On Explanation: Aristotelean and Hempelean
In his recent studies showing Galileo's knowledge of and adherence to the deductive standards of explanation in science set forth by Aristotle, Wallace (1) remarks that this Aristotelean theory must not be confused with the contemporary deductive-nomological theory of Hempel and Oppenheim. (2) There are, of course, important differences between the classic works of Aristotle and Hempel, for twenty-three centuries lie between them. But the differences are not as great as might be expected, and, as current discussions of the metatheoretical issues of explanation are generally ahistorical, I believe an attempt to compare these two intellectual mileposts in our understanding of scientific method should prove useful.
The most obvious and interesting similarities between the two metatheories of science lie in their deductive character, and this is where their significant contrasts lie as well. Aristotle had developed two major deductive systems: the hypothetical and categorical syllogisms. Of these, he thought only the latter suitable to the demanding rigors of scientific knowledge, whose first characteristics he saw to be 'certainty' and 'necessity'. (3) There are some problematic elements in just what Aristotle took these concepts to mean, but I postpone discussion of that to a later stage.
The categorical syllogism, preferably in the familiar "Barbara" of the first figure of the first mood, Aristotle sees to be the ideal supplier of both the certainty and the necessity, with the scientific conclusion being the conclusion of the syllogism. Like Hempel and Oppenheim, he insists that the premises be true, from which it is evident that the conclusion could not fail to be certainly and necessarily true. The syllogism itself, as an argument, then stands as an explanation. Inasmuch as the deductive system of the categorical syllogism can be seen now to be a significant subset of the first-order predicate calculus, which is the deductive system prescribed by Hempel and Oppenheim, the difference between the deductive requirements of the two metatheories is really only that of the greater scope, power, and elegance of the more recent logic. But it remained for Hempel and Oppenheim to point out the bidirectional properties of this explanatory model, in the sense that taking the direction of the deduction to the conclusion may yield prediction (or retrodiction), while looking back from the conclusion on the completed deduction may provide the explanatory power.
That brings us to ask what Aristotle meant by 'necessity' and 'certainty'. A good answer is available only for the former, so let us take that first. Necessity, Aristotle writes in explicit language, inheres in that "which could not be otherwise." And this brings us to the chief difference between the Aristotelean and Hempelean views. For there are plainly two sorts of things which "could not be otherwise" lying at the heart of the scientific task.
The first of these is the necessity of the successful deductive process. A conclusion validly deduced cannot be otherwise, whether in the ground-breaking system of Aristotle's categorical syllogism, or more recent formalisms. Further, deduction is truth-conserving, hence the importance both Aristotle and Hempel placed on the methodological requirement that the premises be true, for that would produce a conclusion that was not only necessary, but also true. I will suggest later that this requirement is deceptive for both metatheories, but the considerations that led to its adoption were overwhelming at the time, and have not much diminished in their attractiveness since. In any case, this is the sort of necessity that, by Hempel's day, all philosophers (except those in the Hegelian tradition) recognized as 'logical', and, in terms which go back to Hume, (4) describe as the kind of necessity which rules out the truth of self-contradictory propositions.
The second sort of necessity of things "which could not be otherwise" is that of natural laws, in terms of which causal connections and the persistent patterns of events in nature can be expressed. Its distinction from logical necessity goes back at least to the work of Galileo, (5) and was reiterated in forceful terms by Hume, after Leibniz had turned back in the direction of
Its properties are most commonly defined negatively or functionally, and are the subject of wide controversy, including whether and to what extent various formal systems may succeed ine mbodying them.
Aristotle did not distinguish between these two kinds of necessity, and, from the way in which he wrote about the subject, it seems very likely that his joy in the manner in which the tools of logic could be used to track the necessities of nature was founded on the confident assumption that 'necessity' must, at its base, be one. That there are Eleatic, Pythagorean, and Platonic reasons to strengthen such a belief is a matter of more than historical interest, but one that need not be pursued here. It is enough for our purposes to be reminded that Aristotle did not mark out "logical" and "natural" necessities as being of different kinds, and thus, doubtless, took the evident properties of the former as fully explicating the latter. We could say, in the wisdom of hindsight, that he "conflated" them, as though it were an intentional act for which he could be held responsible, but there is no basis for such a view That aside, and in spite of its evident difficulties, there is, nevertheless, something deeply satisfying about Aristotle's position, as may be attested to by the fact that in recent years a number have sought to revive it in one form or another.
