Inductive Logic

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.

2.    The Principle of Induction

Concerning the uniformity principle, which Hume denies, it is admittedly an idea difficult to uphold, in the sense that we cannot readily define uniformity or make a generality of it. We might speak of repetition, of two or more particular things seeming the same to us; but we are well aware that such regularity does not go on ad infinitum. On the contrary, we well know that sooner or later, something is bound to be different from the preceding things, since the world facing us is one of multiplicity.

Therefore, this “principle” may only be regarded as a heuristic idea, a rule of thumb, a broad but vague practical guideline to reasoning. It makes no specific claims in any given case. It just reminds us that there are (or seem to us to be) ‘similarities’ in this world of matter, mind and spirit. It is not intended to deny that there are also (apparent) ‘dissimilarities’. It is obviously not a claim that all is one and the same, a denial of multiplicity and diversity (in the world of appearances, at least[14]). To speak of uniformity in Nature is not to imply uniformity of Nature.

We might also ask – can there be a world without any ‘uniformities’? A world of universal difference, with no two things the same in any respect whatever is unthinkable. Why? Because to so characterize the world would itself be an appeal to uniformity. A uniformly non-uniform world is a contradiction in terms. Therefore, we must admit some uniformity to exist in the world. The world need not be uniform throughout, for the principle of uniformity to apply. It suffices that some uniformity occurs.

Given this degree of uniformity, however small, we logically can and must talk about generalization and particularization. There happens to be some ‘uniformities’; therefore, we have to take them into consideration in our construction of knowledge. The principle of uniformity is thus not a wacky notion, as Hume seems to imply. It is just a first attempt by philosophers to explain induction; a first try, but certainly not the last. After that comes detailed formal treatment of the topic. This proceeds with reference to specifics, symbolized by X’s and Y’s, and to strict logic.

The uniformity principle is not a generalization of generalization; it is not a statement guilty of circularity, as some critics contend. So, what is it? Simply this: when we come upon some uniformity in our experience or thought, we may readily assume that uniformity to continue onward until and unless we find some evidence or reason that sets a limit to it. Why? Because in such case the assumption of uniformity already has a basis, whereas the contrary assumption of difference has not or not yet been found to have any. The generalization has some justification; whereas the particularization has none at all, it is an arbitrary assertion.

It cannot be argued that we may equally assume the contrary assumption (i.e. the proposed particularization) on the basis that in past events of induction other contrary assumptions have turned out to be true (i.e. for which experiences or reasons have indeed been adduced) – for the simple reason that such a generalization from diverse past inductions is formally excluded by the fact that we know of many cases that have not been found worthy of particularization to date.

That is to say, if we have looked for something and not found it, it seems more reasonable to assume that it does not exist than to assume that it does nevertheless exist. Admittedly, in many cases, the facts later belie such assumption of continuity; but these cases are relatively few in comparison. The probability is on the side of caution.

In any event, such caution is not inflexible, since we do say “until and unless” some evidence or argument to the contrary is adduced. This cautious phrase “until and unless” is of course essential to understanding induction. It means: until if ever – i.e. it does not imply that the contrary will necessarily occur, and it does not exclude that it may well eventually occur. It is an expression of open-mindedness, of wholesome receptiveness in the face of reality, of ever readiness to dynamically adapt one’s belief to facts.

In this way, our beliefs may at all times be said to be as close to the facts as we can get them. If we follow such sober inductive logic, devoid of irrational acts, we can be confident to have the best available conclusions in the present context of knowledge. We generalize when the facts allow it, and particularize when the facts necessitate it. We do not particularize out of context, or generalize against the evidence or when this would give rise to contradictions.

Hume doubted the validity of generalization because he thought that we adopt a general proposition like All X are Y, only on the basis of the corresponding particular Some X are Y. But if the latter was sufficient to (inductively) establish the former, then when we were faced with a contingency like Some X are Y and some X are not Y, we would be allowed to generalize both the positive and negative particulars, and we would find ourselves with a contradiction[15] in our knowledge, viz. with both All X are Y and No X are Y.

