I’ve decided to start a series on the problem of universals as I’m slowly working through Marilyn McCord Adams’s massive two-volume work on Ockham.
I’ll blog my way slowly through each of the myriad alternative medieval positions and maybe if I get ambitious I’ll try to say something comparing and contrasting medieval and contemporary positions.
Right now the plan is:
- Part I. Introduction.
Motivating the Problem
A universal is a type that is multiply instantiable and particulars are tokens of those types. The word “rabbit” contains six letter tokens, but only five types. There are six individual letters, but there are two instances of the same kind. Consider Socrates and Plato who are both human beings. They are numerically distinct individuals. But they are the same kind of thing (they are specifically identical). The problem of universals is to say what accounts for Socrates and Plato’s being the same kind of thing, even though they are two different particulars.
Why is this problem important? Well, in his excellent SEP article on this topic Gyula Klima points out that knowledge of universals is crucial to the Aristotelian conception of science. He offers a mathematical example:
How do we know, for example, that the Pythagorean theorem holds universally, for all possible right triangles? Indeed, how can we have any awareness of a potential infinity of all possible right triangles, given that we could only see a finite number of actual ones? How can we universally indicate all possible right triangles with the phrase ‘right triangle’? Is there something common to them all signified by this phrase? If so, what is it, and how is it related to the particular right triangles?
What we know when we learn the Pythagorean Theorem is something about the natures of triangles and hence it is true universally and necessarily, which is exactly the sort of thing we want our scientific knowledge to be. There are at least two really interesting interrelated questions here. The first is a semantic question: What does the phrase “right triangle” in “Let ABC be a right triangle . . .” refer to? What does “man” in the sentence “Socrates is a man” refer to? There is also the metaphysical question I’ve already mentioned above: Just what is a nature and how is it possible that the same nature could exist in two numerically distinct instantiations?
Modern discussions of the problem of universals tend to treat the metaphysical problem exclusively and ignore the connection to the semantic problem and the epistemological/philosophy of science problem of how necessary knowledge is possible. This concern for the systematic interconnection of the different problems is what I find really helpful about the medieval approach.
Different Types of Solutions
In his second commentary on Porphyry’s Isagoge, Boethius points out that there are four big families of positions on the metaphysical status of universals.
- Universals do not subsist; they are in the understanding alone. Nominalists.
- Universals subsist outside the understanding and are corporal. Roscelin’s view.
- Universals subsist and are incorporeal and “separate from” the particulars. Plato.
- Universals subsist and are incorporeal and they are “in” the particulars. Aristotle.
I’ll have the most to say about options 1 and 4, because those are the two positions that attracted the most attention in the Middle Ages.