The method of contraries

1. The uses of contrary accounts

People may favour various accounts of aspects of the world. These may be straightforwardly factual accounts, as when someone favours an account of the dynamics of galaxies that assumes the existence of dark matter or an account of the American Civil War that emphasis economic causes. Or they may concern concepts rather than concrete reality, as when someone favours a particular account of knowledge or of value. We do however mean to exclude positions that are not accounts of how things are, for example the position that people should live in accordance with Aristotelian virtues or the position that there should be an unlimited right to free expression.

Our topic is a way to clarify the contents of accounts and the intensions of the terms that are used when giving them.

Someone who wishes to argue for an account may well spend time arguing against contrary accounts. This is not surprising. Rivals must be vanquished if the chosen account is to triumph.

There is another reason to explore contrary accounts. Doing so can help to clarify the favoured account. This, and not defence against rival accounts, is the reason we shall explore here. We shall call this use of contrary accounts the method of contraries.

Our focus on clarification means that we are not interested in how one might arrive at an account by a process of dialectic. More generally, our interest is in what to do once one has a favoured account to convey, rather than in any zetetic activity - although in practice we may of course modify an account because difficulties emerge as we try to clarify it.

We deliberately speak of contrary accounts, not contradictory ones. The reason is that clarifying a contradictory account, in the strict sense of an account that was the negation of a favoured account, would be precisely as challenging a task as clarifying the favoured account. It would require colouring in the territory on the other side of the same boundary.

When it comes to concepts, it is usual to speak of definitions that give the intensions of the corresponding terms. But we shall speak of accounts of the intensions of terms, accounts that may be rather more discursive than is normal for definitions. One reason is that in the humanities and sometimes in the social sciences, definitional precision is unavailable for lack of a complete and precise vocabulary to use in giving definitions. We can only say more or less about the intension of a term, not give a precise definition. Another reason is that we want to discuss a single method of contraries that straddles accounts of the intensions of terms and accounts of aspects of the world.

2. Where contrary accounts are used

In mathematics and the natural sciences, we can mostly say what we mean without saying what we do not mean. At the other extreme, there is a tradition of apophatic theology. So little can be said about God, either with confidence or without inappropriately limiting God, that theologians in this tradition resort to saying what God is not. They do so in the hope of somehow conveying something about God. And one could extend the practice to other areas of deep unclarity, outside theology.

Our interest is not in either of these extremes, but in the middle ground where entities discussed and concepts that are applied to them are sufficiently well understood for plenty to be said in a positive way, but there is still not enough clarity or precision to give favoured accounts in a wholly satisfactory way without reference to contrary accounts. It is in the humanities and the social sciences that we can expect to observe this phenomenon.

3. Examples

We shall now consider some examples. They differ from one another markedly. But they do share the use of contrary accounts to clarify as well as defend favoured accounts.

3.1 The Theaetetus

Plato's dialogues are replete with argument and counter-argument. Accounts of the topic under consideration are put up and shot down, and these turn out to be contraries of accounts proposed later. The final result may not be a positive conclusion. Sometimes the aporia remains. But each account still helps to show what is meant by some later account to which it is a contrary.

This kind of content of the dialogues is the result of applying Socratic questioning, a tool of pedagogy and research. Our concern will however be with the results, accounts and the contrasts between them, rather than with the process.

Early in the Theaetetus, the method of contraries is used to clarify what is sought. This is a unified account of knowledge itself, as opposed to a list of types of knowledge (146c-147c).

Then the extended discussion of perception as knowledge which ends at 160e lays the groundwork for bringing out the required distinctions between knowledge and perception (164b), and between knowledge and opinions that may differ from one person to another (169d-171e). These contrasts not only guide the discussion. They also indicate an essential element in knowledge, the truth of what is believed. The discussion also draws attention to the cases where different opinions can happily coexist (as when a wind is hot for one person but cold for another), and to the contrasting cases where there is a matter of fact that is independent of people's opinions so that if two people think different things, at least one of them must lack knowledge (179a-d).

Immediately after that point we are reminded of the use that has been made of the method of contraries, when Socrates notes that the task is to find out what knowledge is, not what it is not. He says we must wipe out everything up to now and start afresh (187a-b). But our view of the problem has already been thoroughly shaped by the dialogue up to this point.

There are also small examples. For example, when Socrates wants to investigate mistakes about the sum of 5 and 7, he emphasises that he means the numbers themselves, not 5 men and 7 men or anything like that (195e-196a). Here the method of contraries is used to show what is meant by abstract numbers. They are not collections of concrete objects. The distinction is obvious to us now, but it may not have been obvious in the early days of science and reflection on science.

3.2 The Renaissance

Our next example comes from historiography. Jacques Le Goff, in his book Must We Divide History Into Periods?, argues against accounts that impose on history a division into periods which would see a significant leap from the medieval period to the Renaissance. He favours an account that would acknowledge significant changes in the fifteenth and sixteenth centuries, but would also recognise that there was too much continuity across the supposed leap and not enough radical change to take the traditional view of the Renaissance as a distinct historical period.

In order to make his case, Le Goff makes extensive use of the method of contraries. At the highest level he sets out the traditional conception of the Renaissance, particularly as developed in the work of historians of the last 200 years, so as to be clear about what he is arguing against and therefore about what he is arguing for. At a more detailed level he identifies several allegedly transformational developments and argues against traditional views that they were revolutionary. He measures their significance as somewhat less but not trivial.

His position may be summarised in two quotations from the book. The first is: "However reasonable it may seem to mark it off as a discrete segment of historical time, I do not believe that the Renaissance can truly be said to constitute a separate period. It seems to me instead to constitute the last renaissance of a long Middle Ages" (page 58). The second is: "My own view is that the transition from one period to another, in this case at the end of a long Middle Ages, is to be situated in the mid-eighteenth century" (page 105).

Use of contraries is inevitable when one wants to argue that something did not exist, or was not of the nature commonly supposed. One has to set out what the thing would have been if it had existed, or what its commonly supposed nature was. Nonetheless, we have here perfectly good examples of the method of contraries in our sense. The positive thesis is set out in opposition to the rejected common view. It is then clarified by being set against specific elements in the common view.

3.3 Globalisation

Turning to an example from the social sciences, globalisation may be conceived in different ways by different authors. One example that brings out use of the method of contraries is supplied by Jan Aart Scholte (Globalization: A Critical Introduction, second edition, chapter 2).

Here the favoured account and contrary accounts are accounts of the intension of a term that may be useful, a term that might be thought to be entirely the invention of social scientists in order to help them understand developments in the human world. There is a contrast with knowledge as regarded in the Theaetetus. Plato takes it that there is such a thing as knowledge out there in the (human) world, the nature of which is to be discovered. The term "knowledge" is not one merely invented by philosophers, to have its intension modified as they may find useful.

Nonetheless, the idea of favouring a particular account of a term's intension remains. It is just that the basis of favouring is usefulness rather than correctness. And the role of the method of contraries in giving the favoured account also remains. So does the aptness of speaking of accounts rather than definitions that we noted in section 1. It may seem more legitimate to give precise definitions if one thinks one is using a term for a concept of one's own invention than if one thinks one is trying to fit a concept to something out in the world. But a desire to come up with something that is truly useful in understanding the world may lead one to hold back from providing a definition that by its rigidity may generate too many inconvenient exceptions to its applicability. There is also the point that in the humanities and to some extent in the social sciences, the available vocabulary often does not provide the words that would be needed to give precise definitions.

Scholte rejects accounts of the intension of "globalisation" in terms of internationalisation, liberalisation, universalisation, and westernisation (pages 54-58).