But since contradiction is error, according to the 2^nd law of thought, it follows that a particular is not by itself enough to confirm a generality. To do so, we need also to first adduce that the opposite particular is not currently justified. Note well what we have shown here: this criterion for generalization follows from the law of non-contradiction. Hume and his skeptical successors did not take this additional criterion into account. They noticed the aspect of ‘confirmation’, but ignored that of ‘non-rejection’.

The uniformity principle ought to be viewed as an application of a much larger and important principle, which we may simply call the principle of induction (in opposition to the so-called problem of induction). This all-important principle could be formulated as follows: given any appearance, we may take it to be real, until and unless it is found to be illusory.[16]

This is the fundamental principle of inductive logic, from which all others derive both their form and their content. And indeed, this is the way all human beings function in practice (with the rare exception of some people, like Hume, who want to seem cleverer than their peers). It is, together with Aristotle’s three laws of thought, the supreme principle of methodology, for both ordinary and scientific thought, whatever the domain under investigation[17].

Indeed, we could construe this principle of induction as the fourth law of thought. Just as the three laws proposed by Aristotle are really three facets of one and the same law, so also this fourth law should be viewed as implicit in the other three. Induction being the most pragmatic aspect of logic, this principle is the most practical of the foundations of rational discourse.

The principle of induction is a phenomenological truth, because it does not presume at the outset that the givens of appearance are real or illusory, material or mental, full or empty, or what have you. It is a perfectly neutral principle, without prejudice as to the eventual content of experience and rational knowledge. It is not a particular worldview, not an a priori assumption of content for knowledge.

However, in a second phase, upon reflection, the same principle favors the option of reality over that of illusion as a working hypothesis. This inbuilt bias is not only useful, but moreover (and that is very important for skeptics to realize) logically rock solid, as the following reasoning clearly shows:

This principle is self-evident, because its denial is self-contradictory. If someone says that all appearance is illusory, i.e. not real, which means that all our alleged knowledge is false, and not true, that person is laying claim to some knowledge of reality (viz. the knowledge that all is unreal, unknowable) – and thus contradicting himself. It follows that we can only be consistent by admitting that we are indeed capable of knowing some things (which does not mean everything).

It follows that the initial logical neutrality of appearance must be reinterpreted as in all cases an initial reality that may be demoted to the status of illusion if (and only if) specific reasons justify it. Reality is the default characterization, which is sometimes found illusory. Knowledge is essentially realistic, though in exceptional cases it is found to be unrealistic. Such occasional discoveries of error are also knowledge, note well; they are not over and above it.

If we did not adopt this position, that appearance is biased towards reality rather than illusion, we would be stuck in an inextricable agnosticism. Everything would be “maybe real, maybe illusory” without a way out. But such a problematic posture is itself a claim of knowledge, just like the claim that all is illusory, and so self-inconsistent too. It follows that the interpretation of appearance as reality until and unless otherwise proved is the only plausible alternative.[18]

If appearance were not, ab initio at least, admitted as reality rather than as illusion or as problematic, we would be denying it or putting it in doubt without cause – and yet we would be granting this causeless denial or doubt the status of a primary truth that does not need to be justified. This would be an arbitrary and self-contradictory posture – an imposture posing as logical insight. All discourse must begin with some granted truth – and in that case, the most credible and consistent truth is the assumption of appearance as reality unless or until otherwise proved.

We may well later, ad terminatio (in the last analysis), conclude that our assumption that this appearance was real was erroneous, and reclassify it as illusory. This happens occasionally, when we come across conflicts between appearances (or our interpretations of them). In such cases, we have to review in detail the basis for each of the conflicting theses and then decide which of them is the most credible (in accord with numerous principles of adduction).

