The aim of this book is to analyse and defend the claim that the first four chapters of Darwin’s Origin constitute an argument by analogy from artificial selection to natural selection, situating that argument in Darwin’s thought as a whole: just as human beings by their selective practices in domestic settings can make new varieties of plants and animals, so the struggle for existence in the wild can make new varieties and even new species of plants and animals. This claim has been frequently made, but also latterly contested. However, both the defenders and the opponents rarely spell out in detail what the argument is supposed to be, and, insofar as they do so, usually work with an inappropriate account of what an argument by analogy is thought to be.

Therefore, before turning to Darwin himself, we need, in this chapter and the next, to examine the idea of an argument by analogy. We begin in classical Greece where the concept of analogy was introduced, before turning in the next chapter to the emergence of a completely different conception of analogy, and with it a completely different account of argument by analogy. We shall argue that although the later account has become the most popular understanding of ‘argument by analogy’, it is the classical account which is the appropriate one to account for the text of the Origin.

The point is that the word ‘analogy’ has historically been understood in two quite different ways. The word was initially introduced in Pythagorean mathematics (‘ἀναλογια’) and then extended into the empirical domain, above all by Aristotle. Here, the word always designated a proportionality (‘A is to B as C is to D’), and the interest was in the rich variety of uses to which appeals to analogies of this kind could be put, as against simple similarities (‘A and B share some intrinsic properties’), whose uses were very limited. The contrast between analogy and simple similarity was always observed and insisted upon. However, beginning in the seventeenth century, in large part as a reaction against mediaeval scholasticism, this contrast was ignored – or, at most, it was noted that this distinction was important but only in mathematics. Elsewhere ‘analogy’ was treated as a near synonym for ‘similarity’. Insofar as the two were distinguished, it was not in accord with Greek usage, but talking of ‘analogy’ was treated as most appropriate when A and B shared several similarities.

Corresponding to these two different ways of understanding the word ‘analogy’ were two completely different accounts of what constituted an argument by analogy. Without at this stage analysing them in detail, we may look at the following two supposed uses of ‘argument by analogy’. Consider first the following ‘anti-democratic’ argument ascribed by Aristotle to Socrates,Footnote ¹ where Socrates is protesting against the use of a form of lottery in the appointment of certain offices of state (a procedure deemed ‘democratic’ because every citizen had the same chance of holding office):

When we realise why it would be absurd to choose athletes or helmsman by lot, since there are skills vital to being a successful athlete or helmsman, we see that by analogy it is absurd to choose magistrates by lot. What we have here is an argument by analogy that is valid, given the tacit premise that there is a range of skills necessary to carry out the tasks of a magistrate successfully.

Contrast this with:

Both of these arguments clearly need tightening up: in the first case, we need to show that the analogy holds in all relevant respects, and in the second, we need, for instance, to find a way to exclude characteristics that are irrelevant to the point at issue. But even after tightening up, what we have here are two radically different arguments. The first argument can be developed into a fully valid argument, but the second, though not worthless – it is obviously sensible to avoid the berry – is at best a probabilistic argument, beset with difficulties in attempting, for example, to quantify the probabilities involved. Because of this, it is clearly crucial when we come to examine Darwin’s presentation of his argument by analogy in the first four chapters of the Origin to be clear which of these two patterns of argument is involved. This is particularly true since the vast majority of commentators, both those claiming that these chapters do constitute an argument by analogy and those who contest this, have assumed that there is thereby meant an argument of the second sort, whereas it is the central contention of this book that a careful examination of Darwin’s text shows him as presenting a near perfect argument of the first sort.

Therefore, before turning to our main subject – an exegesis of Darwin’s use of the analogy – we look further at the two different forms of argument. In this chapter, we look at the introduction of analogy as proportionality in classical Greece, including the prototype of the first form of argument by analogy, the development in Euclid VI of the theory of similar triangles, and hence, by extension, the simplest of all analogical models – the scale model. Then in the next chapter, we look at the centuries immediately prior to the Origin, where we find two things: the emergence and eventual great popularity of the second form of argument, while alongside this we shall see continued exploration of analogy as classically understood, culminating in the work of Richard Whately, and following him John Stuart Mill.

The First Introduction of the Concept of Analogy

Euclid V: Analogy and Incommensurable Magnitudes

The analogical relationship, interpreted as the identity of the relative magnitudes of two lengths ($\mathrm{A}/\mathrm{B}=\mathrm{C}/\mathrm{D}$), first appears in Greek mathematics as an element in Pythagoras’ theory of musical harmonics. However, for our purposes, we are concerned with a later use in which it becomes a key concept in Euclid V where it has a fundamental role in the solution to the problem posed by the discovery of incommensurable magnitudes, thereby marking a key stage in the development of mathematics.

