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Bence Tarr

The Question of Induction in Hume's Enquiry


Induction, in logic is the process of moving from the particular to the general, and as such is not demonstrative; which means, it does not prove its conclusions through a logical process, like deduction. Ever since induction has been noticed, many philosophers have either been apologetic about it for not being demonstrative, or have tried to show that somehow it really is demonstrative in a roundabout way, or at least respectable in spite of not doing what deduction does. Hume belongs to the group of philosophers who cannot be placed in either of these categories, since his method of dealing with this problem is not a logical one. Since he deals with the problem through the theory of causality in the terms of constant conjunction in the past, despite its general logical usage, induction is not purely a logical problem. Therefore we should look at Hume’s approach to this problem and see, whether he is right in dealing with the problem in a 'psychological' way.

While I will try to focus on Section IV entitled Sceptical Doubts concerning the operations of the Understanding, which deals with the problem of induction, I will have to make a short survey on how he reached this problem:

In the Introduction to the Treatise, Hume says that 'as the science of man is the only solid foundation for the other sciences, so the only solid foundation we can give this science itself must be laid on experience and observation.' In the current Cartesian tradition of his time, laying the foundation of the science of man on experience and observation meant, for Hume, doing something, that would lift the veil off metaphysics, showing ‘that this science is uncertain and chimerical’. [1]  The reason for this intent was, that philosophy of his time has become something very obscure, which with the use of ‘metaphysical jargon being mixed up with popular superstition, renders it in a manner impenetrable to careless reasoners, and gives it the air of science and wisdom.’ [2]  So his purpose was to set up a science free from superstition, through the only method he thought would free learning, which for him meant ‘to enquire seriously into the nature of human understanding, and show, from an exact analysis of its powers and capacity.’ [3]

Of course the only way was adopting a reformulated version of Locke's Way of Ideas, and explaining the relation of ideas in terms of ‘association’. He reformulated Locke's term of idea, by using two words, ‘impressions’ and ‘ideas’ where Locke has used one, distinguishing between what is present to the mind when we employ our senses or are actuated with passion, and what is present to the mind when we exercise thought and reflection. He names the former impressions, meaning ‘all our more lively perceptions, when we hear, or see, or feel, or love, or hate, or desire, or will’ ; and names the later ideas, ‘which are the less lively perceptions, of which we are conscious, when we reflect on any of those sensations or movements above mentioned’. [4]  So he draws a distinction between these two kinds of perception, of which impressions are those that have more force and violence. Though he brings the two together by saying that ideas, unless created by fiction, are derived from impressions, there is a clear distinction between the two.

The second main ingredient in Hume's ‘empirical’ science of man is his theory of the Association of Ideas. Of course this also goes back to Locke’s remark on the subject. Although Locke neither thought it worthwhile to list the ways in which ideas come to be associated (though the principle of association in his ‘trunk-dancing’ [5] example is plainly that of contiguity), nor gave the association of ideas any useful, and identical, role to play in how everyone's mind works, it is clearly contained in his writings. Hume gives two other principles of association, besides contiguity: resemblance (which Locke regarded as a natural connection, since resemblance of ideas is the result of nature making things alike), and causation.

David Hume

Whereas Locke disparaged the association of ideas as a chance affair, and concentrated on how dissimilar associations in different people make the opinions and actions of other people seem odd, Hume concentrated on showing how contrasted ideas being associated in accordance with universal principles are used to explain how it is that different people make similar associations. Particularly concerning the cases, when simple ideas are being associated to form complex ones. It's clear that simple ideas in their first appearance are derived from impressions, but complex ideas need not to resemble impressions. For instance, we can imagine a winged horse without ever having seen one, but for Hume it is clear that the constituents of this complex idea are all derived from impressions. Thus whereas the association of ideas is an afterthought in Locke's philosophy it plays a central role in Hume's.

