The Lagoon Page 13
THE
INSTRUMENTS
ELAPHOS – RED DEER – CERVUS ELEPHAS
XLII
EVERY SCIENTIST HAS a conception of what constitutes ‘good science’. It is a sense, as firmly held as it is poorly articulated, of which causal claims are sound and which aren’t. It’s not, of course, that scientists necessarily agree on the soundness of any given claim. If you have ever contemplated the reviews of a manuscript, submitted with such hope to Nature or Science (for at the gates to these journals hope truly does spring eternal), you will know that your peers’ notions of what constitute sound causal claims are often very different from your own and really quite confused.
Aristotle also faced the problem of securing causal knowledge from observation, but he faced it alone. Behind him lay generations of speculative theories about the causes of the natural world; at his feet stretched the world itself. He saw, and saw as no one before him had, the need for a way to connect them. So he developed one.
In Book I of Historia animalium he alludes to it. First, he says, we have to get the facts about the different features of animals, then we have to work out their causes. Doing things in that order, he continues, will make the subject and target of our demonstrations clear. It seems like a rather banal introductory statement. It isn’t. For, when Aristotle talks of ‘demonstration’, he means an intellectual structure of daedal complexity whose foundations are sunk in metaphysical bedrock and whose pillars are constructed of steely formal logic. He means his scientific method.
XLIII
ORGANON MEANS ‘TOOL’ or ‘instrument’.* It’s the title often given to six of Aristotle’s books. It’s an apt one for they are tools for the production of knowledge. One of these books, the Posterior Analytics, contains his scientific method.
Aristotle distinguishes the rules for debating opinions from the rules for constructing scientific explanations. The first he called ‘dialectic’, the latter ‘demonstration’ (the Greek is apodeixis). By ‘demonstration’ he means exactly what a modern scientist means when he says, ‘we have demonstrated that A is the cause of B’ – that is, he and his collaborators have shown that the presence of A is a necessary and sufficient condition for B. He had a high notion of the power of scientific demonstrations: he thought that they delivered truth. That’s because they are the products of logical operations. Aristotle invented the theory of inferential logic known as his syllogistic. It was his greatest technical achievement and dominated the subject for millennia even if it was incomplete and, in parts, wrong. His syllogistic aimed to deduce new conclusions from established premises where the premises are propositions that contain a subject and a predicate, e.g. ‘All octopuses [subject] are eight legged [predicate].’ To analyse such statements he invented a formalism that substituted letters for the terms, e.g. ‘All A are B.’ This formalism allowed him to speak generally of all propositions of a given form, manipulate them and derive the many results that he did.
For Aristotle, a scientific demonstration rests upon a syllogism. But to qualify as a demonstration a syllogism must meet certain conditions. First, the premises of the syllogism must obviously be true. Second, the premises of the syllogism must be more immediate, more empirically apparent, than its conclusion (at least in natural science as distinct from geometry). Third, it must concern universals rather than particulars. In fact, Aristotle thinks that it’s impossible to have scientific knowledge of individuals. To say that this octopus has eight legs gets us nowhere; scientific knowledge can only begin once we’ve established that all octopuses have eight legs – or at least that all normal octopuses do. Finally only universal, assertive and assertoric propositions can form the basis of demonstrations: ‘All A are B; all B are C; therefore all A are C.’ Logicians refer to such syllogisms as being in the ‘mood’ of ‘Barbara’.
Such logical strictures may seem remote from the modern scientific method and so, in a way, they are. But Aristotle’s reason for grounding scientific knowledge in his syllogistic is, I believe, one familiar to any modern scientist. I suggested that, far from being a natural history or a taxonomy, Historia animalium is a search for associations among the traits that animals possess; that it is, in fact, a data trawl. His syllogistic, then, provides a powerful way of securing those associations – of showing that they are true. Secure associations, in turn, demand causal explanations – which his syllogistic also identifies.
A lovely bit of modern biology can be pressed to illustrate this strategy. In the bays and estuaries of Northern Europe and America there lives a small fish called the three-spined stickleback, Gasterosteus aculeatus. The binomial translates as ‘bony stomach with spines’, which is apt since it has a pelvic girdle with spines on its belly. Although the stickleback usually lives in the sea, it’s a versatile fish and, in the last ten thousand years, has invaded freshwater lakes many times. The lake fish have evolved rapidly and have lost their pelvic girdles and spines. Recently, several beautiful studies have shown that the lake sticklebacks carry a mutation in an enhancer of a gene called Pitx1, a mutation that their marine relations do not have. Had he known them, Aristotle would have surely wondered about the connection between these facts, but before investigating it, he might have proved its existence, so:
All lake sticklebacks lack pelvic spines;
All sticklebacks that lack pelvic spines have a Pitx1 mutation, therefore,
All lake sticklebacks have a Pitx1 mutation.
