1. Maximality Distinguished from Optimality

We certainly need disciplined reasoning in the pursuit of ethics in general and in the evaluation of claims about justice in particular. Within the need for discipline is an understanding of what would constitute a well-formulated argument for an ethical proposition. In a widely used approach, reasoning is taken to be incomplete until a conclusion emerges that is at least as satisfactory as every other conclusion. Formally, this is an insistence on ‘optimality’ – the identification of an ‘ideal’ – or ‘best’ – alternative. This has to be distinguished from ‘maximality’, seeking a conclusion that is no less satisfactory than any other conclusion (an alternative that cannot be bettered).

The distinction between maximality and optimality is often overlooked in presentations on reasoned ethics, but it is a very major contrast. An alternative is optimal if it is at least as good as every other alternative. In contrast, an alternative is maximal if there is no better alternative. To illustrate the contrast, when there are two alternatives x and y neither of which is judged to be better than the other, then in that pair of alternatives, both are maximal, but neither is optimal.

While optimality entails maximality, the converse does not hold, and the two demands need not coincide even for well-behaved transitive rankings. The distinction is well discussed in Bourbaki's classic book, Éléments de Mathématique [insert diacritical marks] (1939). With special assumptions, such as there being no unranked pair (in addition to the ranking being transitive), the maximal will also be optimal, and the difference will vanish. But there is no analytical reason, nor any practical necessity, why the ranking of alternative conclusions must take that form.

Even though the contrast between the maximal and the optimal may seem like an esoteric mathematical issue, the distinction is of enormous practical importance for decisional analysis as well as moral and political philosophy. Indeed, I would argue that this formal, or methodological, issue is absolutely central to the nature of substantive ethical arguments, including the assessment of the respective claims of alternative theories of justice.

It should also be noted that decisional incompleteness may co-exist with total valuational completion. More specifically, our complete success in identifying a determinate truth value – giving a ‘true or false’ answer to every valuational question about the respective alternatives – may not eliminate the need to go beyond valuational reasoning in reasoned decision-making.

In his recent book Being Realistic about Reasons,Footnote ⁴ Thomas Scanlon has presented a strong defence of his diagnosis that ‘claims about reasons can be correct or incorrect, and such claims are fundamental – not reducible to or explainable in terms of claims of other kinds’ (14). My arguments about decisional reasoning, including the distinction between maximality and optimality, are quite compatible with a reason-based foundation of ethical decisions – in fact even with what Scanlon calls ‘reasons fundamentalism’. They are also compatible with what has come to be known as ‘normative cognitivism’. But I should add here that my contentions, which are mainly methodological, would hold also for non-cognitivist approaches to ethics. The formal issue has relevance for all reasoned resolutions of valuational questions, whether or not ‘claims of other kinds’ play a foundational role in the reasoning invoked (so that the distinction made here is not dependent on the belief, which I do in fact share, that claims of other kinds can become relevant only through reasoning).

2. An Illustration

Let me begin with an example. Consider a person, Ashraf, with a strong anti-terrorism commitment in contemporary West Asia who is considering the possibility of two terrible events, both of which a terrorist group has threatened to carry out. One threatened event – let us call it x – is the total destruction of the historic city of Nineveh (with, however, no one being killed), and the other – called y – involves the killing of a thousand people at a different spot (without any destruction of Nineveh). Both are hugely bad things to happen, and Ashraf is considering what can be done to stop them. If it turns out that he and his fellow anti-terrorists can prevent one of the two ghastly events, but not both, then his decision would have to be about choosing between x and y.

The point is not only that it is a difficult choice, nor that the considerations involved in the two alternatives are quite different: one is the prevention of the murder of a large number of people (a thousand in this example) and the other the preservation of a great historical sight which can be thought to be valuable in itself, but would also be hugely valued by a great many generations to come. The point rather is that we may have good reasons to give decisional priority in one direction, or alternatively in the other – a plurality of answers that need not be eliminated by what Rawls calls a ‘reflective equilibrium’. It may be quite acceptable, and yet not obligatory, that by the force of reasoning Ashraf will decide in favour of one of the alternatives, rejecting the other (for example, choosing to sacrifice a thousand human lives, for preventing the destruction of Nineveh).

