Book 1. Hume’s Problems with Induction
Chapter 12. Some further remarks on causal logic
The following notes are intended to amplify my past writings on causality.
The fallacy of reductionism. In my research on the logic of causation, I established that “a cause of a cause of something is not necessarily itself a cause of that thing” (see list of valid and invalid causative syllogisms for the precise conditions when this applies and when it does not).
It occurs to me that this result can be interpreted as a formal proof that “reductionism” does not always apply.
When we try to ‘reduce’ something to its constituent parts, we are saying that the laws that apply to the parts ultimately apply to the whole; i.e. we are saying that the whole is no more than the sum of its parts. This is sometimes true, but it is not always be true. It is true when the following syllogism is valid, and untrue when it is not.
Y causes Z, and
X causes Y,
therefore, X causes Z.
In some cases, I say, though the whole (Y) have a certain property (Z), it does not follow that the part (X) has that same property (Z). In such cases, the whole may logically be said to be more than the parts. For example, though the whole of a live human organism has consciousness and volition, it does not follow that any of its parts has these powers.
It should be added that this insight of causal logic is valid for all modes of causation. That is, it can be equally said of natural, extensional, spatial, temporal, or logical causation. Thus, reduction or irreducibility has as many senses as there are modes of modality. It follows that something may be reducible in one sense, but irreducible in another.
We thus have, precisely listed in my work The Logic of Causation, the formal rules for impartially settling debates about reduction in specific cases. Reductionism is sometimes applicable and sometimes not; and we have a way to tell just when it is and when it is not. Reductionism is a fallacy, note well, not because all reduction is fallacious, but because reduction is in some cases fallacious.
Incomplete listings of causes. It should be added that the above schema is not the only way reduction occurs fallaciously. Sometimes, reduction consists simply in declaring a number of things to be partial or alternative causes of a phenomenon. The possible fallacy in such cases consists in incomplete listing of partial or possible (i.e. contingent) causes. Even though the things proposed as causes are indeed causes – the list proposed is incomplete. The effect of such too-short listing is to narrow our vision and multiply our wrong causal judgments. That is why we must call it a fallacy: because it makes us reason wrongly.
For example, the expression “nature or nurture” is usually understood as signifying that the causes of physiological and psychological phenomena are genetic and/or environmental. But there is a third possibility or partial determinant: viz. volition. Volition signifies personal choice and effort, self-generated change; it is quite distinct from and even antithetical to physical and mental causations. To omit it from the list is to bias judgment away from it, towards more deterministic biological and psychological forms of explanation.
This missing disjunct might be generously understood as implicit in the others, but in truth it is not so. Often, when people speak of nurture, they have in mind the influence of other people – for instance, parents and teachers in the learning process. This is indeed ‘nurture’, though we must keep in mind that it refers to acts of volition by other people, which influence the volition of the subject. However, to think in such terms alone puts insufficient emphasis on the subject’s will – in this instance, the subject’s will to learn. To classify this too as ‘nurture’ would be inappropriate. It is definitely a third factor, viz. personal choice and effort. Thus, we should always speak of “nature and/or nurture and/or volition” when explaining human behavior.
Note that the disjunction “genetics and/or environment” is even worse than “nature or nurture”, because the word ‘environment’ need not imply any human interference at all, whether that of others or one’s own. It connotes the effects of the weather, food composition, agents of disease – anything but human action. The choice of this word is rarely accidental. There is a tendency among many modern scientists (biologists, physicians, psychologists, etc.) to deliberately avoid any explicit mention of volition in their explanations. They think that mention of volition would make their discourse unscientific, and are afraid to lose credibility among their peers. So even if they think of volition as a relevant factor, they keep all references to it tacit. Such discursive behavior is not honest or intelligent.
A common causal argument. Quite incidentally here, while on the topic of causal logic, when we say that something (X) is the causative of something else (Y) in an individual case, we mean that from all the possible causes of Y in general, the cause X is in this case the one applicable. For example, to say that John died of a heart attack, we need only verify that John’s heart had a serious enough problem, and no other possible cause of death occurred in this instance; and thus, by demonstration and elimination, we conclude that John died of a heart attack.