Scholte then homes in on his preferred account in terms of a spread of connections between people across the planet (pages 59-65). A key contrast with the rejected accounts is set out in these words: "In this fifth usage, globalization refers to a shift in the nature of social space. This conception contrasts with the other four notions of globalization discussed above, all of which presume (usually implicitly rather than explicitly) a continuity in the underlying character of social geography" (page 59). He reinforces the point in the words: "Whereas international relations are inter-territorial relations, global relations are trans- and sometimes supra-territorial relations" (page 65). These quotations highlight the importance of the method of contraries. In order to give his preferred account of the intension of "globalisation" in a way that gives the term sufficient (although still imperfect) precision, and to highlight the importance of a change in the nature of social space, the author has to give rejected accounts.

4. Why is the method of contraries useful?

4.1 The natures of disciplines

It is in the humanities, and to a lesser extent in the social sciences, that we are most likely to see the method of contraries doing work for which it is the only or the best tool. In mathematics and the natural sciences the method is likely only to have pedagogical uses, except perhaps in those natural sciences that are at a considerable distance from physics and chemistry.

The explanation lies in the nature of the humanities and to some extent the social sciences. It can easily be impossible to give a favoured account precisely if one gives it only in a positive way. Recourse must then be had to the method of contraries. The result may still not be fully precise, but it may be markedly more precise.

We shall now consider ways in which the natures of disciplines may give a role to the method of contraries.

4.2 The extensions of terms

Sometimes the difficulty in making precise positive statements will arise from imprecision in the extensions of terms. There may be borderline cases. It may not be possible to spell out necessary and sufficient conditions for entities to fall within the extensions of terms in ways that could in practice be applied to settle every case.

Here the method of contraries may help by picking off some borderline cases as outside the extensions of terms that are used in the positive statement of the favoured account. But the assistance may not be great, and in any case this would be a narrow and relatively uninteresting use of the method of contraries.

4.3 The intensions of terms

A more interesting source of difficulty is that there may be unclarity as to even the broad meaning of the favoured account on account of substantial unclarity as to the intensions of some significant terms. We may expect use of the method of contraries to make a significant contribution to the resolution of difficulties of this type.

Lack of clarity as to an intension may arise because a term is novel and not already well-embedded in the relevant discourse, or because it is being used in a novel sense. This helps to explain why the method of contraries has a much wider role in the humanities than in the natural sciences. In the natural sciences, when new terms are introduced, they are given places in rich networks of inter-definition, with implications between the possession of various sets of properties by entities that can be almost as strong as logical entailment. (Such implications are not verbal artefacts of definition. They need to be discovered by painstaking work. But once the results of research are in, the network of terms will be formulated or modified to fit the results. And the closer we get to physics, the more it is a feature of how the world works that use of terms which fit the world allows strong implications to be identified.) In the humanities and in much of the social sciences, tightly drawn networks of implication are rarely available. New terms must be given their senses in some looser way.

The method of contraries can help in that task. One may display contrary intensions of terms by giving accounts of some rejected intensions of those terms. If the main favoured account is an account of the intension of a term, then the accounts of contrary intensions will simply be contraries to that main account. And if the main favoured account sits above that level, and uses terms with potentially unclear intensions, the accounts of contrary intensions will be contraries to accounts that would convey the intensions of terms as they are used in the main favoured account.

We can see this sort of thing by returning to the examples we gave in sections 3.2 and 3.3.

Jacques Le Goff makes clear what sense of renaissance he will countenance largely by considering the traditional conception and denying its applicability to the relevant period of history. If we analyse his whole argument in our terms, we can see him first making clear what sort of change he has in mind under the term "renaissance", a significant but not necessarily revolutionary change, by presenting the contrary conception of a great transformation. Then he can build an account of the relevant stretch of history, an account that includes several renaissances in his sense but no great transformation of the type that is central to traditional accounts of the Renaissance.

That example is largely one of giving us a sense of the position of the Renaissance on a scale of radicality. And scale is at least in principle a quantitative variable, even if it is hard to measure when it means something other than any kind of physical scale. The example of globalisation is more complex, because the distinctions that Jan Aart Scholte wishes to draw are not in any significant aspect quantitative. Instead he wants to focus on different forms of interaction between entities and barriers to such interactions, before homing in on connections between people.