It should be stressed that this stage of reconciliation between conflicting appearances is not a consequence of adopting reality as the default value of appearances. It would occur even if we insisted on neutral appearances and refused all working hypotheses. Conflicts would still appear, and we would still have to solve the problem they pose. In any case, never forget, the assumption of reality rather than illusion only occurs when and for so long as no contradiction results. Otherwise, contradictions would arise very frequently.

Note well that I do not understand appearance in quite the same way Edmund Husserl does, as something ab initio and intrinsically mental; such a view is closer to Hume or even Berkeley than to me.

The ground floor of Husserl’s phenomenology and mine differ in the primacy accorded to the concepts of consciousness and of the subject of consciousness. My own approach tries to be maximally neutral, in that appearances are initially taken as just ‘what appears’, without immediately judging them as ‘contents of someone’s consciousness’. Whereas, in Husserl’s approach, the wider context of appearance is from the start considered as part and parcel of the appearance.

For me, some content comes first, and only thereafter do we, by a deduction or by an inductive inference, or perhaps more precisely by an intuition (an additional, secondary, reflexive act of consciousness), become aware of the context of consciousness and conscious subject. At this later stage, we go back and label the appearance as a “content of” consciousness, i.e. as something whose apparition (though not whose existence) is made possible by an act of consciousness by some subject. Content is chronologically primary; the context is secondary.

Whereas in Husserl’s philosophy, the fact of consciousness and its subject are present from the start, as soon as the appearance appears. Husserl’s mistake, in my view, is to confuse logical order and chronological order, or ontological and epistemological. Of course, logically and ontologically, appearance implies consciousness and someone being conscious; but chronologically and epistemologically, they occur in succession.

As a result of this difference, his approach has a more subjectivist flavor than mine, and mine has a more objectivist flavor than his. Note, however, that in his later work Husserl tried more and more to shift from implied subjectivism to explicit objectivism.

We have seen the logic of induction in the special case of generalization. Given the positive particular ‘Some X are Y’ (appearance), we may generalize to the corresponding generality ‘All X are Y’ (reality), provided we have no evidence that ‘Some X are not Y’ (no conflicting appearance). Without this caveat, many contradictions would arise (by generalizing contingencies into contrary generalities); that proves the validity of the caveat. If (as sometimes occurs) conflicting evidence is eventually found (i.e. it happens that Some X are not Y), then what was previously classed as real (viz. All X are Y) becomes classed as illusory (this is called particularization).

Induction is a flexible response to changing data, an ongoing effort of intelligent adaptation to apparent facts. Few logicians and philosophers realize, or take into consideration, the fact that one of the main disciplines of inductive logic is harmonization. They discuss observation and experiment, generalization and adduction, and deduction, with varying insight and skill, but the logic of resolving contradictions occasionally arrived at by those other inductive means is virtually unknown to them, or at least very little discussed or studied. This ignorance of, or blindness to, a crucial component of induction has led to many foolish theories[19].

Notice well, to repeat, the conditional form of the principle of induction: it grants credibility to initial appearances “until and unless” contrary appearances arise, which belie such immediate assumption. Thus, in the case of the narrower uniformity principle, the initial appearance is the known few cases of similarity (or confirmation) and the fact of not having to date found cases of dissimilarity (or conflicting data); this allows generalization (or more broadly, theory adoption) until if ever we have reason or evidence to reverse our judgment and particularize (or reject, or at least modify, the theory).

The principle of induction may likewise be used to validate our reliance on intuition and sensory and inner perception, as well as on conception. It may also be applied to causality, if we loosely formulate it as: order may be assumed to exist everywhere, until and unless disorder appears obvious. However, the latter principle is not really necessary to explain causality, because we can better do that by means of regularity, i.e. with reference to the uniformity principle, i.e. to generalization and adduction.

In any case, the principle of induction is clearly a phenomenological principle, before it becomes an epistemological or ontological one. It is a logical procedure applicable to appearance as such, free of or prior to any pretensions to knowledge of reality devoid of all illusion. The claims it makes are as minimal as could be; they are purely procedural. It is for this reason as universal and indubitable as any principle can ever be.

