Inductive Logic

A Thematic Compilation by Avi Sion

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35. Some LC Phase Three Insights


1.    History of My Causation Research

I have been dreaming of systematizing causal logic since my teens, I think, when I first studied works on logic and philosophy.

My first book, Future Logic (1990), mentions the manifest modal foundations of causality and indeed the tacit causal foundations of modality, stressing that different types (or modes) of causality exist reflecting the different types of modality. And of course, knowing approximately the basic definitions of causation in terms of conditional propositions, the work done on the latter in Future Logic was incidentally work on the logic of causation.

Moreover, having understood the formal continuity between categorical and de re conditional propositions, and indeed between the different modes of modality (including the logical), the work done with regard to factorial induction of categoricals was also significant in the long run to induction of conditionals – and thence to that of causative propositions (which are, after all, just conjunctions of selected conditional and categorical ones).

I made some general remarks relating to causal logic in my book Judaic Logic, first published in 1995, showing my continuing interest.

My research efforts into the logic of causation per se started in earnest in the late 1990s, with a macroanalytic approach to the problem. My purpose then was, simply put, to clearly define all the varieties of causation (its determinations, indicative of degrees of causation), then correlate them all (oppositions, eductions) and work out all syllogistic reasoning possible between them (which necessitated the development of matricial analysis). It was, I believe the first time anyone had ever tried so ambitious a project in this field of logic. This first phase of the research was published in October 1999 as The Logic of Causation. However, I soon realized that there were some problems in these initial results, and tried to improve on them in a second edition published in July 2000.

But it was by then clear that I needed to develop a much deeper and more systematic approach to obtain reliable results. It was, I think, not until the later half of 2002 that I found the time to proceed with microanalysis of causation, the second phase of my research. The massive amount of work involved was completed rather quickly, because I devoted all my time and concentration to it. By about March 2003, I was able to publish the results. This work involved very many painstaking manual ‘calculations’, and produced a very profound understanding of causation, which allowed me to formally settle some age-old difficult issues concerning it.

Thus, various “laws of causation” traditionally proposed were examined and evaluated. Criticisms of causation as such, such as those of Nagarjuna or David Hume, were rebutted. The notion of natural spontaneity used in modern quantum physics, as well as the Buddhist notion of interdependence were scrutinized and judged. And a critical analysis of J. S. Mill’s proposed methodology for identifying causation was made possible. In same period, I wrote two other works which had some bearing on the understanding of causality, namely Buddhist Illogic (2002) and Phenomenology (2003).

However, even as I was completing this new phase of the research, it was clear to me that some uncertainties remained, due to the manual method of calculation used (subject in principle to human error, though all results were double-checked) and because some problems could not be solved by considering only three items. It was clear to me that a third phase of research, involving a more mechanical approach (using spreadsheets, database software or ad hoc programming) to increase reliability, and a larger scope (i.e. at least four items) to increase reliability, were needed. There and then, I started doing some work in that direction; but ran out of time, having to deal with many mundane matters.

In 2004, I devoted my time to writing Volition and Allied Causal Concepts, a study relevant to causation by implication. I continued thinking about causation in 2005, writing down my insights in Ruminations, and even made some effort to advance phase III causation research. In 2006, my time was taken up writing Meditations, and in 2007-8 writing Logical and Spiritual Reflections. The latter work including some insights relating to causality (notably in book 1, chapters 3 & 6, and book 3, chapter 11). I also made some more effort in 2008 to advance phase III research, but was soon stopped by other concerns. The year 2009 was devoted to improving my website and to creating an online bookshop to sell my books.

I first posted some phase III results in my website,, in October 2009, partly to encourage myself to pursue the matter further. In January 2010, I decided to try and complete phase III – and the work done is described in the following pages.