The problem of incommensurable magnitudes arises as follows. We start out with the Pythagorean theory of relative magnitude, which says that we can specify the relative magnitude of any two lengths by two whole numbers (at this stage the phrase ‘whole numbers’ is pleonastic – the only numbers recognised are the positive whole numbers). Thus, for any two lengths, A and B, (∃m)(∃n)($\mathrm{mA}=\mathrm{nB}$), where, importantly, this formula can be given a straightforward geometrical interpretation: if you extend A to m times its length and B to n times its length, you arrive at two lines that are the same in length.

However, this simple theory received a death blow with the discovery of incommensurable magnitudes – the discovery that it was possible to construct a pair of lines for which it was impossible to satisfy this formula. The proof of this was a simple corollary of Pythagoras’ theorem. Consider an isosceles right-angled triangle, with hypotenuse of length H, sides of length S. By Pythagoras’ theorem, ${\mathrm{H}}^2=2{\mathrm{S}}^2$. If the Pythagorean theory of magnitude is correct, there exist two numbers p and q such that $\mathrm{H}/\mathrm{S}=\mathrm{p}/\mathrm{q}$ where p and q have no common factors, from which it follows that ${\mathrm{p}}^2=2{\mathrm{q}}^2$. Now, the square of an odd number is odd, and of an even number even, so that p must be even $=2\mathrm{r}$, say, giving us $4{\mathrm{r}}^2=2{\mathrm{q}}^2$, or $4{\mathrm{r}}^2=2{\mathrm{q}}^2$, giving us in turn that q must also be even, contradicting our assumption that p and q have no common factors.

This discovery constituted what may be regarded as the first crisis in the foundation of mathematics: it was now possible to specify lengths for which there could be no answer to the question of their relative magnitude. The task was thus to replace the Pythagorean theory of magnitude by one that was equally applicable to incommensurable and commensurable magnitudes. The two mathematicians who proposed solutions to this problem were Theaetetus,Footnote ² and Eudoxus of Cnidus. It is the latter who concerns us here, and specifically the opening definitions in Euclid Book V that have been traditionally ascribed to Eudoxus. The most relevant definitions for our purposes are the following:

Definition 3. Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity.

Definition 5. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second and the fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth, and if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth, and if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth.

Definition 6. Magnitudes which have the same ratio are called proportionals (analogous). When four magnitudes are proportionals (analogous), it is usually expressed by saying the first is to the second as the third is to the fourth.

Definition 8. Analogy, or proportion, is the similitude (equality) of two ratios.

In the first of these, definition 3, where initially the notion of a ratio is left to be specified further in the subsequent definitions, the important thing to notice is the phrase ‘of the same kind to one another’ – you can talk of the ratio of one length to another length, or the ratio of one time to another time, but not of the ratio of a time to a length. It is the abandonment of this restriction when we come to extend analogy beyond its mathematical application that marks what is the most significant difference between the mathematical and the non-mathematical concepts of analogy.

The key definition is definition 5, which may be easier to understand if we render it in modern notation:

Given four magnitudes A, B, C and D, $\mathrm{A}/\mathrm{B}=\mathrm{C}/\mathrm{D}$ if and only if the following condition is satisfied:

$\left(\forall \mathrm{m}\right)\left(\forall \mathrm{n}\right)(\left(\mathrm{m}\times \mathrm{A}>\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}>\mathrm{n}\times \mathrm{D}\right)$

$\&\left(\mathrm{m}\times \mathrm{A}<\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}<\mathrm{n}\times \mathrm{D}\right)$

$\&\left(\mathrm{m}\times \mathrm{A}=\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}=\mathrm{n}\times \mathrm{D}\right))$

where the quantifiers range over the natural numbers.

The strategy adopted here anticipates the strategy that was used in the nineteenth century to define real numbers. There you specify a real number by specifying which rational numbers are greater than it, which less, and which equal to it. Here you specify a relative magnitude by specifying which commensurable relative magnitudes are greater than it, which less, and which equal to it. The basic strategy here, which represents the high point of Greek mathematics and paves the way for modern mathematics, may be put as follows: it has been shown that we cannot in general specify the relative magnitude of any two lengths by citing a simple arithmetical formula for that magnitude, but we can nevertheless specify the relative magnitude of an arbitrary pair of lengths in the following sense. We can say when that relative magnitude is the same or different from the relative magnitude of any other pair of lengths. That is to say, we give the truth conditions of the formula $\mathrm{A}/\mathrm{B}=\mathrm{C}/\mathrm{D}$. This breakthrough was widely celebrated and led to a widespread interest in the concept of analogy, including, as we shall see, interest in the possibility of extending the concept beyond the realm of mathematics.

