Jan. 16, 2004
Chapter 2: The problem of induction and other problems with inductivism
Naïve inductivism: observations made in a variety of circumstances are to be recorded impartially and then induction is used to arrive at a general law.
-Many scientists have claimed to follow this method
-It explains the alleged objectivity of scientific method (observation without assumptions).
-It keeps scientific knowledge deeply entrenched in experience.
Two questions:
- Does inductivism seem to be the method that has actually been followed by particular individuals in the history of science?
In other words, is that the method that scientists in fact use?
- Would the inductive method produce knowledge if we did se it?
In other words, regardless of whether or not it has been used in the past, does this method work?
We will tackle the second question today by looking at David Hume’s (1711-1776) criticism of induction.
A thought experiment:
Let us suppose that we are a bunch of geneticists that managed to get our hands on a few cells of Albert Einstein, and we decided that the world would be better of if there was another Einstein, and so we made a clone of him. We grow him in a tank until he is fully mature, and while we are at it, we find a way to download into his memory the content of a basic dictionary (not an encyclopaedia) so that he will be able to talk when he goes out of the tank, which he eventually does.
Now, as you surely know, a clone is not absolutely identical to the original, nor does it share the memories and knowledge of the original. A clone is like an identical twin: they have the same genetic make-up, but the rest is different. Even their fingerprints are different. So to differentiate our Einstein from Albert, we call him Frank, Frank Einstein.
So our Einstein is fresh out of the tank. We tell him his name and ours and we sit him in a wheelchair because he hasn’t learned how to walk yet, and we start asking him questions about what he knows.
Supposing that Frank is as bright and intelligent as Albert, what do you think he knows?
He knows relations of ideas: A horse is a kind of animal; bachelors are unmarried; checkmate is the end of a game of chess; triangles have angles totalling 180o.
He doesn’t know matters of fact: snow is white (if it is defined only as falling particles of frozen water); Paris is the Capital of France; all metals expand when heated;the Confederation was in 1867.
What is the difference between the two kinds of knowledge?
The first can be known by deduction, because its negation will imply a contraction (by using a reduction ad absurdum). Definitions are conventions. They are arbitrary in the sense that it is humans who decided that, say, a bachelor is unmarried. We do not really learn anything about the world.
The second are about the world, but can only be derived by experience (or by someone telling us, which is a kind of experience) because the ideas are unrelated and so not deductively provable.
Hume calls the first kindrelations of ideas, and the second matters of fact.
By the way, Hume, a Scottish, is part of the British Empiricists, which include English John Locke (1632-1704) and Irish George Berkeley (1685-1753). All of them thought that there are no innate concepts and that all our knowledge of the world is derived from, and justified by, our sensory perceptions. In other words, they deny that a priori (i.e., “before the fact”, without experience) knowledge of matters of fact is possible.
Now, obviously at least some of our knowledge of matters of fact is based on experience: it is sunny outside; this blackboard is green; there is a piano in this room; all this we know by our present experience.
Other things we know are things we learned in the same way in the past. Our present knowledge of these things is thus based on our memory of our perceptions.
What about things we have not observed ourselves? How do we know that the sun will rise tomorrow, that the Lake Superior is the largest freshwater lake in the world, and that your hand will freeze instantly if you put it in liquid oxygen?
Let us suppose Frank is now steadier on his feet, and we decide to go play a billiard game with him. We explain the rules to him, and get ready to play. Will he know what will happen when the white ball strike another ball? What about the second time? How do we know that the second ball will start moving in the opposite direction, rather than going in any direction at random, or not moving at all? How do we know that the white ball will not just get tired of being pushed around and will not jumped over the next ball it encounters?
Hume’s answer: causal relations
There is no logical relation between matters of fact; that’s why there is no logical contradiction if a matter of fact was false. In the same way, there is no logical inconsistency in thinking that the sun will not come up tomorrow, or that the white billiard ball will jump over the next ball it encounters. So the only way to connect these ideas is by supposing there is some causal connection between them.
We know that the second ball will move when struck by the white ball because the white ball will cause the second ball to move. Similarly, we know that Lake Superior is the largest freshwater lake in the world because there is a series of causal relations from the person who first measured the area of the lake and determined its fresh water content, up to the person who told us about this fact.
But how do we know when there is a causal relation rather than a mere correlation? Let say we explain to Frank that the white ball will cause the second ball to move, but that he ask us how we know. What do we say?
