Hume, induction and justification
The source for the problem of induction as we know it is Hume's brief argument in Book I, Part III, section VI of the Treatise, (Hume THN). The great historical importance of this argument, not to speak of its intrinsic power, recommends that reflection on the problem begin with a rehearsal of it. The brief summary in sections 10 and 11 of the entry on Hume provides what is needed, and those who are not familiar with the argument are well advised to read them in conjunction with the present section; It will also be helpful in understanding the deceptively simple argument to have some idea of Hume's project in the Treatise. For this section 4 of that entry is most useful. Indeed, the first twelve sections of the article serve as a brief and comprehensive introduction to Hume's theory of knowledge. Reference to this article permits an abbreviated account here of his classic argument.
First two notes about vocabulary. The term ‘induction’ does not appear in Hume's argument, nor anywhere in the Treatise or the first Inquiry, for that matter. Hume's concern is with inferences concerning causal connections, which, on his account are the only connections “which can lead us beyond the immediate impressions of our memory and senses” (Hume THN, 89). But the difference between such inferences and what we know today as induction is largely a matter of terminology. Secondly, Hume divides all reasoning into demonstrative, by which he means deductive, and probabilistic, by which he means the generalization of causal reasoning. In what follows we paraphrase and interpolate freely so as to ease the application of the argument in contemporary contexts.
It should also be remarked that Hume's argument applies just to enumerative induction, and primarily to singular predictive inference, but, again, its generalization to other forms of inductive reasoning is straightforward.
The argument should be seen against the background of Hume's project as he announces it in the introduction to the Treatise: This project is the development of the empirical science of human nature. The epistemological sector of this science involves describing the operations of the mind, the interactions of impressions and ideas and the function of the liveliness that constitutes belief. But this cannot be a merely descriptive endeavor; accurate description of these operations entails also a considerable normative component, for, as Hume puts it, “[o]ur reason [to be taken here quite generally, to include the imagination] must be consider'd as a kind of cause, of which truth is the natural effect; but such-a-one as by the irruption of other causes, and by the inconstancy of our mental powers, may frequently be prevented” (Hume THN, 180). The account must thus not merely describe what goes on in the mind, it must also do this in such a way as to show that and how these mental activities lead naturally, if with frequent exceptions, to true belief. (See Loeb 2006 for further discussion of these questions.)
Now as concerns the argument, its conclusion is that in induction (causal inference) experience does not produce the idea of an effect from an impression of its cause by means of the understanding or reason, but by the imagination, by “a certain association and relation of perceptions.
” The center of the argument is a dilemma: If inductive conclusions were produced by the understanding, inductive reasoning would be based upon the premise that nature is uniform; “that instances of which we have had no experience, must resemble those of which we have had experience, and that the course of nature continues always uniformly the same.” (Hume THN, 89) And were this premise to be established by reasoning, that reasoning would be either deductive or probabilistic (i.e. causal). The principle can't be proved deductively, for whatever can be proved deductively is a necessary truth, and the principle is not necessary; its antecedent is consistent with the denial of its consequent. Nor can the principle be proved by causal reasoning, for it is presupposed by all such reasoning and any such proof would be a petitio principii.
The normative component of Hume's project is striking here:
That the principle of uniformity of nature cannot be proved deductively or inductively shows that it is not the principle that drives our causal reasoning only if our causal reasoning is sound and leads to true conclusions as a “natural effect” of belief in true premises. This is what licenses the capsule description of the argument as showing that induction cannot be justified or licensed either deductively or inductively; not deductively because (non-trivial) inductions do not express logically necessary connections, not inductively because that would be circular. If, however, causal reasoning were fallacious, the principle of the uniformity of nature might well be among its principles.
The negative argument is an essential first step in Hume's general account of induction. It rules out accounts of induction that view it as the work of reason. Hume's positive account begins from a constructive dilemma: Inductive inference must be the work either of reason or of imagination.; Since the negative argument shows that it cannot be a species of reasoning, it must be imaginative.
Hume's positive account of causal inference can be simply described: It amounts to embedding the singular form of enumerative induction in the nature of human, and at least some bestial, thought. The several definitions offered in (Hume EHU, 60) make this explicit:
[W]e may define a cause to be an object, followed by another, and where all objects similar to the first are followed by objects similar to the second. Or, in other words, where, if the first object had not been, the second never had existed.
Another definition defines a cause to be:
an object followed by another, and whose appearance always conveys the thought to that other.
If we have observed many Fs to be followed by Gs, and no contrary instances, then observing a new F will lead us to anticipate that it will also be a G. That is causal inference.