Moreover, the principle of induction (and likewise its corollary the uniformity principle) applies equally to the material, mental and spiritual realms. It is a valid method of dealing with data, independently of the sort of data involved, i.e. irrespective of the ‘substance’ of the data. Many people associate induction exclusively with the physical sciences, but this is misconceived. Inductive logic sets standards of judgment applicable in all fields – including in psychology and in moral and spiritual concerns.

3.    Causation, Necessity and Connection

One of the main battlegrounds of Hume’s attack on induction is his treatment of causation. This is no accident, since one of the most important functions of induction is to find and establish causal relations. If we now turn our attention to this issue, we find almost exactly the same error on Hume’s part.

He defines causation as “constant conjunction,” ignoring the equally important inverse (a contrario) aspect of it. In truth, causation (in its strongest determination) of Y by X would be defined as follows: “X is always accompanied or followed by Y” (the positive aspect), and “not X is always accompanied or followed by not Y” (the negative aspect).

The constant conjunction of the presences of X and Y would not by itself convince us there is causation between them; we would also have to find that the absences of X and Y are likewise related. This is at least true in the strongest determination of causation, known as complete and necessary causation. There are in truth lesser determinations, but these similarly include both a positive and a negative side, so the argument holds for them too[20].

To define causation, as Hume did, only with reference to the positive aspect of it, would necessarily make the bond involved seem flimsier. The negative aspect is what gives the positive aspect its full force. The coin is two-sided. If one focuses only on the complete causation and ignores the underlying necessary causation, it is no wonder that one (like Hume) sees no “necessity” in causation.[21]

The idea of causation thus involves not just one but two generalizations, viz. a seemingly constant conjunction between X and Y, and a seemingly constant conjunction between the negation of X and the negation of Y. Note this well, one cannot refer to “constant conjunction” without admitting generalization.

And one cannot refer to causation without considering both the presences and the absences of the putative cause and effect. I say ‘putative’ because it is not right to call the two events or things concerned a cause and an effect till they have been formally established to be so[22]. A cause is generally understood to be something that makes a difference to, i.e. has an effect on, something else. If something has no effect on anything it cannot rightly be called a cause.

Another way to express this is to point out that “constant conjunction” is a very ambiguous term, because it does not specify direction. At first sight, it means that the cause (X) is always followed (or accompanied) by the effect (Y) – i.e. ‘if X, then Y,” But upon reflection, it also might refer to the reverse direction, viz. that the effect always implies (or presupposes) the cause – i.e. “if Y, then X,” And in the last analysis, the correct understanding (for the strongest form of causation) is that both those directions should be intended – for that would ensure the above-mentioned double condition of causation; i.e. that the relation have both a positive and negative side (since “if Y, then X” can be contraposed to “if not-X, then not-Y).

“Constant conjunction” would be a correct description of (complete necessary) causation, only if the expression were understood in this double manner. The vagueness of the phrase makes it possible for Hume to treat it as if it only meant “every occurrence of C has an occurrence of E attached to it” – while at the same time the phrase subconsciously impinges on us as meaning a two-way constancy of conjunction, i.e. as including “every occurrence of E has an occurrence of C attached to it,” Because of this theft of tacit meaning, many of Hume’s skeptical statements about causation seem superficially credible when they are not in fact so.

As a result of the vagueness of his treatment, Hume seemingly considered only complete causes to be causes – and simply did not take into consideration partial causes. Moreover, he seems to have totally ignored necessary and contingent causation. These suspicions are suggested by his definition of causation as ‘constant conjunction’. Such a definition fails to take into account partial causes on the positive side, and necessary and contingent causes on the negative side. It covers just one corner of the domain of causation. (And of course, as we shall see later, it also ignores indeterministic causality, i.e. volition.)

