This post is a part of my ongoing series, "A few things wrong about the cosmological argument." Previously, I gave several examples of actually infinite sets of objects in physics. The next logical step is to argue that these objects are "real" objects, thus showing that real objects can be actually infinite.
But wow, arguing over what is real just seems like the the pinnacle of metaphysics silliness. It belongs in the same category as questions like, "If you replace all the wood of a boat plank by plank, is it the same boat?" or, "What if you're just a brain in a vat?"
It's not clear to me that there is any consensus about the definition of "real". Thus, I think that any argument which hinges on the details of the definition of "real" is a flawed argument, since it assumes something we don't agree on. I'm not sure there is any point to arguing over such a thing, so I think I will just muse about physics instead.
Physicists use "real" in a number of distinct ways.
Sometimes, we simply mean "that which is not caused by instrumental artifacts and experimental errors". For example, if we use a digital caliper to measure some lengths, we might read the numbers 0.015, 0.330, 0.845. The lengths are discrete (in multiples of 0.005 inches), but this is only a limitation of our device. Thus we would say that the discreteness is not real, and that lengths are really continuous.
Other times, "real" means "actualized in nature", as opposed to "maybe self-consistent, but not actualized in nature". Neutrinos are real, but tachyons probably are not. Minkowski space is real, classical space is not. Stable carbon nuclei are real, stable uranium nuclei are not. And so on. This definition is used to talk about theories which seem self-consistent, but are nonetheless false in our universe. Note that all these theories are basically mathematical,* so I have no problems with saying that a mathematical concept is real. In fact, I have more problems with the claim that there is anything real which is not mathematical.
*Neutrinos and tachyons have different four-velocities, Minkowski space has a different geometry from classical space, carbon and uranium are defined by different numbers of protons.
We might also use "real" to mean "that which is most fundamental". Of course, the most fundamental object in physics is the universal wavefunction, which specifies the state of the universe. The universal wavefunction is a ray in Hilbert Space, which is (you're going to like this) a space with an infinite number of dimensions, each of which can take on an infinite number of values.
But what does fundamental mean? A fundamental theory is one that is valid everywhere, and from which other theories can be derived (though it may be too difficult to actually derive them).We can also talk about theories which are more or less fundamental. The more fundamental a theory is, the larger its range of validity, and the more things can be derived from it. Particle physics is more fundamental than statistical physics, which only applies to systems much larger than our ability to calculate. Statistical physics is more fundamental than biology, which only applies when there is a particular large-scale pattern of molecules. Biology is more fundamental than psychology, which is more fundamental than sociology, and so forth, you know the deal.
We could define "real" as "that which is sufficiently fundamental", given some arbitrary threshold for fundamental-ness. If I happen to think baseball is real, I have to say sociology, psychology, biology, and physics are real too, since they're all more fundamental than baseball.
I'm pretty sure that physicists are not using the same definitions of "real" that philosophers are. But that's the point. There are lots of sensible definitions of "real", and not all of them allow the cosmological argument to work. So if we consider the premise, "Infinities may not exist in reality," we must know what definition of reality applies.
The applicable definition of "reality" is decided by how we argue for the premise! If the argument involves instrumental artifacts in experiments, then the applicable definition is "that which is not caused by instrumental artifacts." If the argument involves theories which are self-consistent, but not true in nature, then the applicable definition is "that which is actualized in nature". If the argument is just hand-waving, then we don't know what the applicable definition is, and the cosmological argument is flawed.
(I will also make a weaker argument, that I cannot think of any non-pathological definition of "real" which has the qualities that the cosmological argument requires. William Lane Craig thinks that there are a finite number of past events which are real, and that future events are not real. But on a fundamental level, the past and future are equally real.* And the idea of a finite number events seems contingent on what we, with all our human biases, consider to be events or not. Incidentally, in physics, an "event" is just a point in space-time, which is a far more objective definition. By this definition, there are an infinite number of events in the past, present, and future. Lastly, one of my examples of real infinities was particles which are beyond our observable range. It would take an unusual definition of "real" to exclude objects simply because we cannot see them.)
*I note that my favorite physics blogger said exactly the same thing earlier this month, and it's clear he's not even thinking about the cosmological argument.
"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one
7. Uncertain beginnings
8. Entropy: The unsolved problem
9. Kalam as an inductive argument
10. Getting from First Cause to God