Inductive Logic

A Thematic Compilation by Avi Sion

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25. Some LC Phase One Insights


1.    The Significance of Certain Findings

Let us review how we have proceeded so far. We started with the paradigm of causation, namely, complete necessary causation. We then abstracted its constituent “determinations,” the complete and the necessary aspects of it, and by negation formulated another two generic determinations, namely partial and contingent causation. We then recombined these abstractions, to obtain all initially conceivable formulas. Some of these formulas (mp, nq) could be eliminated as logically impossible by inspecting their definitions and finding contradictory elements in them. Others (the lone determinations, obtained by conjunction of only one generic determination and the negations of all three others) were eliminated on the basis of later findings not yet presented here. This left us with only five logically tenable specific causative relations between any two items, namely the four joint determinations (the consistent conjunctions generic determinations) and non-causation (the negation of all four generic determinations).

When I personally first engaged in the present research, I was not sure whether or not the (absolute) lone determinations were consistent or not. Because each lone determination involves three negative causative propositions in conjunction, and each of these is defined by disjunction of the negations of the defining clauses of the corresponding positive form, it seemed very difficult to reliably develop matrixes for them. I therefore, as a logician[1], had to assume as a working hypothesis that they were logically possible. It is only in a later phase, when I developed “matricial microanalysis” that I discovered that they can be formally eliminated. Take my word on this for now. This discovery was very instructive and important, because it signified that causation is more “deterministic” than would otherwise have been the case.

If lone determinations had been logically possible, causation would have been moderately deterministic. For two items might be causatively related on the positive side, but not on the negative side, or vice-versa. Something could be only a complete cause (or only a partial cause) of another without having to also be a necessary or contingent one; or it could be only a necessary cause (or only a contingent cause) of another without having to also be a complete or partial one. But as it turned out there is logically no such degree of freedom in the causative realm.

If two things are causatively related at all, they have to be ultimately related in one (and indeed only one) of the four ways described as the joint determinations[2], i.e. in the way of mn, mq, np, or pq. The concepts m, n, p, q are common aspects of these four relations and no others. There is no “softer” causative relation. Causation is “full” or it is not at all; no “holes” are allowed in it. We can formulate the following “laws of causation” in consequence:


  • If something is a complete or partial cause of something, it must also be either a necessary or (with some complement or other) a contingent cause of it.
  • If something is a necessary or contingent cause of something, it must also be either a complete or (with some complement or other) a partial cause of it.
  • In short, since a lone determination is impossible, if something is at all a causative of anything, it must be related in the way of a joint determination with it.

These laws have the following corollaries:

  • If something is neither a necessary nor contingent cause of something, it must also be neither a complete nor (with whatever complement) a partial cause of it.
  • If something is neither a complete nor partial cause of something, it must also be either neither a necessary nor (with whatever complement) a contingent cause of it.
  • In short, since a lone determination is impossible, if two things are known not to be related in the way of either pair of contrary generic determinations (i.e. m and p, or n and q), they can be inferred to be not causatively related at all.


  • The complement of a partial cause of something, being also itself a partial cause of that thing, must either be a necessary or (with some complement or other) a contingent cause of that thing.
  • The complement of a contingent cause of something, being also itself a contingent cause of that thing, must either be a complete or (with some complement or other) a partial cause of that thing.


With regard to the epistemological question, as to how these causative relations are to be established, we may say that they are ultimately based on induction (including deduction from induced propositions): we have no other credible way to knowledge. Causative propositions may of course be built up gradually, clause by clause (see definitions in the previous chapter).

As I showed in my work Future Logic, the positive hypothetical (i.e. if/then) forms, from which causatives are constructed, result from generalizations from experience of conjunctions between the items concerned (which generalizations are of course revised by particularization, when and if they lead to inconsistency with new information). The negative hypothetical (i.e. if/not-then) forms are assumed true if no positive forms have been thus established, or are derived by the demands of consistency from positive forms thus established. In their case, an epistemological quandary may be translated into an ontological fait accompli (at least until if ever reason is found to prefer a positive conclusion).