My initial idea with regard to phase III research was to develop a computer program capable of ‘calculating’ the value of causative propositions and syllogisms directly from the matrix relating the items concerned[1]. Realizing that in the absence of professional help such programming was beyond my immediate capabilities, I thought instead of using database software, such as Access. I began indeed doing so, but soon realized I had difficulty visualizing the interrelationships involved, not having made use of such software for many years. I therefore decided that the best way for me to proceed was through the use of spreadsheets, namely Excel software; and this is what I did.

In the present, final chapter, I will try and provide readers with a practical guide to the logic of causation. That is, after all, the purpose of the whole exercise. This book was written over a period of many years (on and off) more as a research report than as a text book. Most readers, I assume, are not very interested in the details of how I got to such or such a result, but just want to learn how to reason correctly with causative propositions. The validations are more of concern to logicians. Lay people want practical guidance. Thus, do not expect here a systematic summary of all findings, but rather a highlighting of some of the main points.


2.    What is Causation?

What is causation? This term refers to a concept – an abstraction through which we can order empirical facts in a way that makes them more comprehensible to us and helps us makes predictions. Like every reasonable concept, causation does indeed signify an existing fact – namely the fact that sets of two or more facts are often evidently related in the ways we call causation. Causation refers to certain observable or induced or deduced regularities in conjunction or non-conjunction between two or more things. By ‘things’ (or preferably, henceforth, ‘items’) here, understand any domain of existence: material, physical, bodily, mental, abstract, spiritual; any category of existent: substance, entity, characteristic, quality, change, motion, event, action, passion, dynamic, static, etc. – anything whatever.

As with all concepts, the concept of causation varies somewhat from person to person, and over time in each person. At one end of the spectrum, there are people for whom the concept of causation is a vague, subconscious notion, which often produces erroneous judgments. At the other extreme, there are those who clearly understand causation and use it correctly in their thinking. The purpose of causative logic, i.e. of the present detailed theory of causation and its relevance to thought, is to improve people’s understanding and practice.

Causation can thus be defined, broadly – and more and more precisely, as our study of it proceeds. But can causation as such be ‘proved’ to exist? Yes, indeed. Causation relies first of all on the admission that there are kinds of things. For, generally, we establish causation (as distinct from volition, which is indeterministic causality) not for individual items, but for ‘kinds’, i.e. for sets of things that resemble each other in some way. When we say that X causes Y, we mean that instances of the kind X are related in a certain way to instances of the kind Y.

Now note this first argument well: if there were no kinds, there would be no causation. That is, if nothing could be said to be ‘the same’ as anything else, kinds would not exist and causation could not be established. But if we claim, “Nothing is the same as anything else in any respect,” we are engaged in an inextricable self-contradiction, for that very statement is full of assumption regarding the existence of kinds. Therefore, such a claim is logically untenable, and we must admit that kinds exist, i.e. that our concepts have some empirical basis.

Now, causation refers to the possibility or impossibility of various combinations of things (or their negations). For example, to say that X is never found in conjunction with not-Y and that not-X is never found in conjunction with Y, is a statement of ‘complete necessary’ type of causation. We can certainly argue, regarding a particular pair of items X and Y (e.g. irrational behavior and mental suffering), as to whether or not they indeed fit in this relational format; merely asserting it as fact does not of course make it fact.

But no one can logically deny that there exist some pairs of things in this world that do indeed fit this pattern of relation. It would mean that we deny that there are possibilities and impossibilities of conjunction. Note this second argument well: if we claim, “No conjunction of things is possible,” we are saying that the conjunctions implied by this very statement are impossible; and if we claim, “No conjunction of things is impossible” we are saying that contradictions are possible. All the more so, if we claim that nothing is possible or that nothing is impossible, we are involved in logically unacceptable self-contradictions. When a thesis is self-contradictory it must be abandoned, and replaced by its contradictory thesis.

Therefore, the definitional bases of causation as such – i.e. the fact that there exists the modalities of possibility and impossibility, and thence of necessity and unnecessity – and the fact that some conjunctions in the world are bound to be related by one or the other of these modalities (nothing else is even conceivable) – are indubitable. Thus, causation, which refers to different combinations and permutations of such modalities of conjunctions, is indubitable. There are no ifs and buts about it.

