Inductive Logic

A Thematic Compilation by Avi Sion

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33. More Reflections on Induction


1.    The Psychology of Induction

Hume tried his best to do away with the science of induction by psychologizing our understanding of it. Of course, there is a psychology of induction, since humans have a psyche and induce. But Hume attempted to reduce induction to psychological mechanisms, i.e. to substitute a psychology of inductive thought for the logic of inductive thought. He proposed a description that effectively eliminated the possibility of evaluation and prescription. He sought to permanently undercut all attempts to validate induction.

With this goal in mind, Hume proposed a psychological theory of generalization. Generalization was to him a mere quasi-mechanical or instinctive reaction of expectation due to repeated imprints in the mind; it was, effectively, an acquired habit. Essentially, Hume was arguing that the repeated experience of cases of X that are Y drives us to conclude that all X are Y (i.e. to expect that yet unseen cases will conform to past experience), even though in principle things might well (and often do) turn out otherwise.

But according to inductive logic, Hume’s theory is just a hypothesis that has to, itself (like all hypotheses), be confirmed repeatedly and never infirmed. Hume cannot regard it as somehow exempt from or transcending inductive logic. It is subsumed by it like any other theory. In fact, there is no psychological drive such as Hume projects – and his theory is itself proof of that, since he himself is aware that things might (and often do) turn out differently than expected.

It is important to notice that, in practice, while we do frequently generalize, we often do so tentatively fully aware that we might have reason to change our minds later on. Moreover, we often abstain from generalizing, because we do not want to proceed hastily or because we are already aware of contrary evidence. Also, we often particularize after having generalized, due to coming across new evidence to the contrary.

It follows from such simple considerations that Hume’s claim to a psychological law is empirically inaccurate. It is a false observation, an overly hasty generalization from limited or selective introspection. Not only does it not explain the phenomenon of generalization, nor replace the need for a logical and epistemological treatment of the issue, it is an erroneous psychological claim, incorrect psychology.

Another attempt at reductive psychologizing was Hume’s attempt to write-off causation as mere association of ideas. Basically, this suggests, Hume had personal difficulty distinguishing the fact of causation from our way to knowledge of causation; because he confused the two issues, he tried to conflate them.

Underlying Hume’s notion of association of ideas was of course his belief that what we perceive (when we seem to perceive the world) are not things in the world out there but images of such things produced in the mind through sensations. Due to this erroneous (because internally inconsistent, self-contradictory) analysis of the experiential process, he seems (in some people’s eyes) to have some credibility in affirming causation as mere association of ideas.

For Hume effectively adopted John Locke’s theory of human knowledge as his starting point. This theory admittedly seems like common-sense: we have senses and they obviously somehow produce images and memories in us. However, this is the basis of the worldview that has come to be called Naïve Realism (or uncritical materialism). It seems reasonable, but upon reflection it is found to be wobbly.

If the senses truly produce images in our minds of the world beyond them, it follows that we have no direct knowledge of the world out there at all, but only knowledge of the said images (this term here intends all phenomenal modalities, i.e. not only sights, but also sounds, smells, tastes, and various touch sensations). In that case, how do we know of the bodily senses at all, and on what basis could we at all affirm a world beyond them? It is a seemingly inextricable dilemma.

At first glance, to affirm that our cognitive relation to the world out there is mediated by ideas seems innocuous. It seems obvious enough that our ideas, or most of them, somehow ‘represent’ or ‘correspond to’ the world. But upon reflection, such a view of how our knowledge is constituted and justified is logically untenable. How can we claim our ideas representative or correspondent to reality if we have no immediate contact with it by which to make this judgment? How indeed can we even claim our ideas not to represent or correspond to reality? We are seemingly doomed to utter ignorance.

To his credit, Hume (unlike Locke[1]) became aware of the insuperable difficulty that the common-sense theory of knowledge raised. Less to his credit, Hume derived a deep skepticism from this puzzle, because he effectively assumed there was no other approach. That is, rather than considering Locke’s particular theoretical approach to have caused the dilemma, he viewed the problem as a definitive cause for doubting all human knowledge as such.