It cannot, however, be a requirement of disciplined reasoning, or a necessity of a ‘reflective equilibrium’, that Ashraf must be able to rank the two alternatives x and y in one direction of the other – even to judge them to be equally good (in fact, equally bad, in this case). If Ashraf equilibriates in the position that neither can he say that saving Nineveh would be at least as good as allowing a thousand people to be killed, nor that stopping a thousand murders would be at least as good as saving Nineveh from being gutted, then he has what is technically called an incomplete ranking, on the basis of his completed – and possibly complete – reasoning. It is important to recognise that the presence of an incompletely ranked pair does not indicate that Ashraf is not making use of as much reasoning as he can invoke, or even what can possibly be invoked.

It is also important to note that consistently with this, Ashraf may be able to rank many other pairs of alternatives in quite a definite way. For example, he may be able to find reason enough in favour of, say, allowing Nineveh be destroyed rather than the whole of Syria (not to mention Iraq, where Nineveh itself is situated). Reasoned valuational rankings can co-exist with valuationally unranked pairs, even after taking reasoning as far as it would go. This is not an argument for slackening one's attempt at reasoning to rank every unranked pair – often with decisive results (there is no advocacy or tolerance of valuational laziness in the claim being made here). But there is no analytical necessity here, nor any practical reason, that guarantees that a complete ranking must emerge. This may not be a comfortable position to be in from a decisional point of view, but Ashraf cannot be accused of intellectual sloth, nor of violating reason, since incompleteness can be – and in this case is – a reasoned conclusion. He has been led to an unranked pair by reasoning, not by any refusal to seek a reasoned resolution.

3. Partial Ordering and Maximality

Note also that while Ashraf has an incomplete ordering, he need not be in a decisional impasse. If both x and y, while unranked vis-à-vis each other, are better than all the other alternatives in a set including a great many other alternatives (including many nastier ones like the whole of Iraq being destroyed), he has reason enough to choose either x or y from that set of alternatives. Each of them is a ‘maximal’ alternative, in Bourbaki's sense. The fact that neither is ‘optimal’ need not leave Ashraf in a decisional impasse. He can sensibly choose either x or y, but not any of the other alternatives.

It may be also be noted that a valuational incompleteness need not entail a valuational impasse. Let me try to bring out the problem more clearly by elaborating on the logical structure of what is involved here. Take a partial ordering of three elements x, y, z in terms of their respective goodness: x is better than z, and y also is better than z, but neither is x better than (or even at least as good as) y, nor is y better than (or at least as good as) x. There is a lot of correctness and incorrectness floating around here, for example that ‘x is better than z’ is correct, and that ‘x is better than y’ is incorrect. Note that in the example given, the correct-incorrect dichotomy can be applied to the comparison of every pair, without exception. In this particular case, the statement ‘x is better than or as good as y’ is incorrect, and so is the statement ‘y is better than or as good as x’. The valuational unrankability here does not show any valuational failure – merely the need to recognise that unrankability is the particular form that the outcome of the valuational exercise here takes. To include the possibility of the unrankability of some pairs of alternatives is an integral part of Bourbaki's foundational mathematics of relations and sets, and it is a reasoned possibility in the analysis of ethical and political evaluation as well.

If it is to be shown that there is something of a mistake in a configuration that includes both these statements (that ‘x is not at least as good as y’ and ‘y is not at least as good as x’), this does not arise from any lack of answer to any pairwise comparison (all such comparisons have definite answers here). We shall have to make some further demand to insist that the correct-incorrect dichotomy ‘must’ – for some reason yet to be specified – take a particular, and analytically highly restrictive, form. Such a special demand may take the form of insisting that if x is not better than y, then y must be – absolutely must be – at least as good as x. If that particular demand were to be made, we have to ask why.