Hume, furthermore, argues that generality of conjunction is not the same as necessity. If two things are constantly conjoined, it does not mean that they must be so. This is true, but to raise this as an objection is to fail to realize the exact logical relation between the actual modality (are) and necessity (must be). They are two modal categories, and their relation is simply this: that necessity is more general than actuality, just as actuality is more general than possibility.

That is to say: to affirm the ‘necessity’ of some relation is to engage in a larger generalization than to affirm its ‘general’ actuality. It follows that if one admits the meaningfulness and validity for a general actual conjunction, one must equally admit them for the more pronounced necessary conjunction. If generalization can go so far, it can in principle go farther still. To accept the one without the other, just because necessity is more abstract (higher up the modal scale) than general actuality, would be arbitrary. There is no logical basis to be choosy like Hume.

Indeed, when Hume denies the possibility of human knowledge of necessity (admitting at best generality, if that), what is he doing in fact other than claiming for himself a necessity? After all, impossibility (i.e. negation of possibility) is simply the negative form of necessity (i.e. it is necessity of negation). Therefore, Hume is here again in a position of inextricable self-contradiction.

Additionally, it is logically impossible to deny the concept of necessity while admitting that of possibility. The moment one admits some things as possible (as their actuality logically implies them to be), one must equally admit some others are impossible. That is, there are limits to all possibilities. If everything were only possible, nothing at all would be possible for contradictories would have to intertwine. Thus, denying all necessity is a logically untenable position.

There is yet another way that Hume’s skeptical approach to causation relates to his problem with induction. He repeatedly asks on what basis we believe in a causal “connection,” According to him, all we observe and can observe are the happenstances of conjunction; we never observe and can never observe any link or tie between the things conjoined.

Connection is not an observable fact that we can generalize from, even granting generalization to be valid. Causation is at best, he implies, a generalization about conjunction – but it tells us nothing of a stronger underlying bond, which is really what we popularly understand by causation. The idea of connection is thus an after-the-fact projection of some obscure force unto an essentially statistical report; it assumes something more than what is empirically given.

In reply, we should first point out that ‘conjunction’ is not a concrete object, but an abstraction. Phenomenologically, it refers to the appearance of two objects side-by-side in some context. The term does not refer to a phenomenon, something with sensible qualities in itself – it refers rather to a relation between phenomena (or, similarly, other appearances or concepts) that we project to unify them for our rational purposes. It is a tool of ratiocination.

‘Connection’ is also an abstract term. We might therefore ask how come Hume acknowledges conjunction but not connection. The answer would be that the latter is a more complex abstraction than the former. Connection is not as immediately related to observation as conjunction. More imagination is needed to grasp it, because it refers to collective rather than to individual properties of things.

It is true, as Hume implies, that causation (i.e. deterministic causality, as distinct from volition) is never known or knowable in individual cases, except through knowledge of the behavior of kinds of things. Therefore, causation cannot be generalization of perceived individual connections, but only generalization from individual conjunctions. Connection is a rational, top-down idea, more than an empirical, bottom-up idea. It is imagined with reference to many observations, rather than simply observed.

Even though Hume correctly realized this, his objection to connection has no weight, because according to inductive logic (viz. the principles of adduction), we can imagine any thing we choose as a hypothesis, and affirm it as true, provided and so long as it remains compatible with all experience (on both the positive and negative sides), meaningful, consistent with itself and all other empirical and abstract knowledge, and more coherent, relevant[23] and credible than all alternative hypotheses.

In other words, what Hume is here refusing to comprehend is that most human knowledge is based on abstraction and imagination. He fails to understand that this is quite legitimate, provided it is properly regulated by the rules of adduction. Generalization directly from experience is just one kind of induction, the simplest. More broadly, we have the process of adduction, i.e. of forming fancy or complex hypotheses and testing them repeatedly both experientially and rationally.

The idea of causal connection (or tie or link or bond) is just one such hypothesis. It is indeed not a direct generalization from experience like “constant conjunction,” but is a quite legitimate and ordinary adduction from experience. It is a rational construct we find useful for our understanding, both consistent with all evidence we have from experience and internally consistent. That is, the genesis of the concept of connection accords with the scientific method.