But the deductive-nomological metatheory of Hempel and Oppenheim-even in its very name-distinguishes what Aristotle did not, thus following the path of Galileo and Hume. In terms of the predicate calculus, it expresses natural laws in terms of universal operators ranging over predicate variables. This is a technique which, if successful, portrays the properties as they are associated, without enlightening anyone as to the "necessity" of the association. When pressed as to what this might consist in, the defenders of this view can only reply: that is what our investigations of the world have so far revealed as to which things are repeatedly observed together on specific occasions. Here the two sides reach a stand-off, with the critics of the Galilean-Humean view insisting that this reveals no "necessity" distinguished from coincidence, while its defenders urge that there is no more to it; that only further testing could distinguish the natural necessity from the accidental coincidence, and that to seek more is to go beyond the observable to the dark abyss of "metaphysics." There are, of course, many other factors to be considered in this complex issue, but the superficially satisfying aspect of the Aristotlean identification may well be playing a part here, which is all the more difficult to confront because it is never clearly expressed.
Be that as it may, we must now return to look more closely at the requirement that the premises be true: a requirement shared by the ancient and contemporary metatheories. Its purpose, alike in both, to ensure the truth of the conclusion, has already been remarked. Aristotle asks how this can be determined, and quickly narrows the possibilities down to two: the truth of the premises may have been established by their character as conclusions of earlier scientific syllogisms, or noninferentially through perception and intuition. He tells us the latter must be a possibility, since were the former the only source of knowledge, it would either force us back into a bottomless regress or a vicious circle. Neither of these would produce knowledge, and that would leave unexplained the knowledge he took us to indubitably possess. We must have a nonsyllogistic way of arriving at some of our premises.
At first he is not hopeful about perception being the source of such knowledge, on the grounds that it yields information only about a particular case, while a syllogism requires at least one universal premise. Seeing no other source, however, and taking examples from everyday life, from astronomy, and from physics, he finds that humans have the capacity, under certain conditions, to observe a universal in the particular. Using memory, and paying special attention to the likenesses and differences of events otherwise similar, we may, he says, see a set of particulars as an instance of a universal, much as soldiers in a rout, by first one making a stand, then another, and another, rebuild their original formation. The formation is the universal seen first in the original stand, and then, in its reappearance after the rout. One of his astronomical examples is to imagine an observer placed over the planetary system and seeing the earth blocking the sun's light from the moon, and then recognizing that it must always be so in a lunar eclipse.
If this strikes the reader as an extremely compressed and phenomenological account of the methods of agreement and difference, so be it. My concern here is to point out that these premises are to be what, twenty-three centuries later, we call 'empirical'-even 'verifiable' in the rough sense of the early use of that word. That we are not so sanguine as Aristotle about the frequency of the success of such methods is, perhaps, the result of the great deal of experience mankind has had since then in using and further perfecting them. In any case, with the empirical character of these premises, we find another of the requirements of the Hempel and Oppenheim metatheory shared with its ancient and honorable predecessor.
All in all, therefore, the two have in common their most outstanding features, which is remarkable considering the enormous period of history which separates them. Most important, and in some ways the most remarkable of all, is that both model science on the deductive process itself. In Aristotle's version, this promises to enable him to provide science with what he sees as its most important qualities: certainty and necessity. In that of Hempel and Oppenheim these ideals have become attenuated, although they seem to remain motivating, if tacit, elements, as in the project of logical atomism, to which the deductive-nomological theory is related.
Yet, while the practice of the scientific enterprise from ancient times to our own has occasionally reached truly startling successes of long term accuracy of predictions in physical geometry, astronomy, physics, and even biology-successes which may lead their practitioners to conclude they have reached both certainty and necessity in these realms-the actual details of the history of science lead to a more sober view. For although our methods are not nearly so hopeless as Feyerabend would have us think, our powers of intuiting the universal from the particular do not warrant the unlimited confidence Aristotle (and, much later, Husserl) placed in them either. The history of science, whatever else we may think of it, is also a history of our errors, and we have no reason to believe that our posterity will find this situation to change.