Of course, the central mathematical interest here is the way that it gives us a general theory of magnitude at an altogether more sophisticated level than the Pythagorean theory that it replaces. However, for our purposes, we are concerned with other features of the formula $\mathrm{A}/\mathrm{B}=\mathrm{C}/\mathrm{D}$ that emerge in the course of the subsequent mathematical investigations. Primarily we are interested in the way in which in Euclid Book VI this formula is used in the construction of analogical models and the development of a style of argument by analogy that will concern us throughout this book, including providing a clue to the form of the argument of the Origin. But before turning to that, there are two other features of the formula $\mathrm{A}/\mathrm{B}=\mathrm{C}/\mathrm{D}$, as defined by Eudoxus, which are also important for our purposes.

In the first place, one key characteristic of the idea of a ratio, as we have been looking at it so far, is the restriction contained in the phrase ‘magnitudes of the same kind’. So that, for instance, it permits us to compare one length to another, one time to another, one volume to another and so on, but not one length to a time. However, we frequently in fact want to compare things in different categories. To take a simple example, to arrive at a concept of velocity requires us to compare the distance travelled to the time taken. It is the concept of analogy, as just explained in definition 5, that permits us to make sense of such comparisons between things in different categories. If we look again at that definition

$\left(\forall \mathrm{m}\right)\left(\forall \mathrm{n}\right)(\left(\mathrm{m}\times \mathrm{A}>\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}>\mathrm{n}\times \mathrm{D}\right)$

$\&\left(\mathrm{m}\times \mathrm{A}<\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}<\mathrm{n}\times \mathrm{D}\right)$

$\&\left(\mathrm{m}\times \mathrm{A}=\mathrm{n}\times \mathrm{B}\to \mathrm{m}\times \mathrm{C}=\mathrm{n}\times \mathrm{D}\right))$

we see that although we can only give a meaningful interpretation of it if A and B are ‘of the same kind’, there is no reason why A and C need be of the same kind. Thus whereas a theory of magnitude expressed purely in terms of ratios would make it impossible to compare a distance with a time, once we replace the Pythagorean theory with a theory expressed in terms of analogy, we can make sense of comparisons between things in different categories, and thus, e.g., find it possible to construct a concept of velocity, which precisely rests on comparing the distance travelled and the time taken. This leads us to an idea that, as we shall see, is stressed by Aristotle and indeed is crucial for making sense of subsequent applications of analogy, including those which we find in the Origin: there are two different ways of comparing two entities A and B. The first, a direct comparison, only enables us to compare A and B if they are the same sort of thing, but the second, an indirect comparison resting upon an introduction of two other terms, C and D, and using the formula ‘A is to C as B is to D’, enables us to compare entities that, as Aristotle puts it, are remote, whether a distance to a time, an elephant’s trunk to a hand, the opening chapters of a book to the opening shots in a battle, or a desert permitting only the most drought-resistant plants to survive to a racehorse owner permitting only the fastest horses to go to stud.

Archytas of Tarentum: Analogy and Definition

Almost all of the ideas necessary for the analysis of the argument of the Origin can already be derived from that which we have found in Euclid, and that argument is simply an application of the argument by analogy that we found in the case of similar triangles. However, within Euclid, the formula ‘A is to B as C is to D’ is always to be interpreted in purely mathematical terms – ‘the ratio of A to $\mathrm{B}=$ the ratio of C to D’. For our purposes, we need to be able to give other, empirical, interpretations of this formula. We therefore need to look at subsequent developments in Greek thought to see whether and how we can extrapolate from the mathematical case to empirical interpretations of the analogical formula. Above all, we need to look at Aristotle’s uses of analogy.

We look first at a use of analogy that is not prefigured in Euclid – the use of analogy to generate and define new concepts. For this, we need to consider Archytas of Tarentum. Archytas (428–347 BC) was a Pythagorean mathematician and statesman. Although only a few fragments of his writings survive, he is an important figure in the history of the concept of analogy. Not only was he a major influence on both Plato and Aristotle in their exploitations of analogy, it is in the slender evidence that survives that we find for the first time someone who is exploring the possibility of extending the concept of analogy beyond its original mathematical use.

