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Logical and Spiritual REFLECTIONS

Book 1. Hume’s Problems with Induction

Chapter 1. Hume’s “problem of induction”

In the present essay, I would like to make a number of comments regarding Hume’s so-called problem of induction, or rather emphasize his many problems with induction. I am mindful of Hume in all my writings. In at least two places, I devote some attention to Hume’s particular viewpoints[1]. If elsewhere I often do not mention him, or I just mention him in passing[2], as one proponent of this or that doctrine under discussion, it is because my emphasis is on proposing coherent theories rather than lingering on incoherent ones.

David Hume[3] is undoubtedly a challenging and influential philosopher. In his works, he repeatedly attacks many common concepts, such as the validity of induction (notably, generalization); the existence or knowability of natural necessity or law, causal connection or causation; and the existence or knowability of a self or person; that will is free of determinism and indeterminism; that an “ought” may be derived from an “is” or is a special kind of “is”.

These are of course essentially various facets of one and the same assault against common sense, against human reason. I will briefly now reply to each of these skeptical objections. The central or root question here is, I believe, that of the validity of induction. For the other problems are solvable mostly by inductive means. So that if induction is invalid, it is indeed difficult to see how the various other basic ideas of reason could be justified.

With regard to Hume’s problem with generalization: Hume[4] doubted the validity of generalization on the ground that having in the past observed certain regularities is no guarantee that in the future such regularities will hold. To appeal to a principle of Uniformity of Nature would, according to him, be a circular argument, since such a principle could only itself be known by generalization.

In Hume’s view, a generalization is just a mental knee-jerk reaction by humans (and even animals, though they do it non-verbally), an expression of the expectation formed by repeated experiences of a similar kind, a sort of psychological instinct or habit rather than an epistemologically justifiable scientific methodology.

This might all seem credible, were we not to notice some glaring errors in Hume’s understanding of generalization, and more broadly of induction[5].

Hume’s error was to concentrate on the positive aspect of generalization and totally ignore the negative aspect of particularization.[6] Since he unconsciously equated inductive reasoning solely with generalization from past regularity, he naturally viewed the fact that some breach of regularity might indeed (as often happens) occur in the future as evidence that generalization as such is flawed. But this is just a misapprehension of the nature of induction on his part.

He should have known better, since Francis Bacon had (some 80 years before, in his Novum Organon)[7], already clarified the all-importance of the “negative instance” as a check and balance against excessive generalization and in other forms of induction. Because Hume failed to grasp this crucial insight, we can say that his understanding of induction was fragmentary and inadequate.

All generalization is conditional; we may infer a generality from similar particulars, provided we have sought for and not found evidence to the contrary. To generalize to “All X are Y” we need to know two things, not just one: (a) that some X are Y, and (b) that no X to date seem not to be Y. Though the latter condition is usually left tacit, it is absolutely essential[8].

If we did find such contrary evidence early, before we generalized, we would simply not generalize. If we find it later, after we generalized, we are then logically required to particularize. Synthetic generalities are not meant as static absolutes, but as the best available assumptions in the given context of knowledge. Generalization is a dynamic process, closely allied with particularization; it is not a once and for all time process.

The same logic applies to other forms of induction[9], notably adduction. The latter refers to a broader concept of induction, from any evidence to any derived hypothesis (which may contain different terms than the evidence). The hypothesis is not merely confirmed by the evidence it explains, but equally by the absence of contrary evidence and by the absence of better alternative hypotheses.

Note this well: the data that confirm a hypothesis do not suffice to make us believe it. The simple proof of this is that when a hypothesis is rejected for some reason, the data that in the past confirmed it continue to logically confirm it, yet the hypothesis is thrown out in spite of that. There are essential additional conditions, which make our inductive conclusion unassailable thus far, namely (to repeat) that we have to date no data that belies it and no more fitting hypothesis.[10]

Inductive truth is always frankly contextual. It is absurd to attack induction as “unreliable” because it does not yield truths as certain and foolproof as deduction is reputed to do. To argue thus is to claim that one has some standard of judgment other than (or over and above) the only one human beings can possibly have, which is induction.

When inductive logic tells us: “in the given context of knowledge, hypothesis X is your best bet, compared to hypotheses Y, Z, etc.” – it is not leaving the matter open to an additional, more skeptical posture. For what is such skepticism, but itself just a claim to a logical insight and a material hypothesis?

If one examines skepticism towards induction, one sees it to be nothing more than an attempted generalization from past occurrences of error (in other domains), one that pays no heed to past and present non-occurrences of error (in the domain under consideration). That is, it is itself a theory, open to inductive evaluation like any other.

Inductive logic has already taken that skeptical hypothesis into consideration and pronounced it inferior, because it does not duly take into consideration the specific current evidence in favor of X rather than all other alternatives.

Even if a scientific theory is not absolutely sure forevermore, we must stick by it if it seems at this time to be the closest to truth. The skeptic cannot come along and object that “closest is not close enough” – for that would mean he considers (nonsensically) that he has a theory that is closer than closest!

Hume foolishly ignored all this reasoning. He focused only on the positive aspect, and rightly complained that this could not possibly be regarded as logically final and binding! Under the circumstances, it is no wonder that he could see no “proof” of generalizing or adductive reasoning. If we wrongly define and fail to understand some process, it is bound to seem flawed to us.