Why, then, you may ask, are the likes of David Hume or Nagarjuna, and all their modern followers and imitators, so convinced of the illusoriness of causation? The answer is that they are clearly not committed to reason or logic, but merely express their cognitive or psychological problems; or they are not very intelligent. Nagarjuna relied heavily on fallacious reasoning to support his alleged critique of causation. Hume’s search for an empirically observable phenomenon of ‘connection’ or ‘bond’ was a red herring; it implied that causation is something concrete, i.e. tangible or otherwise materially detectable. No wonder he could not find it! No: to repeat, causation is an abstraction, through which we order our empirical observations and predict similar events of the same sort[2].

Hume admits as much when he defines causation as ‘constant conjunction’ between things. However, that definition is flawed inasmuch as it draws attention to only the positive side of causation; it ignores the crucial negative side (the constant conjunction between the negations of the things). Hume also ignores the different determinations or degrees of causation. And in attempting to ‘explain away’ causation by referring it to habitual associations of ideas, he contradicts himself – since such explanation is itself an appeal to causality; i.e. it purports to tell us ‘why’ we assume causation. Causation is formally the same whether it is assumed to occur in the material surrounds or in the mind, i.e. whether it correlates things or ideas. The fact that causation is usually induced by means of generalizations does not allow us to equate it to association of ideas. And anyway, association of ideas can occur even where causation is doubted; so, these concepts cannot be the same in our minds.

As shown above, the concept of causation rests on two pillars, two fundamentals of human knowledge. The one is the fact of similarity and the other is the fact that conjunctions may be possible or impossible.

You can deny that two or more particular objects are similar, but you cannot deny that there are somewhere similar objects and that we are able to identify them in principle. You can deny that two or more particular objects are sometimes or never conjoined, but you cannot deny that there are somewhere objects that are sometimes or never conjoined and that we are able to identify them in principle. When I say: “you cannot deny,” I mean you cannot do so without self-contradiction – i.e. you cannot do so with the sanction of logic, i.e. you do so against logic.

Ontologically, causation occurs because not everything is possible in the world. If nothing was impossible, everything could proceed every which way. The limitations that exist in Nature constitute obstacles in its free flow, and ‘force’ it to flow along specific routes. Nature’s course is determined by where it cannot go, rather than by where it must go. The stream of events follows the groove formed by the limits set.

There are as many modes of causation as there are modes of modality. Rational argument refers to the logical (de dicta) mode of causation. Extensional causation is based on extensional modality. Natural, temporal and spatial causation likewise are based on these (de re) modes of modality. It is logically inconsistent to admit one mode of causation (e.g. the logical) and refuse to admit the others (e.g. the natural mode). There is formally no reason to discriminate between them.

In conclusion, causation is a mental overlay through which we order observed reality. But this overlay does not force reality into any arbitrary patterns; it is not an invention of ours. It is merely an acknowledgement that certain patterns do observably occur, and our task in causative reasoning is to identify when they do occur as well as possible. The overlay is not a distortive filter or a hindrance to knowledge. It is based on experience of the world and helps us to more correctly and profoundly discern and understand the world, and thus also to better predict and deal with it.

The concept of causation has no doubt a long history, dating from the beginnings of humanity, if not earlier still in its wordless animal ancestors. Certainly, the moment our ancestors thought or said “because…” or “therefore…” they displayed their belief in or knowledge of causation. The study of the concept is a much later development, of course, which coincides no doubt with the dawning of philosophy, especially in ancient Greece. But it is, I think, in modern times that people began to look for applications of causation in a very conscious manner. I refer of course to the advent of modern experimental science in Europe.

Two important philosophical figures in this context were Francis Bacon and John Stuart Mill. Not because they discovered causation theoretically or the ways to find it in practice, but because they sought to verbalize causative logic. However, neither of these thinkers asked all the right questions or gave all the right answers. Surprisingly, no one made a big effort to follow up on their work, discouraged perhaps by the skepticism instilled by David Hume. It is not until the present study of causation that we have a full analysis and practical guide to causative reasoning, a truly formal logic of causation. This is really a historic breakthrough.