We may first, by such induction (or deduction thereafter), propose one of the four generic determinations in isolation. The proposed generic determination is effectively treated as a joint determination “in-waiting,” a convenient abstraction that does not really occur separately, but only within conjunctions. We are of course encouraged by methodology to subsequently vigorously research which of the four joint determinations can be affirmed between the items concerned. In cases where all such research efforts prove fruitless, we are simply left with a problematic statement, such as (to give an instance) “P is a complete cause, and either a necessary or a contingent cause, of Q,”

But, since lone determination does not exist, we can never opt for a negative conclusion, like “P is a complete cause, but neither a necessary nor a contingent cause, of Q,” We may not in this context effectively generalize from “I did not find” to “there is not” (a further causative relation). We may not interpret a structural doubt as a negative structure, an uncertainty as an indeterminacy.


In the history of Western philosophy, until recent times, the dominant hypothesis concerning causation has been that it is applicable universally. Some philosophers mitigated this principle, reserving it for ‘purely physical’ objects, excepting beings with volition (humans, presumably G-d, and even perhaps higher animals). A few, notably David Hume, denied any such “law of causation” as it has been called.

But in the 20th Century, the idea that there might, even in Nature (i.e. among entities without volition), be ‘spontaneous’ events gained credence, due to unexpected developments in Physics. That idea tended to be supported by the Uncertainty Principle of Werner Heisenberg for quantum phenomena, interpreted by Niels Bohr as an ontological (and not merely epistemological) principle of indeterminacy, and the Big-Bang theory of the beginning of the universe, which Stephen Hawking considered as possibly implying an ex nihilo and non-creationist beginning.

We shall not here try to debate the matter. All I want to do at this stage is stress the following nuances, which are now brought to the fore. The primary thesis of determinism is that there is causation in the world; i.e. that causal relations of the kind identified in the previous chapter (the four generic determinations) do occur in it. Our above-mentioned discovery that such causation has to fit in one of the four specific determinations may be viewed as a corollary of this thesis, or a logically consistent definition of it.

This is distinct from various universal causation theses, such as that nothing can occur except through causation (implying that causation is the only existing form of causality), or that at least nothing in Nature can do so (though for conscious beings other forms of causality may apply, notably volition), among others.

We shall analyze such so-called laws of causation in a later chapter; suffices for now to realize that they are extensions, attempted generalizations, of the apparent fact of causation, and not identical with it. Many philosophers seem to be unaware of this nuance, effectively regarding the issue as either ‘causation everywhere’ or ‘no causation anywhere’.

The idea that causation is present somewhere in this world is logically quite compatible with the idea that there may be pockets or borders where it is absent, a thesis we may call ‘particular (i.e. non-universal) causation’. We may even, more extremely, consider that causation is poorly scattered, in a world moved principally by spontaneity and/or volition.

The existence of causation thus does not in itself exclude the spontaneity envisaged by physicists (in the subatomic or astronomical domains); and it does not conflict with the psychological theory of volition or the creationist theory of matter[3].

Apparently, then, though determinism may be the major relation between things in this world, it leaves some room, however minor (in the midst or at the edges of the universe), for indeterminism.

We will give further consideration to these issues later, for we cannot deal with them adequately until we have clarified the different modes of causation.


2.    Highlights of Findings

I will stop the first phase of my research on the logic of causation at this point. Not just because I do not think it is worth going further into minutiae. I in fact do not consider that all the important formal issues have been covered. However, I do regard the logical techniques applied so far to have come close to the limits of their utility. That is why I have been developing more precise techniques, which I will publish eventually as Phase Two. Let us meanwhile review some of our main findings thus far in Phase One, and what information we are still missing.

We have succeeded in defining the various determinations of causation, by means of propositional forms already known to logic. These forms involve conjunctions (‘and’), conditionings (‘if-then’), modalities (‘possibly’, ‘actually’), and of course negations of all those (‘not’).

The mechanics of these various source forms are thoroughly treated in my work Future Logic, and need not be reviewed here. Since we already know the deductive properties of these underlying forms (how they logically interact) and how they can ultimately be induced from experience (abstraction, adduction, generalization and particularization, factorial analysis, factor selection and formula revision), these formal problems are in principle already solved for causative propositions. It is only a question of finding ways and means to extract the implicit information systematically and reliably.

I have tried to perform just this job in the preceding pages. The difficulties encountered are never such as to put the whole enterprise in doubt, note well. They are only due to the complexity of forms involved, since each positive causative is a conjunctive compound of several simpler forms, and all the more so in the case of negative propositions, which are disjunctive compounds of such simpler forms. The main problem is thus one of volume of information to be treated; there is so much data to sort out, order and organize, that we can easily get lost, forget things, make minor errors with numerous hidden repercussions.