It is clear, says Hume, that we do make inductive, or, in his terms, causal, inferences; that having observed many Fs to be Gs, observation of a new instance of an F leads us to believe that the newly observed F is also a G. It is equally clear that the epistemic force of this inference, what Hume calls the necessary connection between the premises and the conclusion, does not reside in the premises alone:
All observed Fs have also been Gs,
and
a is an F,
do not imply
a is a G.
It is false that “instances of which we have had no experience must resemble those of which we have had experience” (Hume EHU, 89).
Hume's view is that the experience of constant conjunction fosters a “habit of the mind” that leads us to anticipate the conclusion on the occasion of a new instance of the second premise. The force of induction, the force that drives the inference, is thus not an objective feature of the world, but a subjective power; the mind's capacity to form inductive habits.
The objectivity of causality, the objective support of inductive inference, is thus an illusion, an instance of what Hume calls the mind's “great propensity to spread itself on external objects” (Hume THN, 167).
It is important to distinguish in Hume's account causal inference from causal belief: Causal inference does not require that the agent have the concept of cause; animals may make causal inferences (Hume THN, 176–179; Hume EHU, 104–108) which occur when past experience of constant conjunction leads to the anticipation of the subsequent conjunct upon experience of the precedent. Causal beliefs, on the other hand, beliefs of the form
A causes B,
may be formed when one reflects upon causal inferences as, presumably, animals cannot (Hume THN, 78).
Hume's account raises the problem of induction in an acute form: One would like to say that good and reliable inductions are those that follow the lines of causal necessity; that when
All observed Fs have also been Gs,
is the manifestation in experience of a causal connection between F and G, then the inference
All observed Fs have also been Gs,
a is an F,
Therefore, a, not yet observed, is also a G,
is a good induction. But if causality is not an objective feature of the world this is not an option. The Humean problem of induction is then the problem of distinguishing good from bad inductive habits in the absence of any corresponding objective distinction.
Two sides or facets of the problem of induction should be distinguished: The epistemological problem is to find a method for distinguishing good or reliable inductive habits from bad or unreliable habits. The second and deeper problem is metaphysical. This is the problem of saying what the difference is between reliable and unreliable inductions.
This is the problem that Whitehead called “the despair of philosophy” (Whitehead 1948, 35). The distinction can be illustrated in the parallel case of arithmetic. The by now classic incompleteness results of the last century show that the epistemological problem for first-order arithmetic is insoluble; that there can be no method, in a quite clear sense of that term, for distinguishing the truths from the falsehoods of first-order arithmetic. But the metaphysical problem for arithmetic has a clear and correct solution: the truths of first-order arithmetic are precisely the sentences that are true in all arithmetic models. Our understanding of the distinction between arithmetic truths and falsehoods is just as clear as our understanding of the simple recursive definition of truth in arithmetic, though any method for applying the distinction must remain forever out of our reach.
Now a
s concerns inductive inference, it is hardly surprising to be told that the epistemological problem is insoluble; that there can be no formula or recipe, however complex, for ruling out unreliable inductions. But Hume's arguments, if they are correct, have apparently a much more radical consequence than this:
They seem to show that the metaphysical problem for induction is insoluble; that there is no objective difference between reliable and unreliable inductions. This is counterintuitive. Good inductions are supported by causal connections and we think of causality as an objective matter: The laws of nature express objective causal connections. Ramsey writes in his Humean account of the matter:
Causal laws form the system with which the speaker meets the future; they are not, therefore, subjective in the sense that if you and I enunciate different ones we are each saying something about ourselves which pass by one another like “I went to Grantchester”, “I didn't” (Ramsey 1931, 241).
A satisfactory resolution of the problem of induction would account for this objectivity in the distinction between good and bad inductions.
It might seem that Hume's argument succeeds only because he has made the criteria for a solution to the problem too strict. Enumerative induction does not realistically lead from premises
All observed Fs have also been Gs
a is an F,
to the simple assertion
Therefore, a, not yet observed, is also a G.
Induction is contingent inference and as such can yield a conclusion only with a certain probability. The appropriate conclusion is
It is therefore probable that, a, not yet observed, is also a G.
Hume's response to this (Hume THN, 89) is to insist that probabilistic connections, no less than simple causal connections, depend upon habits of the mind and are not to be found in our experience of the world. Weakening the inferential force between premises and conclusion may divide and complicate inductive habits, it does not eliminate them. The laws of probability alone have no more empirical content than does deductive logic. If I infer from observing clouds followed by rain that today's clouds will probably be followed by rain this can only be in virtue of an imperfect habit of associating rain with clouds...
http://plato.stanford.edu/entries/induc ... 2HumIndJus 