When Hume discovered the unreliability of induction as he conceived it, he should have looked for a flaw in his own view of induction, and modified it, rather than consider induction as invalid. That would have been correct inductive behavior on his part. When one’s theory leads to absurd consequences, our first reaction should be to modify our particular theory, not theorizing as such. Instead of doubting his own thinking, Hume attacked human knowledge in general, whining that it cannot be “proved”.[11]

But of course, logic – by that I mean deductive logic this time – cannot tolerate such self-contradiction. If someone claims the human means to knowledge, which includes induction as well as deduction, is flawed, then that person must be asked how come he arrived at this supposedly flawless proposition. One cannot reasonably have one’s cake and eat it too.

The argument against generalization is itself a generalization, and so self-contradictory. We cannot say: since some generalizations are evidently erroneous, therefore all generalization is invalid (i.e. we cannot be sure of the validity of any generalization, which makes it as good as invalid) – because, of course, this argument is itself a generalization, and therefore is invalidated by itself! What we can say for sure is that a generalization (like that one) that leads to a contradiction is deductively invalid.

When one discovers a contradiction in one’s thinking, it is not logic as such that is put in doubt but only one’s current thinking. It is silly to cling to a particular thought and reject logic instead. Hume had greater faith in his particular logical notions (which were not, it turns out very logical) than he had in logic as such. The true scientist remains humble and open to correction.

Our ideas and theories have to be, as Karl Popper put it, not only verifiable but also falsifiable, to be credible and trustworthy. Albert Einstein likewise remarked[12]:

“The belief in an external world independent of the perceiving subject is the basis of all natural science. Since, however, sense perception only gives information of this external world or of “physical reality” indirectly, we can only grasp the latter by speculative means. It follows from this that our notions of physical reality can never be final. We must always be ready to change these notions – that is to say, the axiomatic basis of physics – in order to do justice to perceived facts in the most perfect way logically.”

If one examines Hume’s actual discourse in his books, one sees that even as he explicitly denies the reliability of induction he is implicitly using induction to the best of his ability. That is, he appeals to facts and logic, he conceptualizes, generalizes and proposes theories, he compares his favored theories to other possible interpretations or explanations, he gives reasons (observations and arguments) for preferring his theories, and so forth. All that is – induction. Thus, the very methodology he rejects is the one he uses (albeit imperfectly) – and that is bound to be the case, for human beings have no other possible methodology.

To say this would seem to suggest that self-contradiction is feasible. Not so, if one considers how the two aspects, viz. the theory and the practice, may be at odds in the same person. When Hume says that induction is unreliable, he of course means that induction as he sees it is unreliable; but he does not realize that he sees it incorrectly[13], i.e. that a quid pro quo is involved. Indeed, he does not seemingly realize that the way he views it affects the way he gets his views of it, i.e. that he misleads himself too.

While he consciously denies the validity of induction, he unconsciously and subconsciously naturally continues to use it. However, because he has (prejudicially) chosen to deny induction in principle, he cannot study it as openly, impartially and thoroughly as he would otherwise have done, and he is led into error both in his understanding of it and in his actual use of it. Bad theory generates bad practice. And the converse is of course also true, wrong practices promote wrong theories. He is trapped in a vicious circle, which requires a special effort of objectivity to shake off.

We must always keep in mind that what seems impossible or necessary to a philosopher (or anyone else, for that matter) depends on how he views things more broadly. Every philosopher functions within the framework of some basic beliefs and choices. These are not an eternal prison, but they take time and effort to overcome. Sooner or later, a philosopher gets locked-in by his past commitments, unless he takes great pains to remain open and inquisitive.

[1] Namely, in Phenomenology, chapter II (section 5), and in Ruminations, part I, chapter 8 (sections 4-7).

[2] See mentions in: Future Logic, chapters 65 and 67. Phenomenology, ch. I, V, VI and VII. Judaic Logic, ch. 2. Buddhist Illogic, ch. 7. The Logic of Causation, ch. 3, 10, 16 and app. 1. Volition and Allied Causal Concepts, ch. 2. Ruminations, part I, ch. 9, and part II, ch. 1, 6, 7. Meditations, ch. 32.

[3] Scotland, 1711-76.

[4] In his Treatise of Human Nature (1739-40), and subsequent works. The Treatise is posted in full at http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/hume/treatise1.html.

[5] I here refer the reader to Future Logic, Part VI, for a fuller understanding of the issues. Read at least chapters 50 and 55.

[6] This error has, I have read, already been spotted by Karl Popper.

[7] England, 1561-1626. The full text (1620) is posted on the Internet at http://etext.library.adelaide.edu.au/b/bacon/francis/organon/complete.html.

[8] Still today, many writers, philosophers and teachers fail to realize and mention this essential condition when they define or discuss generalization. It should nevermore be left tacit, to avoid the perpetuation of Hume’s error.

[9] Indeed, in the very act of concept formation, we do not merely include certain cases into it, but also (if only tacitly) exclude other cases from it. There is always both a positive and a negative aspect to thought, though the latter is often less manifest. Integration is always coupled with differentiation.

[10] The logical calculus involved is thus not a simple dependence on “confirmation”, but a much more complex and global set of considerations, including “non-rejection” and “competitiveness”. See in this regard my detailed essay “Principles of Adduction” in Phenomenology (chapter VII, section 1).

[11] Hume’s egotistical thinking in this and many other matters was very similar to that of certain philosophers much earlier in India (notably the Buddhist Nagarjuna). Not to mention Greek sophistries.

[12] I cannot say just where – having gleaned this quotation out of context somewhere in the Internet.

[13] Or at least, incompletely – being for instance aware of the positive side (e.g. apparent constancy), but unaware of the negative side (e.g. testing for inconstancy).

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