I am only human, and may well have made some mistakes in this process. A major annoyance for me is that I am often forced to interrupt my research work due to the need to earn my living by other means. In such circumstances, my attention is diverted for long periods; my mind loses its thorough concentration on the subject matter, and I have to later re-learn it all. Hopefully, I have nevertheless succeeded in spotting and removing all eventual inconsistencies. Certainly, I have tried: always making consistency checks, painstakingly reviewing large bodies of data and long chains of reasoning, doing what I call “quality control,”

The best way to do this is to arrive at the same results using different means. That is one reason why, although the above Phase One work apparently stands up well on its own, I will not be entirely satisfied until Phase Two is complete and I arrive there at consistent results. But to return for now to our findings thus far…


It must be understood that this research has not been idle reshuffling of information and symbols. It had both practical and theoretical purposes in mind.

The practical questions relate to everyday reasoning about causes and effects. One of the principal questions we posed, you will recall, was whether the cause of the cause of something is itself a cause of that thing or not, and if it is, to whether it is so to the same degree or a lesser degree. This issue of causal (or effectual) chains is what the investigation of causal syllogism is all about. What our dispassionate research has shown is that it is absurd to expect ordinary reasoning, unaided by such patient formal reflections, to arrive at accurate results. The answer to the question about chains is resounding and crucial: the cause of a cause is not necessarily itself a cause, and if it is a cause it need not be one to the same degree. Once the scientific impact of this is understood, the importance of such research becomes evident.

But this syllogistic issue has not been the only one dealt with. We have in the process engaged in many other investigations of practical value. The definitions of the determinations causation by means of matrixes can help both laypeople and scientists to classify particular causative relations, simply by observing conjunctions of presences and absences of various items. Generalizations may occur thereafter, but they should always be checked by further empirical observation (at least, a readiness to notice; eventually, active experiment) and adjusted as new data appears (or is uncovered).

Another interesting finding has been the clarification of the relationships between positive and negative, absolute and relative causative propositions: for instance, that we may affirm partial or contingent causation, while denying it of a particular complement. One very important principle – that we have assumed in this volume, but not proved, because the proof is only possible in the later phase of research – is that (absolute) “lone determinations” are logically impossible. This means that we may in practice consider that if there is causation at all, it must be in one or the other of the four “joint” determinations.

Another finding worth highlighting is that non-causation is denial of the four genera (or four species) of causation, and before these can be definitely denied we have to go through a long process of empirical verification, observing presences and absences of items or their negations in all logically possible conjunctions. It is thus in practice as difficult to prove non-causation as to prove causation! Indeed, to be concluded the former requires a lot more careful analysis of data than the latter. Of course, in practice (as with all induction) we assume causation absent, except where it is proved present. But if we want to check the matter out closely, a more sustained effort is required.

With regard to the theoretical significance of our findings, now. By theoretical, here, I mean: relevant to philosophical discussions and debates about causality. Obviously, so far we have only treated causation, and said nothing about volition and allied cause-effect relations, so we cannot talk about causality in its broadest sense.

What our perspective makes clear is that the existence of “causation” is indubitable, once we apprehend it as a set of experiential yes or no answers to simple questions, leaving aside references to some underlying “force” or “connection” (which might be discussed as a later explanatory hypothesis). If we look upon causation in a positivistic manner, and avoid metaphysical discussions that tend to mystify, it is a simple matter. Causation is an abstraction, in response to phenomenologically evident data. It is a summary of data.

It is not purely empirical, in the sense of a concept only summarizing presences of phenomena. It involves a rational element, in that it also summarizes absences of phenomena. Affirmation may only be acknowledgment of the empirically apparent. But negation, as I have stressed in my work Phenomenology[4], is a partly rational act (a question is asked: is the thing I remember or imagine now present to my senses?), as well as a partly empirical act (the answer is no: I see or hear or otherwise sense nothing equivalent to that image!). Absence does not exist independently like presence, but signifies an empirically disappointed mental expectation.