The way to bring out the form of interaction that is germane to Scholte's approach is to contrast it with other forms of interaction. The points of contrast between the favoured notion of globalisation and notions that are centred on other forms of interaction are not the only points that could be brought out by the method of contraries. But by choosing other notions that have been thought to do the same job of understanding the specific phenomenon of the world's becoming more socially and economically connected, the author can make it likely that he will bring out the points about his favoured notion that will be most significant in doing that job of understanding the phenomenon.

4.4 The favoured account as a whole

There are cases in which the difficulty in giving a favoured account purely positively is not a consequence of imprecision in the extensions or the intensions of terms that are brought together to give the account. Rather, it is a consequence of potential unclarity in the account as a whole when those terms are brought together to give it.

We can see this in the example of the Theaetetus that we introduced in section 3.1.

The goal, a unified account of knowledge itself, is clarified by contrast with a list of types of knowledge. Without this clarification, it would not be clear that a unified account would not even be given by a list of types together with a statement that the list was complete. It would also not be clear that Plato saw a fundamental difference between the intension and the extension of the term "knowledge" which would exist even if there was only one kind of knowledge.

The discussion of perception, about which the perceiver is not mistaken, provides the background for an argument that the intension of "knowledge" must allow for beliefs that do not count as knowledge. That need is then turned back on the proposal to define knowledge as perception, showing its inadequacy.

5. How good a tool is the method of contraries?

We shall now consider whether the method of contraries is a good tool.

On the positive side, the method works. This is indicated by numerous examples of its use. If it did not work, it would have fallen out of use.

It is the negative side that should concern us. Does use of the method of contraries present a high risk of misleading understandings of accounts or terms?

Abstractly, it would seem that it does. If we indicate what is meant partly by saying what is not meant, we are at risk of choosing the contraries that happen to occur to us because they are the ones that we thought of in the context of discovery, when we were still exploring accounts and terms. The contraries chosen in that way may not be the contraries most needed to convey a good understanding. And neglected contraries might have changed our assessment of the adequacy of the favoured account or the appropriateness of the terms used. We could only have full confidence in the results of using the method of contraries if we could be confident that we had identified and made use of all the contraries that would contribute significantly to an understanding and assessment of the account or the terms.

Concretely, there is less reason to worry than might at first appear. This is because of what is achieved in the humanities, and to some extent in the social sciences. The human world is not as amenable to precise characterisation as the physical world, and it is the possibility of precise characterisation that makes the demand that our accounts and terms should match the world an unforgiving demand. Without that possibility, we should not expect a total ordering of accounts by quality. So use of one selection of contraries need not lead us to an inferior result to use of another selection.

Moreover, adding some contraries to a selection may not yield an understanding that is better to any worthwhile extent. It may even muddy the waters. It may be some clear statement that B is neither C nor D that gives insight to the reader. Adding that B is also not E may take the edge off the contrast with C and D. That might seem to be a merely psychological consideration, but such considerations matter when the goal is Verstehen rather than, or at least in addition to, Erklären.

Indeed the tendency we have to cite the contraries that appear most salient, either because they show the reason for homing in on the intended target as distinct from other ones or because they rule out the obvious misunderstandings of the intended target, means that use of the method of contraries should improve accounts in respect of their conferring an understanding of the world. That is a different function from finding out some single and precise way that the world is, a function that is in any case beyond the scope of the humanities.

This is not to say that use of the method of contraries is without risk. We could pick contraries idiosyncratically and thereby mislead ourselves. And citing contraries, while it improves readers' sense of what is meant, does not take us all the way to unambiguous statements or definitions. It may however be the best we can do.

References

Le Goff, Jacques. Must We Divide History Into Periods?, translated by M. B. DeBevoise. New York, NY, Columbia University Press, 2015.

Plato. Theaetetus.

Scholte, Jan Aart. Globalization: A Critical Introduction, second edition. Basingstoke, Palgrave Macmillan, 2005.