3.    How is Causation Known?

We have in the previous section explained that causation is an ‘abstract fact’ and established that it is knowable by humans. Our definitions of the various types and degrees of causation provide us with formal criteria with which we are able to judge whether causation is or is not applicable in given cases. But to affirm that causation as such is definable and knowable does not tell us just how to know it in particular cases.

Can we perceive causation? Not exactly, since it is not itself a concrete phenomenon but an abstract relation between concrete phenomena (and more broadly, other abstractions). It has no visual appearance, no color, no shape, it makes no sound, and it cannot be felt or tasted or smelled. It is an object of conception.

Can it then be known by direct conceptual ‘insight’? This might seem to be the case, at first sight, before we are able to introspectively discern our actual mental processes clearly. But eventually it becomes evident that causation must be based on concrete experience and logical process. We cannot just accept our insights without testing them and checking all the thinking behind them. The foundation of causative knowledge – i.e. of knowledge about causation between actual things – is evidently induction.

That is to say, quite common and ordinary processes like generalization and particularization or, more broadly, adduction (the formulation and empirical testing of hypotheses). These processes are used by everyone, all the time, though with different degrees of awareness and carefulness. The bushman who identifies the footprints he sees as traces of passing buffalo is using causative logic. And the scientist who identifies the bandwidth of rays emanating from a certain star as signifying the presence of certain elements in it is using the same causative logic. The bushman is not different from or superior or inferior to the scientist. Both can make mistakes, if they are lazy or negligent; and both can be correct, if they are thorough and careful.

How is a given causative relation induced? Take for instance the form “X is a complete cause of Y,” This we define as: “If X, then Y; if not X, not-then Y; and X and Y is possible,” How can these propositions be established empirically? Well, as regards “X and Y is possible,” all we need is find one case of conjunction of X and Y and the job is done. Similarly for “if not X, not-then Y;” since this means “not-X and not-Y is possible,” all we need is find one case of conjunction of not-X and not-Y and the job is done.

This leaves us with “If X, then Y” to explain. This proposition means “X and not-Y is impossible,” and we cannot by mere observation know for sure that the conjunction of X and not-Y never occurs (unless we are dealing with enumerable items, which is rarely the case). We must obviously usually resort to generalization: having searched for and never found such conjunction, we may reasonably – until and unless later discoveries suggest the contrary – assume that such conjunction is in fact impossible. If later experience belies our generalization, we must of course particularize and then make sure the causative proposition is revised accordingly.

Another way we might get such knowledge is more indirectly, by adduction. The assumption that “X and not-Y is impossible” might be made as a consequence of a larger hypothesis from which this impossibility may be inferred. Or we may directly postulate the overall proposition that ‘X is a complete cause of Y’ and see how that goes. Such assumptions remain valid so long as they are confirmed and not belied by empirical evidence, and so long as they constitute the most probable of existing hypotheses. If contrary evidence is found, they are of course naturally dropped, for they cannot logically continue to be claimed true as they stand.

Another way is with reference to deductive logic. We may simply have the logical insight that the items X and not-Y are incompatible. Or, more commonly, we may infer the impossibility of conjunction – or indeed, the whole causative proposition – from previously established propositions; by eduction or syllogism or hypothetical argument or whatever. It is with this most ‘deductive’ source of knowledge in mind that the complex, elaborate field of causative logic, and in particular of causative syllogism, is developed. This field is also essential to ensure the internal consistency of our body of knowledge as a whole, note well.

Additional criteria. It should be added that though causation is defined mainly by referring to various possibilities and impossibilities of conjunctions – there are often additional criteria. Space and time are two notable ones. Two events far apart in space and time may indeed be causatively related – for example, an explosion in the Sun and minutes later a bright light on Earth. But very often, causation concerns close events – for instance, my eating some food and having a certain sensation in my digestive system. In the both these cases, the effect is temporally after the cause. In the latter case, unlike the former, the cause and effect are both ‘in my body’.