In effect, this would be an attempt to establish that there simply could not be partial orderings of normative valuation that allow incompleteness of ranking – an unusually restrictive demand. Note that, contrary to an often made presumption (typically implicit), this is not an analytical necessity, and if for some substantive reason such a demand should be made, then we must be given a reason as to why that necessity arises. To say that this would be helpful for decision-making would, of course, be to beg the question, aside from reflecting a failure to recognise that maximality is adequate enough for reasoned choice.

Two and half centuries of work on ‘social choice’ has provided many practical examples of what can be called ‘equilibriated incompleteness’.Footnote ⁵ Even in terms of general principles there is no particularly compelling reason to presume ‘completeness’ of all binary relations of normative judgment. And there is no great analytical or practical difficulty in having systematic and reasoned choice with maximality, rather than optimality, even though the two yield quite different structures of compatible axioms.Footnote ⁶

4. Not an Issue of Non-commensurability

Before I move on to the far-reaching implications of the distinction between maximality and optimality, let me make a quick clarificatory remark. The issue of unrankability must not be identified with the so-called problem – a much over-hyped issue – of ‘non-commensurability’. As a matter of fact, we very frequently make perfectly reasoned choice over non-commensurable alternatives. If I love bananas and hate apples, I would not be deterred from going for a banana by the extremely peculiar worry that bananas and apples cannot be measured in the same unit, which is what commensurability is concerned with.

The real source of unrankability is not the absence of co-measurability, which is a very common and entirely mundane occurrence. In contrast, in the case I am discussing, the alternatives not only involve distinct components (as most alternatives do), but – and this is the crucial issue here – our reasoned valuation cannot put one alternative over another, despite our best effort at reasoning.

5. Assertive and Tentative Incompleteness

Incompleteness of a ranking can arise not only from judgmental unresolvability (which I have tried to illustrate), but also from unbridgeable gaps in information (not just unbridged gaps, but unbridgeable in practice). In fact, in any decisional choice the consequences of which would come in the future (and many – indeed most – decisional choices are of this type), we have to guess, not always confidently, what the consequences would in fact be. In many cases, the future effects may well be easy to guess, and in some cases, we can deal with uncertainties through some acceptable procedure of reasoning under uncertainty (for example, with probability-weighted ‘expected values’, if there are reliable probability distributions and if we accept the foundational axioms that make the discipline of expected valuation a sensible way to proceed). But there is nothing extraordinarily odd if, in many cases, we cannot find reason to bridge the informational and judgmental gaps to arrive at a reasoned complete ordering.

I turn now to ‘tentative’ incompleteness. In addition to equilibriated incompleteness that cannot be removed, we also have to deal with provisional incompleteness. Reasoning is a process rather than an instantaneous occurrence. At the moment when a decision has to be taken, we may quite possibly still be looking for more information, or for fuller resolution of contrary considerations. While a partial ranking (or a partial partition) can be of the ‘assertive’ type, it can also be ‘tentative’ – being a contingent assertion at a particular stage of a possibly long drawn out exercise.Footnote ⁷

Consider now the argumentative issues that relate particularly to tentative incompleteness. We may, for example, know that our inability to rank a pair is tentative because it could be resolved – in one direction or other – if and when more information of a particular type can be found, which we presently do not have. Even though this is not a case of assertive incompleteness, there is still a question of reasoned decision making to be faced regarding what should be the right choice given where we inescapably are – at the point of decision making. To say that we should rapidly find more information to eliminate the uncertainty is, of course, an evasion of the question being asked. And so would be any advice to reflect more, if the tentative incompleteness arises not from informational deficit, but form an actual failure to discern the truth because of the problem's complexity. We may, in fact, have good reason to abandon one of the more frequently used assumptions in information theory that assumes that we know everything that is analytically deducible from what is known (like knowing immediately the answer to any mathematical puzzle whenever we are given one!).

