popper saw induction as attempting to establish a universal statement from a singular one, or indeed many singular ones. How can we believe something to be universally true when we can only show it to be true a finite number of times? Even a very large number of singular statements or events will not prove a universal one. The only way to prove a universal statement is by testing it an infinite number of times, which is impossible.

Some have countered that while inductive reasoning may not guarantee actual truth, it at least provides a greater probability of truth. Popper demonstrates that this view is false. Even probability is not certain. If we are to grant a certain amount of probability to a statement we have to invoke another instance of induction, and granting this statement a degree of probability forces yet another invoking of induction, and so on. Using ‘probability logic’ leads to either an infinite regress, or an a priori belief. The logic behind induction is based on the doctrine of non est factum. We are assuming something to be a fact when it has not yet been established. Probability only works in a closed system, as does induction. Even if we extrapolate from sample-to-population, we are still dealing with a closed system. An example of this is the simple opinion polls that are conducted before elections. A small sample of the population is surveyed and these results are extrapolated to the general population as a prediction of the election result. But this is a form of probability, and thus induction, in a closed system of all those who vote on the day.

What Hume and then Popper were getting at was the lack of justification for induction in an open system, i.e. the universe. Defenders of induction often misunderstand this point. For example, it has been argued that we are able to use induction based on probability, for things such as the blackness of crows. If we observed a large sample of crows, all of which were black, we could justifiably induce that most if not all crows, are black. This is because we are assuming there is a finite population of crows. We are unconsciously defining crows as a certain species of bird that lives on our planet at this particular point in time. We are doing exactly what Popper said we would have to do. We are accepting a priori that crows exist only on the Earth. An a priori belief is something we assume to be true before we experience it. We have yet to properly explore the planets of our own solar system, let alone any other. In a universe that for all intents and purposes is infinite, can we be sure that all crows are black? No; because for all we know, no matter how improbable it seems, evolution may have produced the identical species of crow on a planet on the other side of the universe, a breed of which may be white. If this seems to be a bit unfair to the probability argument, consider the real problem for physics. Physicists have assumed, through induction, that the laws of physics are the same at all points in the universe. We cannot use the probability argument to justify this belief, as we cannot impose an artificial boundary on this system. The universe has no boundary. The sample-to-population argument is acceptable for certain types of inductive reasoning, but not for laws of nature.

Herein lies the essence of my dilemma. Whether Popper liked it or not, induction is still used by scientists to conduct research, and by everyone to make sense of the world in their everyday lives (most sane people assume that the sun will rise on the morrow as it did the day before). Although Popper has amply refuted any logical reason to accept induction, at least for universal laws, it does seem to work quite well. The probability argument works for closed systems (though proving a system is closed can be difficult) but is it irrational to believe induction works for universal laws? The use of the word irrational provided the first inkling to a solution. I really do not think it to be irrational for physicists to believe gravity acts the same elsewhere in the universe as it does here. The solution lies in the difference between logical and rational. Although we cannot establish the logical truth of induction, it is possible to establish a rational explanation for why we can utilise it.

A clear distinction needs to be made between what is meant by logical and rational. This is of fundamental importance to my argument. These two words are often used in the same context, but there is a subtle yet extremely important difference. Logical reasoning, in its strictest sense, is valid because of the tautological nature of the statement. If you are introduced to a bachelor, it follows that he is an unmarried man. This is a logical deduction from the premise. Whereas someone suggesting that red is not a colour, is logically false, because by definition red is a colour. A rational explanation is to justify a position by a reasoned and plausible argument. It does not have to contain a logical truth; it just has to be a reasoned statement that is not logically false. For example, it is logically possible that God exists; it is logically possible that God does not exist. Thus it is not illogical to take either of these positions. Even though it is not possible to prove or disprove God with logic, it is possible to hold either of these beliefs rationally. “I believe in God because the universe is ordered and works like clockwork,” or, “I don’t believe in God because I think it is just a human creation we invented as a way of dealing with death.” These are both rational positions for belief or non-belief as they are reasoned statements that are not logically false; but neither of them are logical truths.

