Are you asking for objections based upon current knowledge? If so, atomism had been completely replaced by quantum theory where wave-particles replace particles, and everything is enabled so there v is no clear boundary.

I'm looking at ancient objections rather than modern ones but thank you for that response- it's incredibly interesting.

I'm looking at ancient objections rather than modern ones but thank you for that response- it's incredibly interesting

I presume you will have been given a copy of Lucretius’ De Rerum Natura? That is one of the classic texts of atomism.

One objection to Lucretius’ theory is that, if ‘heat atoms’ indeed transfer heat from the sun to the Earth, where do they all end up? You would think they would accumulate in vast numbers once they had arrived.

Another common objection is that, if atoms truly are ‘dimensionless points’, then how can they come into contact? Because if they can come into contact, then they must have a surface or a side. But if they have a side, then they’re not dimensionless at all. And if they’re not dimensionless, then they can be divided, so they’re not indivisible (which is what atom mean, ‘a’- not ‘tom’ cuttable.)

Ancient objections to atomism are discussed in a chapter of the book The Shape of Ancient Thought, Thomas McEvilly.

Thank you so much. This was incredibly helpful.

And if they’re not dimensionless, then they can be divided, so they’re not indivisible (which is what atom mean, ‘a’- not ‘tom’ cuttable.) — Wayfarer

Not to be contrary, but how does this follow? Let's imagine that the physical world is made of tiny cubes. The cubes are so tiny that our eyes cannot see them individually. Of course we don't have modern technology to rely on either. Just because we could imagine slicing that cube into pieces would not entail that we could in fact do so.

Also:

The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible, and have always been and always will be in motion; that there is an infinite number of atoms and of kinds of atoms, which differ in shape and size. — Wiki

So where does 'dimensionless' come from in the post above? That's what caught my attention. Democritus would not have been plausible at all if his atoms had no volume.

Also:

If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis, or the atomic fact, or whatever you wish to call it, that all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied. — Feynman

Well, I’ll have to go back to my copy of Shape of Ancient Thought to recall the details of the arguments, which are essentially Buddhist (as atomism was also debated in ancient India).

But it seems to me quite logical to say that if something has a physical shape, that even if it is minute in size, then it can’t be thought of as ‘indivisible’. Because if it has a shape, it has aspects, and an aspect is a part. So if it has parts, how can it be partless?

Also, the ancients did not, as far as I know, have any conception of the electro-magnetic field, or indeed of electrical energy as such, although they did know of magnetism. But I think that without the concept of a field, the model of ‘the atom and the void’ can’t be realistic, as the only kind of energy it allows for is kinetic, presumably.

Regarding the Feynmann quote, obviously ‘the atomic hypothesis’ has been extraordinarily fruitful in terms of this history of science. But I think it is still an open question whether there actually is such a thing as ‘an indivisible particle’. Particles are now considered excitations of a field, whatever that is. The ‘standard model’ of particle physics is apparently in something of a crisis at this point, although the arguments are arcane and really not relevant to the study of ancient atomism.

In any case, De Rerum Natura, which I presume the OP is studying, is a philosophical classic and well worth studying even if the underlying ideas have been superseded by later discoveries.

Having volume doesn't mean being dividable Something could occupy volume, but be impossible to divide. ...though there might be insufficient information to know whether it's really indivisible--as atoms were initially expected to be.

Michael Ossipoff

Here is an objection against ancient atomism that I have heard:

Ancient atomism postulates two things - 1. atoms, and 2. void.

Now, between atoms there are two options that may obtain. Option 1 is that there is something between the atoms. Because everything is made of atoms, this something must be just other atoms. Therefore, on option 1, there are only atoms, not void. Option 2 is that there is nothing between the atoms. However, if there is nothing between the atoms, then those atoms are in direct contact, and again, there is no void, only atoms. Either way, there can be only atoms, not atoms and void.

I think this objection was proffered by Zeno.

Here is another objection to ancient atomism that I think I came up with, but maybe I heard it somewhere I don't really recall...

Atoms are either something or they are nothing. If atoms are nothing then there is nothing, not something. But there is something, so atoms must be something. But if atoms are something then they must be made out of something. Since everything is made out of atoms, that means atoms must be made out of atoms. But if atoms are made of atoms then atoms are not indivisible. Therefore, by the definition of atoms, there cannot be any atoms.

At best, antiquated Parmenidean sophistry.

When I wrote these two objections, I thought to myself, "well these objections are quite good." But now that I reflect on the first I think to myself, "perhaps Zeno is confused about the difference between nothing and empty space." For surely there can be empty space between things without there being nothing there. But I must now admit that were Zeno to press the issue and say, "NotAristotle, what is the difference between empty space and nothing?" I will be at a loss to answer. How might we answer him?

If Zeno is engaging in mere sophistry, then he must only be appearing to say something true, but is not saying something true. But he either says something untrue because he does not know the truth or wishes to deceive us as to what is true. But then we have two reasons to answer the question, because by answering we may either avoid deception, or we may help Zeno know the truth. So let us re-examine the matter in earnest. Again I ask, how might we answer Zeno?

[W]hat is the difference between empty space and nothing? — NotAristotle

Empty space is a kind / state of space which, having a property (empty or non-empty), is not nothing.

I hope you do not mind if I am a bit argumentative, but if space is something in the universe, then it must be somewhere, right? But where is space?

The question makes no sense since the universe is itself – is constituted by – space(time). Where (or when) is the universe? :roll:

At best, antiquated Parmenidean sophistry. — 180 Proof

Answering the OP, the fundamental issue from Ancient philosophy is exactly to read Parmenides by Plato. I think you would have to refer to that one. As it states in Parmenides, we don't have the book from Zeno anymore and Plato himself opposed the Eleatic School. Hence our understanding of the Eleatic School is very thin. That @180 Proof calls it sophistry is the mainstream view, although looking at the history of mathematics after the Greeks, the Eleatic schools counterargument was indeed valid. How much you can built a philosophical view upon it is another question.

Mathematics overcame this basically only with limits and the modern interpretation of infinitesimals. That happened far later. And these findings would have surprised the Ancient Greeks, just like they were surprised to find irrational numbers themselves (as they first thought that math had to be so perfect that every number had to be rational).