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LOGICAL AND SPIRITUAL REFLECTIONS

© Avi Sion, 1996-2009 All rights reserved.

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Logical and Spiritual REFLECTIONS

Book 1. Hume’s Problems with Induction

Chapter 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[1].

To define causation, as Hume did, only with reference to the positive aspect of it, would necessarily make the bond involved seem more flimsy. 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.[2]

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[3]. 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[4] 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)[5]. 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[6]. 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.



[1] As I show in great detail in my work The Logic of Causation.

[2] Indeed, if one or both of the things labeled X and Y is/are categorically constant, the constant conjunction of X and Y is formally true even though the two things are independent of each other. For the constancy to be applicable specifically to the conjunction of X and Y, there must be inconstancy in opposite circumstances.

[3] 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. Many fake arguments against causation are based on naming the items under consideration cause and effect before they have been demonstrated to be so.

[4] Relevance here refers to there being more than only compatibility between the thesis and empirical data; for the thesis to be relevant to the data at hand, it must imply some of them and thus conversely be fortified by them. The thesis is thus useful, in somewhat explaining the data. And it must be more useful than others, for if it is only as useful and sound as its alternative(s), it remains problematic (i.e. we cannot decide between them all).

[5] We can then also say that the two phenomena are ‘indirectly’ causally connected through or by the third phenomenon.

[6] To name just one: the notion of “association” of ideas. What is the concrete content of this abstract term? Has “association” a sensible quality, like a color, tune, smell, taste or feel? Clearly not – yet Hume freely uses this abstraction. Indeed, it is to him the main force (another abstraction) in the mechanics of ideas that he wishes to institute for psychology, emulating Isaac Newton’s treatment of physics.

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2016-06-13T11:58:30+00:00