The truth of this syllogism guarantees a connection between several stickleback predicates: living in a lake, a lack of pelvic spines, and the presence of the Pitx1 mutation. A demonstrative syllogism implies not just a logical connection, however, but a causal one that can be expressed as a ‘definition’. We usually think of a ‘definition’ as a description of a word – that is, a nominal definition: ‘a lake stickleback is one that lacks pelvic spines’. Aristotle, however, would point to the middle term of the syllogism – the Pitx1 mutation – as the causal link and give a definition of the following sort: ‘a lake stickleback is one that lacks pelvic spines because it has a Pitx1 mutation’. That’s demonstration, he would say; that’s science. Such definitions are the logos – the ‘essence’ or ‘formula’ of the things he studied. So his scientific method turns out to be a way of expressing the fundamental causal identities of things shorn of all incidental, and hence scientifically uninteresting, features.
STICKLEBACKS – GASTEROSTEUS ACULEATUS ABOVE: MARINE (ANADROMOUS) MORPH FROM CALIFORNIA BELOW: LAKE (BENTHIC) MORPH FROM PAXTON LAKE, BRITISH COLUMBIA
I have been speaking of Aristotle’s ‘theory of demonstration’ as if there is just one of them. In the Posterior Analytics he certainly devotes most space to the method I have sketched. But he also allows that there are other modes of demonstration – though he’s quite vague about how they work. In The Parts of Animals he says that the methods of demonstration in natural science are actually different from those in ‘theoretical sciences’ such as geometry. In biology, he suggests that we should start with the end – the teleological purpose – of an animal and work our way deductively back to infer how the animal’s various parts serve that purpose. Such demonstrations can also, with some twisting, be couched in syllogistic terms.
Although demonstration is the beating heart of his scientific method, Aristotle acknowledges that science rests on various indemonstrable statements. These include the axioms of his syllogistic as well as various primary definitions. For example, geometry requires a definition of ‘spatial magnitude’ and arithmetic a definition of ‘unit’. The axioms and primary definitions of biology are less obvious but include statements such as ‘nature does nothing in vain’ – an apophthegm that he puts to hard use. Aristotle isn’t clear how such ideas can be justified, and suggests that their truth is just apparent by induction (epagōgē), but argues nonetheless that they’re needed if science is to get off the ground.
This is certainly right. In our day there are people who think, all evidence to the co
ntrary, that science is just one system of beliefs among many. Aristotle had to contend with them too. Some people, he says, claim that scientific knowledge is impossible because any inference we make must rely on some previous inference, and that must rely on another, and so on to infinity so that, ultimately, we can know nothing. Other people, he continues, claim that anything can be demonstrated: everything is true hence nothing is true.
Aristotle recognizes that both thoughts are lethal to the possibility of science, and he deals with them briskly. No, there isn’t an infinite regress of inferences, nor is it true that everything can be demonstrated, because our arguments ultimately begin with axioms and our perception of the empirical world. His language is combative. It has to be. He has to show against his opponents, not just Plato but the sophists with their razor-sharp dialectic, that it is possible to extract real knowledge from the sensible world. We may wonder whether he succeeded. Modern science rests on fundamental axioms no less than Aristotelian science, and scientists mostly justify them by the fact that they work. But Aristotle could hardly defend his assumptions, as a modern scientist can, by flicking on a light.*
XLIV
ARISTOTLE’S THEORY OF demonstration isn’t without its problems. Every science undergraduate learns that ‘correlation does not equal causation’. Nor does it: which is why we do experiments. To their get their work published in Science, Chan et al. not only had to show that the Pitx1 mutation is coextensive with a missing pelvic spine; they also had to show experimentally that the Pitx1 mutation really does cause spine loss – and (rather heroically) made a transgenic stickleback to do so. Aristotle, who never did controlled experiments, is much less cautious. Having identified a coextensive set of features, he tends to jump to the causal relationship. Perhaps it can be shown syllogistically that having horns, an incomplete set of teeth and many stomachs is completely coextensive (i.e. that ruminants and only ruminants share these features), but are they really causally related in the direct way that Aristotle says they are? In the absence of other evidence, we may be inclined to doubt it.
Another problem lies in the direction of causation. ‘Horn-bearing animals have many stomachs because they do not have a complete set of teeth.’ Maybe – but why not the other way around? Surely it’s just as plausible that they have incomplete teeth because they have many stomachs? In the case of the sticklebacks we are confident that the arrow of causation runs: invade lakes → gain Pitx1 mutation → lose pelvic spines because two theories, the theory of evolution by natural selection and the fundamental dogma of molecular biology, tell us that it must be so and not the other way around. Aristotle considers the problem in the Posterior Analytics but doesn’t solve it. In practice the directions in which he aims his causal arrows also depend on all sorts of theoretical beliefs independent of the syllogisms upon which they are based.
Finally, Aristotle argues that all demonstrative claims can be stated in the form of a syllogism. Some certainly can, but all? Much modern science depends on mathematical models that posit quantitative phenomena and relations. Tests of such models require measurement and a probabilistic theory of inference. Aristotle’s models, by contrast, are invariably qualitative and he seems never to have measured a thing.
