The four determinations of causation

The four determinations of causation
Causation, which is deterministic causality, involves four generic determinations, two strong and two weak[1]:
Complete causation (symbol m): If C, then E; if notC, not-then E; where: C is possible.
Necessary causation (symbol n): If notC, then notE; if C, not-then notE; where: C is unnecessary.
Partial causation (symbol p): If (C1 + C2), then E; if (notC1 + C2), not-then E; if (C1 + notC2), not-then E; where: (C1 + C2) is possible.
Contingent causation (symbol q): If (notC1 + notC2), then notE; if (C1 + notC2), not-then notE; if (notC1 + C2), not-then notE; where: (notC1 + notC2) is possible.Note the precision of these definitions and the symmetries in this list. Causation is defined with reference to positive and negative hypothetical (or conditional) propositions. A proposition of the positive form ‘if X, then Y’ means ‘X without (or not followed by) Y is impossible (in the mode of modality concerned)’; a proposition of the negative form ‘if X, not-then Y’ means ‘X without (or not followed by) Y is possible (in the mode of modality concerned)’.
Note that the two strong determinations are composed of two hypothetical propositions, one positive and one negative, plus a modal categorical; the two weak determinations involve one positive and two negative hypothetical propositions, plus a modal categorical[2]. All the stated elements are needed to define each of these compounds; no element is redundant. Since no other determinations of causation are logically conceivable, this list is exhaustive.
Further analysis proves that only four specific combinations of these four generic determinations are logically consistent, namely: complete-necessary causation (mn), complete-contingent causation (mq); necessary-partial causation (np), partial-contingent causation (pq). These four joint determinations are (to repeat) exhaustive, and (moreover) mutually exclusive, so that we may safely say that: nothing can be said to be a cause or effect of something else, in the causative sense, if it is not related to it by way of one – and indeed, only one – of these four species of causation.
Having thus arrived at an exhaustive listing of the forms that causation may logically take, we can gradually develop a thorough logic of causation. This must begin by interpreting the specific negations of the four forms of causation, and thence the general negation of causation. Note well that we cannot theoretically define non-causation except through negation of all four forms of causation, which have to be defined first”[3].
Next the oppositions and eductions of the four forms are investigated, and various issues such as parallelism of causes and causal and effectual chains can be discussed. Thereafter, syllogistic reasoning involving causative propositions can be systematically investigated. This is to guide us in deduction and to ensure consistency in one’s knowledge. The formal solution of all deductive problems is by no means easy, and requires successively more and more complex techniques[4].
As regards the induction of causation, this seemingly difficult problem is reduced to the easier problems of induction of the conditional and categorical propositions which together make up a causative proposition. To fully understand the issues involved in induction of causation, it is first necessary to realize that there are different modes of causation, corresponding to the different modes of modality. This means that there are four full determinations of causation for each of the modes of modality.
In the above definitions, the if-then statements are not intended as exclusively logical, but as generic, being applicable to logical conditionals, extensional conditionals, natural conditionals, and temporal (and similarly spatial) conditionals. The deductive and inductive formal logics of these various modes of conditioning are treated systematically and in great detail in FL. The work of clarification and validation of induction of causation is thus already formally done.
Briefly put, we can describe the induction of causation, i.e. of a proposition like ‘A causes B’, as follows. Consider, say, two events A and B. If A is always in our experience so far found to be followed by B, i.e. never followed by not-B, then we can by generalization induce (i.e.  infer by inductive logic) that A implies B, until if ever we come across even a single case of A not followed by B, in which case we must particularize our previous proposition and conclude instead that A does not imply B[5]. The same process applies to the negations of these same terms, viz. to not-A and not-B, which also need to be considered before any sort of causation can be declared. If not-A is always in our experience so far found to be followed by not-B, i.e. never followed by B, then we can by generalization induce that not-A implies not-B, until if ever we come across even a single case of not-A not followed by not-B, in which case we must particularize our previous proposition and conclude instead that not-A does not imply not-B[6]. Once we have settled both these issues, one way or the other, and combined the results, we can formulate a causative proposition of whatever degree.
The induction of non-causation, i.e. of a proposition like ‘A does not cause B’, is much more difficult. Granting we have by the above said means arrived at the conclusion that ‘A does not imply B and not-A does not imply not-B’, we might well first conclude that ‘A is a partial and contingent cause of B’ before concluding that ‘A does not at all cause B’. The former, more positive conclusion presupposes that there are some additional causal factors involved, which we have already identified or expect to readily identify; whereas the latter, negative conclusion presupposes that additional causal factors were diligently sought but couldn’t be found. In either case, the conclusion can only be inductive, as it could easily be overturned at some later stage.[7]
We thus arrive at a full and indubitable development of the concept of causation. This permits us to examine and if necessary to criticize past and present discourse regarding causation with masterly finality. Some past and current works on this subject deserve attention and praise, even if they are not exhaustive. Some past and current works deserve criticism and can be rejected in a decisive manner once and for all. We thus move from mere opinion and controversy to genuine scientific discourse.
One thing that the above-described analysis proves authoritatively is that causation exists and can be known. It is not a figment of our imaginations, as some (notably David Hume, as we shall see) have contended. The forms of causation proceed logically and inevitably from modality and the categorical and hypothetical forms that naturally emerge from it which are the bases and means of all rational discussion. No one can attack these rational means without using them and thus putting his own discourse in doubt and indeed invalidating it. It may in the past have seemed possible to criticize causation when we had no precise idea of its exact nature; but now that we know precisely how it is constructed out of simpler discursive elements, it can no longer be doubted or rejected without self-contradiction. Skepticism regarding causation’s very existence and knowability is no longer an option.
Furthermore, although causation is something abstract, it is still something objective, i.e. it exists independently of our knowledge (or not) of it. Immanuel Kant’s attempt to respond to Hume’s skepticism by proposing that causality is a ‘category’ imposed by us on empirical data implied causality to be something subjective. This was not a solution, but an additional layer of error. Both these philosophers have had a devastating effect on the theoretical understanding of causal thinking.
Another important finding is that the much touted ‘law of causation’, according to which everything must have a cause, in the deterministic sense of the term, is not formally guaranteed. It may be true; but then again it may not. We cannot, through our logically established definitions of causation and non-causation, prove that spontaneity is impossible; nor for that matter that it is possible. Thus, logic must make formal allowance for the idea of spontaneity, i.e. of natural spontaneity and/or human volition (freewill). Then, when we speak of causality in the widest sense, we should bear in mind not only causation (the deterministic variety of causality), but also natural spontaneity and volition (the indeterministic varieties)[8]. In that case, we can formulate a more open ‘law of causality’, such that everything must be caused in one or more of these three senses.
 

[1]              The symbols m, n, p, q, are derived from the words coMplete, Necessary, Partial, and Qontigent. Note in passing that a complete cause is often, in common discourse, referred to as a sufficient cause; the two terms mean the same. The word ‘cause’ may, in the context of causation, be replaced by the more specific word ‘causative’. Here, the symbols C and E refer, of course, to putative causes and effects until they fall within one of the valid definitions of causes and effects.
[2]              The positive hypothetical alone cannot define causation, since formally it could be combined with another positive hypothetical with the same antecedent and the opposite consequent; the negative hypothetical(s) is (are) needed and used to eliminate this logical possibility. The modal categorical ensures that the antecedent C or notC, or (C1 + C2) or (notC1 + notC2), has a basis. In the event of partial or contingent causation, the terms C1 + C2, etc. refer to combination of only two causes; but when there are more than two they can gradually be redefined as two.
[3]              The importance of this statement is that all past attempts to deny causation (such as Nagarjuna’s or David Hume’s) are worthless, since they do not even first accurately define what it is they are trying to deny.
[4]              This work takes up most of my work The Logic of Causation and need not concern us here.
[5]              Needless to say, if we know from the start that A is not always followed by B, we do not bother generalizing and particularizing, but go straight to the negative conclusion.
[6]              Again, if we know from the start that not-A is not always followed by not-B, we do not bother generalizing and particularizing, but go straight to the negative conclusion.
[7]              I would like to one day develop software for causative logic, made available online, which could be used by scientists and everyone else to determine the best logical conclusions about causation given certain combinations of raw data, based on my detailed work in The Logic of Causation.
a) In any given knowledge context, the information currently available concerning three variables (P, Q, R) or four variables (P, Q, R, S), or more, would be introduced, and the program would determine which causative relation is the most fitting. Until new data is found, the chosen causative relation (mn, mq, np, or pq) would be declared the most probably true one.
b) Then, given two or more such probable causations, arguments would be used by the program to draw conclusions. These conclusions would predict the probable causative relations between items for which we did not previously determine the relation in the manner (a).
c) At this point, we would want to empirically verify the latter findings. If they turned out to be wrong (i.e. if the outcome of an (a)-type proposition is not in accord with the outcome of a (b)-type inference) we would of course conclude that one or both premises giving rise to our conclusion in (b) needs revision.
d) In such event, we would be called upon to do further empirical research on the doubtful items. In this way, the program would generate consistency checks and when necessary further research.
Not being able myself to produce such software, I am hoping someone else will eventually do it. Or maybe the job will eventually be easily done using AI.
[8]              Here regarding the causal relation of ‘influence’ as a concept within the domain of volition, because it only has significance in relation to volition.