We have seen it in the past, and by induction, we know it will happen again. But how do we know induction work? Is induction a relation of ideas or a matter of fact? That’s not a relation of ideas, so we cannot know it by deduction. Induction is a matter of fact, and so we must know it by experience. But what kind of experience can justify induction?
All we can observe, according to Hume, is constant conjunction of phenomena. To say that A causes B means that A is always conjoined in our experience with B. Whenever we experience A, we also experience B, and so we suppose that it will always be the same in the future. Whenever I move my arm, I see the arm of my shadow move similarly, and I am naturally inclined to think that it will always be so.
Hume’s analysis of causation (see p.36):
1-Events of type A precede events of type B in time.
E.g., I eat a pizza, and then I’m no longer hungry. Eating caused me to not being hungry. However, it is not always obvious that the cause precede the effect. E.g., the beams causing the roof to stay up.
2-Events of type A are constantly conjoined in our experience with events of type B.
That’s the point we discussed before. Up until now, whenever we A happened, B happened too. Our belief that it will also be the case in the future rests on our belief that the future will be like the past.
3-Events of type A are spatiotemporally contiguous with events of type B.
Usually, when A causes B, A and B are close by physically in time and space. If they are not, then they are connected by a chain of causes and effects, each member of which is spatiotemporally close to the next. However, this condition is not universal: Hume does not claim that there is always contiguity when a causal relation is postulated.
4-Events of type A lead to the expectation that events of type B will follow.
The crucial word here is “expectation”. According to Hume, there is no necessary connection between a cause and its effect, it is only an expectation or an inclination that we have. Thus, causality is a psychological phenomenon, not a physical one.
Of course, Hume knows that many philosophers have argued that if X causes Y, then there is a necessary connection between X and Y. But he responds that we do not experience anything beyond the constant conjunction, and so all there is is a constant conjunction.
Here is the argument in short: compare two theories about causation. One is Humean: there are only the four features identified by Hume. The other says that there is all that Hume said, plus a necessary connection between A and B. Now, both theories fits equally well with experience, and there is no crucial experiment or pejorative instance à la Bacon that we could find to help us decide between the two. Since both theories fit the facts equally well, Hume thinks that his theory is superior, because it does without a metaphysical complication. Thus, implicitly, he appeals to a principle called “Occam’s razor”, according to which whenever we have two competing hypotheses, then if all other considerations are equal, we should take the simpler of the two.
Hume’s problem with induction is that whatever the number of observation we have made in the past, the future can always be different. E.g., the swans example. Even the more sophisticated Principle of Induction we saw last time (which includes consideration of a variety of settings, as well as negative instances) presupposes that the future will be like the past. Since apparently the only way to justify this latter belief is by using induction (in the past, the future has always been like the past, therefore in the future the future will always be like the past), which is a circular reasoning, then there is no way to have justified belief about the future.
Solutions and dissolutions of the problem of induction
According to Hume, induction is not rational, but is simply a psychological tendency of human being. As humans, we just have to form beliefs about what has not been observed yet on the basis of what has been observed. So Hume expects that even after his argument, people will still use induction in science and in their everyday lives. So to accept Hume’s argument does not mean that, as individuals, we will start wondering whether or not the sun will come up tomorrow. But it does mean that we cannot have knowledge of what has not yet been observed.
Unsurprisingly, most philosophers are unsatisfied with such a sceptical view, and many different strategies have been used to defuse Hume’s argument.
(1) Induction is rational by definition
The crude version: in everyday life, we use the term ‘rational’ to apply to more than just deductively valid inferences, in particular to include inductive inferences. It is part of what everyone means by ‘rational’ that induction is rational.
E.g., compare three methods to predict whether Sophie will do well at her final exam. (1) The first method is to look at the behaviour of her cat: if he is grumpy the morning of her exam, she will do badly, but if he is happy, she will do well. (2) The second method is to look back at the previous assignments and exams Sophie did for this class. If she did well for the previous assignments exams, she will do poorly on the final, and conversely. (3) The third method is to look back at the previous assignments and exams Sophie did for this class, and to infer that if she did well in the past, she will do well at the final, and conversely. Now, the third method is the one we will call rational, yet it is the one involving induction. Thus, this is what we means by rational; induction is rational by definition.
Objection to the crude version: just because everyone calls induction rational does not make it rational. When we call something rational, we mean that it meets some requirements that make it rational. If induction happen not to meet these requirements, then it is not really rational, whatever people call it.