Some scholars have suggested that when we open his actual scientific works, The Parts of Animals say, we should see Aristotle’s scientific machine at work; that we should see axioms and syllogisms neatly arrayed as in a treatise of geometrical proofs. They are puzzled by the fact that we don’t. All the treatises are a messy mixture of data, arguments and conclusions (a messiness that, given its pervasiveness, cannot be blamed on their having been scrambled in transmission). If we look hard enough, traces of Aristotle’s machine can be found throughout his scientific works. They may not contain syllogisms, but they contain their results. His works are filled with causal definitions: ‘The horn-bearing animals have many stomachs because they do not have a complete set of teeth’; ‘selachians have skin that is rough because they have cartilaginous skeletons’; ‘the ostrich has toes rather than hooves because it is large’ – all these are quotes from The Parts of Animals. Still, he never spells out the syllogisms themselves. Why not?
Perhaps he felt he didn’t need to. Or perhaps he felt that he’d only do so when he understood the causes of everything, once his work was complete, but he never did, it never was, and so he didn’t. But I think that he didn’t express his causal claims as syllogisms because he couldn’t. In Aristotle’s demonstrative logic the predicates of his syllogisms are typically coextensive, but in real animals they’re not. Horns, multiple stomachs, cloven hooves and missing teeth merely tend to go together. The camel has all of these features except one: horns. The problem with syllogistic reasoning is the same problem that monothetic classification has: some creature or other always spoils the show.
It is the problem that our theory of probabilistic inference – statistics – addresses. When we search for associations among attributes, we demand that they be not fully coextensive but only correlated. Indeed, Chan et al. do not claim that living in lakes, lack of pelvic spines and possession of a Pitx1 mutation are fully coextensive; they show (remarkably strong) statistical associations and warn that other genetic factors may be at work. Aristotle’s solution is simply to say ‘many [italics mine] of the cloven-hoofed animals have horns’ and then give a patently ad hoc explanation for why the camel doesn’t. In fact, he’ll often assert that some association or other is true ‘for the most part’.
I think that the Posterior Analytics sets a gold standard for scientific knowledge. It establishes the conditions under which we really know a given causal relationship to be true. But, in practice, natural science – and by this I mean, as Aristotle did, the study of the natural world rather than mathematical or geometric objects – rarely admits of rigorous proofs. Most of it depends on much weaker forms of inference, the claim that this explanation is the best one around. Data are incomplete, results are tentative, causes are complicated and inferential gaps yawn at every turn. It is so for us; it was for Aristotle too. The result is that his practice is more casual and dialectical or, to give it a positive spin, much more reasonable and probabilistic than the rigours outlined in the Posterior Analytics. In the Nicomachean Ethics (for ethics is an Aristotelian science as well, even if not a natural science) this ambiguity is explicit:
Here, as in all other cases, we must set down the appearances [phainomena] and, first working through the puzzles, in this way go on to show, if possible, the truth of all the beliefs we hold about these experiences; and if this is not possible, the truth of the greatest number and most authoritative. For if the difficulties are resolved and the beliefs are left in place, we will have done enough demonstration.
Untangled, this amounts to the following: start with some ordered information about some part of the world, identify the problems that it presents, collect the best explanations for those problems and then demonstrate which of those explanations are coherent and which aren’t. Those left standing are the answer.
Although this passage appears to be about ‘demonstration’ it actually suggests a quite different procedure from the theory of the Posterior Analytics. That’s shown by Aristotle’s use of the word phainomena. The syllogistic theory of demonstration requires that the premises of the argument be indisputably true. If they’re not, then you can’t prove anything. But phainomena don’t have that kind of epistemological certainty since, according to Aristotle, they include opinions – the opinions of ‘wise’ and ‘reputable’ people to be sure – but opinions nevertheless. We are in the realm of dialectic, which, it turns out, isn’t that far from demonstration after all. Most of his biology lies in this twilight realm.
That is the consequence of the world’s messiness. But Aristotle has another, deeper strategy for coping with a lack of coextension. He recognizes that if a group of individuals (or kinds) share some feature, but that this feature is differentially associated with other features, then multi
ple causes may be at work. In such cases, he suggests, we should divide our classes and search for the common cause, and keep doing so until we have identified a single cause for each.
Quite a lot of modern biomedical science follows exactly this recipe. Melanomas of the uvea – a part of the eye – afflict about one in 167,000 Americans. How shall we aid them? The answer – one upon which researchers have bet their working lives – is by searching for the cause of the disease, its definition, its formula, its essence. It’s a cancer so it’s probably caused by a particular mutation or combination of mutations. But there are at least two ‘species’ of uveal melanoma, each of which has its own mutational ‘formula’. Class 2 tumours have mutations in a gene called BAP1, while Class 1 tumours do not. This has consequences since where Class 1 tumours can be treated, Class 2 tumours currently cannot, are aggressively malignant and nearly always kill. Even these two classes are heterogeneous and can be subdivided further by the presence and absence of other mutations. And so oncogeneticists, searching for the causes of this disease – or rather, of these several diseases – chase the formulas ever deeper, subdividing as they go. Actually, Aristotle alludes to just such a case: