This is a complex argument because it involves Philosophy of Mathematics, Reism (i.e., reification), Zeno's Paradoxes, and Abstract Objects rolled up into one.

Philosophy of Mathematics

Does mathematics simply REPRESENT reality or is mathematics more than our mental depiction of things or phenomena in reality - a particular an actual thing or phenomenon itself? In other words, is some phenomenon that is exquisitely described in mathematics with its attendant high correspondence to an observable physical phenomenon really two sides of the same coin? Does mathematics exists in the concrete world in and of itself?

"At first blush, mathematics appears to study abstract entities. This makes one wonder what the nature of mathematical entities consists in and how we can have knowledge of mathematical entities. If these problems are regarded as intractable, then one might try to see if mathematical objects can somehow belong to the concrete world after all." (Philosophy of Mathematics - Stanford Encyclopedia of Philosophy (SEP))

Dever seems to be doing just that, taking a mathematical object (i.e., infinity) and seeing if they somehow "...belong to the concrete world..." (Philosophy of Mathematics - SEP) So how did Dever do this concretization? His conclusion tells us:

*"But when we consider his arguments with an eye to understanding why there should be this mismatch between the mathematical possibility and the physical impossibility of the actually infinite, we discover at every stage that the bond between math and reality is too tightly woven to allow separation." (Dever, n.d.) Dever further elaborates his elimination of distinctiveness in footnote 8, which is on the same page as his conclusion. It states, "That there can be a distinction between what can be accomplished by a particular act in a task and what can be accomplished the whole task is a familiar thought from other areas. Thus, in the area of vagueness, the addition of no particular grain of sand transforms a non-heap into a heap, even though the process of adding all the grains does effect that transformation. Or, in the area of emergent properties, the firing of no particular neuron transforms the non-mental into the mental, even though the process of all the firings does effect that transformation." (Dever, n.d.)*

In other words, Dever simply says there is no line or a geometrically pure one-dimension line between mathematical reality and physical reality. He also says, that one thing or act is sufficient to change states or conditions to their grander version (i.e., a little thing or action can switch states to categorical opposites). If such is the case, then anything found in the mathematical reality can be found in physical reality. So, I should be able to sense [abstract] numbers in the world, let alone infinity. Not two things, but the number two itself because two can cross over now from the abstract realm of mathemics to the real world. Any one seen two or any other number running around lately (see Abstract Objects section below)?

Reism

"Reism is the doctrine that only things exist." (SEP). If there is such a thing as an actual or physical infinity, then it must be a thing. As a thing we must be able to locate it in space and time. More practically, what is this thing - actual or physical infinity - composed of or filled with? Additionally, where would this infinite thing fit into our observable finite space/time universe? This is a contradiction, therefore an infinite thing cannot exist in a finite universe on this basis.

Zeno's Paradoxes

In many ways Dever's argument looks suspiciously similar to Zeno's Paradoxes at least on the possibility of infinity coming from the finite. I am not saying Dever is plagiarizing Zeno, but I am saying it is the same kind of argument for our better understanding and analysis.

"2.1 The Argument from Denseness

If there are many, they must be as many as they are and neither more nor less than that. But if they are as many as they are, they would be limited. If there are many, things that are are unlimited. For there are always others between the things that are, and again others between those, and so the things that are are unlimited. (Simplicius(a) On Aristotle's Physics, 140.29)" (Zeno's Paradoxes - SEP)

Here is the more common explanation of the above argument:

"Assume then that there are many things; he argues that they are both ‘limited’ and ‘unlimited’, a contradiction. First, he says that any collection must contain some definite number of things, neither more nor fewer. But if you have a definite number of things, he concludes, you must have a finite—‘limited’—number of them; he implicitly assumes that to have infinitely many things is to have an ‘indefinite’ number of them. But second, imagine any collection of ‘many’ things arranged in space—imagine them lined up in one dimension for definiteness. Between any two of them, he claims, is a third; and in between these three elements another two; and another four between these five; and so on without end. Therefore the limited collection is also ‘unlimited’, which is a contradiction, and hence our original assumption must be false: there are not many things after all." (Zeno's Paradoxes - SEP)

This is similar to an Infinite Regress argument or what I would call an Infinite Progress (i.e., division or zooming in) argument. Essentially, according to Zeno, this is how you can get infinity from a finite. I would refer the reader to Zeno's Paradox - SEP for further explanation and other similar paradoxes of Zeno. However, this creation of the infinity from finite space does not make that space infinite and the infinity creation is still happening wholly in the mathematical realm.

Abstract Objects

"The abstract/concrete distinction has a curious status in contemporary philosophy. It is widely agreed that the distinction is of fundamental importance. And yet there is no standard account of how it should be drawn (emphasis mine). There is a great deal of agreement about how to classify certain paradigm cases. Thus it is universally acknowledged that numbers and the other objects of pure mathematics are abstract (if they exist), whereas rocks and trees and human beings are concrete. Some clear cases of abstracta are classes, propositions, concepts, the letter ‘A’, and Dante's Inferno. Some clear cases of concreta are stars, protons, electromagnetic fields, the chalk tokens of the letter ‘A’ written on a certain blackboard, and James Joyce's copy of Dante's Inferno." (Abstract Objects - SEP) Dever draws no distinction between Abstract and Concrete objects by saying the one-dimensional line that separates the two is so thinless (i.e., zero width) or seamless (i.e., Dever states "...tightly woven...")that to make the distinction between the abstract and concrete is really arbitrary or some kind of personal choice. So, if I liken, by the Transitive Law, Abstract with Products of Mind with Imaginary Creations, I should be able to bring into physical existence my hearts desires since there is no real or arbitrary distinction between my imagined pile of gold and a concrete pile of gold. Really?

Just my two cents and I am expecting change back.