His primary contribution, in the fragments for which we have evidence, is in the theory of definition, contained in these two quotations from Aristotle:

Taking these two passages together, we may see Archytas as proposing a new way of defining concepts based upon analogy. We specify a concept not by noting properties belonging to all objects falling under that concept, but by grouping together as falling under a single concept a range of objects that are related analogically. Thus, to take one of Archytas’ examples, the concept calm. We may talk of a calm sea, and a calm sky – and further of a calm mind, or of streets that are calm after a riot. These extremely heterogeneous entities have no obvious properties in common, but windlessness is to the sky as wavelessness is to the sea, as contentment is to the mind. Such concepts are extremely widespread, including open, long, difficult, principle, and typically permit us to group together objects that are different in kind (a long novel, a long pause, a long railway …). It is clear that Archytas’ approach has far greater explanatory power for such concepts than the frequent superficial appeal to ‘family resemblances’.

This represents a major advance in the theory of definition. The then standard account had been offered by Plato – the method of division. There you began with a class and then subdivided until you had specified the concept required, producing definitions such as ‘man is a rational, sensitive, animate substance’. Although this is an excellent start in the theory of definition, it is extremely limited in its application and very few scientifically fruitful concepts can be defined by this means. By contrast, a wide range of important concepts, both within and outside science, are susceptible of being explained along the lines outlined by Archytas. A major part of the greater power of such definitions – the part that will be stressed by Aristotle – is the capacity of such definitions to gather together and make scientifically significant comparisons between highly disparate phenomena.

When we come to the Origin, we shall find that two of Darwin’s central concepts, ‘struggle’ and ‘select’, are paradigm cases of concepts that are best handled by Archytas’ method.

Plato: The Informal Use of Analogy

Plato was a friend of Archytas, and was clearly familiar with his work.Footnote ⁵ There is, however, not the rigorous use of analogy that we find either in the mathematics or that we shall encounter in Aristotle. There is also no theoretical discussion of the concept. What we find instead are several informal arguments by analogy based on an intuitive use of analogical models, such as ‘the cave’Footnote ⁶ and ‘the line’.Footnote ⁷ By looking at one, the most famous of these, we can see how we may transpose the idea of argument by analogy to a non-mathematical setting. This argument may be used to give us a preliminary indication of the form such an argument should take. Also, as it stands, Plato’s argument is at best suggestive, and by seeing why it falls short of being a fully rigorous argument, we may use it to identify those features that would be required of such arguments by analogy to make them watertight.

The argument that we shall consider is the extended argument that constitutes the Republic. This argument is intended to demonstrate that it is better to be just than unjust. It is put forward as a reply to a challenge made by Glaucon and Adeimantus, who argue that, the nature of the world being such as it is, it is the perfectly unjust man who flourishes, but not only that, since he needs to appear to be just to carry out his nefarious schemes, he will become a benefactor of humankind. By contrast the perfectly just man will be condemned to a life of misery, and since he will not be concerned to appear to be just, will be constrained from behaving in ways that are to the obvious benefit of the rest of humankind.

The argument rests on using the state as an analogical model for the soul. We are then invited to infer that the ideal state having such-and-such a structure, so too the ideal for the soul will have an analogically corresponding state. The state is seen as having three components – a ruler, a group whose task is to ensure that the people obey the laws of the ruler, and the people. In the ideal state, the ruler will be the philosopher king, who knows ‘the form of the good’ – what is right should be done, and then there are guardians who have true beliefs about what should be done and whose task is to make the general public carry out the wishes of the king. It is then argued that the soul has also three components – reason, a ‘spirited’ part, and appetite. This is shown by the fact that we are sometimes torn between different courses of action, and in particular between what reason dictates that we ought to do, and what our appetites tell us that we want to do, and, further that in such cases we can by an act of will control our appetites. This enables us to use the state as an analogical model for the human soul. We then argue that just as the best state – the just state – is one in which the philosopher king is in power and the guardians ensure his laws are obeyed, so the best soul – the just soul – is one in which reason always controls the passions.

There is clearly much that is questionable about this argument. Is a society in which the majority of the people have no control over their lives and are simply made to do what the ruler dictates really an ideal society? However, we are concerned with the question how well the argument stands up as an analogical argument. That will give us a preliminary indication of what needs attending to in assessing any purported analogical argument. Even if we grant Plato his premise that he has shown the republic to be the just society – that is not our present concern, which is whether if we accept that as a premise, he is entitled to infer his conclusions as to what it is for the soul to be just. If we were to accept Plato’s argument we would clearly need to be satisfied about two things. Firstly, we would need to ask whether we have here a genuine case of an analogical model. That is to say, is it really the case that the relation between a ruler and the citizens was the same as the relation between reason and appetites in the soul: that the ruler: the citizens :: reason: appetite? To be convinced of that we would need to accept Plato’s argument that the best way to explain being torn in different directions as to what to do is to hypostasise three different aspects of the soul, in such a way that we can take seriously the idea of one of these aspects governing another. Secondly, once we had established that there was indeed an analogical model here, we would then need to show that being just was a feature that was invariant under analogy – that if the state were just, it would follow that a soul with the corresponding structure would also be just. It is here perhaps that the argument is most vulnerable: there is something like an equivocation on the word ‘just’ here. We are talking about something very different when we describe a state as just and when we talk about an individual as just. For a state to be just is for there to be just treatment of the citizens within the society, for instance, for there to be equality before the law; however, for an individual to be just concerns their relations with other people: in one case we are concerned with the internal relations within the state, in the other with the external relations of the individual.