That such a radical doubt in turn cast doubt on his own faculty of knowledge and conclusions apparently did not cross Hume’s mind (or not sufficiently). For, though henceforth fundamentally a skeptic, he continued seeking and claiming knowledge. But he did not try very hard to find a solution to the inherent problem. He never discovered the solution made possible by a phenomenological approach.[2]

This approach is encapsulated by the aforementioned principle of induction, which starts the enterprise of knowledge with regard to appearances rather than to sense perceptions. ‘Appearances’ refers to the contents of consciousness irrespective of their source, so this term does not have presuppositions like ‘sense perceptions’. It is not a verbal issue, but one of ordering of knowledge, note well. In a phenomenological perspective, Locke’s theory regarding sensations and ideas is just that – one attempted explanation of certain appearances. Seen in this light, the difficulties it presents seem far less threatening.[3]

Now, all this is said here only to explain why Hume was more or less bound to opt for a reduction of causation to ‘association of ideas’. Since his viewpoint effectively divorced ideas from their objects, he could not talk about the objects themselves without some nagging discomfort, and he was pretty well cornered into rather discussing ideas.

But it must be stressed that for us, who are free of the dilemma posed by Locke’s theory thanks to a more phenomenological approach, the scenery looks very different. We can logically distinguish ideas from the objects they intend – be these objects physical, mental or spiritual. Although ideas might conceivably always appear in certain sequences, this is not for us sufficient reason to declare the objects they intend to be causally related.

Here again, we must apply deductive and inductive standards to judge the issue.

For a start, it is worth pointing out that the concept of association of ideas is inherently one of causation. Leaving aside Hume’s view of causation as mere constant conjunction as against connection, to say that ideas are associated in some way is to claim a connection of some sort between them. If we think in terms of one idea ‘giving rise to’ another, or we use any other such expression, we are thinking causation. The implication may be tacit, but it is clearly there.

That the causal sequence concerns the specific kind of thing we call ideas, rather than the kind of thing we call objects, is irrelevant to the relation itself, which is conceived as technically the same irrespective of the kind of thing related. Causation is a certain kind of relation between terms or theses, which has nothing to do with their actual contents.

To say that the idea of X causes the idea of Y is as much a claim to causation as to say that X causes Y. The formal proof is that we can call “the idea of X” a special case of X, and “the idea of Y” a special case of Y. In formal logic, X and Y are symbols for any two terms; they are not reserved for objects as against ideas. For this reason, the principles developed with regard to X and Y are universal.

If we formally admit a causative relation between ideas (or impressions, sensations, concepts, beliefs, thoughts, or any such mental phenomena), there is no reason for us not to admit a causative relation between other kinds of things (i.e. between non-ideas, viz. the objects of most ideas). To accept the one and refuse the other, as Hume does, can only be arbitrary, for there is nothing to formally distinguish the two. The variables differ, but the underlying relation between them is the same.

In short, our use of the word association in one case and causation in the other is a mere verbal embellishment. Hume’s main argument is thus based on a superficial verbal distinction. And here again, his attempt to substitute psychology for logic is implausible. The truths of logic are independent of any psychological thesis.

Secondly, Hume is incoherent when he formulates a concept of association of ideas that is meant to exclude a concept of causation between the objects the ideas refer to. Such an exclusive contrast between the two concepts commits the stolen concept fallacy. For to invalidate the association of ideas, i.e. to point out that ideas may be erroneously associated, we need to have a more objective knowledge to compare to. It is logically impossible to claim associations of ideas to be occasionally or inherently wrong, without claiming separate knowledge of the true causation between the objects concerned.

In the very act of downplaying or denying causation between objects by positing association of ideas, Hume is relying on his and our past experience that sometimes associations do not match causations. If we had no such past experiences, we could not comprehend Hume’s argument, or be convinced by it. Hume’s discourse tacitly implies his and our ability to grasp causation independently of association, i.e. that we all have access to some objective reality.[4]

Hume is here committing the same silly error Kant would later commit when claiming that things as they really are (“in themselves”) are radically different from things as they appear. How could he know it? No one can consistently postulate a conflict between reality and appearance without having access to both. If someone accuses humans of total delusion, he forfeits all logical right to discuss the presumed ‘real’ world, for all such discussion (even hypothetically) would be self-contradictory, since it is itself a claim to some knowledge.

The critic cannot claim to be an exception to the general rule he posits. We cannot project a scenario that excludes us – but some people keep trying to! We admittedly all have some illusions sometimes; none of us are infallible – but this is a far cry from total delusion.

It should be noticed that we are well able to distinguish the two classes, i.e. ideas and objects. Hume does so in practice, though he denies our ability to do so theoretically. Indeed, how could his discourse be at all meaningful to him and us, if we could not all make the distinction? If apparent objects were truly no more than ideas, it is doubtful we could even imagine such a distinction; certainly, it would be logically self-contradictory in the way that Kant’s dichotomy later was.

Thirdly, let us consider the facts of the case in more detail. Note that we ordinarily pass no time wondering whether our ideas are repeatedly conjoined, but only concern ourselves with their objects. Moreover, we might ask whether any two ideas are ever in our actual experience constantly conjoined; the answer seems evident to me – it is no. On the other hand, many objects do seem to us constantly conjoined.

Moreover, if we introspect sufficiently, we easily notice that ideas may become associated in our minds for reasons that have nothing to do with the objects they intend. Such association is not based on constant conjunctions, but on a single coincidence. The strength of mental association is not due to statistical frequency. For instance, a certain musical tune reminds me of a certain woman, just because it happened to be playing in the restaurant where we sat the day I met her. I may well have heard the same tune a hundred times before, without any association occurring.

This means that in our common everyday experience, without reference to Hume, the conjunction of ideas and the conjunction of the objects they intend are two quite different issues. Even if we observed our ideas and found them constantly conjoined, we would not necessarily conclude that the objects they intend are causally related; we are not (most of us) that stupid. As well, we are well able to believe two objects to be causally related even while our ideas relative to these objects do not readily arise together.

It is also worth pointing out that, intuitively, we have the volitional power (often if not always) to arouse or suppress ideas, whereas we do not seem to have similar power relative to apparent objects. We can ignore objects, or forget them, but that does not wipe them out: if we look for them again they reappear or someone else might still see them. But in the case of ideas, or more precisely many memories and derived imaginations, we experience a greater power of manipulation. On this basis, we expect the associations between ideas to be more tenuous: they depend more on our will.

All such simple observations and arguments again take us to the conclusion that Hume indulged in an excessively hurried generalization, from very little introspection and reflection. He was either lazy or dishonest, focusing on the data that supported his pet theory and ignoring the data and reasoning that contradicted it. The matter is open to objective judgment – it is not my word against his: everyone can carefully consider the data and judge independently.

The philosophical sciences of logic, phenomenology, epistemology and ontology provide the blueprint and guidelines for induction. There is of course additionally the need to consider the psychology of induction, since after all induction is an activity of the human psyche. Through such a complementary study, we can better comprehend how induction actually occurs. But psychology and logic are two very different fields.

Briefly put, I would describe the psychology of induction as follows. The human soul has powers of cognition, volition and valuation. All three of these functions come into play in every inductive act. The end is cognitive; the means is volitional (combined with non-volitional elements, provided by the nervous system, mainly the brain); the motivation comes from the valuing of knowledge, or the things or events that knowledge can serve as a means to.

The relation between the said philosophical sciences (including logic) and the psychology of induction (in an individual at a given time) is that the sciences (to the extent that they are known to the person concerned and kept in mind) influence the inductive activity of the person. They do not determine it, note well, but they influence it. This relationship thus leaves room for the cognitive, volitional and value-oriented factors of induction.

If the person has a low degree of knowledge or understanding of the scientific underpinnings of induction, he or she will naturally often make errors. However, even without formal training and reflection on the issues of induction, most people do subconsciously frequently think logically and thus a lot of the time have some measure of success in their inductions. Humans, after all, have considerable natural intelligence; else they would not have survived till now. The said sciences are, after all, very recent productions of the human mind.

The root of Hume’s problem with induction is perhaps his misconception as to what ideas[5] are. I suggest that in his mind’s eye, ideas are clouds of ‘mental stuff’ produced by sensation. These perhaps very often look like the objects that generated our sensations, but we cannot be sure of that since we have no access to such objects other than through ideas. Thus, what we actually perceive and know are only ideas. Thus, ideas are veils that separate us from reality, rather than conduits to reality.

