Happy new year first of all, to anyone who happens to be reading this. One of my new years’ resolutions is to make an effort to finally understand some concepts that I’ve always struggled to get my head around. I am going to start with the concept of ‘dialectics’. The term ‘dialectic’ comes from the Ancient Greek word dialektikḗ, and referred originally to a dialogue between people holding different points of view about a subject but wishing to arrive at the truth through reasoned argument. The word was given a more technical meaning by the German philosopher Georg Hegel in the early 1800s. In Hegel’s philosophy, the term takes on the specialized meaning of development by way of overcoming internal contradictions.
In the later 1800s, Marx and Engels adapted the Hegelian dialectic method into a materialist philosophy which became known as ‘dialectical materialism’. This theory forms the basis of ‘historical materialism’, their materialist view of history. Although clearly based on Hegel’s approach, Marx claimed his own dialectic method to be the “direct opposite” of Hegel’s, which he considered too abstract and insufficiently rooted in material conditions. The class struggle between capital and labour is the primary contradiction considered as part of Marx’s dialectics because of its central role in the social and political lives of a society. Another key contradiction is that between the use value and exchange value of commodities, on which more below.
In a recent (2023) paper, the British philosopher Graham Priest provided a formal definition of the dialectic method. Priest begins by pointing out that dialectics, in the sense of both Hegel and Marx, involves the study of dynamic processes in which contradictions arise and are ‘aufgehoben’ – an impossible word to translate into English as it means both removed and preserved. (This highlights a perennial problem that arises when translating philosophical texts from the language in which they were originally written.) The closest word we have in the English language is ‘sublation’. Priest aims to answer two questions with his approach: (1) how, exactly, do these contradictions arise? and (2) what exactly is meant by sublation?
The dynamic processes Priest refers to are known as ‘dialectic progressions’. These be thought of as a sequence of stages, which we may label as stage 1, stage 2, stage 3, and so on. All of these stages concern a predicate: a function P() from a set X to the set {0,1}, with the interpretation that P(x) = 1 means that x has the property specified by P(), and P(x) = 1 means that it doesn’t. We start by fixing some element x in the set X. In stage 1, P(x) = 1, in stage 2, P(x) = 0, and in stage 3, P(x) = 1 and P(x) = 0; thus, stage 3 involves a contradiction. Stage 4 involves introducing a new predicate, P’(), with the property that for any x’ in the set X, P’(x’) = 1 if and only if P(x’) = 1 and P(x’) = 0. Thus, in particular, we have P’(x) = 1 and P’(x) ≠ 0.
The predicate P’() has in a sense removed the contradiction we had in stage 3, as P’(x) no longer entails a contradiction; but it has also retained this contradiction, as it was baked into its very definition! Thus, the predicate P’() formalizes the concept of sublation (or aufgeheben). We can continue this process by fixing some element x’ in the set X (which may be equal to x). In stage 4, P’(x’) = 1, in stage 5, P’(x’) = 0, and in stage 6, P’(x’) = 1 and P’(x’) = 0; thus, stage 6 also involves a contradiction. This contradiction can be sublated again by defining a new predicate P’’(), with the property that for any x’’ in the set X, P’’(x’’) = 1 if and only if P’(x’’) = 1 and P’(x’’) = 0. The process can then be repeated again indefinitely, neatly capturing the logical relations involved a dialectic progression.
The process is best illustrated with some examples. The first example involves the development of money. Let us take X to be the set of all commodities, and define the predicate P() by P(x) = ‘x is a use value’. Then at stage 1, P(gold) = 1, as gold is something that is used (as jewellery, etc.). At stage 2, P(gold) = 0, as gold becomes an exchange value (as people trade it). At stage 3, P(gold) = 1 and P(gold) = 0, as gold becomes both a use value and an exchange value. Now define the predicate P’() by P’(x) = ‘x is commodity money’. Then P’(gold) = 1, and at stage 4, P’(currency) = 1, as the value of currency is linked to the value of gold. At stage 5, P’(currency) = 0, as we move away from the gold standard; this is the stage we are currently at.
The second example involves the development of capitalism. Let us take X to be the set of all labourers, and define the predicate P() by P(x) = ‘x is bound’. Fix some generic labourer x. Then at stage 1, P(x) = 1, as the labourer is bound by their feudal chains. At stage 2, P(x) = 0, as the labourer is feed from their bonds. At stage three, P(x) = 1 and P(x) = 0, as the freed labourer is forced to sell their labour-power. Now define the predicate P’() by P’(x) = ‘x is a wage labourer’. Then P’(x) = 1, which completes the first round of the progression. There is of course much more to be said about the development of capitalism, just as there is much more to be said about the example above. In particular, this model says nothing about why these progressions occur. However, I think it nicely summarizes the logical structure involved.