Contradictory and contrary opposites in a philosophical analysis of dialectical thinking

One basic difference between philosophical logic and cognitive psychology is that while the latter concerns ways of thinking in the broad sense (including perceptions, emotions, and dreaming) and strives to describe their characteristic features empirically, philosophical logic is a theory of valid inference, in which inference is not a thought process. This means that it is difficult if not impossible to derive conclusions pertaining to philosophical logic from how people, mature or immature, think. In the following, we shall describe this difficulty first from the viewpoint of the notion of contradiction that is also central in the abovedescribed dialectical theories of human cognitive development.

In the psychological descriptions, mature adult ways of thinking are said to be more tolerant towards or even more capable of accepting logical contradictions (Kramer, 1983) than youthfill ways of thinking. This might be taken to imply that mature adult thought is not logically two-valued. Two-valued logic acknowledges only two truth-values as possible: true or false. It is important to stress that this question is distinct from the question of whether and how we know which claims are true and which ones false. This means that a claim can have a truth-value even if we do not know what it is. This is because truth depends on how things are, not on whether we know how they are. If I do not know whether it is raining in Finland at place x on 30 June 30, 2017 at 13:45 Greenwich time — let us call this time t — it does not mean that the claim “it is raining in Finland at place x at time f” would lack a truth-value, i.e., that it is not true or false. It simply means that I do not know whether it is true or not.¹⁷

In the psychological discussion of two-valued versus many-valued logic, the cognitive development of adults has been compared to Hegel’s “logic” in which the Spirit progresses through thesis, antithesis, and synthesis and this is called “dialectic” (Kramer, 1983, p. 94). It is important to note that Georg W. F. Hegel’s “logic” concerns the progress or development of Spirit through history, whereas philosophical logic, as generally understood, is a theory of valid inference.¹⁸ Therefore, we shall use “logic” in quotation marks here because Hegel’s dialectic is not a logical theory in the sense of being a theory of valid inference. For developmental psychology and the philosophical analysis of its central notions, the important point is that a mature adult way of thinking will not assume that one must only accept either the thesis or the antithesis but aims at a wider synthesis of the claims made in both. As mentioned, this is sometimes taken to imply that mature adult thought is capable of embracing logical contradictions (Basseches, 1984). Next it will be argued why we should avoid such a description and rather maintain that adult cognition is capable of recognising contradictions that are only apparent and making a difference between contrary and contradictory opposites.

Let us consider the following example to illustrate the claim. Imagine a community in which the notion of orange colour is not known and two members of the community are debating about the colour of oranges (the fruit).¹⁹ One is arguing that oranges are yellow, the other one that they are red. This is a contradiction in the sense that the claim that oranges are yellow and that they are red cannot be true at the same time. However, it is not such a contradiction that exhausts a two-valued logical space (yellow and not yellow) and therefore no third truth-value needs to be introduced in addition to truth and falsity. This is simply because both claims (i.e., the one that oranges are yellow and the one that they are red) are false. Let us then assume that a third person from outside the community enters the scene and says that the colour is orange. This new, enhanced conception of the colour in a sense incorporates the two antithetical views within it because the orange colour is a mixture of yellow and red. However, no many-valued logic is needed to analyse this example because the new claim (oranges are orange) is true, whereas both the antithetical claims (oranges are red, oranges are yellow) are false.

Those views are, in a sense, closer to truth than the claim that oranges are black, for example, but this observation causes no problems for two-valued logic.

Real controversies are of course more complicated than this imagined debate about the colour of oranges. However, a mere increase in complexity does not imply modifications to logic. Rather, it seems that one central feature in adult mature ways of thinking is exactly the capacity to recognise logical space, i.e., the capacity to see that there are possible claims that are perhaps true, in situations of debates analogous to that about the colour of oranges. For instance, the question of whether light should be understood as waves or particles could be a similar case. Although in terms of logic both cannot be true at the same time, they might both be false, analogously, to the claim about oranges as yellow or red. A new perspective might be found that allows one to reconcile between the two interpretations and find a new, more accurate one. In general, recognising the possibility that two opposing views are not necessarily the only alternatives, i.e., that the alternatives in a certain debate can both be false, allows one to form a new, better informed view that is capable of integrating the essential elements from the earlier antithetical views.