Aristotle: Two Ways of Comparing Things

It is in the use that Aristotle makes of the concept of analogy, rather than the more informal uses that we find in Plato, that we find the full potential of the concept once it is extended beyond its mathematical origins. Aristotle shows how appeals to analogy can be made to do important work in research in the varied contexts – in rhetoric, in his researches into living things, in metaphysics, in the theory of justice and in the theory of definition. In each of these cases, he is typically precise and rigorous, with a surefooted understanding of what analogy can, and cannot, do for us. However, for our purposes, we shall not look in detail at each of these particular applications: only two of these applications will prove to be of importance in eventually understanding the role of analogy in the Origin: that of the relation of analogy to metaphor, and that of the question of method in biology.Footnote ⁸ We shall look at Aristotle on metaphor in the course of Chapter 6, and before looking at the biological writings, we shall identify and examine some of the themes that recur in all these applications.

We begin with what may be regarded as a key theoretical statement: ‘Yet a further method of selection is by analogy: for we cannot find a single word applicable to a squid’s pounce, fish spine and bone, although these too possess common properties as if there were a single osseous nature.’Footnote ⁹ In a way this is simply a repetition of what we found in Archytas, but it is worth interpreting it in the context in which Aristotle introduces the idea. The major part of the Posterior Analytics is concerned with definition by the method of division, where a definition proceeds by taking a large class, dividing it, then subdividing until you have specified the class of things that interest you, producing such definitions as ‘Man is a rational, sensitive, animate substance’. He is working here against a Platonic background, in which there were ways of ‘carving nature at the joints’,Footnote ¹⁰ producing natural kinds, and where natural kinds could always be defined by the method of division.

But at the same time, even at the stage of his enquiry represented by the Posterior Analytics, there is something that will assume central significance in the Parts of Animals: even within the science of biology there is a need for concepts that do not pick out natural kinds. He proposes that such concepts can be defined by analogy, along the following lines. We start by defining the species of animals by the method of division, setting up a Porphyry tree branching downwards, with the different species at the bottom. We then cut across the tree picking out functionally corresponding parts of different animals. In the example he gives, we take the example ‘bone’, where we have monkey bone, fishbone and cuttlebone. These are composed of completely different substances and thus do not form a natural kind. They are however analogically related: monkey bone is to monkeys as fishbone is to fishes and as cuttlebone is to cuttlefish, in that in each case we are dealing with substances that can provide the skeletal structure for their host. In order to provide such a skeletal structure, they must share those properties, such as hardness, that are necessary or useful in performing their function. In this way, we arrive at an ‘as-if’ natural kind, which can be the subject of scientific investigation.Footnote ¹¹

The governing idea that runs through all the diverse applications that Aristotle makes of the concept of analogy is that there are two fundamentally different ways of comparing two things, A and B: there is, firstly, making a direct comparison, which is a matter of noting common properties of A and B, and secondly, making an indirect comparison, in which we introduce third and fourth terms, C and D, such that A is to C as B is to D. This contrast is highly flexible and may be adapted in a way that is appropriate to the topic of research. Thus, Aristotle shows how exploitation of this contrast can illuminate questions concerning the nature of justice, explain the difference between successful metaphors and lifeless metaphors, be fundamental to comparative anatomy and throw light on the question what could be meant by equality in the state. In each of these examples, the analogical relation ‘A: B :: C: D’ is to be understood in a way that fits the topic in hand. In every case apart from metaphor, it is clear how the formula is to be interpreted and Aristotle holds rigorously to that interpretation.Footnote ¹³ Thus in the case of justice and equality in the state, Aristotle contrasts arithmetical equality – everyone is paid the same – and analogical equality in which everyone is paid proportionally to their role within society; in the case of metaphor, we have a contrast between metaphors based upon a transfer from species to species or genus to species and metaphors based on analogy; and in his researches into living things there is a contrast between parts of animals that differ by the more and the less and parts of animals that are only related by analogy.

