Science and Induction

science

We give “scientific knowledge” a special status in popular discourse. Once something is covered in the garb of scientific authority, it gains a certain legitimacy in the eyes of the public.  And that’s because science “works”. Whether it’s through medicine, technology, or understanding, there’s no denying that science has improved our lives by leaps and bounds. Yet whenever anyone tries to explain what science is or what makes it special, things quickly fall into vapidness and confusion. People start talk about nonsense like the “scientific method” and other absurdities. After sifting through all of these twisted explanations, it’s clear is that nobody, including scientists, can adequately explain what makes sciences an unique enterprise.

Induction

When most people discuss the nature of science, they usually talk about “the facts”. What separates science from other forms of inquiry is its emphasis on the facts and the objectivity of those facts. In Science and its Backgrounds, H.D. Anthony’s description of Galileo captures this view:

It was not so much the observations and experiments which Galileo made that caused the break with tradition as his attitude to them. For him the facts based on them were treated as facts, and not related to some preconceived idea, as we saw in the case of Kepler’s Harmony of the Spheres. The facts of observation and experiment might, or might not, fit into an acknowledged scheme of the universe; but the important thing, in Galileo’s opinion, was to accept the facts and build the theory to fit them. If he was unable to produce the latter, he declared it better “to pronounce that wise, ingenious and modest sentence, ‘I know it not'” (Anthony 1948: 145)

This description of Galileo is reminiscent of the “scientific method” we learn in primary school, conjuring up images of white coats, fancy instruments, and laboratories:

The scientist begins by carrying out experiments whose aim is to make carefully controlled and meticulously measured observations at some point on the frontier between our knowledge and our ignorance. He systematically records his findings, perhaps publishes them, and in the course of time he and other workers in the field accumulate a lot of shared and reliable data. As this grows, general features begin to emerge, and individuals start to formulate general hypotheses – statements of a lawlike character which git all the known facts and explain how they are casually related to each other. The individual scientist tries to confirm his hypothesis by finding evidence which will support it. If he succeeds in verifying it he has discovered another scientific law which will unlock more of the secrets of nature. The new sea in then worked – the new discovery is applied wherever it is thought it might yield fresh information, Thus the existing stock of scientific knowledge is added to, and the frontier of our ignorance pushed back. (Magee 1985: 14-15)

This method of reasoning is known as induction or inductivism. Inductivism in it’s most crude and naive form says we can generalize from a collection of observations to a general conclusion. When we observe a large number of Xs under a wide variety of conditions, and when all observed Xs have been found to cause Y, then naive inductivism says that it’s logically valid to say that all Xs cause Y. So in the example above, our scientist starts with his experimental observations and uses them to derive some general scientific principle. It might look something like this.

 

Screen Shot 2016-03-23 at 8.02.14 PM

 

On face value, inductivism seems like a perfectly reasonable principle. It captures many of the commonly held intuitions on scientific knowledge, i.e. its reliability and objectivity. This is why for most people, including many scientists, induction is considered the hallmark of science.

The Problem of Induction

In The Problems of Philosophy, Bertrand Russell poses this question about induction; “Do any number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future?” If we answer “no”, then we have no grounds for induction and we can’t confirm that Newton’s laws or any other scientific “facts” will continue to hold in the future.

So how do we justify induction?  We can’t logically prove that induction is a valid way of reasoning. If we could then it wouldn’t be induction, but rather deduction (the process of reasoning from one or more premises to reach a logically certain conclusion). The character of inductive arguments is that they proceed from statements about some events to statements about all events. As Alan Chalmers puts it, “General scientific laws invariably go beyond the finite amount of observable evidence that is available to support them, and that is why they can never be proven in the sense of being logically deduced from that evidence” (Chalmers 1999: 45). After all, if induction was just like deduction, then science wouldn’t be any different from math, philosophy, and a host of other disciplines.

To put it another way, think about David Hume’s distinction between relations of ideas and matters of fact:

The former [relations of ideas] are propositions whose content is con- fined to our concepts or ideas, such as a horse is an animal, bachelors are unmarried, and checkmate is the end of a game of chess. (Hume also included mathematics in this category, so triangles have angles totaling 180° is another example.) Propositions concerning matters of fact are those that go beyond the nature of our concepts and tell us something informative about how the actual world is. So, for example, snow is white, Paris is the capital of France, all metals expand when heated, and the battle of Hastings was in 1066 are all propositions that concern matters of fact. (Ladyman 2002: 32)

Consider the proof for infinitely many prime numbers. First, we assume that there are a finite number of prime numbers. Then we use this proposition with other assumed facts about prime numbers (a prime number is a natural number with exactly two distinct divisors, 1 and itself) to derive a contradiction. The concepts are self contained, have a logical relation to one another, and are therefore provable by deduction. The same cannot be said for matters of fact, which are contingent on the nature of existing things:

Take the proposition that Everest is the tallest mountain on Earth.  The concepts involved – mountain, tallest, Earth, and that of some specific mountain in the Himalayas – have no logical relation to each other that determines the truth of the proposition, and there is no contradiction in supposing that some other mountain is the tallest. Hence, it is not possible to find out if the proposition is true merely by reasoning; only by using the senses can the status of such propositions be investigated. (Ladyman 2002: 33)

Since we can’t justify induction by using deduction, that leaves us with another option, an appeal to experience. Newton’s laws have a proven track record, therefore they are justified by experience. However, as we can clearly see, we are using an inductive argument to justify induction. We are assuming what we are trying to prove (i.e. begging the question). 

This predicament is known as the problem of induction and ever since the days of David Hume, it’s been a well known problem in philosophy:

The general principles of science, such as the belief in the reign of law, and the belief that every event must have a cause, are as completely dependent upon the inductive principle as are the beliefs of daily life. All such general principles are believed because mankind have found innumerable instances of their truth and no instances of their falsehood. But this affords no evidence for their truth in the future, unless the inductive principle is assumed (Russell 1912).

This isn’t a critique of the practice of science or the idea that science is a unique form of enquiry. The problem of induction won’t stop scientists from conducting their experiments, building their theories, and making our lives materially better. However, for those who think that “the scientific way of knowing” is the best way of knowing (or as some scientists argue, the only way of knowing), then this famous dilemma is a unavoidable hurdle. I would argue that until we solve this problem (or get around it), people have no basis to say that their theories are true in any sense, at least on the grounds of induction. At best, scientific theories are useful bodies of knowledge with a good track record, a far cry from “true knowledge”.

Links:

1. John Wilkins Defends Philosophy: Begging the Question by Larry Moran

2. Why are there infinitely many prime numbers?

3. The Problem of Induction

4. Hume: Empiricist Naturalism

References:

1. Anthony, H.D. Science and its Background. Macmillan, 1948. Print.

2. Chalmers, A. F. What Is This Thing Called Science? Indianapolis: Hackett Pub., 1999. Print.

3. Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: U of Chicago, 2003. Print.

4. Ladyman, James. Understanding Philosophy of Science. London: Routledge, 2002. Print.

5. Magee, Bryan. Philosophy and the Real World: An Introduction to Karl Popper. La Salle, IL: Open Court, 1985. Print.

6. Papineau, David. Methodology: The Elements of the Philosophy of Science. In A. C. Grayling, Philosophy 1: A Guide Through the Subject. OUP Oxford, 1998. Print

7. Russell, Bertrand. The Problems of Philosophy. New York: H. Holt, 1912. Print.

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