The same applies to the concept of change. In the dialectical theories of human development, change is identified as a central feature of reality that dialectical thinking is claimed to reflect. The following simplified example shows why change as such does not require many-valued logic. Consider, for instance, an apple that is first green, then ripens and turns red. In a sense, this entails that the apple is both green and red, which are two conflicting properties that cannot belong to the apple at the same time but come to belong to it at different instances of time. However, recognising this does not influence the way in which we should analyse what logically follows from what. The apparent contradiction is solved simply by recognising that the two conflicting properties belong to the apple at different points of time. It might be a sign of the kind of attitude characteristic of youthful thinking to create a controversy about the colour of the apple on the basis of the evidence, sticking vigorously to the claim that the apple is either red or green. A more mature thinker, by contrast, would be prepared to accept that, at this moment, in this light and under these conditions the apple seems, say, green, but that this does not imply that it should permanently be so. It might change or there might be other lighting conditions in which it appears to be of a different colour.

One additional example can be introduced to illustrate the ways in which mature cognition is able to transcend simplified dichotomies. Sometimes debates are construed in a way that two views are opposed to each other and the impression is created that these views are, as the philosophical terminology puts it, exhaustive. Being exhaustive means that there are no alternatives to the views that are presented. Many classical moral dilemmas are construed in this way. A standard example is the so-called “trolley problem”. In the scenario, a trolley is approaching a rail switch between two tracks. On one track there are five people and on the other only one person. The scenario is that one must choose to guide the trolley on either of the two tracks, i.e., to choose between killing one or five people. Moral theories are often tested with respect to their capacity of offering solutions to these kinds of problems.²⁰ However, some philosophers have criticised these scenarios and suggested that in situations of a moral dilemma one should look for a third alternative.²¹

There is a structural similarity in these dilemmas to the above example about the debate of the colour of oranges. Both assume that two conflicting alternatives (i.e., such that they cannot be true at the same time) exhaust the space of (logical) possibilities. While in principle there could be a pragmatic restriction, the cases are such that there are always other logical possibilities. This means that although the orange cannot be yellow and red in the same respect and at the same time, or that one cannot navigate the trolley on two distinct tracks at the same time,²² the alternatives do not exhaust what is possible from a logical point of view. Orange is a possible answer to the question about the colour of an orange and some moral philosophers argue that we should answer trolley problems in a similar way: look for a third alternative and do everything you can to stop the trolley, for example. There are no logical constraints that would narrow the options down to taking the orange as being either yellow or red or having to choose between running over one person or five people. Unfortunately, logic does not prevent people from sometimes having to face tragic decisions between two or more terrible outcomes. However, such decisions are not a matter of logic, and adding truth-values to logic does not help in saving one from possibly tragic decision-making. It seems, however, that maturity of thought helps one in seeing beyond simplified dichotomies and recognising that there are more options than initially might appear.

Therefore, from the point of view of philosophical logic, there is one central difference between youthful and mature thought: it is the capacity to recognise which oppositions or conflicts are exhaustive and which are not. By contrast, on the basis of the psychological descriptions starting from Piaget’s analysis and criticism to it, youthful thought tends to see all conflicts and oppositions as exhaustive. Often this means a tendency to confuse between contrary and contradictory opposites. Confusing between these two might thus lead one to assume that from one pair of contrary opposites the other pair logically follows. This is not the case because contrary opposites can both be false. For example, if one maintains that the world is not good it does not follow that it is bad because both claims can be false at the same time. The world might be in essence neutral with respect to being good or bad. However, not all conflicting notions that youthful thought might assume to exhaust the logical space are contrary opposites. They might be like yellow and red in our example above. Those are conflicting notions in the sense that they cannot be true at the same time. However, they can be false, and thus it would be erroneous to assume that a debate between such notions is exhaustive, i.e., that there are no other alternatives. As we have suggested above, one crucial difference between youthful and mature ways of thinking could be that the latter can recognise which oppositions are which and whether some conflicting notions exhaust the logical space or not, while the former tends to see all conflicts as ones in which it is necessary to choose between two given options.