Sophisticated version: We are more certain of the validity of induction than of the validity of Hume’s argument. Therefore, if the two conflicts, the problem must be with Hume’s argument (even if we do not know where exactly the problem is), rather than with induction itself.
(2) Hume is asking for a deductive defence of induction, which is unreasonable.
To say that induction is unjustified because it is not deductively valid is to assume, without any argument, that deduction is the only possible source of justification for all beliefs other than those we directly experience or remember. Of course induction is not deduction, but Hume should not automatically prevent induction to be a source of justification.
Reply: Hume does not object to induction simply because it is not deduction. Rather, he objects to induction because we have no independent reason to think that the future will resemble the past, yet induction assumes this principle to work.
(3) Induction is justified by the theory of probability
Another strategy is to give an account of induction based on the mathematical theory of probability. The problem is that to apply a purely mathematical theory to the world requires further assumptions about how the world behaves, and it is these assumptions that now must be justified. How do we know that these assumptions will hold true in the future?
(4) Induction is justified by a principle of induction or the uniformity of nature
One easy solution to the problem of induction is to transform induction into a deduction by adding a Principle of Induction into our argument.
(1)N As have been observed under a wide variety of conditions and all were found to be Bs.
(2)No As have been observed to be non-Bs.
(3)If N observations of As under a wide variety of conditions have been made, and all were found to be Bs, and no As have been found to be non-Bs, then all As are Bs.
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Therefore, all As are Bs.
This makes the argument deductively valid, because if the premises are true, the conclusion has to be true.
However, one problem is that, whatever the N we choose, this creates the weird situation where we have no justification whatsoever for our conclusion at N-1, and then full justification at N. What makes N so important? Solution: change to probable with proportionality of probability and N. (But see strategy 9)
Another problem is that we do not have any justification for the principle of induction. It is not a relation of ideas, but a matter of facts, and so, according to Hume, we should justify it by experience. This brings us back to the original problem.
One possible reply is that not all matter of facts must be justified by experience. Immanuel Kant (1724-1804), a German philosopher who has been influenced by Hume’s writings, argues that some matters of facts are known a priori (before experience) because they are necessary principles of the way our minds work. One such principle is that every event has a cause; others are those implied by Euclidean geometry and Newtonian physics. Unfortunately, although Kant’s idea seemed pretty good in the 18th and 19th century, now that we know that neither Euclidian geometry nor Newtonian physics accurately describe the world, the idea of matters of facts known a priori seems improbable.
(5) Hume’s argument is too general. Since it does not appeal to anything specific about our inductive practices, it can only be premised on the fact that induction is not deduction.
Even the naïve inductivism’s principle of induction is more complex than simply presupposing that the future will resemble the past. When we perform induction, we take into account all of our relevant knowledge: sometimes we infer after just one case, sometimes we take our time and makes lots of experiments before concluding. This suggests that induction is must more complicated than what Hume claims.
Still, it is probable that some part of our inductive practices depends on the fact that the future will resemble the past, and this is probably enough for Hume to say that induction is not justified.
(6) Induction is really (a species of) inference to the best explanation, which is justified.
We often rely on inference to the best explanation (abduction) to explain a phenomenon. We will talk more about inference to the best explanation in the following weeks, but assuming it is a legitimate strategy, then maybe induction is just a kind of inference to the best explanation and so also legitimate.
(7) There really are necessary connections that we can discover.
Hume says that the idea of necessary connections explaining causality fails because we cannot observe them and so constitute an unnecessary assumption. But one might argue that we do not need to observe these necessary connections to know their existence. One can use inference to the best explanation to justify their existence by saying that these necessary connections are necessary to explain the regularities of the world. (We will talk about this in more details in the following weeks).
(8) Induction can be inductively justified after all, because even deduction can only be given a circular (i.e., deductive) justification.
As we saw with strategy 4, one way to try to justify induction is to include a principle of induction into our justification. But this is circular (question-begging), and so not a good justification, according to Hume.
One reply is to admit that induction cannot be justified without circularity, but to point out that deduction cannot either. How do you convince someone who does not think deductively that deduction is justified? (e.g., Achilles and the Tortoise, Lewis Carroll, 1895). One must already accept deduction for deduction to work, yet we do not think deduction is unjustified or irrational for all that. Thus, if induction is in the same situation, there is no reason to find this alarming.