Is a mortise something? A carpenter on holes, absences and what is really there

This week I cut forty-two mortises for a cedar door. A mortise is the rectangular hole in one piece of wood that receives the tongue, the tenon, of another. My father taught me to cut them by hand, and I still do for the doors that matter. Each one has a width, a depth and a position, all measured to less than a millimetre. Each one can be too big, too shallow or in the wrong place, and when it is, the customer can see the fault and refuse to pay.

And yet a mortise is made of nothing. It is exactly where the wood is not. When I finish cutting, what I have produced is a pile of shavings on the floor and an absence in the board. My nephew, who is studying philosophy in Tetouan, told me that some philosophers say holes do not exist. I laughed. Then I could not stop thinking about it.

The puzzle

The problem is simple to state. We talk about holes as we talk about things. We count them ("three mortises left"), measure them, move them ("cut it two centimetres lower") and blame them ("this mortise is why the door sags"). If we say that something exists whenever we can count it and say true things about it, holes exist. But what are they made of? Not wood, since the wood is precisely what is missing. Not air, since if I pump the air out the hole is still there.

The old Greeks argued about this. Parmenides held that what is not cannot even be thought, so empty space is impossible. The atomists, Leucippus and Democritus, answered that there are atoms and the void, and the void is as real as the atoms. Aristotle, in the fourth book of his Physics, denied that there is any void at all. Many of the Muslim theologians of the kalām, who were atomists, took the other side and allowed empty space between their atoms. So this is not a modern joke. It is one of the oldest quarrels there is.

The modern version I know comes from a short dialogue by David and Stephanie Lewis called "Holes" (1970). One speaker, a materialist, refuses to admit anything immaterial, and so proposes that a hole is really the lining of the hole: the material around it, the inside surface of the cheese or the doughnut. His friend keeps pressing him with objections, and he keeps answering them, more ingeniously each time. Later, Roberto Casati and Achille Varzi wrote a whole book defending the opposite view: holes are real but dependent things, which exist only in a host, as a shadow exists only where there is an object and a light.

What the Indian schools said

The philosophy I found most useful came from further away. The Vaiśeṣika school of India, whose root text is the Vaiśeṣika Sūtra attributed to Kaṇāda, made a list of the basic kinds of thing there are. Later thinkers in the school, and in the allied Nyāya school, added a last category: absence. They did not mean that absence is a ghostly substance. They meant that "there is no pot on the floor" describes something real about the floor, which a careful list of reality must include.

They also divided absences into kinds, and the divisions fit my workshop surprisingly well. There is the absence of a thing before it is made, the prior absence of the door before I begin. There is the absence that follows destruction, the board after it is burned. There is the absence of something that is never in a place at all. And there is the absence that is really difference: this board is not that board.

They then argued about how we know an absence. The Naiyāyikas said that we simply perceive it: I look at the floor and see that the pot is not there. The Mīmāṃsā philosopher Kumārila said that perception needs something to perceive, and so proposed a separate way of knowing, non-perception, by which we know what is missing from where we would expect to see it. When I look into a badly cut mortise and see that it is not deep enough, I think Kumārila describes the experience better. I am not seeing an object. I am seeing that what I expected is not there.

What the bench says

Here is what my trade has taught me about holes, for what it is worth to philosophers.

First, a mortise has its own conditions of identity, separate from the wood around it. If I widen it by a millimetre, it is the same mortise, made larger. If I fill it with a tenon and glue, I do not destroy it; the joint holds because the mortise is still there, occupied. If I plane the whole board thinner, the wood changes but the mortise may not. This is why I cannot accept the hole-lining view. The lining changes every time I pare the walls, and the mortise does not become a new mortise each time.

Second, a mortise depends entirely on its host. Burn the board and the mortise is gone with it. It has no existence of its own. So I agree with Casati and Varzi that holes are real but parasitic. In Aristotle's language, which I learned from my father without the Greek names, a mortise has no matter of its own. Its matter is the wood around it, and what it is is a shape, a form, given to that wood. Perhaps that is the best way to say it: a hole is the form of a thing where the matter is missing.

Third, and this is what my apprentices learn slowly, many of the most important parts of a piece of furniture are absences. A good cedar panel must sit in its frame with a small gap, because wood swells across the grain in the wet months and shrinks in the dry ones. A panel fitted tight will crack the frame by summer. The gap is invisible to the customer. It is the most important measurement on the door.

The card on ontology asks what there is. I would only add, from the bench: there is also what isn't, and much of a craftsman's knowledge is knowing exactly where to leave it.