Having shortly enumerated the problems which led Hume to the problem of induction, we should try to take a look at the problem itself, in the form Hume presents it: To me it seems, that just as Locke had distinguished between ideas which our reason can trace, and ones which are due to chance and custom, so does Hume, in distinguishing between ‘Relations of Ideas’ and ‘Matters of Fact’, right in the first sentence of Section IV. He defines the first as 'the sciences of Geometry, Algebra and Arithmetic; and in short, every affirmation, which is either intuitively or demonstratively certain.' [6] In other terms, all those relations of thought which depend entirely on the ideas, which we can compare, and can change without causing any change in the ideas themselves. For instance, that ‘the three times five’ is equal to ‘the half of thirty’, expresses a relation between these two figures, and is based entirely on our ideas of these two numbers. It is this kind of relation on which demonstrative reasoning can be based. It is what Hume calls intelligible, of which he says:

whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proven false by any demonstrative argument or abstract reasoning a priori.[7] 

On the other hand 'Matters of Fact', which are the second objects of human reason, are not ascertained in the same manner; ‘nor is our evidence of their truth, however great, of a like nature with the foregoing.[8]  With a matter of fact, such as ‘a pair of shoes’ is next to a ‘bed’, there is no basis in our ideas for demonstrative reasoning. The idea of a pair of shoes would be no different were it not next to a bed. An other example, used by Hume, is the problem of the ‘rising sun’: Just because I have seen the sun rise today, how do I come to the conclusion that it will rise tomorrow as well? Hume's answer to this problem, is that all reasoning concerning matters of fact, are founded on the relation of ‘cause and affect’. With his words:

All our reasoning concerning fact are of the same nature. And here it is constantly supposed, that there is connexion between the present fact and that is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious.[9]

This binding is the law of cause and effect. We explain the position of a billiard ball casually: it moved to its present location as a result of having been struck by another billiard ball. But, all our casual relations are such, that they cannot be foreseen from a knowledge of the respective ideas. (It is not even demonstrable that everything has a cause.) Any beliefs we have about causation are based on experience, not demonstrative reasoning. The reason for this, is that Hume looks at the causation as something entirely different, from its cause; presupposing that the effect cannot be contained in its cause. It is worthy to quote his summary:

In a word, then, every effect is a distinct event from its cause. It could not, therefore, be discovered in the cause, and the first invention or conception of it, a priori, must be entirely arbitrary. And even after it is suggested, the conjunction of it with the cause must appear equally arbitrary; since there are always many other effects, which to reason, must seem fully as consistent and natural. In vain therefore, should we pretend to determine any single event, or infer any cause or effect, without the assistance of observation and experience.[10]

This means, that if reasoning about matter of fact is based on casual beliefs, and there were a necessary connection between the cause and effect, then we would be able to infer the effect from the cause a priori. However, there is not the sort of necessary connection we find in mathematics. Besides, when we look at one billiard ball causing motion in another we do not see any necessary connection. So he totally denies the possibility of recognising the general features in the particular case, which would be a sensible solution to the problem of induction. For instance, if I observe the sun rising today and no more, it might seem rash to infer that it will do likewise tomorrow, but if in seeing it rise today, I recognise this fact as linked with the laws of planetary motion (themselves linked with the theory of universal gravitation), then my forecast of sunrise tomorrow is quite conclusive. Now by stating that effect is not contained in its cause, he denies this possibility. I believe he doesn't exclude this possibility straight away, since he states that effect can be concluded from the cause, but clearly states that in opposition with deduction, where only one conclusion can be derived from the premises, there is an infinite number of conclusions to be drawn here a priori. This is very well proved by the famous ‘zöké’ example of Nelson Goodman. [11]

So he clearly concludes that ‘this proposition, that causes and effects are discoverable, not by reason but by experience, will readily admitted.’ [12] But, he also excludes the possibility that repetitious experience would help to determine the necessary connection between the cause and effect. Hume denies the that the inference drawn from experience would be produced by a chain of reasoning. Nor is it by intuition. (Although when speaking of the 'relation of ideas' he left this possibility open.) In his words:

There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument.[13]

According to this he is reversing roles: instead of the inference depending on necessary connection, the idea of necessary connection somehow arises out of the inference, considered psychologically. Seeing the billiard ball moving is an impression, associated by resemblance with the ideas of moving billiard balls seen in the past, each of which is associated by contiguity with the idea of another billiard ball striking it. So, on seeing the billiard ball moving we cannot help but think of the associated idea. The reason we cannot help not to think of the associated idea is simple. Although its exact discussion is in Section V, it does appear in Section IV as well:

We fancy that we were brought, on a sudden, into this world, we could at first inferred, that one billiard ball would communicate motion to another upon impulse; and that we needed not to have waited for the event, in order to pronounce with certainty concerning it. Such is the influence of custom, that, where it is the strongest, it not only covers our natural ignorance, but even conceals itself, and seems not to take place, merely because it is found in the highest degree.’ [14]

So the answer is plain from here: we have a custom-produced propensity to pass from the present impression to the idea of another billiard ball. The passage is the inference, experienced as a felt ‘determination of the thought’; and the idea of a necessary connection is derived from this internal impression, and mistaken for an idea of something objective. There are two reasons for this: 1) the observer believes in the existence of the former billiard balls seen, and since belief is different from mere thought in strength of the idea entertained, the internal impression produced is strong and vivid; 2) the present impression infects the associated idea with its strength, producing the strong internal impression. That what makes the future seem an effect of what is past, and that's what makes us believe that anything else outside of what is immediately present to our memory or senses exists.

Custom, then, is the great guide of human life. It is that principle alone, which renders our experience useful to us, and makes us expect, for the future, a similar train of events which have appeared in the past. Without the influence of custom, we should be entirely ignorant of every matter of fact, beyond what is present to the memory and senses.’ [15]

In a word: Hume believes that all necessary connections drawn between cause and effect are due to experience, and experience alone; and all inductive speculations on general principles are nothing more than custom-produced propensities, that derive their vividity from the strength of the present impression which they are associated with.



[1] David Hume: An Enquiry Concerning Human Understanding  [Edited by Eric Steinberg [Hackett Publishing Company, Indianapolis 1977.] ("Enquiry", Section I - Of the Different Species of Philosophy, page 7.)  All quotations are from this book, therefore not indicated from now on.

[2] In Enquiry, Section I - Of the Different Species of Philosophy, page 6.

[3] In Enquiry, Section I - Of the Different Species of Philosophy, page 6.

[4] In Enquiry, Section II - Of the Origin of Ideas, page 10.

[5] Locke: An Essay concerning Human Understanding - (II. xxxiii 16).

[6] In Enquiry, Section IV- Sceptical Doubts Concerning the Operations of the Understanding -page 15.

[7] In Enquiry, Section IV- Sceptical Doubts Concerning the Operations of the Understanding -page 22.

[8] In Enquiry, Section IV- Sceptical Doubts Concerning the Operations of the Understanding -page 15.

[9] In Enquiry, Section IV- Sceptical Doubts Concerning the Operations of the Understanding -page 16.

[10] In Enquiry, Section IV- Sceptical Doubts Concerning the Operations of the Understanding -page 19.

[11] ‘Zöké’ is a word created by Goodman to mean a certain colour, which he defined in the following manner: A thing is ‘zöké’ if it's colour has been inspected before the year 2000 and it's been found green, or it hasn't been inspected and it's blue. Now all statements, “every sapphire is green”, which is thought generally true, would also be equal to the statement “every sapphire is zöké” (presupposing, that all inspections have been made before the year 2000). But making such a statement, that “every sapphire is zöké” would determine any forecast of the inspections made after the year 2000. Because this would mean that all the sapphires inspected after 2000 will be blue, the ones inspected until 2000 are green, and the ones not inspected until 2000 are blue as well. But if we say “every sapphire is green” then we forecast that we'll find all of them green without taking into consideration the date of their inspection. This example shows, that on an inductive basis we can draw other general conclusions, than the ones proved by experience. Thus we not only have to consider the fact that predictions based on an inductive basis are not a 100% certain, but also, that on an inductive basis other general conclusions can be drawn from evidences known to us. (Example brought in Nigel Warburton: Philosophy. The Basics. - Hungarian ed. Kossuth, Bp. 1993;  p.103.)

[12] In Enquiry, Section IV - Sceptical Doubts Concerning the Operations of the Understanding -page 17.

[13] In Enquiry, Section IV - Sceptical Doubts Concerning the Operations of the Understanding -page 22.

[14] In Enquiry, Section IV - Sceptical Doubts Concerning the Operations of the Understanding -page 18.

[15] In Enquiry, Section V - Sceptical Solution of these Doubts -page 29.

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