This is stated in support of the claim already made that causation always relates to kinds, not to individuals. When we identify causatives in individual cases, we are not identifying the general fact of causation, but its particular application to a given instance. Thus, in our example, we know from general scientific studies that a human being can die from a variety of causes. When a particular human being dies, and we wish to know “the cause of death”, we use our general knowledge in disjunctive form as the major premise in an apodosis with an appropriate minor premise concerning the individual case.
The argument runs as follows:
Death in a human being may be caused by heart failure, or cancer, or… etc.
In John’s case, we found some evidence of heart failure, and no evidence of any other possible cause of death.
Therefore, John (probably) died of heart failure.
Of course, this argument may be found erroneous, if it turns out that the list of causes of death is incomplete, or if it is found that certain other problems in John had not been spotted. For this reason, it is wise to qualify the conclusion as only probable, in the way of reminder of the inductive assumptions behind the deduction.
Positivism may be viewed as a thesis going in the opposite direction to reductionism, or putting a stop to the urge to reduce. It is a (sometimes arbitrary, sometimes wise) refusal to dig any deeper or look any further for underlying causes or explanations.
An example is the Heisenberg principle of uncertainty. This is regarded by some philosophers (notably Neils Bohr), somewhat arbitrarily (in the way of a concession to the 20th Century’s zeitgeist), as an epistemological principle (implying doubt in our very ability to know, since our antennas of knowledge are limited in scope), whereas it is really no more than a principle of physics.
The wave-particle duality is often presented as an empirical refutation of the law of non-contradiction. But this is an unfair interpretation of events. The facts of the case are that an ongoing physical phenomenon may in some circumstances behave with the mathematical properties of a particle and in other circumstances behave with those of a wave. The circumstances involved are certainly not one and the same.
There is empirically no actual superimposition or ‘interbeing’ of wave and particle in the same respect, in the same place, at the same time, in the same perspective of the onlooker. The two states are clearly separated by space, time or other circumstances. Therefore, the law of non-contradiction is in fact never breached. Therefore, no epistemological or metaphysical difficulty arises.
The problem raised by the wave-particle duality is at worst merely rational: it is a surprising inability of our theoretical instruments, i.e. physics theory and experiment as well as mathematics, to fully predict and explain such goings-on of material phenomena.
Thus, we could say in rebuttal to the positivists of uncertainty that what prevents us from full knowledge at the quantum level is one or all of the following:
- Perhaps as they claim the physical world is really so roughly constituted that there are no finer levels of matter in this world than what we observe. In that case, our cognitive faculties are not to blame; the world is like that. But then, how can we know it for sure?
- Perhaps the world in fact has finer, deeper levels, but our sensory faculties and experimental instruments are inadequate to the task of detecting and measuring them. In that case, it is not inconceivable that more sensitive experiments be devised someday that do make physical detection possible, directly or (granting certain physics hypotheses) indirectly.
- Perhaps the mathematical tools currently at our disposal are inadequate. In that case, it is not inconceivable that someday we develop a mathematics sufficiently sophisticated to seamlessly unify the quantum phenomena observed.
Our faculties of perception and our intelligence are, it is true, limited. We might conceivably have had a sensory faculty strong enough to allow us to differentiate particles from waves, but we unfortunately do not. We might have found some indirect way to do so, but we did not – so far, at least. We might have developed a mathematical theory capable of dealing with the problems encountered, but we did not – so far, at least. In that sense at most, the uncertainty principle might be viewed as an epistemological statement.
But people who think thus forget that their conceptual faculties (though also not unlimited) have compensated this sensory and technical limitation, if only enough to realize the (currently apparent) truth of the uncertainty principle. Therefore, the problem is essentially factual rather than epistemological. It does not put in doubt human knowledge as such, but is an expression of it. Our knowledge is limited in scope, but not for that reason necessarily false.
It is important to emphasize in this context the modern tendency to infer an “is” from a “might be”. This fallacy is evident in Bohr’s inference from an uncertainty (as to what lies at a deeper level of matter than what we are ‘on principle’ – at the present development of physics, at least – able to observe) to a certainty of negation (i.e. to a certainty that there is nothing beyond). The same fallacy is found in Goodman’s inference of blue (a specific color) from ‘grue’ (a range of possible colors).
The causation in ‘fields of force’. Someone looking at the definitions and analyses of causation in my book The Logic of Causation might well wonder what all that has to do with the ‘fields of force’, like gravity, electricity and magnetism (to name just the more widely known), which are at the core of modern Physics theory. The answer to that question is already proposed in my Judaic Logic, Appendix 1.3.
We describe the force at each point in a field, around some central ‘particle’ or ‘body’ (collection of many and varied interacting particles), by means of if-then statements. These have roughly the form: “another body with such and such characteristics (e.g. mass, electric charge or whatever appropriate) placed at this point in that field (i.e. at a certain position relative to the central body concerned) will be subject to a force of magnitude and direction so and so, calculated using a certain quantitative formula (a hypothesis previously developed by inductive logic, e.g. an inverse square law)”. Needless to say, this proposition is merely descriptive: it does not tell us why or how such (invisible and remote) force occurs at all – I leave this difficult question for physicists to answer!
Such if-then statements, which are natural or extensional conditional propositions in formal logic, are the underlying causal (or more specifically, causative) propositions analyzed in my causative logic work. It is important to realize that the causative propositions corresponding to fields of force generally relate to partial and contingent causation, since forces may amplify or diminish each other (and in some instances cancel each other out). That is to say, the relation of force operative between two bodies, calculated by means of the pertinent algebraic formula, is applicable to them as is only granting that no other bodies are in their vicinity. It goes without saying that if more forces are involved at the same time, their net effect has to be calculated before we can correctly predict the subsequent motion (if any) of the body or bodies concerned.
Speaking of motion, can the motion emerging from fields of force be described as motion arising from rest? In my Volition and Allied Causal Concepts, chapter 8.1, I suggest that the generation of motion from rest is a distinctive characteristic of volition.
On the surface at least, fields of force would seem to belie this claim of mine. For example, hold a stone above the ground, then let it fall; or again, place two light magnets next to each other well at rest, and when you let them go they will either attract or repel. In such cases, acceleration from rest evidently occurs. Yet this is clearly different from what we suppose volition to do. In the case of gravity or magnetism (or other sorts of field-forces), the movement is preprogrammed, i.e. in the same circumstances it will always be the same in magnitude and direction. Whereas in the case of freewill, the same agent may in the same circumstances choose a different magnitude and direction of will. In the latter sense, volition truly initiates motion from rest.
Notice, too, that in the examples above given, volition was involved in bringing the stone or the magnets in their starting positions, and they were held momentarily stationary there by volition. The motion in these objects is as it were artificially held in abeyance; whence the physics concept of ‘potential’ energy. Motion is the main configuration of the natural world (the domain of deterministic causality, or causation), while immobility in it is due to a temporary balance of opposite forces. In the spiritual world (i.e. the domain of personal causality, or volition), in contradistinction, motion emerges occasionally and somewhat voluntarily from something essentially at rest.
Liebniz’s ‘pre-established harmony’. Hume’s attempt to weaken the bond of causation can be rooted to some degree to the doctrine of ‘pre-established harmony’ found in the philosophy of Gottfried Liebniz. This idea substitutes a sort of parallelism for the common concept of causation. That is to say, according to this doctrine, the putative cause and effect just happen to regularly occur together or in sequence.
The observable regularity is, according to Liebniz, not due to a causal relation or connection between the two phenomena (here labeled putative cause and effect). Rather, each functions independently according to its own nature, yet they happen to (or were programmed by God to) be in phase. This can be illustrated by reference to two clocks that happen to always show the same time, though their mechanisms are not linked.
I mention this doctrine here so as to refute it, for it may have a semblance of truth in it due to common misunderstanding of the nature of causation. For after all, what is what we call the nature of things but the happenstance of their various observed characteristics? But the concept of causation is not based on mere actualities; it relies on modal concepts, i.e. on the concepts of possibility and necessity. And in particular, natural causation is based on the corresponding natural modalities. The concept goes beyond perceptual data, though we try to base it on such data.