This view is, as already pointed out, self-defeating, since it accuses also itself of ignorance and error. However, the point I want to stress here is how ideas are reified in Hume’s discourse. Because he effectively visualized ideas as atoms of mental substance, his view of human knowledge as a whole was completely distorted.

In fact, an idea is something very abstract, an intention[6] towards some object, a relation of pointing in a certain direction, directing our attention hither, rather than a substantial entity. An idea is an idea of an object. It has no existence apart from an object of some sort (although, of course, the object concerned need not be real, but may be illusory).

It is certainly true that the physical processes of sensation play a central role in our noetic relation to a domain beyond our apparent physical body. But it does not follow that what we perceive when we sense this ‘external world’ are sensations or even images[7] of the world.


  • The only coherent theory is that what we perceive is the world itself.
  • The images we form in our minds of such primary perceptions are only ex post facto memories of what we perceived[8].
  • The abstract concepts we form thereafter are not mere manipulations of concrete memories, but relations we intend to the objects initially perceived.


The fact that we perceive external objects, and not impressions or ideas of those objects, is certainly marvelous, so much so that we still cannot understand how that might happen. But our difficulty and failure to explain this marvel of nature is not a reason enough to deny its occurrence. That we perceive the world is obvious enough; how such a thing is possible is a distinct question, which we may never answer. Science does not normally deny the very existence of what it cannot thus far explain.

Note well, we can claim knowledge that we directly perceive the external world itself, without claiming to know yet just how we manage to do so. We know we can, because this is the only consistent theory we can posit, as already explained. But exactly what role the senses and brain play (other than memory production, storage and reactivation) in this evident direct perception is still an open question. The fact that a partial question remains does not invalidate the truth of the partial answer already obtained. There are many issues in the special sciences that remain unsolved to date – and we do not for that reason throw out the knowledge we already have.[9]

It does not follow from such non-skeptical, objectivist theory of knowledge that perception or conception can never be erroneous. Errors in human knowledge are essentially conceptual, and it is the task of logic to minimize them. Perception sometimes seems wrong, after the fact, due to our noticing later percepts that seem to contradict the earlier. In such cases, we realize that in fact we drew some conceptual inference from the initial percepts, which the later percepts make clear was unjustified, and we correct our previous assumption. This is just an application of the laws of thought and the principle of induction to sorting out conflicting perceptions.

Once we comprehend human knowledge in this truly enlightened manner, it becomes clear why Hume was so confused and self-contradictory in his views of induction, and other logical and philosophical issues. If one starts with false premises, one is very likely to end up with false conclusions. He should have been more careful.

Philosophers like Hume have always found the idea that we might indeed be perceiving and conceiving the world out there, and not merely our impressions and ideas of it, difficult to comprehend or explain. This is understandable, because this seeming ability of ours (viz. external consciousness) is something truly surprising and, well, miraculous – no better word for it comes to mind.

But then these same philosophers take for granted that our inner perceptions and conceptions are valid and not in need of explanation. They apparently do not realize that this ability (viz. internal consciousness) is also miraculous – indeed, just as miraculous. For the difference between the two, after all, is just one of distance. And who is to say how big the soul (the subject of consciousness) is or where it is in fact located? Why do they assume that it is more ‘inside’ than ‘outside’ the apparent body?

In both cases, there is something marvelous, inexplicable – namely consciousness, a line of relation between an object and a subject. How can one existent (a soul, a spiritual entity) experience another (a mental or material phenomenon)? In the case of self-intuition, the subject and object are exceptionally one and the same. But even this is a marvelous event, that something can experience itself.[10]

The mere fact of consciousness is the biggest mystery. In comparison to it, the issues of how far consciousness can go, and how in some instances it is aroused and made possible by sensation and yet the body does not block or distort our view – these are relatively minor issues.

Of course, a theory of the exact role of the senses remains highly desirable. Obviously, each sense organ (whether in humans or other animals) somehow gives the overall organism ‘access to’ a range of data of a specific sort, and no other: e.g. human eyes open the window to a range of light waves (the visible spectrum) but not to all frequencies (not to radio waves, ultraviolet rays or microwaves, for instances) and not to other modalities (such as sound or chemical signals). The different sense organs have evolved over millions of years (at different rates and in different directions in different organisms).