One element in the quotation we are now looking at is the idea that analogical comparison, unlike a direct comparison, permits us to compare ‘genera that are remote’. Here the word ‘remote’ should be read as broadly as one chooses: no matter how different in kind two entities may be, an analogical comparison between them may still be possible. We already saw this when we looked at Euclid, showing how Eudoxus’ definition of analogy permitted us to arrive at a concept of velocity by comparing time taken with distance travelled. When we move outside the mathematical context, everyday examples clearly show this to be true. An opening batsman at cricket, the opening chapter of a book, a chess opening and the opening of a new hospital: here we have four entities that share no obvious intrinsic properties that can nevertheless be fruitfully seen as all openings because of the way that they are related to what is to follow. Aristotle himself will show how this can be exploited, e.g., in his theory of justice.Footnote ¹⁴ Suppose you wish to explain what a fair price is for something. You constantly have to compare things that are remote – the price of a house and the price of legal representation in court. A direct comparison of goods that are so different is virtually impossible. Aristotle therefore proposes that we explain a fair exchange by finding an interpretation of the analogy: this much legal representation is to the lawyer as a house is to the builder – e.g., how much it costs each to produce their respective goods.

Finally, Aristotle is claiming that it is the analogical comparisons, as opposed to the direct comparisons, that will characteristically be the scientifically fruitful comparisons. Thus when we come to look at Darwin’s use of analogy, whereas comparing the activities of one breeder with another simply tells much the same story, it is the comparison between a farmer castrating a bull and frost killing a lettuce that leads to the idea of natural selection.

Analogy in Biology

Aristotle’s contribution to the early history of biology is one of his most assured accomplishments with a deep influence on all his successors until Darwin, so that even someone as late as Cuvier will explicitly describe himself as applying Aristotle’s methods in his work. Darwin himself writes in such a way as to indicate that he regarded Aristotle as the greatest of his predecessors.Footnote ¹⁵ There is a widespread opinion that Darwin’s work made Aristotle’s work obsolete. However, that is a simplistic reaction. What is clear is that Aristotle had argued for the fixity of species, and as a result could only account for the high level of functional complexity evident in animals, by positing as an underlying metaphysical principle that nature itself was purposive, leading to the methodological principle that ‘nature does nothing without purpose or makes anything superfluously’.Footnote ¹⁶ The theory of evolution by natural selection enables us to replace the highly counterintuitive metaphysical principle that Aristotle found himself forced into by a simple, purely naturalistic interpretation of the purposiveness that is evident throughout the animal kingdom.

However, even if the metaphysical background to Aristotle’s account of animals and plants may be regarded as refuted by modern evolutionary theory, that leaves the method for biological research that he argues for untouched. As a pioneer, working with limited empirical information, it is inevitable that Aristotle will frequently go wrong in the conclusions that he draws. However in subsequent centuries, further empirical investigations making more refined application of Aristotelian methods are responsible for a large proportion of the advances in pre-Darwinian biology, such as, for example Harvey’s discovery of the circulation of the blood.

Unlike previous explorations in biology, and indeed his own investigations in the Posterior Analytics, in his biological writings properly speaking, Aristotle shows little interest in the question of definition. At Parts of Animals 642b 5ff., he makes a long series of devastating criticisms of the attempt to define animals by the method of dichotomous division, and that is all. Instead, he sets himself a different task, that of discovering why animals are the way they are, where this question must be interpreted in terms of discovering their ‘final causes’. That is to say, the kind of explanation he is after is illustrated by the reply to the question ‘Why do giraffes have long necks?’, ‘So that they can browse the leaves of tall trees’.

To understand how he is to set about offering answers to such questions, we must first look at the way that he is thinking of animals. They are for him the paradigm case of substances, entities that are systems of parts, whose continued existence depends upon the cooperative activity of those parts. They are composed of matter, the stuff they are made of, and form, the principle of organisation of the parts to produce a functioning whole. In the case of living substances, the form of the being is what Aristotle calls its ‘soul’.

This conception is clarified by the simple observation that Aristotle makes at the beginning of the Parts of Animals. There is a range of things that an animal needs to do if it is successfully to live out its life (and reproduce): ‘For genera that are quite distinct still frequently present many identical phenomena, sleep, for instance, respiration, growth, decay, death, and other similar affections and conditions, which may be passed over for the present, as we are not yet ready to treat of them with clearness and precision’.Footnote ¹⁷

If an animal can perform such actions, it must be assembled in such a way that enables it so to do. A part may then be identified functionally, as organ,Footnote ¹⁸ as the feature of the animal that gives it the ability to do certain things.

In the light of this, Aristotle’s question now becomes the questions ‘Why does an animal have the parts it does?’ and ‘Why do these parts have the form they have, and why are they related the way they are?’ To answer such questions, Aristotle makes what is perhaps his most significant contribution to the theory of life, the use of comparative biology. One compares corresponding organs in different species of animals. The similarities between these organs give one a guide as to what is necessary for such an organ to carry out its function, or at least carry out that function well. The differences give one a guide as to the way that such organs are adapted to fit the life of the particular animal.

This enquiry is governed throughout by a major contrast between the ways in which corresponding organs are related: they either ‘differ by the more and the less’ or are ‘related only by analogy’. The term ‘differing by the more and the less’ stems from PlatoFootnote ¹⁹ to signify cases where two things possess the same property but to different degrees. Two things will thus ‘differ by the more and the less’ if all the differences between them can be specified simply by the use of comparatives: one is longer, heavier, hotter … than the other. We can see the straightforward biological application of this idea if we consider the case of beaks. Given any two birds, when we compare their beaks, we find basically the same structure, composed of the same stuff, but in the one case the beak is longer, straighter, more pointed … than the other. By way of contrast, if we consider the case of the horns and tusks of different animals, we have the same kind of organ of defence, but with far greater differences than can be specified simply by the use of the more and the less. These organs are related by analogy, in that they have the same function: horns are to bulls as tusks are to elephants.

The two different ways in which organs are related play opposite roles in Aristotle’s investigations. In the case of parts that differ by the more and the less it is the difference between the parts that are significant but in the case of parts that are related only by analogy, it is the similarities.

In the case of parts that differ by the more and the less, the differences show one the way in which the parts have been fine-tuned to fit the way of life of the various animals:

In the case of parts related by analogy, despite the fact that they are related only by analogy, they will typically also possess a range of common intrinsic properties. These are the properties that an organ of that kind must have if it is to function, or at least function well. Thus if we look at the case of an elephant’s tusk and a bull’s horn, they are, for instance both curved, pointed, of the same texture and attached to the head. By reflecting on such common properties as our investigations identify, we can further our understanding of the part and its function.

In implementing his programme, Aristotle uses these two ways in which corresponding parts of animals are related to divide the animal kingdom into nine major families along the following lines:

Then, in the History of Animals, Aristotle conducts an extensive and meticulous survey of the parts of animals working systematically through the different parts that he has identified, noting in each case the similarities and differences between the corresponding parts in different species of animals. Against that background, he will then in Books II to IV of the Parts of Animals attempt explanations of what his survey has shown.

We may conclude this survey by seeing how such explanations look in the particular case by taking a case where both kinds of comparison are combined in a single part. On the one hand, the elephant’s trunk differs by the more and less from the human nose, and on the other is related by analogy to the human hand:

Here we see the peculiarities of the elephant’s trunk explained in terms both of its interrelationship with the other parts of the elephant and of its life and environment. Because it needs to be able to wade across water, it needs to breathe when it is submerged. Because of its bulk, it cannot readily bob in and out of the water in the way that, say, otters do. Therefore its breathing organ is an elongated flexible tube which can be used as a snorkel. At the same time, because of its bulk its legs must be like pillars. Therefore it is unable to provide itself with forepaws. Therefore it exploits its trunk, as a long and flexible tube, shaped in such a way that it can form an analogy of an arm and hand.

What this example shows, as do many of Aristotle’s examples, both in The Parts of Animals and elsewhere, is the way in which Aristotle’s quest for teleological explanation leads to what can be described in modern terms as a sophisticated form of ‘adaptationism’ – an interplay between three different forms of adaptation: the way the parts of animals are adapted to the animal’s environment, the way they are adapted to its way of life, and the way the parts of the animal are adapted to one another. Of course, Aristotle’s understanding of such adaptation was quite different from post-Darwinian adaptation developed in the context of a theory of natural selection: for Aristotle this was, rather, a consequence of the ‘metaphysical’ principle that ‘Nature always works for the best’. What is also dubious is his apparently taking the further step of thinking that there must be a similar teleological explanation of why a particular species of animal exists.

Although the method of comparative biology that he has evolved depends upon comparing animals that are related only by analogy, the resulting arguments are not arguments by analogy in the sense that interests us in this book, but a form of what we would now call ‘arguments to the best explanation’. Thus, Aristotle asks ‘Why, in every species, no matter how morphologically different their eyes, are the eyes always located in the head of the animal?’, and goes on to argue that this is explained by the fact that it is this placing of the eyes that is best suited for them to carry out their function in enabling the animals to take in their surroundings.

Argument by Analogy

Despite the extensive explorations of the concept of analogy that we find in Aristotle, arguments by analogy are comparatively uncommon. The clearest cases that we find are those in which he exploits analogies between animals and other complex entities such as the city state or, even, in the Poetics tragedy. In particular, he is concerned with the question ‘In what way are such entities integrated and united as a single thing?’

