The medieval problem of universals rules everything around me

The comedian Rob Paravonian’s “Pachelbel rant” is one of the first YouTube videos I remember watching. He complains about how soul-numbingly boring it was to play the cello line in Canon in D: eight notes, over and over. He performs a whole comedy bit on the theme that modern pop songs keep reusing (essentially) that same chord progression so that he feels like he is being haunted by the pre-Enlightenment European composer. I am also being haunted by pre-Enlightenment Europeans: the medieval scholastics who debated the realist and nominalist approaches to the problem of universals.

This post is a joke. However, all the autobiographical events described are pretty much real, and they really did make me feel like the problem of universals was everywhere. I wrote a more serious post introducing this topic here. In that post I talk about how at one point in history students in Paris were attacking each other in the streets over their differing interpretations of this arcane point of metaphysics. This is the closest I've come to understanding why it mattered to them so much.

The problem of universals goes like this: think about the colour of grass, the colour of traffic lights that indicate "go", the colour of emeralds. These things have very little in common, they don't look, feel or behave the same, but they are all recognisably green. How is it that we are able to see instances of these things as particulars falling under the same universal class of "green things?". ¹

A version of this problem appears as early as Plato's dialogues but its precise formulation appears in the early scholastic period shaped heavily by the transmission of Aristotelian logic through Ibn Sina and Ibn Rushd. The main scholastic sources are the early twelfth century debate between Abelard and William of Champeaux, and the early fourteenth century debate between Duns Scotus and William of Ockham. ²

I know what you're thinking, "just stop reading medieval philosophy!". It doesn't matter... the scholastics are following me. It sounds paranoid, but they're following you too - you think about their problems every day.

I recently went to my cousin-once-removed's film night. The kids got bored of K-pop Demon Hunters so we switched to screening the original Transformers animated series. You know... the one where all the good guy giant robots have an "autobot" crests on their chests in order to help you recognise them as the good guys. But as I was squinting at these drawings, I found myself thinking: how is it that we recognise each individual crest as a particular instance of the same universal shape, despite variation in line thickness, angle, or scale? If we couldn't we wouldn't be able to tell the good guys from the bad guys.

On the walk home I decided to listen to a podcast about Kant. I've been trying for years to wrap my head around what is going on in his account of schematism, why did Kant think we needed an account of how categories are applied to intuitions in the first place? Suddenly a thought strikes me... no, it can't be... I pull up a translation on my phone³:

In all subsumptions of an object under a concept the representations of the former must be homogeneous with the latter, i.e., the concept must contain that which is represented in the object that is to be subsumed under it, for that is just what is meant by the expression "an object is contained under a concept." Thus the empirical concept of a plate has homogeneity with the pure geometrical concept of a circle, for the roundness that is thought in the former can be intuited in the latter. Now pure concepts of the understanding, however, in comparison with empirical (indeed in general sensible) intuitions, are entirely unhomogeneous, and can never be encountered in any intuition. Now how is the subsumption of the latter under the former, thus the application of the category to appearances possible, since no one would say that the category, e.g., causality, could also be intuited through the senses and is contained in the appearance?

Is the schematism of the categories the transcendental cousin of the problem of universals? Kant is asking what kinds of particulars could even possibly count as instances of a universal concept like causation. I couldn't stop thinking about it the rest of the journey.

So when I got home I decided to clear my mind with some philosophical logic. Something maximally simple and dry, say, for example basic first-order predicate logic. Volker Halbach's The Logic Manual always makes a perfect antidote to the dangers of medieval scholasticism, or worse, continental philosophy. It's essentially a math textbook. I turn to chapter 4 and start to read:

The argument Zeno is a tortoise. All tortoises are toothless. Therefore Zeno is toothless. is logically valid but not propositionally valid: replacing ‘Zeno is a tortoise’, ‘All tortoises are toothless’, and ‘Zeno is toothless’ (uniformly) with other sentences doesn’t always yield another valid argument. But the validity is independent of the meaning of ‘Zeno’, ‘tortoise’, and ‘toothless’; so in order to capture the validity of this argument, I need to analyse the constituents of the sentences. In the language L2 of predicate logic such arguments can be analysed

Oh no...

Is predicate logic just an account of how something can be true of a given particular in virtue of that particular being a member of some universal class?

Apparently the logicians still do scholastic philosophy like everyone else still does scholastic philosophy. Just to torment me. I've started growing a beard because razors remind me too much of Ockham. The scholastics had this one hit 600 years ago and now it's my cross to bear that everyone is playing it over and over.

If they would just stay away from topics I liked it would be better. But they won't, they are shameless, apparently they will follow me to the ends of the earth.

I read some pragmatist philosophy thinking, no, they couldn't possibly follow me into pragmatism. The pragmatists would never waste time debating whether general categories are "real" beyond the particulars that instantiate them. But you know who was a pragmatist? C.S. Peirce:

Consequently, some general objects are real. (Of course, nobody ever thought that all generals were real ; but the scholastics used to assume that generals were real when they had hardly any, or quite no, experiential evidence to support their assumption; and their fault lay just there, and not in holding that generals could be real.) One is struck with the inexactitude of thought even of analysts of power, when they touch upon modes of being. One will meet, for example, the virtual assumption that what is relative to thought cannot be real. But why not, exactly? Red is relative to sight, but the fact that this or that is in that relation to vision that we call being red is not itself relative to sight ; it is a real fact.

I need to escape this problem once and for all. Analytic philosophy is out. So I figure I'll just study psychoanalysis and Foucault secondary literature for the rest of my life. No dice! Ian Hacking. Historical Ontology. Page 26:

In fact, 'ontology' turns out to be perfect, for we are concerned with two types of being: on the one hand, Aristotelian universals - trauma or child development - and on the other hand, the particulars that fall under them - this psychic pain or that developing child. The universal is not timeless but historical, and it and its instances, the children or the victims of trauma, are formed and changed as the universal emerges. I have called this process dynamic nominalism, because it so strongly connects what comes into existence with the historical dynamics of naming and the subsequent use of name.

My only remaining solace is that I was able to spot this pattern emerging before it got too late. But wait... how was it that I was able to see these different examples as particulars of the same general problem of universa- arrghhhhhh!