The philosopher Daniel Dennett suggested one way of looking at the likelihood of something occurring, or just existing, is by classifying it into a grade of possibility. First is logical possibility, which as before is simply that of a statement not being contradictory to itself. It is logically possible for me to breathe water. Then comes physical possibility. While it is logically possible for me to breathe water, it is not physically possible for me to do this (and live). Following this line of reasoning:

1. It is logically possible that we exist in a universe of a uniform nature, in terms of it having universal laws that explain it.

2. It is also physically possible that we exist in a universe of a uniform nature, in terms of it having universal laws that explain it.

What type of physical phenomena and experiences would we expect to see and have if these were more than mere possibilities, but actual truths? Well for one, induction should work (as it appears to). If we actually manage to stumble across a universal law through experience and/or experimentation, then the principle of induction would work. We would also be able to see the workings of these laws wherever we look in the universe. An example of this is the detection of extra-solar planets orbiting other stars. Astronomers have done this by utilising laws of physics and phenomena that were discovered on the Earth. Newton’s second law of motion and the shifting frequencies of light through the Doppler effect, are used to detect the ‘wobble’ of a star that a planet is thought to be orbiting. If these laws were only valid on the Earth we would not be able to discover things about other areas of the universe.

So far we have no logical proof of induction, but also, there is no logical or physical disproof of induction. The evidence fits the premises; but could not the same evidence fit different premises? Well, yes it could. Hence the problem of induction. We could imagine a great many different states the universe might exist in, which for the moment, are consistent with this evidence. Light may be behaving completely differently at the stars with extra-solar planets, but still give us the impression of behaving as we would expect it.

This looks as if I am refuting my own argument. But remember; this is not an attempt to come up with a logical proof of induction. It is an attempt to build a rational reason for accepting it. The problem with my proposal is that it requires an a priori belief, as Popper would have predicted, so it is not logically valid. But it is not logically invalid, and this a priori principle is acceptable, at least as a rational belief. The principle is Occam’s razor. William of Occam’s original statement of this famous principle was that, “Entities are not to be multiplied beyond necessity.” A more suitable modern version is, “If there are two (or more) conflicting hypotheses for an observed phenomena, which offer equally acceptable explanations, one should choose the hypothesis that requires the least number of steps to explain it.” If you have different explanations for something, all of which can explain it equally well, then you have no reason to choose a complex reason over a simple one. Or as my father always said, “KISS, Keep It Simple Stupid.”

A universe that can be explained in terms of universal laws is the least complex state of affairs we can envision. Any other explanation for our universe cannot be anything but more complicated. If half of the universe can be explained by one set of laws, and the other half explained by another set of different laws; then it is a more complex universe than one governed by a single set of laws. Thus if we accept Occam’s razor, we can dismiss any other explanation for the workings of the universe, simply because they are unnecessarily complicated.

No longer will I fret, for I feel my dilemma has been solved. This is not a logical argument (as it was previously defined) as we have to accept Occam’s razor a priori; but it is a rational one. We can see that the premise of a universe with universal laws is the simplest explanation for the phenomena we experience in our observable region of space. At this stage we have no rational reason to favour any other premise over this one. But we do have a rational reason to give it favour. The acceptance of Occam’s razor allows the rational belief of a uniform universe governed by universal laws, and from this we can accept induction. There are other arguments for the acceptance of induction (e.g. probability) but to my mind at least, this is the most satisfying. Occam’s razor is no guarantee of truth or even of likelihood, but it is not invoked as such. It is a rule of thumb that is used to give provisional acceptance to a hypothesis. The provision is that until evidence comes along to give weight to an alternative hypothesis, it is best to stick to the simplest one. As Occam once said, “It is vain to do with more what can be done with fewer.”

Theo Clark lives in Brisbane, Australia and is studying at Griffith University.