APPENDIXES

1. Some formal logic guidelines

2. Aristotle’s four causes

 

1. Some formal logic guidelines

We have in the course of the present work introduced a great number of propositional forms, such as “A wills W”, “X influences A to will W”, and many more. In some cases, we have been content to broadly define a causal relation without further treatment. In others, we have gone into more detail, preparing the ground for eventual logical treatment. But the present work (unlike the author’s previous works) has not attempted to systematically develop the logic of the various forms introduced in it. This policy was adopted for two reasons: one, to make the text more readable and widely accessible; and two, because the task of formalization is enormous.

This daunting task is left to future logicians. Nevertheless, we shall here make some hopefully helpful comments, in addition to those made in passing throughout the main text. It is always useful to start with a nomenclature. Thus, we have called forms about volition: “volitional propositions”, and forms about influence: “influential propositions”. We may similarly name other forms, like those about velleity or habits or urges.

Next, we must clearly formulate each form, using symbolic variables for the terms (X, Y, Z or the like). The form concerned should then be analyzed into simpler ones, already studied by logicians. I call the larger form a ‘bulk’ form and those it is composed of or reducible to its ‘pieces’; for example, briefly, “X influences A to will W” implies “A willing W requires less effort with cognition of X than without it” among others. The implied form may in turn be reducible; e.g. the form just mentioned may be reworded with the hypotheticals “if X (is cognized while A wills W), then effort E(X) is required (for willing W)” and “if notX, then effort E(notX)”, and the comparative “effort E(X) is less than effort E(notX)”.

The forms thus progressively clarified then need to be systematically studied, if we are to develop a thorough formal logic for them. This means interrelating all the forms of the same family (validating eductions and oppositions), and considering their concatenations (validating syllogisms and other arguments), as regards deductive logic, as well as dealing with inductive ways and means. This is a big job, requiring much patience, which is likely to yield some tasty fruits. Ultimately, forms of different families must also be logically compared and combined; for example, volitional and influential forms. In this way, the logician prepares for all eventual discourse using all possible forms.

Any attempt to develop a thorough formal logic must take non-formal nuances into consideration; otherwise, the treatment will be naïve and ultimately misleading. Many logicians err, because they are too quick getting involved in purely technical issues, before they have sufficiently studied the matter at hand. As I have often argued, excessively ‘symbolic’ logic is pretty well bound to fall into this trap. Better to stick with ordinary language, although it is more bulky to deal with, because one can more easily spot if one is straying from reality.

For example, again briefly: consider the four forms below, willing and its negation, or activity and passivity.

(a) “A wills W” – this refers to an active will of W by agent A.

(b) “A wills notW” – this refers to an active will of notW by agent A.

(c) “A does not will W” – here A minimally does nothing with regard to W.

(d) “A does not will notW” – here A minimally does nothing with regard to notW.

These forms are in a standard ‘square of opposition’, assuming that agent A cannot at once will W and will notW – so that (a) and (b) are contrary. Clearly, (c) and (d) are intended as the formal contradictories of (a) and (b), respectively. It follows that (c) and (d) are subcontrary. When both are true, agent A is can truly be said to be passive. But if (c) is true without (d), then A is active in (b). Similarly, (d) may be true without (c), by implication from (a).

However, it could be argued that (a) and (b) are in fact compatible, although an agent cannot achieve contradictory goals simultaneously, since he can pursue both at one and the same time, provided the respective partial causatives of the two results that he wills into motion at the time concerned are compatible with each other (as sometimes happens). In such case, the square of opposition between the four forms is more dilute: the diagonals still relate contradictories, but the four lateral relations are ‘unconnected’.

We can further complicate the formal issues, if we more closely consider what we mean by “willing”. On the surface, “A wills W” suggests direct will, so that A has but to will in the direction of W and W is brought about. But most objects of will are not attainable at will – A may desire to attain W, and he may do what he thinks is useful to such end, and he may do his best, yet he may be wrong in his assumptions, and his best may not be good enough, and he may end up unsuccessful, or (if W is divisible) only partly successful. Of course, A may try again; but in some cases, W may no longer be attainable, and the opportunity may be lost.

If A wills W and succeeds, then at that moment notW ceases to be. If A wills W and fails, then presumably notW continues to be – although it may be that W is brought into being by some causative or a volitional agent other than A, provided that W is not something within A but further out, granting that as a free agent only A can affect what goes on within himself. (Similarly, mutadis mutandis, with regard to willing notW.)

If A does not will W, he has effectively “allowed” notW to be – i.e. to continue if already present or to occur if it was absent. That is of course not per se equivalent to willing notW, unless A positively intended notW by abstaining from willing W. Here again, that is assuming no other cause or agent can and does bring W, or notW, about – in which case we can only refer to A’s intentions or wishes. (Similarly, mutadis mutandis, with regard to not-willing notW.)

Various reasons may cause A not to actively will W – such as lack of energy, laziness, weak will, cowardice, indifference, lack of motivation, having better things to do, and so forth. All such reasons are influences in relation to the non-will of W by A; they make A’s willing W harder by some degree. All other things being equal (i.e. if no other causes come into play), the inertial result will be notW (i.e. if W is not actively willed, notW will naturally take place). If A now decides to will W, he will have to overcome the said influences against W. Some new influences may however come and facilitate this choice, and make W easier to will than it seemed previously. (The same can of course be said, mutadis mutandis, with regard to notW.)

Apart from influences, one must also consider the terms and conditions provided by the environment more broadly. Influences are only those factors in the environment that have been perceived to be there, or at least are thought to be there. There remain factors that have not been perceived or thought to be relevant – but which in fact have causative significance.

We would similarly need to study the formalities of all other propositional forms, related in one way or another to volitionals, starting with influentials. We have already defined the positive influential forms, but not interpreted their negations. The way this is done is by denying the defining implications of the corresponding positive forms. Thus, at first sight, “X does not influence A to will W’ means “A requires either more or equal effort to will W with cognition of X than without it”. But on closer scrutiny, to arrive at the strict contradictory, allowance must be made for cases where A is neither aware of X nor aware of notX, or where A cannot will W at all, or where A is not a volitional agent. (Similarly, mutadis mutandis for “X does not influence A not to will W”.)

With regard to other oppositions, we would for example declare the forms “X influences A to will W” (meaning “A requires less effort to will W with X than without X”) and “notX influences A to will W” (meaning “A requires less effort to will W without X than with X”) to be contrary, since “less effort with X” equals “more effort without X”, and since “less effort” and “more effort” without X are incompatible (though not contradictory, since “equal effort” remains an option). On the other hand, the obverse forms “X influences A to will W” and “X influences A not to will notW” are not as equivalent as might first appear, since we could argue that “the effort to will W” and “the effort not to will notW” are not necessarily the same (with or without X).

Our distinction between necessary causation and inertial causation (in chapter 2.1) has an important consequence for formal logic. Thus far, we have treated all natural conditional propositions, “When this, then that”, as one, but in fact they are of two sorts. Sometimes we mean that the consequent follows the antecedent with natural necessity; but sometimes we only mean that the consequent invariably follows the antecedent provided no volitional interference prevents it. The latter negative precondition is very often left tacit in practice, but should obviously be taken into consideration in all reasoning processes involving such inertial propositions. For example, in a first figure syllogism with such a proposition as its major premise, we cannot draw a conclusion if this tacit proviso (which is effectively part of the middle thesis) is somehow incompatible with the minor thesis, and if we can draw a conclusion the tacit proviso becomes part of its antecedent.

As such examples illustrate, we should not rush to judgment in formal analysis, but proceed very cautiously, thinking the issues through. Logic is a big responsibility! An error of formal logic by logicians signifies thousands and millions of errors of ‘material’ logic by ordinary practitioners thereafter. It is comparable to mathematicians making a theoretical error, which is carried over into physics, architecture, and so forth, causing havoc in science and technology. Of course, contradictions would soon become apparent.

 

2. Aristotle’s four causes

The Greek philosopher Aristotle proposed four senses of the term cause, four ways with which anything may be explained. These “four causes” were called the material cause, the formal cause, the efficient cause and the final cause. An example would be a man-made statue: its granite is the material cause, its shape is the formal cause, the sculptor’s chiseling away at a stone is its efficient cause, and the image of Hercules the sculptor intended to produce is its final cause.

I have read some modern writer’s claim that nowadays only the efficient cause would be considered rightly named as a ‘cause’ – but that claim is not correct, as we shall now show. All the four causes fit the bill with regard to causality, and all four of them to some extent qualify as causation:

  1. The material cause is a necessary though partial cause, since we can say of it: “without some material, there would be no sculpture; whereas with it, a sculpture becomes possible”. The stone used for the sculpture was thus a causative, although that particular piece of matter could have been replaced by another; i.e. it was only a contingent cause. The stone by itself does not a sculpture make, so it is only a partial causative.
  2. The formal cause is something quite abstract, but can be considered another necessary partial cause, since “without some form, there would be no sculpture; whereas with it, there is”. Again, this particular shape given to the stone is not a necessary causative, since another shape could have been applied. Also, the shape cannot exist without material substrate, so it is not a complete causative.
  3. The efficient cause, in our example, is of course primarily the sculptor – the human agent using his volition. But the term can also be applied to the inanimate chisel and the blows it gave the stone, ignoring for a moment who held it and willed its movements; or equally well, to a sculpting machine built by someone. In any case, the efficient cause can be regarded as a causative – again a necessary one (in the sense that some sculptor or moving chisel was needed) or a contingent one (if we focus on this specific sculptor, or this particular chisel and those particular movements), and in either case a partial causative (since matter to be sculpted was needed too).
  4. The final cause in our example is not essentially a causative, but rather an influential cause, since it is only through its imagination by the sculptor that it has played a role in the genesis of the sculpture. However, we can still reduce this mental goal to a causative, if we consider that had the sculptor not thought of and intended some image, he would probably not have engaged in all these movements of his, and certainly if his movements had been wholly capricious they would not have resulted in such a perfect resemblance of Hercules. Thus, here, we have another sine qua non, and again a partial causation.

Note that it could be argued that in the example we have given the formal and final cause are identical – a certain shape, resembling that of Hercules. But it should be clear that we might equally well posit other intentions of the sculptor as final causes – for examples, his intent to honor Hercules, or to make money by selling the sculpture to the Athens municipality. Any motive involved is a final cause.

Lastly, our example deals with a special case – that of manufacture of some finished product by a conscious, volitional agent. However, Aristotle’s intent is that these four causal categories be used also in the explanation of natural events –in the wider world of living and inanimate objects.

  • Clearly, all such objects must have a material cause and a formal cause; all particular phenomena apparently have substance and form (abstract characters found in common with other particulars in diverse measures). By analogy, we might also apply these concepts to the mental and spiritual domains. The term ‘material’ cause must thus be understood to refer to any assumed concrete substance, and ‘formal’ cause to any conceptual abstraction.[1]
  • With regard to efficient cause, the concept is applicable not only to agents and their acts (i.e. volition), but to non-volitional entities and movements in living matter, and more broadly to non-living matter. For examples: the respiration of oxygen into our blood stream via our lungs is an efficient cause of our continued life; the momentary alignment of the sun, earth and moon is an efficient cause of the phenomenon of eclipse of the moon.
  • As for final cause – the concept may be stretched to fit non-volitional life processes, as explained in our discussion of the quasi-purposive. Such ‘conatus’ is of course a mere abstraction, based on the observation of life perpetuating itself; but it does imply efficient causes at play within the organism. For inanimate matter, no concept of ‘final cause’ is applicable, except in relation to the purposes of some volitional being (including, eventually, God) or with reference to utility for the quasi-purposes of living entities.

Although I here defend Aristotle’s foursome, I do not regard it – by far – as the last word on aetiology. If our intent is to categorize all the senses of the term ‘cause’, there are a lot more things to be said about it. As we have seen, causality is a very broad concept, not limited to causation or even to Aristotle’s four causes however viewed.



[1] It could also be argued that substance and form are both abstractions, i.e. products of conception, anyway, and so ultimately indistinguishable.

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