Further, we know the importance of probabilistic reasoning, and that the exigencies of human action often call for us to proceed on the basis of the "best" knowledge we can get in the circumstances. However, 'best' is a comparative term, and is seldom fulfilled by knowledge that deserves to be called 'certain', nor the unfailing embodiment of even natural necessities. Yet to reject such knowledge as "unscientific" would not only call upon us to thrust out of the pale a large portion of what is taken to be science today, but would also hinder us from rational action, which can seldom wait until "perfect" knowledge is in hand.
That brings us to ask what Aristotle himself meant by the term 'certain'. Unlike the case of 'necessity', the texts we have yield no explicit answer, so we must fall back on his usage and some guesswork. My own guess is that he would agree with what has just been said, not only because he has his own ideas about chance in nature, although these are put in teleological terms, but because his examples of scientific knowledge include such cases as concluding that a person has negotiated a loan from his banker as a result of first seeing them in conversation, and then seeing the banker hand the first party a full purse. This sort of transaction, as viewed from a distance, is so clearly subject to errors of misunderstanding and misinterpretation that it could only be considered as probable, likely, or warranting action which does not risk much. To treat it as scientific, and, hence, deserving to be called 'certain' as well, suggests that Aristotle is thinking of a kind of certainty that is far less than infallibility, although of a sort which may justify certain actions, much in the same way as, later, Daniel Bernoulli used the concept of 'moral certainty'. If so, we can surmise Aristotle would not be unhappy with Hempel's accommodation of probabilistic reasoning as an alternative in some circumstances to the original deductive-nomological view. But, more importantly, it would mean that the certainty of a scientific syllogism could fall short of infallibility.
However that may be, for these and for other reasons which fall outside the scope of this essay, it may be useful to ask what function deduction might serve in the sciences if, contrary to both of these metatheories, we set it aside as the very model of knowledge itself. For both of them, I believe, contain the answer implicitly. The deductions in each begin with laws, axioms, postulates, or premises which are not themselves logical truths. They are laws which, in Galileo's terms, could be set aside by the extraordinary power of God. Natural science is possible to the extent He abstains from such actions, Galileo thought. But these are different from logical truths, for even God lacks the power to make them false. Or, in Hume's terms, they are premises which can be denied without self-contradiction. We arrive at them, well or ill, through a fallible process of observation, reflection, and surmise about nature. When we are able to use them successfully as the foundation for a deductive process, we arrive at conclusions which, because they are valid, we cannot deny without self-contradiction, provided we accept those premises. They may be general or particular in nature, and, may accord or conflict with future observations. Which of these they do has a bearing on the possible truth of the premises from which we started, and those observations can play that role because the deductive process guarantees the necessity of the conclusion given those premises. If the observation is in conflict with that conclusion, their necessary connection warrants our rejection of the premises. Hence the logical necessity serves to enable us to articulate the contents of our theories, but the truth of these theories rests on how well they comport with our experience of the world. It would be well to remind ourselves, also, that this necessity is not our only guide within theories. Some, which contain logical anomalies, avoid these in arbitrary ways, and others confine themselves to probabilistic considerations. In any case, we are without grounds for supposing either that logically necessary connections within theories are models of natural necessities, nor that deduction is the appropriate ideal of the process of scientific inquiry.
Among the consequences of such a view is that it dispenses with one of the needs for the requirement, the same in Aristotle and Hempel, that the premises of a scientific deduction be true. When one recognizes that the intuitions of universals are neither so quick nor so easy as Aristotle suggests, and that the premises are thought true precisely because we find what they lead us to, the prior requirement of their truth begins to appear otiose or circular. Along with other considerations, the above analysis is a step in the direction of showing there is no need for it in those terms.
(1) Wallace, William A., Galileo and His Sources, Princeton, Princeton University Press, 1984.
(2) Hempel, Carl G, Aspects of Scientific Explanation And Other Essays in the Philosophy of Science, New York, The Free Press, 1965.
(3) Aristotle, Posterior Analytics.
(4) Hume, David, A Treatise on Human Nature, London, J M Dent & Sons, Ltd., 1949 (originally published 1738).
(5) Galileo Galilei, Logical Questions, MS 27; See Wallace, op cit., p 112.