Reading debates between philosophers (for example, David Hume’s discussions), one might get the impression that non-causation is an obvious concept, while causation needs to be defined and justified. But, as we have seen here, non-causation can only be understood and proven with reference to causation. Before we can project a world without causation, we have to first understand what we mean by causation, its different determinations, their interactions, and so forth. But the moment we do that, the existence of causation is already obvious. However, this does not mean that non-causation does not exist. Quite the contrary. Since, as we have seen, some formal processes like syllogism with premises of causation are inconclusive, we may say that the existence of causation implies that of non-causation! This finding has two aspects:

  1. The more immediate aspect is inferred from the fact that the cause of a cause of something is not necessarily itself a cause of it: taking any two things at random, they may or not be causatively related. This implication is valuable to contradict the Buddhist notion that “everything is caused by everything,” But the possibility of independence from some things does not exclude dependence on other things. Each of the two things taken at random may well have other causes and effects than each other.
  2. A more radical aspect is the issue of spontaneity, or no causation by anything at all. We can only touch upon this issue here, since we have only dealt with causation so far. But what our formal study of causation has made clear is that we cannot say offhand whether or not spontaneity in this sense is possible. There is no “law of causation” that spontaneity is impossible, i.e. that “everything has a cause,” as far as I can see. Nothing we have come across so far implies such a universal law; it can only be affirmed by generalization. Spontaneity (chance, the haphazard) remains conceivable.

I think the point is made: that formal research such as the present one has both practical and theoretical value. Let us now explain why the research undertaken so far is insufficient.


3.    The Modes of Causation

The observant reader will have noticed that throughout the present study we have concentrated on logical causation, i.e. on causative propositions based on logical conditioning. But of course, this is but one aspect of human aetiological reasoning. To be thorough, we need to consider not only such “de dicta” forms, but also the “de re” modes of causation, i.e. natural, temporal, extensional and spatial causation. In many ways, the latter are more interesting than the former. We have focused our attention on logical causation because it is the most widely known theoretically, although not necessarily the most widely used in practice.

Each of these modes of causation is derived on one of the modes of conditioning. A thorough study of the underlying forms of conditioning may be found in my work Future Logic (Part IV, Chapters 33-42)[5]. What is evident from that study is that natural, temporal, extensional and spatial conditioning, are in most respects similar to logical conditioning, but in significant respects different. The difference is essentially due to the fact that logical conditional propositions (like “if P then Q”) distinctively cannot be made to universally imply the “bases” (i.e. “P is possible, Q is possible”) – because if they were made to, we would not be able to express paradoxes[6]. From this structural difference, various differences in behavior (during inference) emerge.

However, this distinction dissolves in the context of causation, because here logical causation like all other types implies the bases. We have specified this fact as the last clause of each of the definitions of the determinations. Complete or partial causation implied the cause, or the conjunction of causes, and therefore the effect, to be possible; necessary and contingent causation implied them to be unnecessary. It follows that all the logical properties of the different modes of causation will be comparable. The subdivision of each mode of causation into different determinations will be the same, as will the underlying interplay of presences and absences, possibilities and impossibilities, in every conceivable combination and permutation. All the matrixes of their forms will be identical, and all arguments will have the same conclusions.

The only difference between these different logics is simply that the “possibility” and “impossibility” referred to in the definitions and matrices have a different sense in each case. In logical causation, they refer to logical modalities; in natural causation, to natural modality; in extensional causation, to extensional modality; and so forth. The only task left to logicians, therefore, is to more closely examine the interrelationships between these different modes of causation. That is, for instance, how any two natural and extensional causative propositions are opposed to each other, and how they behave in combination (i.e. within arguments). This complex work will not be attempted here.

Nevertheless, I have already in Future Logic clarified the following essential relationships. Logical necessity implies but is not implied by the de re necessities. Logical possibility is implied by but does not imply the de re possibilities. Similarly on the negative side, for impossibility and unnecessity. Thus, the logical mode lies on the outer edges of rectangles of oppositions including the de re modes.

For now, let us only clarify in what context each mode is used. Logical (or de dicta) causation is concerned with causes in the literal sense of “reasons;” that is to say, it helps us to order our discourse and eventual knowledge with reference to logical implications, presuppositions, disconnections, contradictions, or consistencies, between hypotheses and/or apparent evidences. In contrast, the de re modes of causation are more directly object-oriented.

  • The paradigm of natural causation is:

When the individual X actually is, has or does C (the cause),

then it (or some other individual Y) must (i.e. in all circumstances) be, have or do E (the effect);

and when C is not actual, neither is E.