Without these sense organs, we would not (so it seems) be able to sense external reality. So, their role is not only that of memory production, but they are somehow essential to the actual contact between the organism as Subject and material objects it perceives. Even so, to repeat, it cannot consistently be affirmed that what the Subject perceives are internal products of sensation. Nor is the explanation that sense organs serve to filter out some of external reality sufficient. The sense organs must have a more significant role in the Subject-Object interface. But what?


2.    The Induction of Induction


Upon further reflection, my reaction to the anti-inductive trend set by Hume is more muted, as follows.

Deductive logic was largely the discovery and production of one man, Aristotle (who, of course, had a great teacher, Plato). It has grown considerably since then, thanks to the contribution of many, but its founder’s work is still very present at its foundation. Of course, people engaged in deduction before him, but he brought an enormous amount of self-consciousness and precision to such logical thought. Under his direct influence, many people made fewer errors of deduction.

On the other hand, what the history of the logic of induction makes clear is that this basic discipline was not born long ago and in one go. Retrospectively, we can of course say that induction has always been used by humans, and even in a sense by their animal forbears and cousins. We have always practiced induction, with more or less effectiveness, without need of logicians and philosophers to describe and explain it.

Aristotle and his successors were of course conscious of induction to some extent, but not sufficiently to develop a systematic theory of it. The theory of induction dawned in more modern times, with (I would say) Francis Bacon. The latter’s work was more important than many realize. After him, whether under his influence or independently, physical scientists like Galileo, Newton, and many more till this day, both used and understood induction with increasing clarity.

On the other hand, the direct philosophical successors of Bacon, like Locke, Hume, and many others till today, never quite succeeded in bringing the logic of induction he had started up to date[11]. In some respects, they even regressed, rather than progressed. It is really surprising just how widespread skepticism about induction remains. Hume seems to have permanently impressed his disbelief to a great many later thinkers.

To give you one modern example, two hundred years after Hume – A. J. Ayer reports that Bertrand Russell thought that the assumptions of scientific thought had to be taken on faith, and that (in Ayer’s words):

… there is no necessity other than logical necessity, so that there is no such thing as causal necessity. Causality is just a matter of what Hume originally said it was, namely constant conjunction, and is something purely contingent.[12]

Ayer agrees with him. Many other philosophers and logicians similarly assume induction to be without any solid logical basis, and express surprise that it works at all. It is not that they have some bias against inductive reasoning; they would dearly love to prove it, because they are empiricists at heart and supporters of modern science. What the example of Russell makes evident is that they are sincerely baffled.

All this teaches us an important lesson. It is that the induction of a theory of induction has taken time, a lot more time than anyone would have thought it would take. And this is quite normal and okay – the question is not simple, so we should not be too surprised that many have failed to answer it satisfactorily. After all, induction is a trial and error process. It allows for error, and for long spells of blindness and incomprehension.

The history of science is replete with similar situations[13]. Certain facts were (it seems to us, retrospectively) glaringly obvious, yet scientists went through great pains till they saw them. Many facts were for long periods devoid of explanation. Similarly, in the history of logic, although Bacon had well specified and stressed the importance of the negative instance in induction, Hume just ignored the advice in his formulations on induction and causation.[14]

Thus, after due consideration, we should look upon Hume and similar skeptics without bad feelings, with compassion. The modern discovery of induction and the attempts to formulate a theoretical description and justification of it – were all part of a learning process. If many found it difficult, and drew hasty defeatist conclusions, they ought not be blamed. They did their best, albeit without too much success. We are all fallible and none of us all-knowing.

Letting bygones be bygones, now the task is to educate people, to teach the principle of induction and all the methods that derive from it. Enough of negativity, skepticism and pessimism; let us not perpetuate these historical faults. Instead, let us inaugurate a new era of general mental health and good intentions.


3.    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 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.[15]

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[16]. 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[17], 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.

Leibniz’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 Leibniz[18]. 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 Leibniz, 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):


Table 33.1        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.

Leibniz’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 Leibniz 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 Leibniz 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 Leibniz’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.