Between the Sun’s emission of light and its arrival on Earth, there is continuity: the energy is conserved and travels through all the space from there to here, never faster than the speed of light, according to the theory of relativity. But what of recent discoveries (by Nicolas Gisin, 1997), which seem to suggest that elementary particles can affect each other instantly and at a large distance without apparent intermediary physical motion? Clearly, we cannot generalize in advance concerning such issues, but must keep an open mind – and an open logic theory. Still, we can say that in most cases the rule seems to be continuity. When we say: ‘bad food causes indigestion’, we usually mean that it does so ‘within one and the same body’ (i.e. not that my eating bad food causes you indigestion).

As regards natural causation, we can formulate the additional criterion that the cause must in fact precede or be simultaneous with the effect. But this is not a universal law of causation, in that it is not essential in logical and extensional causation. In the latter modes, the causative sequence may be reversed, if it happens that the observer infers the cause from the effect. Although, we might in such cases point out another temporal factor: when we infer (even in cases of ‘foregone conclusion’), we think of the premises before we think of the conclusions. That is to say, there are two temporal sequences to consider, either or both of which may be involved in a causal proposition: the factual sequence of events, and the sequence of our knowledge of these events.

Similarly, quantitative proportionality is often indicative of causation; but sometimes not. Although it is true that if the quantity of one phenomenon varies with the quantity of another phenomenon, we can induce a causative relation between them; it does not follow that where no such concomitant variation (to use J. S. Mill’s term) is perceived, there is not causation. In any case, the curve quantitatively relating cause and effect may be very crooked; ‘proportionality’ here does not refer only to simple equations, but even to very complicated equations involving many variables. In the limit, we may even admit as causative a relation for which no mathematical expression is apparent. An example of the latter situation is perhaps the quantum mechanics finding that the position and velocity of a particle cannot both be determined with great precision: though the particle as such persists, the separate quantities p and v are unpredictable (not merely epistemologically, but ontologically, according to some scientists) – which suggests some degree of natural spontaneity, in the midst of some causative continuity.

Thus, we must stick to the most general formulations of causation in our basic definitions, even as we admit there may be additional criteria to take into consideration in specific contexts. It follows from this necessity that we can expect the logic of causation certain inferences (like conversion, or those in second and third syllogism) where what is initially labeled a cause becomes an effect and vice versa. Keep this in mind[3].

Laws of causation. We should also here mention the cognitive role of alleged laws of causation. We have already briefly discussed laws relating to space and time.

In times past, it seems that some degree of sameness between cause and effect was regarded as an important law of causation. Upon reflection, the proponents of this criterion for causation probably had in mind that offspring have common features with their parents. But apparently, some people took this idea further and supposed that the substance (and eventually some other characteristics) of cause and effect must be the same. But though this criterion may be applicable to biology or other specific domains (e.g. the law of conservation of matter and energy in physics could be so construed), it is not generally regarded as universal. Formally, I see no basis for it.[4]

The law of causation most often appealed to (at least in Western thought) is that ‘everything has a cause’. But though it is evidently true of most things that they have causes, and the belief in this law often motivates us to look for or postulate causes (i.e. even if none is apparent, we may assume one to exist), we have not in our study found any formal grounds to affirm such a law as universal. Admitting the fact of causation does not logically force us to admit its universality. This does not prove that it is not empirically universal; and it does not prevent us from formulating such universality as an adductive hypothesis. In any case, today, as evidenced by quantum physics and big-bang cosmogony, it seems generally assumed by scientists that this law is indeed not universal (which does not mean it is not very widely applicable).

