Vasubandhu seems to make arguments in this article against the concept of atoms to prove all is appearance in consciousness. But doesn't this go against modern science,even if his arguments are logical? I mean modern science says that atoms exist.
This idea is well known in Mahayana literature, one could say it's a standard idea. What the argument is about, though, is not whether atoms exist at all, but whether they exist as something substantial. Similarly, we are not questioning the existance of rainbows, rainbows do happen - they just don't exist as something solid one could touch.
You won't argue that atoms are not solid nor made from smaller pieces of matter. Even the planetary model is a vast simplification. And of course, the elementary particles that atoms are made from - are not substantial either.
The point of the argument presented by Vasubandhu and others is that as you go down to the microscopic level, you won't find any matter, nor anything substantial at all, nor will it be static and stable, as everything under closer examination is a dynamic system made up of something else, of some interactions.
The statement an extended, part-less whole—is incoherent is correct, but it is not against experimental science. It's against Metaphysics or some over-extended theoretical physics which asserts the existence of a building block for matter.
Experimental scientist are still splitting the smallest particle, and they never claim the existence of a part-less whole. They just follow reason and reason tell us that anything spatially extended can be split in half.
What the Buddhist say is... go on split but don't expect to find the final smallest particle, because that small which can't be cut in half but is extended in space doesn't exist and if the part doesn't exist the whole heap is a dream.
Quoted below is Shadtideva ...
As long as a collection of conditions lasts, the body appears like a person. Likewise, as long as it lasts with regard to the hands and the like, the body continues to be seen in them.
In the same way, since it is an assemblage of toes, which one would be a foot? The same applies to a toe, since it is an assemblage of joints, and to a joint as well, because of its division into its own parts.
Even the parts can be divided into atoms, and an atom itself can be divided according to its cardinal directions. The section of a cardinal direction is space, because it is without parts. Therefore, an atom does not exist.
What discerning person would be attached to form, which is just like a dream? Since the body does not exist, then who is a woman and who is a man?
(Skt.). An atom, being the smallest unit of matter posited in Buddhism and defined as a speck of matter which is partless and indivisible. Standard Abhidharma doctrines hold that each paramāṇu is a composite of various dharmas or their ‘seeds’, but this view was criticized by Mahāyāna followers of Yogācāra andMadhyamaka who maintained that such atoms were conceptual fictions as their existence was logically incoherent.
Both is correct according to Theravāda Abhidhamma.
Paramāṇū's elements are exist, when they are arising an still not vanish and still possible to exit when their origins still available to cause them (AbhidhammatthaSaṅgaha Chapter 8 PaccayaNiddesa).
But the Paramāṇū is concept, illusion of those elements. We imagine Paramāṇū from the elements we known in 6 doors. The concept, illusion, is not exist (AbhidhammatthaSaṅgaha Chapter 8 PaññattiNiddesa).
Why Paramāṇū is not exit?
Because Paramāṇū never arise and vanish, never be, never caused by any origins. It is in only imagination, but never arise and vanish. In MahāsatipaṭṭhānaSutta, the buddha taught students to analysis the body to be Dhātu to purge Paramāṇū into 4 elements which really caused by origins.
If we find the origins of concept, illusion, in dependent origination the the practitioner is going to think "there is a thing which has no cause no origin and controllable, self". But if the practitioner analysis everything into elements, they see the truths "every element is depending many origins, and every origin causes many effects. Every elements vanish immediately when it arising because it is depending on uncountable unstable origins. No real self which one can really control."