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(Full disclosure: I’m neither a philosopher nor a logician. What follows is my own inadequate and incomplete understanding of predicate and dialectical logic.)

I was going to call this post “Classical and Dialectical Logic”, and to begin with the syllogism, that form of logical argument which can take many forms, but which follows the basic format: major premise - minor premise - conclusion. For example:

All humans are mortal
All Greeks are humans
All Greeks are mortal

The syllogism explicitly does not concern itself with the truth of either of the premises, simply that the conclusion necessarily (logically) follows from the combination of the major premise and the minor premise. In the 19th Century, this kind of reasoning was superseded by first-order or predicate logic, coming out of the work of Gottlob Frege, but predicate logic still retains some of the flavour of the syllogism.

Predicate logic begins with sets of propositions made on a particular domain. The propositions take the form “there exists an x such that x is a…”. The part of the proposition “x is a…” contains the predicate relationship, familiar to us in the terms of Linked Data triples: subject - predicate - object. For example, in Linked Data we might make the following propositions:

Jane Austen is an author (predicate here is “is”)
Jane Austen wrote Pride and Prejudice (predicate here is “wrote”)

As with the syllogism, we can infer from these two propositions a conclusion:

Pride and Prejudice has_author Jane Austen

This conclusion (called an “inference” in linked data and similar conceptual systems) follows necessarily from the propositions. Similarly, in predicate logic, the modus ponens is also logically valid, and can be thought of as the modern form of the syllogism:

if p then q
p (is true)
therefore q

These logical systems, both classical and predicate, are based on a few foundational principles:

  • The principle of identity (A is A; A = A)
  • The principle of non-contradiction (A is not not-A)
  • The principle of the excluded middle (Either A is true, or not-A is true, and there is no third option)

We use this kind of logic formally in math and science and even parts of librarianship all the time, but we also use it informally so often that the three principles of classical logic form an unconscious fabric of our intellectual engagement in the world. When I go to the grocery store I know there is a thing called milk that I want to buy and that milk is milk (principle of identity), milk is not orange juice (principle of non-contradiction), and that I either buy milk or I don’t (excluded middle). For many things in the world this kind of logical approach works because many things have a more-or-less stable identity (milk is milk).

But there are many things in the world that we deal with materially and intellectually which do not have a stable identity, whose identity changes in two ways: over time, and in relationship to other things. Actually, when we look closer, milk is an interesting example. Milk is milk in relationship to mammals, but is it still milk in relationship to soy beans, almonds, or oats? Colloquially it remains “milk”, but according to certain regulations in the EU for example, non-mammal “milk” is not milk. Milk also changes over time, eventually becoming not-milk in the nutritional sense (i.e. it goes bad). So even seemingly stable identities start to break down when we look at them in particular ways.

I think of this kind of like the laws of Newtonian physics: at an everyday level and a particular human-scale they work fine, but with a different perspective they break down, lose their coherence, and have to be replaced by different laws.

If, when we look carefully, predicate logic is inadequate to account even for something as simple as milk, how much less adequate is it for dealing with the messy realities of human life and society? What is the identity of abstract concepts (“freedom”, “democracy”)? Political formations? Gender and sexuality? The stable comfortable binaries of predicate logic (A or not-A, man or woman, and no third option) break down completely in many of these cases.

One of the different perspectives on logic that takes relationality and change over time into account is the dialectical logic developed by Hegel in the early 19th century. I am drastically over-simplifying Hegel’s logical theory here, but in general, what Hegel argued was as follows:

Every identity automatically implies its own negation (if there’s something called milk there must also be something [or many things] that is not milk). The presence of milk and not-milk at a given moment is unstable, dissonant, and this instability sets change in motion. The motion of things involves the mutual adjustment of milk and not-milk until something that is different from either comes into being.

A good example might be as follows:

There is milk and there is acid (not-milk)
Putting the milk in contact with the acid produces an unstable situation
The unstable situation leads to the milk curdling and the production of a third thing: buttermilk

Now, two things are important to bear in mind about Hegel’s dialectical logic. In the first place it is an idealist theory, which means that Hegel considered thought and being as the same thing, so that mental or intellectual operations were the same as operations in the real world. He would not likely have used an example like buttermilk, but instead used, for example, particular ideas or political categories (like the State) to illustrate his logic. In the second place, Hegel’s dialectic is teleological: he predicts a time when all contradications (that is, the confrontation of a thing with its negation) are resolved in a higher-order perfection. For example, he saw human political history as the working out of various contradictions, and that the achievement of a perfect state (which he equated with the Prussian state of the 19th century) meant the end of political change, that is, the end of history. We are unable to take such teleological theories seriously anymore, but this doesn’t mean that the dialectical process has become obsolete. Rather, it means that the chain of dialectical reconciliation simply goes on: change is permanent.

