Is Existence a Property?

Describe a hundred-pound note as completely as you can. Give its serial number, the exact wear on its corners, the position of every fibre. Now add that it exists. Have you said anything further about it?

The question is not idle. If existing is a way of being, like being crumpled or being blue, then a description that leaves it out is incomplete, and a description that includes it says more. If it is not, then a great deal of ordinary philosophical practice is misdescribing what it does, and one famous argument for the existence of God collapses immediately.

The argument that provoked the question

The ontological argument attempts to establish that God exists from the concept of God alone. Descartes gives a compact version in the Fifth Meditation: the concept of a supremely perfect being includes every perfection, existence is a perfection, so a supremely perfect being exists. The argument needs existence to be a property that a thing can have or lack, because it needs existence to be among the perfections a concept can contain.

Kant's own statement of the point runs: "Thus when I think a thing, through whichever and however many predicates I like (even in its thoroughgoing determination), not the least bit gets added to the thing when I posit in addition that this thing is." He concluded that being is not a real predicate, while allowing that it functions as a logical one, so that "God exists" is a grammatically respectable sentence which nonetheless does not attribute a feature.

The distinction Kant is drawing is between predicates that determine a thing, narrowing down which thing it is, and the bare positing of the thing so determined. Blue determines. Crumpled determines. Existing does not narrow anything down, because it does not distinguish one candidate from another: every candidate is already fully specified before the question of existence is put.

Making the objection precise

Kant said what existence is not. Saying what it is instead took another century, and the answer came from Gottlob Frege, who supplied the machinery that lets the claim be stated exactly rather than merely felt.

Start with the two levels the account depends on.

The examples make the level shift easy to see. Being a horse is something individual horses have. Being had by many things is not something any horse has; it is something the property of being a horse has. Once the two levels are separated, Frege's proposal can be stated in one line: existence belongs to the second level.

"Horses exist" is not a claim about each horse. It is a claim about the property of being a horse, namely that something has it. "Unicorns do not exist" is the corresponding claim that nothing has the property of being a unicorn. Frege put the point in terms of counting: affirmation of existence, in his words, is in fact nothing but the denial of the number nought.

That is Kant's objection with the vagueness removed. Kant's point was that existence does not determine a thing. Frege's account explains why not: existence is not at the level where determining happens.

The predicate

This is the technical payoff, and it explains why "some horses exist" and "there are horses" say the same thing while looking so different. In the regimented notation there is no separate word for existing. The existential quantifier does the work, and it does it at the second level, saying of a condition that something satisfies it.

It also disposes of the difficulty from the first article of this tier. "Pegasus does not exist" looked like a sentence about Pegasus, and therefore looked as though it needed a Pegasus to be about. On the Fregean treatment it is a sentence about a property, saying that nothing has it, and no Pegasus is required for that to be true. The tangle dissolves without admitting a single non-existent object.

What follows for the subject

Three consequences are worth carrying forward.

The ontological argument, in the form Descartes gave it, does not survive the analysis. Later versions recast in modal terms are a different matter, and philosophy of religion takes them up.

Existence claims are claims about whether conditions are satisfied, which means that the ontological question about any kind is the question whether anything satisfies the condition of being of that kind. This is what makes the paraphrase strategy powerful: change the conditions your theory says are satisfied, and you change what your theory says exists.

Existence is not a way of being among others. Nothing has existence as a feature alongside its shape and mass, and so nothing is available to be sorted into degrees or modes of existing. Views that do want such degrees, and there are some, have to fight the Fregean analysis rather than assume it away.

The last article of this tier makes the second of these precise, and gives it the name it carries in the rest of the subject.