In this context, C and E are qualities, properties or activities of any sort, relative to some individual entity X (or pair of individuals X, Y, respectively). Presence, here, is called “actuality” to refer us to the underlying natural modality. Necessity, here, means in all circumstances relative to this X in the antecedent. The implied basis of such propositions is that “this X can both C and E” (or “X+C and Y+E is potential for the individual(s) concerned,” as appropriate) – no need of additional clauses in that respect. The antecedent and consequent may be static or dynamic, and may or may not be temporally separated.

  • The paradigm of temporal causation is very similar, save that “must” becomes “always” (all units of time) in the body of time concerned. The form is “When… at some time, then… at all times,”
  • The paradigm of extensional causation is a bit different:

In such cases as class X in some instance is, has or does C (the cause),

then it (or another instance of class X or an instance of some other class Y) must (i.e. in all instances) be, have or do E (the effect);

and in such cases as C does not have an instance, neither does E.

In this context, C and E are qualities, properties or activities of any sort, relative to some class of entities X (or pair of classes X, Y, respectively). Presence, here, is called “instancing” to refer us to the underlying extensional modality. Necessity, here, means in all instances of X in the antecedent. The implied basis of such propositions is that “some X are both C and E” (or “X+C and Y+E is extensionally possible for the class(es) concerned,” as appropriate) – no need of additional clauses in that respect. The antecedent and consequent may be static or dynamic, and may or may not be temporally separated. They distinctively need not be actualities, but may be potentialities or necessities, note well, since extensional conditioning refers only to quantity.

The paradigm of spatial causation is very similar, except that “must” becomes “everywhere” (all units of space) in the body of space concerned. The form is “Where… at some place, there… at all places,”

What I want to make sure here is that the reader understands that there are different modes of causation, and that the differences between them are significant to ordinary and scientific thought or discourse.

For example, the theory of Evolution is based partly on observation or experiment on individual biological specimens (spatial, temporal and natural causation) and partly on putting together the jigsaw puzzle of scattered findings relating to a class of individuals in different times and places (extensional causation), as well as partly on theoretical insights about consistency and implications between postulates and experiences (logical causation). All these involve induction and deduction, hypothetical reasoning and generalizations, but their focal center changes.

When, for instance, we take note of the structural or even genetic similarities of all vertebrates, and presume them to have a common ancestor, we are engaged in extensional causative reasoning. We would be engaged in natural causative reasoning, only if we could trace the ascendancy from individual child to individual parent all the way back to the first vertebrate specimen. In the extensional mode, the different individuals (e.g. paleontological findings) are regarded as expressions of a single class (genus, species, variation, whatever). In the natural mode, our focus is on the life of individuals as such (irrespective of their class appurtenance).

People, and even scientists, often confuse these different ways of thinking, and remain unaware that they may lead to different conclusions, or at least nuance our conclusions considerably. For this reason, the study of the modes of causation needs to be carried out in appropriate detail.


Drawn from The Logic of Causation (I:1999-2000), Chapters 3:3 and 10:1-2.



[1]             The logician must keep an open mind so long as an issue remains unresolved. Logic cannot at the outset, without good reason, close doors to alternatives. Where formal considerations leave spaces, we cannot impose prejudices or speculations. The reason being that the aim of the science of logic is to prepare the ground for discourse and debate. If it takes arbitrary ‘metaphysical’ positions at the outset, it deprives us of a language with which to even consider opposite views. So long as formal grounds for some thesis is lacking, its antithesis must remain utterable.

[2]             It is interesting to note that, although J. S. Mill did not (to my knowledge) consider the issue of lone determinations, he turned out to be right in acknowledging only the four joint determinations.

[3]             Note incidentally that to say that G-d created the world does not imply that He did so specifically as and when the Bible seems to describe it; He may equally well have created the first concentration of matter and initiated the Big-Bang. Note also, that Creationism implies the pre-existence of G-d, a 'spiritual' entity; it is therefore a theory concerning the beginning of 'matter', but not of existence as such. G-d is in it posited as Eternal and Transcendental, or prior to or beyond time and space, but still 'existent'. With regard to such issues, including the compatibility of spontaneity and volition with Creation, see my Buddhist Illogic, chapter 10.

[4]             This final chapter of Phase One was written in 2003, after publication of Phenomenology.

[5]             I do not there treat spatial modality, but it is easy enough to do eventually.

[6]             In paradox, either P or Q is implied impossible. See Future Logic, chapter 31.

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