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In the early days, atoms existed according to Democritos. I think Democrites just hypothesized this to build up his world view.

Probably there would have been also philosophers who claimed that everything was divisible to infinity (was perhaps Aristotle such a person?)

But when asking in nowadays physics it is said that elementary particles can't be divided anymore, because the just decay in certain given other particles.

But is this view of nowadays physics the truth? There are muons electrons quarks and neutrino's which can't be divided anymore. But why should this be true? Why can't a particle be split into infinity? Ok, it is probably hard to do so, but is there a more profound 'law' which does state this view?

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    "But why should this be true? " Until a new, more complex theory will be discovered/invented showing that we can split them.
    – Mauro ALLEGRANZA
    Mar 16, 2017 at 20:07
  • AFAIK, the ancient idea of "infinite divisibility" is that matter is a continuum so that if you have a clump of earth, you can cut it in half and now have two clumps of earth. Talk about splitting a particle such as an atom into very non-atom-like subparticles such as protons, neutrons, and electrons, and then splitting protons into very non-proton-like particles such as quarks is qualitatively an extremely different idea.
    – user6559
    Mar 16, 2017 at 22:35
  • There is also string theory. Quantum particles being composed of strings. But, what are strings made of? What is the source of that thing?
    – takintoolong
    Mar 17, 2017 at 2:10
  • My first thought is that if a particle has extension it has parts and if it is unextended it does not. Thus any extended particle is divisible (in principle at least), and until it ceases to be extended it continues to be divisible. Whether we can actually divide it in practice is not an important philosophical question.
    – user20253
    Dec 13, 2017 at 14:12
  • @PeterJ: I think Aristotle would carefully distinguish between the possibilities of potentially divisible, but actually not; and potentially divisible, and actually divisible.
    – Mozibur Ullah
    Dec 14, 2017 at 18:29

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This is more of a physics question than a philosophy question, but the answer sketch is that things like protons appear to have internal structure and were eventually shown to be made out of smaller particles, whereas the things we call elementary particles instead appear to be point particles.

Nonetheless, people do theorize that even those are made out of smaller constituents, although there is no current evidence to support anything like that.

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  • it isn't, there is no experiment that could show satisfyingly that all matter is ultimately indivisible/divisble
    – Lukas
    Mar 16, 2017 at 21:48
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Your questions belongs to mereology, the (part philosophical, part mathematical) theory of part and whole. We should begin by distinguishing between parthood and proper parthood. Something is a proper part of some other thing iff the first is part of the second, and the two are not identical. Something is a part of something else iff the first thing is a proper part of the second, or both are identical.

Let's call something that has no proper parts a simple, and everything that has proper parts a composite object. Then the view you ascribe to physics is the view that the fundamental objects are simple, while the others, you and me, chairs and tables, are composite.

There are philosophers who think that everything is infinitely divisible (Anaxagoras would be an ancient example). This idea, or stuff that is infinitely divisible, is often called 'gunk'. For gunky objects it is true that every part again has a proper part. (Lewis introduced this term in his book Parts of Classes.) There is also a wiki-article for gunk.

As to the contemporary state of physics, I'd like to point to the efforts of Arntzenius (2008), who argues that a point-free physics can get around some problems. Instead of points (which are indivisible) Arntzenius proposes gunky space or spacetime, which is thought to have

the advantage of collapsing certain distinctions to which the laws of nature are insensitive, for example the distinction between open and closed regions. (Sider 2013)

Literature:

Arntzenius, F. (2008): Gunk, Topology and Measure, in: Oxford Studies in Metaphysics: Volume 4. Oxford University Press.

Sider, T. (2013): Against Parthood, in: Oxford Studies in Metaphysics: Volume 8. Oxford University Press.

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The "law" is Atomic Theory, which states that all of matter is built up from discrete indivisible pieces. They may not be what you or I call "atoms," for we know that we have "split the atom," but rather they use the word to describe its original intent of being indivisible.

Atomic Theory is, of course, not a proven theory but rather a set of assumptions which have a history of being useful for physics and chemistry. Its profoundness is not so much that it is "true" as that it is "useful." It's also very versatile. While a modern Quantum Mechanical treatment of a photon recognizes that it does not have one specific position and one specific velocity, it does assume that you can treat the photon as a single entity with a state (typically represented as a tensor). Even in the strange world of QM, atomic theory proves useful.

One major aspect of atomic theory which is important is its relationship to mathematics and set theory. If you don't assume Atomic Theory, you have to be careful not to tread beyond the realm of the set theory that is typically used as the foundation of the mathematics behind science. Modern set theory forbids a set to contain itself (there are some non-mainstream set theories which relax this rule). With Atomic Theory, it's quite easy to remain within that safe domain, because you build up from indivisible atomic elements -- a rather safe construction approach. Without Atomic Theory, you do have to pay attention to make sure you don't accidentally create a theory which depends upon sets that are not sets. (Source: personal experience and a solid 2 months of philosophizing down the drain)

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Seems like a rather old fashioned and poorly researched question to me. There are no "particles" in the sense of pointlike, indivisible pieces of matter. The branch of physics dealing with this scale is ironically still called particle physics but is essentially the QFT which expands QED and QCD. The mathematical formalism rigorously provides results that agree to incredible accuracy with observation through every experimental test. As such, it is accepted within the cutrent standard model and is therefore the best fit theory physicists have at this time. The dynamic properties of fields, then, may be expressed and detected by experiments designed to identify the values at a point in space. These experiments may yield results that are congruent with an intuitive presumption of particular nature.

'divisibility' requires a notion of internal complexity. This complexity is evident in the proportional quantised energy states from the ground state to its next available. For example, a proton can be excited with smaller ratio of energy to its ground state, due to the fact it is composed of quark gluon ensemble which have far many more arrangements to be possible with given energies - An electron would require far more energy to reach a higher state so therefore is far less internally complex and currently considered 'fundamental' until such time as high energy experiments are possible (maybe they wont ever be) to probe this scale.

a math-light, elementary description is given by Susskind in Stanford uni youtube series on string theory.

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