In terms of idealism, it was Marx who “set Hegel right side up” by coming up with a materialist version of dialectical logic. In other words, Marx sees not only intellectual or mental constructs as subject to the dialectical process, but everything in existence. Engels formulated the laws of this “dialectical materialism” in his book Dialectics of Nature:

  1. The Law of Unity and Conflict of Opposites (i.e. things enter into contradiction with other things).
  2. Over time, quantitative changes become qualitative changes.
  3. The Law of the Negation of the Negation (i.e. the negation of the milk is the acid, the negation of the acid is the buttermilk).

Now, when Marxists talk about the dialectic, there is often an idea that they are rejecting predicate or classical logic. However, as I’ve said, predicate logic fits with many everyday, real-world situations. However, there are many cases in which predicate logic becomes a barrier to understanding; generally cases which involve relationality and change over time. Relationality is different from a predicate relationship. In dialectical logic, the act of writing Pride and Prejudice changes Jane Austen, a change which cannot be represented by making the proposition “Jane Austen wrote Pride and Prejudice” or even recording new predicates which indicate how she changed in the writing. In a very real sense Jane Austen becomes not-Jane Austen through the writing of Pride and Prejudice.

By thinking dialectically we are able to keep track of relationality (the relation of Jane Austen to Pride and Prejudice affects both of them) and change over time (Jane Austen after P&P is not identical to Jane Austen before P&P), but we are also able to keep track of “the negation of the negation”. Dialectical logic requires that we constantly search for the higher unity of any pair or set of contradictions. When, for example, people argue for one or another electoral system (proportional representation or first-past-the-post, etc), dialectical logic requires that we see all of those alternatives as part of a larger unified category (elections, or representative democracy), which leads us to think about contradictions and negations in those categories, and so on. This is why in dialectical thinking the totality is so important. It is impossible to really understand, say, electoral reform in isolation from all the other institutions of representative democracy, which leads us to think about all our other political and legal institutions, which leads us to think about broad relations of power, which leads us to see how electoral reform fits into the totality we can understand as society or (in Marxist terms) a mode of production.

For many people predicate logic is the only logic, because it is easily representable symbolically, which means it was easy to formalize and eventually automate. Computers are the automation of predicate logic - a bit is either 1 or 0 and there is no third option - and all our algorithms bear the traces of predicate logic (“All doctors are men; this gym member is a doctor; therefore this gym member is a man”). But predicate logic has very real limitations, which can be overcome by the application of dialectical logic. (I’m also a fan of applying non-logic or irrationality to problems, but that’s a different post).

The usefulness of dialectical logic becomes more and more apparent the more we think in those terms. Whenever we see something proposed as a binary opposition (either/or), we should suspect that those things are more related than is being let on. Whenever we see something being looked at in isolation, we should suspect that the larger context will be instructive. Whenever we see something posited as unchanging and eternal (capitalism, for example, or gender, or language), we should suspect that those identies are much less stable over time than is being let on. Sometimes there is an intellectual reason for sticking with predicate logic, but more often than not there is a political reason, and so dialectical logic (especially in a Marxist context) helps to look at the bigger picture to see who benefits from insisting on stable identities and isolated analysis. This in itself should suggest that predicate logic and dialectical logic cannot be thought of as two stable, isolated systems, but interrelated ones in productive contradiction with each other. Only predicate logic sees the division between the two logical systems as strictly defined, sees each system as isolated, self-sufficient, and incompatible.

People - especially engineers and computer scientists - tend to really like predicate logic as a way of understanding the world because it is unambiguous and stable. Predicate logic is comforting and comfortable. But the world, and not just the social world, but the natural world as well, is not unambiguous and it is unstable. It is constantly changing, adapting, reconciling contradictions and producing new contradictions. Hiding from that ambiguity and instability behind predicate logic may be comforting, but it has particular social and political effects, and these effects are generally pernicious precisely because they are not in line with the way the social or the material world actually works.

Addendum: I should add that what I said above about algorithmic systems being being conditioned by predicate logic is also true of knowledge representation systems in general. If predicate logic underpins how we intellectually relate to the world, then it underpins how we know and how we represent knowledge. Many of our social relationships get reified first as stable identities and then in our KR systems. Many of the problems identified with classification systems like Dewey and LCSH come down to the reification of particular racist, sexist, and colonial identities through predicate logic.

NOTE: Two books which I found really helpful on the relationships between predicate logic, dialectical logic, and materialism are:

Richard Norman and Sean Sayers, Hegel, Marx, and the Dialectic (Harvester Press, 1980).

John Bellamy Foster Marx’s Ecology: Materialism and Nature (Monthly Review Press, 1999).


Sam Popowich

Discovery and Web Services Librarian, University of Alberta

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