Hylomorphism

Aristotle's hylomorphism

In a previous post I discussed the problem of universals. Briefly, Plato held that universals (like redness, roundness and numbers) exist in a higher realm of the Forms.

On the other hand his pupil, Aristotle, held that universals are immanent in particular things in the everyday, natural world. In fact, he considered every physical thing (termed a particular or a substance) to be an inseparable compound of matter and form. This view is called hylomorphism, where the Greek word hule means matter and morphe means form.

Consider a coffee cup. It has a round rim. For Aristotle, the roundness of the rim (a universal) is part of the form of the cup. So too are the cup's other identifiable characteristics such as its color and weight. But the cup also has a material aspect - it's made of ceramic. Without that material there would be no cup. Similarly, without the form, there would also be no cup. Thus the cup necessarily consists of both matter and form. It's not possible to extract the roundness of the rim or the weight of the cup - the form is inseparable from the cup.

Nonetheless we can think about the roundness of the rim or the weight of the cup. We can even think about a circle as a geometric shape separate from any particular thing at all, consider its geometric properties, and transform it to, say, an oval. This is a process of abstraction. The form is in the cup, but we can think about it in a purely formal manner separate from the cup. That separation is epistemic, not ontological - there are no formal circles floating around the universe apart from the particular cups, checker pieces and rings that exhibit that form.

For Aristotle, hylomorphism is applicable to all things, from atoms to plants, animals and humans. In the case of human beings, Aristotle is the particular (or primary substance), his body is the matter and his soul is the form. The species and genera are secondary substances. So human being and animal are secondary substances of Aristotle.

It's interesting to compare Aristotle's view to the modern view where the hard sciences are considered to be concerned primarily with matter, hence the prominence of materialism. Aristotle's broader naturalism, on the other hand, fully includes notions of purpose, meaning, morality, intentionality and everyday experience. For Aristotle, all things are a holistic integration of form and matter. And it is in our experience of things that we discover their true form (nature).

The problem of universals

This apple is red and so is that stop sign. Bob has two arms and two legs.

The apple, the stop sign and Bob are all individuals or particular things. When we say that the apple is red or that Bob has two arms, we are predicating something of those individuals. And when the same thing can be predicated of more than one individual, then that thing (say, redness or the number two) is termed a universal. A universal is just a general characteristic that those individuals have in common.

Now the status of individuals seems straightforward. We say that there is an apple there - it exists and we can see it and also eat it. But the status of universals seems less obvious. Is redness something real? If so, how does it happen to be in many places at once, in both the apple and the stop sign? And also, the number two seems very abstract, not a physical kind of thing that can exist like the apple and Bob do.

In philosophy, this is called the problem of universals. Plato was the first to discuss the issue in depth and proposed that universals do exist, but they exist in a higher realm of the Forms. So there is an ideal or perfect form for redness, a form for the number two, and a form for every other universal. The (imperfect) individual things that we can see around us are said to participate in those perfect forms. This view is called Platonic realism.

Aristotle (who was Plato's student) strongly disagreed with Plato on this issue. In his view, universals were indeed real, but they were not separable from the individuals that they were found in. That is, there is no redness independent of particular things that are red. This view is called moderate or immanent realism - the universals are immanent within the individuals.

A third view, nominalism, denies that universals are real at all. There are only the names we use and there is no universal quality that they have in common.

My own view is that Aristotle's immanent realism best captures what we implicitly mean when we assert things about individuals. The characteristics that the individuals have in common are not merely naming conventions or the creations of humans. Instead they are necessary for the individuals to be observable in any form at all. Granting that, there also seems to be no good reason to posit a non-natural realm for universals to reside in. They are simply features or aspects of the natural world that we experience, albeit at a more abstract level that requires human intelligence to be able to identify and reflect on them.

The image above shows part of the School of Athens fresco by the Italian Renaissance artist Raphael. It depicts Plato pointing towards the heavens where he supposed the ideal forms to be. It also depicts Aristotle gesturing downwards to the here-and-now world that he held universals were a part of.

A simple solution to the Gettier problem

Long ago, Plato proposed that knowledge is justified, true belief. That is, your beliefs count as knowledge if you have good evidence for them and they are actually true. Otherwise they are either mere opinions or false beliefs.

This definition seemed to reflect the common use of the term through history. However, in more recent times, Edmund Gettier provided counterexamples showing that if a belief relies on a false premise, then it won't commonly be regarded as knowledge. For example, you may believe the correct time by looking at the clock on your wall. But your belief doesn't count as knowledge if your tacit assumption that the clock is working is mistaken.

My amendment to Plato's definition is to recognize that for a conclusion to be known, any essential premises also need to be known. This is a slightly stronger formulation than William Lycan's excellent no-essential-false-assumptions analysis.

My proposal for the definition of knowledge: For S to know that P is true means that:
(1) P is justified
(2) P is true
(3) P is believed
(4) S knows that the essential premises of P (if any) are true

One intuition for this definition is that knowledge is constructed hierarchically like building blocks. If a low-level building block fails, then building blocks that sit on it are not supported and so also fail.

Square quotes

How would you measure, with a ruler, the square root of the number two?

One way to figure it out is by reading Plato. In Meno, Socrates shows how you can construct a square with an area of eight feet from a square with an area of four feet (that is, with two-foot sides). To do this, join four squares with four-foot areas together to make a larger square with a sixteen-foot area. Then draw a line between the midpoints of the adjacent sides of the sixteen-foot square to make a new interior square (see diagram). This cuts each four-foot square in half along the diagonal. Since you have cut each four-foot square in half, you now have eight two-foot triangles, with four of the triangles joining together to make a square with an eight-foot area.

You can follow a similar procedure to create a square with a two-foot area from a square with one-foot sides. Since the area of a square is equal to the side length squared, the side length of a square with an area of two feet is the square root of the number two, now easily measurable.

Or you could skip the philosophy and just read Pythagoras instead! The square of the hypotenuse is equal to the sum of the squares of the other two sides.