4.    Addenda (2009)

The principle of uniformity

Concerning the principle of uniformity, discussed earlier on, it should be noted that the underlying assumption of this principle is the particular proposition “some things (whether elements of experience or products of abstraction) have some characteristics in common,” This is clearly not a generalization, because it is not a generality! It is merely an admission that the world we face seems to have some repetitiveness in it, without any prejudice as to the extent of such repetition

And as to how this particular proposition is known to be true – it is not so much by experience as by logic. For if we tried to claim its contradictory, i.e. that “nothing has any characteristic in common with anything else,” we would be guilty of self-contradiction, since the use of any concept whatsoever (like “thing,” “has,” “characteristic,” “in common,” etc.) relies on a supposition that two or more things have certain characteristics in common, thanks to which we may give them a common name. And it cannot be said that things have nothing in common other than the name we conventionally apply to them (Nominalism), since even appeal to a common name implies that the two or more instances of the name concerned are recognizably “the same” name, so that is an inconsistent objection.

Thus, the principle of uniformity is based on a logically necessary particular proposition.

Thomas Reid

In the discussion of sensory perception earlier on, I forgot to mention Thomas Reid (Scotland, 1710-96). Although modern histories of philosophy tend to ignore him or gloss over him, this contemporary and fellow countryman of David Hume’s was during his lifetime more respected than the latter, because of his common-sense approach to philosophy. Reid rejected Hume’s (and others’) skeptical claim that what man perceives are internal impressions, i.e. mental products of the physiological process of sensation, and ably defended the direct realist view that what man perceives are outer physical causes of the sensations. Hume was aware of Reid’s criticism of his work, but remained indifferent to his arguments although they were more perspicacious and reasonable than his own. Later, too, Immanuel Kant (a younger contemporary of Reid’s) paid little heed to Reid’s arguments.

It should be noted that direct realism is sometimes wrongly confused with naïve realism. These are in truth not identical philosophical concepts, though they may on occasion overlap. Naïve realism essentially refers to the worldview of the common man, who takes for granted the reality and materiality of the world apparently around him without asking questions as to the veracity and substantiality of such appearance. Direct realism is perhaps logically implied by naïve realism, but certainly does not reciprocate such implication. Direct realism is the view, as already stated, that we perceive the world itself and not alleged mental representations of the world.

Opponents of direct realism claim that advocacy of this philosophy can only be arbitrary say-so or circular argument. However, this accusation is untrue. The main justification of direct realism is the manifest logical inconsistency of the opposite view, advocated by Hume, and John Locke before him and Kant after him. Impressions, ideas, representations divorced in principle from external objects lead inevitably to self-contradiction – and are therefore far more flawed methodologically. One cannot claim ideas or impressions to represent (i.e. give indirect access to) anything beyond representation if one first claims to have no direct access to anything beyond them. As of the moment the advocate of direct realism has thus (and in many other ways) argued his case, he can no longer accurately be accused of naïve realism. His realism must be labeled (relatively) subtle, instead.

However, the most important and precise distinction between naïve realism and subtle realism lies not in the self-contradiction of the antithesis of direct realism, but with reference to phenomenology. If the direct realist is content to claim that sensory perception is perception of physical reality (as against representations of it), he is still functioning on a relatively naïve level. His understanding is fully subtle only when he comes to understand that the preceding is an inductive hypothesis (better than any other) that admits the phenomena perceived as ab initio mere appearances (i.e. not as necessarily realities or necessarily illusions, but as possibly realities and possibly illusions).

Thus, though Reid’s common-sense approach to direct realism was logically preferable to Locke’s, Hume’s and Kant’s absurd representational cognitive philosophies, it was perhaps not the final word on the subject, since phenomenology was still not very developed. That is not to say there was no phenomenology in Reid’s approach, but only that it was not a thoroughgoing phenomenology. Reid, in any case, did not claim to have answered all questions regarding direct realism, and indeed to date many crucial problems have remained unsolved (as explained my main text).


Drawn from Logical and Spiritual Reflections (2008), Book I, Chapters 4,10b,12,13:1-2.



[1]             I am stereotyping things a bit, because in truth Locke was somewhat aware of the problem, and so was Berkeley after him (and before Hume). Perhaps the philosopher most to blame should be Descartes. But I cannot here get into the fine details of history.

