Inductive Logic

1.    Causation

Causality refers to causal relations, i.e. the relations between causes and effects. This generic term has various, more specific meanings. It may refer to Causation, which is deterministic causality; or to Volition, which is (roughly put) indeterministic causality; or to Influence, which concerns the interactions between causation and volition or between different volitions.

The term ‘causality’ may also be used to refer to causal issues: i.e. to negative as well as positive answers to the question “are these things causally related?” In the latter sense, negations of causality (in the positive sense) are also causality (in the broad sense). This allows us to consider Spontaneity (i.e. causelessness, the lack of any causation or volition) as among the ‘causal’ explanations of things.

A study of the field of causality must also include an investigation of non-causality in all its forms. For, as we shall see, even if we were to consider spontaneity impossible, the existence of causality in one form or other between things in general does not imply that any two things taken at random are necessarily causally related or causally related in a certain way. We need both positive and negative causal propositions to describe the relations between things.

In the present work, The Logic of Causation, we shall concentrate on causation, ignoring for now other forms of causality. Causative logic, or the logic of causative propositions, has three major goals, as does the study of any other type of human discourse.

1. To define what we mean by causation (or its absence) and identify and classify the various forms it might take.
2. To work out the deductive properties of causative propositions, i.e. how they are opposed to each other (whether or not they contradict each other, and so forth), what else can be immediately inferred from them individually (eduction), and what can be inferred from them collectively in pairs or larger numbers (syllogism).
3. To explain how causative propositions are, to start with, induced from experience, or constructed from simpler propositions induced from experience.

Once these goals are fulfilled, in a credible manner (i.e. under strict logical supervision), we shall have a clearer perspective on wider issues, such as (d) whether there is a universal law of causation (as some philosophers affirm) or spontaneity is conceivable (as others claim), and (e) whether other forms of causality (notably volition, and its derivative influence) are conceivable.

Note well, we shall to begin with theoretically define and interrelate the various possible forms of causation, leaving aside for now the epistemological issue as to how they are to be identified and established in practice, as well as discussions of ontological status.

We shall thus in the present volume primarily deal with the main technicalities relating to reasoning about causation, and only later turn our attention to some larger epistemological and ontological issues (insofar as they can be treated prior to further analysis of the other forms of causality). The technical aspect may at times seem tedious, but it is impossible to properly understand causation and its implications without it. Most endless debates about causation (and more generally, causality) in the history of philosophy have arisen due to failure to first deal with technical issues.

2.    The Paradigmatic Determination

Causation, or deterministic causality, varies in strength, according to the precise combinations of conditioning found to hold between the predications concerned. We may call the different forms thus identified the determinations of causation.

The paradigm, or basic pattern, of causation is its strongest determination. This has the form:

If the cause is present, the effect is invariably present;

if the cause is absent, the effect is invariably absent.

Our use, here, of the definite article, as in the cause or the effect, is only intended to pinpoint the predication under consideration, without meaning to imply that there is only one such cause or effect in the context concerned. Use of an indefinite article, as in a cause or an effect, becomes more appropriate when discussing a multiplicity of causes or effects, which as we shall later see may take various forms.

We may rewrite the above static formula in the following more dynamic expression:

If the cause shifts from absent to present, the effect invariably shifts from absent to present;

if the cause shifts from present to absent, the effect invariably shifts from present to absent;

We shall presently see how this model is variously reproduced in lesser determinations. For now, it is important to grasp the underlying principle it reflects.

The essence of causation (or ‘effectuation’) is that when some change is invariably accompanied by another, we say that the first phenomenon that has changed has “caused” (or “effected”) the second phenomenon that has changed. In the above model, the changes involved are respectively from the absence to the presence of the first phenomenon (called the cause) and from the absence to the presence of the second phenomenon (called the effect); or vice versa. We may, incidentally, commute this statement and say that the effect has been caused (or effected) by the cause.

Now, some comments about our terminology here:

The term “change,” here, must be understood in a very broad sense, as referring to any event of difference, whatever its modality.

• Its primary meaning is, of course, natural change, with reference to time or more to the point with respect to broader changes in surrounding circumstances[1]. Here, the meaning is that some object or characteristic of an object which initially existed or appeared, later did not exist or disappeared (ceasing to be), or vice-versa (coming to be); or something existed or appeared at one place and time and recurred or reappeared at another place, at another time (mutation, alteration or movement). This gives rise to temporal and natural modalities of causation.
• Another, secondary sense is diversity in individuals or groups. This signifies that an individual object has different properties in different parts of its being[2]; or that a kind of object has some characteristic in some of its instances and lacks that characteristic (and possibly has another characteristic, instead) in some other of its instances. This gives rise to spatial and extensional modalities of causation.
• Tertiary senses are epistemic or logical change, which focus respectively on the underlying acts of consciousness or the status granted them: something is at first noticed and later ignored, or believed and later doubted, or vice-versa, by someone. This gives rise to epistemic and logical modalities of causation.

Regarding the terms “present” and “absent” (i.e. not present), they may be understood variously, with reference to the situations just mentioned. They may signify existence or appearance or instancing (i.e. occurrence in some indicated cases) or being seen or being accredited true – or the negations of these.