Buridan's ass faced just such a problem when the famous donkey could not figure out which of the two hay stacks facing it was the better one to go for, and – as the tragic story runs – the ass died of starvation. Very likely one of the hay stacks was indeed larger – or more luscious – than the other, but if the ass could not figure out which one that was, it would surely have been better for the ass to go for either of the stacks, rather than die of starvation. So even with unranked stacks and no identified best alternative, there is a reasoned approach to choice for Buridan's ass, to wit, to go for either hay stack, rather than ending up starving to death.Footnote ⁸

Evaluation of justice may well have to deal with firmly fixed equilibriated incompleteness, but even a hardy case of tentative incompleteness may require us to go beyond the standard – and often repeated – recommendation of choosing a best alternative. A best alternative may not exist, but even when it does, we may not be able to identify it, even if such an alternative could be expected to emerge when the informational – or reflectional – gaps are overcome, perhaps over time. To go for an alternative that is not necessarily better than (or as good as) all the others may well be a departure from the frequently used rules of reasoned choice, but it is what reasoning would clearly demand, namely to go for one of the ‘maximal’ alternatives (that is, choose an alternative to which there is no identifiably better alternative). But which one of the maximal alternatives – each unbeaten by all the others – we choose cannot be guided by reasoning alone. We need not shred tears for having that degree of latitude consistently with all that reasoning demands from us, when the point of decision making comes.

6. Theories of Justice

I turn now to reasoning about justice in particular, and what a theory of justice should sensibly demand. In my book The Idea of Justice, I have argued for a departure from the long tradition of situating the analysis of justice in the framework of a so-called ‘social contract’. The social contract approach weaves the idea of justice around the idea of an imagined contract – for bringing about an ideal choice – that the population of a sovereign state are supposed, or imagined, to have endorsed and embraced. This approach was pioneered by Thomas Hobbes in the seventeenth century, and major contributions were made in this line of thinking by those who followed him, including John Locke and Jean-Jacques Rousseau, among others.Footnote ⁹

Rawlsian ‘justice as fairness’ is a species of the general approach of social contract, with a carefully constructed ‘original position’ satisfying demands of impartiality, reflecting Rawls's characterization of fairness. The approach concentrates on selecting appropriate ‘principles of justice’, chosen unanimously in the original position (taking for granted that with the imagined elimination of the influence of people's vested interests, they would completely agree on a unique set of principles of justice). These principles identify the ‘just institutions’ that form the basic structure of a just society. Growing further, the parties – or imagined parties – to the social contract in the original position are all expected to behave compliantly, in line with the principles of justice unanimously adopted in the original position. The choice of the principles of justice that govern the identification of perfectly just institutions, backed by compliant human behaviour, has ended up being the principal – and often the only explicitly specified – assignment in the theory of ‘justice as fairness’.

In contrast with contractarian theorists, a number of other Enlightenment thinkers (beginning with Adam Smith, the Marquis de Condorcet and Mary Wollstonecraft, and extending later to Karl Marx and John Stuart Mill, among others) took a variety of approaches that differed in many ways from each other, but shared a common interest in making reasoned comparisons between different ways in which people's lives may go, jointly influenced by the working of institutions, people's actual behaviour, their social interactions, and other factors that significantly impact on what actually happens. The analytical discipline of ‘social choice theory’, which had its origin in the works of French mathematicians in the eighteenth century, in particular the Marquis de Condorcet, but also others like Jean-Charles de Borda, and which has been revived and reformulated in our time by Kenneth Arrow,Footnote ¹⁰ belongs robustly to this second line of investigation.

As I have argued in The Idea of Justice, we can make extensive use of the insights presented by non-contractarian Enlightenment thinkers, such as Adam Smith, Condorcet, Mary Wollstonecraft, and others. Judgments of justice have to be linked with the lives of the people – their well-being and freedom. The focus has to be on making comparative judgments on the elimination of identified injustices in alternative states of affairs. There is, in particular, no presupposition that all alternatives can be ranked by a given person, even with all the reasoning within his or her command. The basic ingredient of social judgment can be expected to be a partial ordering a person can reasonably defend, after taking note of the reasoning of others, and trying to be as objective as he or she can be.