If we return to Aristotle’s conception of animals as substances, on his account animals are united as a single entity in a way that is quite different from the way in which a rock, say, is a single thing. In both cases we can talk of them as entities with parts, but for Aristotle this is so in completely different ways. A rock is a continuous lump of uniform material with a surface separating what is inside from what is outside the rock and a part of the rock is any continuous lump of material wholly contained within the surface of the rock. However, when Aristotle talks of the parts of substances, such as animals, he conceives of such parts quite differently. Here the parts are identified by their function in enabling the whole to flourish: eyes are the part that enables a man to see, etc. An animal is then to be seen as a system of such parts, organised in such a way as to permit the animal successfully to live out its life cycle. The way the parts are organised for this to be possible is the form of a substance. In the case of a living being this is its ‘soul’ (ψυχὴ): that form of organisation that permits it to live.

In this way, an Aristotelian substance is dependent upon the proper functioning of its parts for its successfully continuing to thrive. The contrasts between such a substance and another entity such as a rock and between an Aristotelian part and a material part is sharp. What unifies a rock as a single entity is its being a continuous piece of matter, with clear boundaries. What unifies an animal as a single entity is its being a system of parts that cooperate to produce something that can live. If a material part is cut out of a rock, it simply continues to exist as a smaller rock. If an Aristotelian part of an animal is removed or damaged, the whole animal is impaired or disabled. Anything that can be removed or damaged without affecting the whole animal is not to be counted as a part of that animal.

In the light of this account, we can see how Aristotle models his account of the structure of tragedy, and in particular what it is for a tragedy to be a unified whole by transferring elements of that account. Having first argued for the centrality of plot in his account of tragedy, at 1450a 39 he establishes an analogy between a tragedy and a living organism as follows: ‘So the plot is the source and (as it were) the soul (οἷον ψυχὴ) of tragedy.’

Aristotle will then pursue this analogy in his accounts of both the ‘magnitude’ and above all the unity of a tragedy:

We see here Aristotle directly redeploying by analogy principles from his account of living organisms in his analysis of tragedy: that which makes a successful tragedy being understood by analogy with that which makes a healthy animal.

There is a major problem still to address. Let us suppose that we have established that A is an analogical model of B, and that A has feature F. How do we know whether F is one of the features of A that can be transferred to B? Within Euclid answering this question was straightforward. A series of a priori geometrical proofs can prove which features of similar triangles must be shared, and which need not be. However, once we consider arguments by analogy, no such a priori proofs are possible, and need replacing with empirical answers to this question. What makes one uneasy about Plato’s use of analogy is that he nowhere addresses this issue.

In the case of Aristotle, there is one passage which needs to be considered in this connection, with two reservations: although the argument he considers can clearly be presented as an argument by analogy, he himself describes it as ‘παράδειγμα’ (‘example’)Footnote ²⁷ and also it is a passage whose interpretation is controversial. This is Prior Analytics, II/24 (68b 39–69a 19).

This is extraordinarily compressed. Cast as an argument by analogy it would run: ‘War by Thebes against Phocis is bad. Thebes is to Phocis as Athens is to Thebes (both being neighbours). Therefore war by Athens against Thebes is bad.’ If this argument is to go through, we need to consider Aristotle’s justification: ‘we must be satisfied that war against neighbours is bad. Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.’ As it stands, this is inadequate, and fails to do justice to what Aristotle has in mind in his discussions of ‘example’: we are meant to discern a general truth in a clearly understood particular case. However, the facts that Thebes waged war against Phocis, that Thebes and Phocis were neighbours and that this turned out badly for Thebes does not as yet suggest the general truth that going to war against a neighbour will turn out badly. To arrive at the general truth, we need also what Aristotle fails to capture, some link between the fact that Thebes and Phocis were neighbours and that the war turned out badly: what we need is for the example to show why it is bad to make war against a neighbour. The task of replacing Aristotle’s inadequate formulation with something more precise lies ahead of us. In fact it is not until the end of the eighteenth and beginning of the nineteenth centuries that we find attempts being made to resolve that task, and we shall be turning to that towards the end of the next chapter.

Retrospect: Analogical Models and Argument by Analogy

Analogy beyond Mathematics

In the final stage, possibly beginning with the Pythagorean mathematician, Archytas of Tarentum, there are explorations of the possibilities opened up if we extrapolate the idea of analogy from the mathematical to the empirical domain. For this, we take the formula ‘A is to B as C is to D’ – or more explicitly, ‘($\mathrm{ARB}=\mathrm{CRD}$)’ but now interpret the formula, according to context, with a variety of different accounts of the relation ‘R’. This possibility was taken up and developed, even if in very different ways by both Plato and Aristotle.