The term “phenomenon” is here, likewise, intended very broadly, to include physical, mental or spiritual phenomena (things, appearances, objects), concrete or abstract. Also, a phenomenon may be static or dynamic: that is, the changing cause and effect need not be a quality or quantity or state or position, though some such static phenomena are always ultimately involved; the cause and effect may themselves be changes or events or movements. For instance, motion is change of place, acceleration is change in the speed or direction of motion. What matters is the switch from presence to absence, or vice-versa, of that thing, whatever its nature (be it static or dynamic). The cause and effect need not even be of similar nature; for example, a change of quality may cause a change of quantity.

Another term to clarify in the above principle is “accompanied,” Here again, our intent is very large. The cause and effect may be in or of the same object or different objects, adjacent or apart in space, contemporaneous or in a temporal sequence. The definition of causation contains no prejudice in these respects, though we may eventually find fit to postulate relatively non-formal rules, such as that in natural causation the effect cannot precede the cause in time or that all causation at a distance implies intermediate contiguous causations[3].

Indeed, it is in some cases difficult for us, if not impossible, to say which of the two phenomena is the cause and which is the effect. And this often is not only an epistemological issue, but more deeply an ontological one. For, though there is sometimes a direction of causation to specify, there is often in fact no basis for such a specification. The phenomena named ‘cause’ and ‘effect’ are in a reciprocal relation of causation; the terms cause and effect are in such cases merely verbal distinctions. All that we can say is that the phenomena are bound together, and either can be accessed through the other; the labels applied to them become a matter of convenience for purposes of discourse.

Finally, the term “invariably” has to be stressed. How such constancy is established is not the issue here; we shall consider that elsewhere. In the paradigm of causation given above, it would not do for the conjunction of the cause and effect, or the conjunction of their negations, to be merely occasional. We would not regard such varying conjunctions as signifying genuine causation, but quite the opposite as signs of mere coincidence, happenstance of togetherness. Post hoc ergo propter hoc. The problem is complicated in lesser determinations of causation; but as we shall see it can be overcome, a constancy of conjunction or of non-conjunction is always ultimately involved.

In this context, a warning is in order. When something is invariably accompanied by another, we say that the first (the presence or absence of the cause) “is followed by” the second (the presence or absence of the effect). This refers to causal sequence and should not be confused with temporal sequence; the term “followed” is ambivalent (indeed, it is also used in relation to spatial or numerical series). Even though causal and temporal sequence are often both involved (which is why the term “to follow” is equivocal), causal sequence may occur without temporal sequence (even in natural causation) or in a direction opposite to temporal sequence (though supposedly not in natural causation, certainly in logical causation, and by abstraction of the time factor also in extensional causation). The context usually makes the intent clear, of course.

Now, for some formal analysis:

In our present treatment of causation, we shall focus principally on the logical ‘mode’ of causation, note well. There are (as we shall later discuss) other modes, notably the natural, the temporal, the spatial and the extensional, whose definitions differ with respect to the type of modality considered. Having investigated modality and conditioning in detail in a previous treatise (Future Logic, 1990), I can predict that most of the behavior patterns of logical causation are likely to be found again in the other modes of causation; but also, that some significant differences are bound to arise.

Returning now to the paradigm of causation, it may be expressed more symbolically as follows, using the language of logical conditioning (as developed in my Future Logic, Part III):

If C, then E; and

if notC, then notE.

A sentence of the form “If P, then Q” means “the conjunction of P and the negation of Q is impossible,” i.e. there are no knowledge-contexts where this conjunction (P + notQ) credibly occurs. Such a proposition can be recast in the contraposite form “If notQ, then notP,” which means “the conjunction of notQ and the negation of notP is impossible” – the same thing in other words.

Such a proposition, note, does not formally imply that P is possible or that notQ is possible. Normally, we do take it for granted that such a proposition may be realized, i.e. that P is possible, and therefore (by apodosis) Q is possible and the conjunction “P and Q” is possible; and likewise, that notQ is possible, and therefore (by apodosis) notP is possible and the conjunction “notQ and notP” is possible.

However, in some cases such assumption is unjustified. It may happen that, though “If P, then Q” is true, P is impossible, in which case “If P, then notQ” must also be true; or it may happen that, though “if P, then Q” is true, notQ is impossible, in which case “If notP, then Q” must also be true. These results are paradoxical, yet quite logical. I will not go into this matter in detail here, having dealt with it elsewhere. It is not directly relevant to the topic under discussion, except that it must be mentioned to stress that such paradox cannot occur in the context of causation (except to deny causation, of course).

Therefore, when discussing causation, it is tacitly understood that:

C is contingent and E is contingent[4].

That is, each of C, E is possible but unnecessary; likewise, by obversion, for their negations, each of notC, notE is possible but unnecessary. If any of these positive or negative terms is by itself necessary or impossible, it is an antecedent or consequent in valid (and possibly true) propositions, but it is not a cause or effect within the causation specified. This is, by the way, one difference in meaning between the expressions cause/effect, and the expressions antecedent/consequent. We shall see, as we deal with lesser determinations of causation, that their meanings diverge further. All the more so, when the terms cause/effect are used in other forms of causality.

Furthermore, as above shown with reference to “P” and “Q,” granting the contingencies of C and E, each of the propositions “If C, then E” and “If notC, then notE” implies the following possibilities:

The conjunction (C + E) is possible; and

the conjunction (notC + notE) is possible.

All this is hopefully clear to the reader. But we must eventually consider its implications with reference to statements dealing with lesser determinations of causation or statements denying causation.

Drawn from The Logic of Causation (I:1999-2000), Chapter 1.