Different persons’ reasoned partial orderings may diverge, and public reasoning can be used to resolve differences to the extent it is possible to do, using epistemic as well as evaluative arguments. When there is an agreement between the people involved on the ranking of any particular pair (possibly after interactive reasoning with others), the agreed ranking can be seen as having a specially endorsed status. But there is no embarrassment in the possibility that many pairs may remain unranked. The incompleteness of an ordering need not be seen as the result of abandoning reasoning, but can, in fact, be as much as reasoning can deliver, given what is known and what valuational priorities have been sorted out. At the decisional level, it is an invitation to make reasoned choices for maximality, guided by personal reflections and public discussion.

It is quite possible that even in what Rawls calls ‘the original position’ – with specified conditions of an imagined state of primordial equality – there may not be a complete agreement on the identification of ‘just institutions’ to be reflected in Rawlsian ‘principles of justice’ as a crucial building blocks of his approach of ‘justice as fairness’. This is a serious problem for the Rawlsian approach, since in the absence of a complete identification of the perfectly just institutions (in the form of the ‘basic institutional structure’ of the society), the elaborate stage-by-stage unfolding of justice, so elegantly formulated by Rawls, need not even get started.

And yet there can be, even with such unrankability, a social agreement that is enough to generate an agreed partial ordering of justice, which could be the basis of many important social decisions about institutions and – to go further away from Rawls – also about behavioural priorities. Our disagreements arise not only from our vested interests, which the ‘veil of ignorance’ in the original position may do its best to eliminate for the imagined exercise of the choice of a ‘social contract’, but also from possibly diverse priorities on distinct concerns, such as the relative weights to be attached to economic equity and personal liberty (when they push us in divergent directions). We can agree on the importance of both economic equity and personal liberty and yet not attach exactly the same relative weights on them.

In his later writings Rawls himself discusses the possibility of plural beliefs – and by implication of surviving disagreements – in the original position. Indeed, in his Justice as Fairness: A Restatement, Rawls notes that ‘there are indefinitely many considerations that may be appealed to in the original position and each alternative conception of justice is favoured by some consideration and disfavoured by others’, and also that ‘the balance of reasons itself rests on judgment, though judgment informed and guided by reasoning’.Footnote ¹¹ Rawls does not, however, tell us much about how the much discussed stage-by-stage procedure in ‘justice as fairness’ – beginning with an unanimously agreed social contract chosen in the original position – would be modified to accommodate disagreements in the original position.

The existence of disagreements in the Rawlsian original position may be a foundational problem for Rawlsian justice as fairness, but a partial agreement is quite adequate for many policy choices and political decisions under other approaches to normative social choice. For example, Adam Smith's analysis of the pursuit of justice through the invoking of the ‘Impartial Spectator’ does not insist that there must be any kind of unanimity on the identification of all the right institutions (or right behaviour patterns). The thought experiment of the Impartial Spectator can significantly the reach of reasoning and broaden the respective perspectives of each person (this was Smith's presumption), but these different perspectives need not become altogether congruent as a result. And yet there could be enough of an agreement on what to do, and what institutions to have, to yield coherent and cohesive decisions in many important areas of social choice through shared partial orderings.

7. Maximality and Theories of Justice

I end by making some brief comments on the principal departures of the kind of non-contractarian approach to justice I have tried to advance in The Idea of Justice, compared with Rawlsian and other contractarian theories First, rather than following the contractarian tradition of beginning the exercise by asking what is perfect justice (or what principles should govern the choice of perfectly just institutions for the society), I argue, following Condorcet and Smith and Wollstonecraft, for the identification of clear cases of injustice, on the urgency of removing which there could be a general consensus, on the basis of public reasoning. The removal would not yield anything like an agreed optimality (or something that anyone really takes to be the best of all possible worlds). But a general acceptance that some changes would make matters better could be the basis of social action, even though what is achieved in this way need not be, in any sense, a realisation of perfect justice.

