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Eleventh post in the ongoing series on important innovations in logic theory to be found in my works. In this and the next few posts, I will write about the logic of causation, which I have just finished researching over a period of 12 years on and off. The following is an extract from the last chapter of my newly published book The Logic of Causation.
We have in the previous post 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 quantatively 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. (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.)
For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm
For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm
To purchase the book, go to: http://stores.lulu.com/thelogicianbooks