[2]             This has come much later in the history of philosophy. Even Immanuel Kant, Hume’s intellectual successor, never grasped phenomenology, but instead produced a complicated system of philosophy that increased the appearance-reality chasm. Note that when I use this term, I do not necessarily mean the Hegelian or Husserlian attempts at phenomenology, though these two later philosophers certainly played important roles.

[3]             The reader is referred to my work on phenomenology for more on this topic.

[4]             Hume obviously in fact believed in the existence of the external world, since he invested so much of his time writing and publishing books for others to read!

[5]             Whereas Locke used the word idea very generally (including all mental phenomena, even emotions), Hume distinguishes primary impressions from derivative ideas, i.e. simple empirical sensations from the more complex mental constructs made with them. However, I here use the term idea much like Locke, because Hume’s finer distinction does not affect the issue at hand.

[6]             The word “intention” is very well chosen here, note well. It is not the idea, or the name for it, that intends the object – it is us, we the subject, who do. The word does not refer primarily to an act of consciousness, in the sense that Husserl defined consciousness with reference to some mysterious “intentionality,” Consciousness is not essentially an action, but rather a receptive event. No, intending refers to an act of volition. The subject (I, you) programs such an intention into every notion or symbol he produces. The subject wills his attention (awareness, consciousness) in the direction of the object concerned when he again comes across that idea or word. When we communicate, we pass such guides to mental action to each other.

[7]             A verbal problem to always keep in mind is the equivocation of the word “sensations”: used in a general sense it refers to all sensory material, whereas more specifically it makes us think of touch sensations. Likewise, the word “images” tends to evoke visual images, but in the present context it is meant to refer to any resemblance, i.e. equally to auditory and other sensory phenomena. Such equivocations may seem anodyne, but they mislead many people.

[8]             More precisely, memories are physical items (produced by sensations of visual and auditory phenomena) stored in the brain, which, when (voluntarily or involuntarily) reactivated, project mental images or sounds that we inwardly perceive and recognize as previously directly perceived (in the physical world, when that is the case). In the case of smells, tastes or tactile phenomena, I suspect we cannot in this way ‘recall’ past or present perceptions, but only ‘recognize’ them as familiar, so the term memory has a slightly different meaning. Note well that we do not commonly confuse our perceptions of material things and events with our memories of such perceptions; it is only armchair philosophers like Locke and Hume who equate these two experiences, quite unthinkingly.

[9]             For example, just what is a “force” like gravity in physics? Or just what is “energy”? Isaac Newton admitted his ignorance, saying “hypotheses non fingo” (meaning, I have no explanation); and even after modern developments in physics, like the Relativity and Quantum theories, we still do not know just ‘what’ these abstractions refer to concretely or ‘why’ these processes occur. Despite this partial (and even crucial) ignorance, we do not consider physics less of a science. For what is science? It is not omniscience, but merely a guarantee that our current opinions are the best possible in the current context of experience – because the most rigorously induced.

[10]            I leave open whether we can experience other souls. Some people suggest it is possible, i.e. claim a sort of other-intuition. Some people claim even to have experienced God.

[11]            While scientists were showing enormous ingenuity in the design of experiments and more broadly in the formulation and selection of theories in their respective fields, the general understanding and justification of induction by philosophers and logic specialists have often lagged far behind. In modern times, the likes of Karl Popper have of course brought greater balance between the theory and the practice of induction.

[12]            See Magee, pp. 313 and 315.

[13]            Stephen Jay Gould documents many such stories and gives us illuminating methodological comments on them, in a set of essays I strongly recommend. See for instance his comments on pp. 96 and 97, on the “long struggles to think and see in new ways” and on “shining a light of logic into the most twisted corners of old conceptual prisons, into the most tangled masses of confusing observations.”

[14]            It is a bit shocking to discover, upon close scrutiny, just how often errors of reasoning and plain ignorance occur in Hume’s work – and indeed in the work of many other great and lesser princes of Western (and for that matter, Eastern) philosophy. I remember my similar surprise and disappointment when, after completing The Logic of Causation, I revised my analysis of J. S. Mill’s “methods of experimental inquiry,” and discovered how many mistakes a very educated and intelligent man like him could make.

[15]            See also for example, Gould, p. 283.

[16]            See for example, Gould, p. 288.

[17]            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.

[18]            Germany, 1646-1716.

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