A common objection is: “night follows day and day follows night, but we do not say that day causes night or vice versa,” Indeed, more generally, every impermanent thing is sure to be followed sooner or later by its negation; but we do not consider such sequences of events as consequential. Sequence is not always consequence. Hence, causation is something more to us than mere repeated togetherness. We need a concept of connection, over and above that of mere constant conjunction, to be able to express this important thought. No tautology is involved.

We could further suggest that “connection” is not commonly thought of as something general, the same abstract ingredient in all particular cases of causation. In practice, something specific and relatively concrete is in each case identified as the operative connection. A more precise analysis is required in each case, to determine where the connection lies. For instance, in the case of day and night, the common ingredient is that of the sunshine and earthly rotation, with some exceptions during eclipses due to the moon.

Thus, the phenomena of day and night may be said to be due to the operation of common causatives. Their constant conjunction is due to them both being alternative effects of certain other phenomena. They must succeed each other, because they cannot occur at the same time. Under certain circumstances, the one occurs; under the remaining circumstances, the other occurs. Sun plus earth facing this way and moon in that position gives day; the same with earth facing the other way gives night; and so on.

We may generalize this example by saying that we should regard constant conjunction as only a first indicator of causation. It is indicative of causation in most instances, as the initial default categorization. But in some instances, we must admit that the conjoined phenomena succeed each other due to some third factor (or collection of factors), with which they are indeed both in turn constantly conjoined. They have some common cause(s), or constant conjunct(s), which more precisely explain their surprising regularity of succession.

In such cases, we would not call the two phenomena ‘directly’ causally connected (even though they invariably alternate). We would, however, instead consider each of them as indeed directly causally connected to the third phenomenon (or set of phenomena)[24]. Thus, our idea of causal connection is a subcategory of constant conjunction, rather than a mysterious universal additive to it. For this reason, we need two distinct concepts.

If we take the trouble to analyze Hume’s own discourse, we are sure to find thousands of concepts and beliefs in it as abstract as that of causal connection that he so derides[25]. His will to attack this particular abstraction is just an arbitrary refusal to give credence to perfectly rational arguments. He gives no evidence or solid reason to show us that this concept is more tenuous than any of those he himself accepts. We must not condone such double standards.

Generalization and adduction are equally justified, and logically not very different processes. Indeed, each could be viewed as a special case of the other. One cannot admit the one and reject the other. One cannot more or less admit the one, and more or less reject the other. They are essentially the same. Both are indispensable and inescapable means of human knowledge, which is mostly conceptual and theoretical. No one can claim to rationally criticize them without using them.

The likes of Hume have this fastidious dissatisfaction with the inherent tentativeness and uncertainty of induced knowledge, because their narrow minds are firmly set on the notion that only deduction yields “proof,” Nothing could be further from the truth. Most or all apparently deduced truths depend to some extent on induction from experience. Deduction is just one tool among others in the essentially inductive enterprise of human knowledge. Even the fanatic empiricist cannot formulate any idea without using induction.

The validity (as well as need) of induction is equal to that of deduction. Deduction is not somehow superior to induction. The validation of deduction (i.e. the science of deductive logic, including the laws of thought) depends on a host of inductions. The validation of induction depends on a host of inductions, too. In either case, we rely on our logical insights, on what seems or does not seem logical and credible, as well as on a mass of information.

Skeptics cannot refuse such logical insights without appealing to this very same faculty in us. When a skeptic says that this or that idea or belief is or is not logical, or credible, or reliable, or convincing, or provable, or valid, or anything or the sort, he is claiming a logical insight and asking us to have the same logical insight. We may agree or disagree. He cannot in any case claim to function over and above logical insight. He is not superhuman, graced with special privileges.

Drawn from Logical and Spiritual Reflections (2008), Book I, Chapters 1-3.