Concepts of Existence: An Intuitive Introduction

Concepts of Existence

Consider the following: some dogs are brown.

(In what follows, I use the phrases, property, first-order property, predicate, first-order predicate, as synonyms. They each mean roughly: a feature of some individual object. So a second-order property or second-order predicate is a property or predicate of an individual's first-order property. The considerations below suggest that 'existence' is best understood as a second-order property and not a first-order one. This will all be more understandable after you read below!)

Given the truth of the above it seems to follow that some dogs exist. We do not need to add to the above claim: Some dogs are brown and they exist. Once we know that some dogs are brown, we already know that they exist. So, existence is not really a property of anything in the way that, say, being brown is a property of some dogs.

So, it looks like thinking existence is a property is either unnecessary or incoherent. If x is F, then x exists. Indeed, x’s being F presupposes that x exists. x cannot be F without existing. So saying that x is F and x exists is either unnecessary or incoherent.

Think of it like this: existence cannot be a property of a red ball. If it was a property or a first-order property (same thing) then we would have to say something like the following:

            x is a ball and x is red and x exists.

So, we have a ball that has the property of being red attached to it, and the property of being existing attached to it.  But what the heck is existence attaching itself to? The ball? But it has to exist for it to have the property of being red. Doesn’t it have to exist for it to have the property of being existing. It looks like we are double-counting or worse. In saying that a red ball exists we are really just saying that something is a red ball. Something is both red and a ball. There is something that is both a ball, and it is red. And this simply amounts to the following logically perspicuous way of putting:

            (3x)(x is a ball & x is red)

OR

            (3x)(Bx & Rx), where B = __is a ball, and R = ___is red

The above just says: There is an x such that x is a ball and x is red.

Not only do we not need a separate property of being existing, adding that property is, in reality, either unnecessary or incoherent. The fact that something is a ball and is red assumes that it exists.

Suppose existence really is a property (a first-order property). If it is, then (many people think) non-existence is a property too. In general, many people think that if F is a property, then ~F is a property. Or more strongly, F is a property just in case ~F is a property. But now denying the existence of something is incoherent.

Pegasus does not exist. That is true. But not, it seems, if non-existence is a property. For if non-existence is a property, and if in order for something to have properties it must exist, it follows that Pegasus has to exist in order to have the property of non-existence. So, assuming that existence is property and that for any property F, F is a property just in case ~F is a property, implies that Pegasus both exists and does not exist. Yikes!

Question: What do you think?

Question: How can the advocate of The Thomistic Proof reply?