Do Abstract Objects Exist?


Do numbers “exist”? What about properties? I know my red apple exists, but does “redness” itself exist?

The existence of abstract objects seems, at first, like a deep metaphysical question. In fact, it’s a question of the pragmatics of language.

A couple of quick definitions. The view that abstract objects do exist is called “Platonism.” The view that they don’t is “nominalism.” Those who think they do exist, but only in the mind, are “conceptualists.”

Let’s take the case of numbers. A typical nominalist argument says that while you may bump into two apples somewhere along your travels, you’re never going to bump into “2.” There is no such thing independent of our descriptions of states of affairs. And that’s all abstract objects are – descriptions. They exist only in language.

The conceptualist replies: the fact that they exist even just as descriptions demonstrates that they do exist – in the mind. Abstract objects are mental fictions, and as such, they exist.

The Platonist’s retort: how do you explain that we all come up with the same mental fictions? When you and I speak of “the number of apples here,” we’re not talking about two different fictions that each of us came up with and which we happened to give the same name to. We’re speaking about the same thing: the number 2!

The Platonist may add that science corroborates the existence of numbers. Science predicts reality, and it does so through the use of numbers. This verifies the fact that numbers aren’t just some arbitrary or socially conditioned way of interpreting the world.…

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I Am God (And So Are You)

That title might sound like a rather mystical, woo-y claim. Maybe it is. I have an argument for it – it comes down to an argument for Indra’s net. All you need to grant me are some standard intuitions about causality and properties, and a particular definition of “God.”

An object is the necessity of every thing else

We’ve got an object – let’s call it “@1” – at some give instant in time, T. There are two ways we can describe @1. We can point to it, or draw some imaginary spatial boundaries, and stipulate that “whatever is there is @1.” This is useful for reference, but it doesn’t tell us anything substantial about @1.

We can also describe @1 by listing out properties. We can say that @1 is at location X, is Y shade of red, has such and such shape and size, is made up of W particles, etc. If we could list out every property of @1, we would say everything that there is to say about it. There is nothing about @1 that couldn’t be conveyed through a property.

Every property of @1 is caused by something. Think of it this way. Every thing is the way that it is because of the arrangement of its subatomic particles along certain basic parameters: location, velocity, mass, charge, etc. If something changes, it is because the arrangement of subatomic particles that constitutes it changes.…

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Zeno’s Arrow

I wrote about Zeno’s Achilles paradox – along with the Dichotomy (a.k.a. Racetrack) and the lesser know Plurality – here. You should read that before reading this. In that post, I didn’t mention Zeno’s other very famous paradox: the Arrow. Though a huge majority of philosophers think Zeno’s other paradoxes were cleared up by calculus and set theory, many consider the Arrow still unsolved. I’ll be arguing that the Arrow, though it appears to deal with separate issues, is really the same Achilles paradox in a different form.

Consider an arrow traveling down a trajectory. Take a snapshot at one static instant. In this one duration-less instant, the arrow is at rest. It is not moving, insofar as motion requires movement from one point to another, and this arrow is, in this one instant, in only one spot. So the arrow is at rest in one instant, at rest again in the next, at rest again in the next. If the arrow is at rest at every instant along its journey, how can we say that the arrow is in motion? When exactly does this arrow travel?

One aspect of the Arrow is simple enough to dissolve: being at rest, defined as “not being in motion,” only makes sense over some duration of time. Motion is defined as distance traveled over some period of time, so it makes no sense to even inquire as to whether motion is happening or not happening when we’re limited to a time range of 0.…

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