I wonder anyway if it was ever really regarded as universal. I would say that in the 19th Century, this law was assumed universal for physical phenomena – but not necessarily for mental phenomena; human volition was generally taken to be an exception to the rule, i.e. freedom of the will was acknowledged by most people. Paradoxically, in the iconoclastic 20th Century, while the said law of causation was denied universality for material things, every effort was made to affirm it as regards human beings and thus forcefully deny freedom of the will[5]. Intellectual fashions change, evidently. But as far as I am concerned, while I admit the possibility that this law may not-be universally true of matter, I have no doubt that it is inapplicable to the human will[6].

Another alleged law of causation that should be mentioned here (because of the current interest in it, in some circles) is the Buddhist notion that ‘every thing is caused by everything’. As I have shown in the present volume, this idea of universal ‘interdependence’ is logically untenable. It is formally nonsensical. Indeed, if you just think for a moment, you will realize (without need for complex formal analysis) that to affirm interdependence is to deny causation, or at least its knowability. Every concept relies on our ability to distinguish the presence and absence of the thing conceived; if it is everywhere the same, it cannot be discerned. I think the Buddhist philosopher Nagarjuna can be said to have realized that; and this would explain why he ultimately opted for a no-causation thesis. However, that does not mean that causation can logically be denied: as already explained earlier, it cannot.

Well, then. Are there any ‘laws of causation’? Of course, there are, a great many! Every finding concerning the formal logic of causation in this volume is a law of causation, a proven law. For instance, the fact that not all positive causative syllogisms yield a positive conclusion of some sort is an important law of causation, teaching us that a cause of a cause of something is not necessarily itself a cause of that thing.


Drawn from The Logic of Causation (III:2008-10), Chapters 17:1 and 24:1-2.


[1]             This is why I have called this phase that of Software Assisted Analysis, although of course its ultimate motive is to investigate the 4-item framework.

[2]             To give an example: a subcategory of causation in physics is the concept of ‘force’. This is in no way thought of as something substantial – yet we consider it to be a reliable scientific reference, because it is an abstract inductive postulate through which we are able to order and predict various physical phenomena. Even if a particle theory of force is developed, it depends on the causative understanding that such particles obey certain abstract laws of behavior.

[3]             It is interesting to note here that J. S. Mill’s definitions of causation use the expression: “is the effect, or the cause” – meaning he had in mind the general forms.

[4]             If we want to go more deeply in the history of ‘laws of causation’, we would have to mention, among others, the Hindu/Buddhist law of karma, according to which one’s good and bad deeds sooner or later have desirable or undesirable consequences, respectively, on oneself. It is the popular idea that ‘what goes around must come around’. Though I would agree this is sometimes, frequently or even usually empirically true, we must admit that it does not always seem confirmed by observation – so it is at best a hopeful generalization (to a life after this one) intended to have positive moral influence. In any case, I see no formal basis for it. The same can be said concerning reward or punishment by God – though it might well be true, it is not something that can readily be proved by observation or by formal means; an act of faith is required to believe in it (I do, on that basis). In any case, the latter can hardly be called a ‘law of causation’, since the free will of God is thought to be involved in bringing about the effect.

[5]             Actually, both these changes were (I suggest) consciously or subconsciously motivated by the same evil desire to incapacitate mankind. Their proponents effectively told people: “you cannot control matter (since it is ultimately not subject to law) and you cannot control yourself (since you have no freewill) – so give up trying,” People who believed this nonsense (including its advocates) were influenced by it to become weaker human beings. Virtue was derided and vice was promoted. We see the shameful results of this policy all around us today.

[6]             I argue this issue elsewhere, in my Volition and Allied Causal Concepts. It should be mentioned that an analogue to the law of causation is often postulated, consciously or not, for the mind. We tend to think that every act of volition has a cause, in the sense of being influenced or motivated, by something or other. Though largely true, this assumption taken literally would exclude purely whimsical volitions; thus, I tend to doubt it, for reasons explained in my said book. In any case, do not confuse this ‘law of influence’ with the ‘law of causation’ here discussed. These are very distinct forms of causality, which cannot be lumped together.

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