In arguing, for example, for the abolition of slavery, as Smith, Condorcet and Wollstonecraft all did, they did not have to seek an agreement on the nature of the perfectly just society, or on the characteristics of ideally just social institutions. Smith would have, I imagine, made more room for market-based institutions in the post-slavery world than what Mary Wollstonecraft would have seen as ideal, and yet the two could agree firmly – yielding an agreed partial ranking – on the need to end slavery. We can completely agree on the manifest injustice of particular institutions and behaviour patterns, and on the urgent need for their removal, even without having the same view of an ideally just society, or of perfectly just institutions. The demands of removing famines and global undernourishment, or the elimination of preventable epidemics, or the remedying of acute human insecurity and suffering, and many other issues in pursuing global justice are much more fruitfully discussed by looking for a reasoned consensus on tentative maximality, rather than seeking an agreed optimality.

Second, our focus need not be only on institutions, in contrast with the social contract approach. We can go beyond institutions – important as they are – to pay direct attention to the nature of the lives that people are actually able to lead and the actual freedoms they enjoy, which would depend on a variety of influences – not just institutions. How things work out for what people actually get – what well-being, what freedom – taking all the influences into account made Smith deeply critical of ending the specification of what needs to be done in terms only of institutions (as he repeatedly argued both in The Wealth of Nations and in The Theory of Moral Sentiments). If the object of the exercise includes how the lives of the people are going (a subject in which Rawls too was deeply interested), then the analysis of justice has to be carried beyond what can be derived from focusing only on the choice of ideal institutions. The problem of incompleteness may well be substantially more present when we are trying to work out what exactly can be expected to happen in the world – or even in a country – as a result of the interaction of institutions, motivations and behaviours. The need to make do with partial ordering could be much greater when we are looking for assessment of realized justice, rather than stopping at choice of institutions only, in an imagined world.

Third, the assumption of compliant behaviour on the part of all to advance the agreement made in the original position eliminates some of the most important aspects of the pursuit of justice. An approach to justice should not fail to say anything at all about, say, corruption, and more generally about how to think about the demands of justice in a world where institutional and behavioural response to non-compliant behaviour must be among the more important – and more difficult – parts of the pursuit of justice. And here again partial ordering would have a particularly important role.

Fourth, unlike the social contract approach which, by construction, must be confined to the people of a particular sovereign state, the alternative approach I am trying to present can involve people from anywhere in the world, since the focus is on reasoned agreement on certain identifiable features of removable injustice, rather than on a state-based social contract to install ideal institutions for that particular state. The departure makes reasoning on ‘global justice’ possible and momentous, and this is essential for addressing such problems as global economic crises, or global warming, or prevention and management of global pandemics, such as the AIDS or Ebola epidemic. Our agreements may be only partial, even after as much public reasoning as we can have. This is so across the boundaries of states, but also within each country itself. And the ways and means of the implementation of the reasoned agreements can also involve considerable plurality. Mary Wollstonecraft made a pioneering contribution on how the rights of women – and of men – can be pursued not just through the laws of a nation state, but also by many non-legal means, including active public discussion and exchange of news as well as views within and across the boundaries of the state.Footnote ¹²

While advocating a different kind of theory of justice from the Rawlsian theory of ‘justice as fairness’ – more comparative, more realization-oriented, more behavioural, more global, and more cognizant of the possible diversity of impartial reasoning – I have to concede that the likelihood of incompleteness would be inescapably larger in what I am proposing than in the imagined Rawlsian world of total agreement in the original position and of perfectly compliant behaviour.

I do not see this as a fault, since – as I have discussed earlier – both tentative incompleteness and assertive incompleteness are very much within the domain of reasoned choice. And if it is important to note that not all issues of decisional justice can be fully resolved by agreed reasoning on values, it is also crucial to recognise that a great many of those issues do not need anything beyond an agreed partial ordering for reasoned resolution. Some of the most urgent problems in the world do not ask for the emergence of an agreed complete ordering (either of institutions, or of states of affairs, or of social realizations). Nor need we wait for a world government to be able to talk about reducing global injustice, or enhancing global justice.

There is surely some reason for satisfaction in the thought that the discipline of reasoning does not make unreasonable demands on us.