That is to say, to claim that (for instance, using the strongest determination of causation as our example) P is a ‘complete and necessary cause’ of Q is not merely a claim that presences of P are accompanied by presences of Q and that absences of P are accompanied by absences of Q. No – it is a claim such togetherness or sequence of events does not merely not-vary, but is invariable. It is necessary; i.e. in the case of natural modality: it is a natural necessity. Or in other words: its negation is impossible by the nature of the things concerned. If no such claim is being made, we cannot truly say that we are discussing causation.
This can be made clearer if we look at the matricial analysis for the determination in question, i.e. the following simple table (drawn from my book The Logic of Causation):
Matrix of “P is a complete and necessary cause of Q”.
In this macroanalytic table, the “1” and “0” under the items P and Q signify respectively presence and absence of those items in different combinations. But the “1” and “0” under the relation “mn” (symbolizing complete and necessary causation) mean respectively “possible” and “impossible”. That is to say, in the latter case, mere continued non-occurrence of the PQ combination concerned is not sufficient to prove the stated causation, there has to be an assumption that such combination will never occur, because it cannot occur. Such proof is logically possible thanks to the principle of induction, and it is possible only by this means.
Liebniz’s doctrine effectively accepts temporal causation, spatial causation, extensional causation, and even logical causation, but arbitrarily rejects natural causation. These various modes of modality and thence of causation are all identical in principle, differing only in the basis of generalization (and if need be particularization) they involve. Temporal necessity (‘is always’) requires generalization from some to all times of some existent; spatial necessity (‘is everywhere’), from some to all places of it; extensional necessity (‘is in all cases’), from some to all instances of some concept; logical necessity (however expressed), from some to all contexts for some knowledge.
The only distinction of natural necessity (again, however verbally expressed) is its requirement of generalization from some to all circumstances surrounding some event. If one sort of generalization is admitted, there is no technical justification for rejecting any other sort; the epistemological process and inductive argument is identical in every case. As already explained, individual acts of generalization may turn out untrue, but the process cannot be denied in principle without self-contradiction. Hume makes the same error, as earlier shown.
It should be added that Liebniz concocted this non-modal (i.e. exclusive of natural necessity) causal theory to buttress his bizarre theory of “monads”, according to which the world is populated by entities (called monads) existing and functioning entirely independently of each other. To explain how come, despite their claimed mutual independence, we can observe seemingly coordinated behavior patterns among things, he postulated the idea of pre-established harmony.
Moreover, this was not, in his view, mere coincidence, but an illusory order deliberately programmed by God. It apparently did not occur to Liebniz that the concepts of independence and Divine programming of the monads required a modal understanding of causality for their formulation. He was effectively saying that worldly events do not cause each other, but do have as common cause God; that is still an admission of causality as such. He was thus tacitly involved in concept-stealing or self-contradiction – unless we consider that he was not like Hume denying causality de jure (in principle), but only de facto (in a limited field).
The deeper problem with Liebniz’s theory of independent monads is its imposition of a grand ‘purely rational’ construct on reality, irrespective of experience. This is an example of what Boorstin has aptly called “the German a priori method” (p. 237). We find the same psycho-epistemology in Kant and Hegel, and many other (though not all) German philosophers – a propensity to build massive intellectual systems (based on a few tendentious observations and insights, and blithely ignoring contrary empirical data and logical limitations). This is not only a failure of due empiricism, but more broadly of understanding the many demands of objective human induction. These thinkers – for all their intelligence and valuable contributions – get romantically carried away by their arcane conceptions, without regard for their obscurities and anti-empirical aspects. They are emotionally driven by the ambition to be the Big Genius who solved all the problems in one sweep, and so easily enthused by apparent panaceas.
 See also for example, Gould, p. 283.
 See for example, Gould, p. 288.
 Physicists might eventually, or maybe already have, come up with a more dynamic vision of the workings of fields. Some theories seem to suggest they involve particles or waves of some sort in motion (e.g. gravitons). But here, let us take fields at their face value, so to speak.
 Germany, 1646-1716.