Three questions about fundamental particles
First: Are fundamental particles mereological atoms?
Fundamental particles are 'the ultimate constituents of the world', those upon whose properties and relations everything else supervenes. Many of us believe that the instrinsic properties of complex things supervene upon the properties and relations of their consituents. Then maybe the fundamental particles can be identified with the ultimate constituents of the world, if there are any. In fact, when we find that some things are composed out of smaller things, we will usually not call the complex things 'fundamental particles'. I think it is in this sense that fundamental particles are supposed to be indivisible -- not because we lack the means to break them into parts, nor because it is impossible 'in principle' to break them, but simply because they lack (proper) parts.
Second: Can an extended thing be a mereological atom?
On the one hand, assume that some thing exactly occupies two adjacent spacetime regions A and B. Then how could it fail to be the mereological sum of two smaller things, one occupying just A, the other B? It thus seems that mereological atoms would have to be as small as the smallest units of spacetime, that is, as points. On the other hand, if some thing A is the mereolgical sum of B and C, I would have thought that A occupies the spacetime region occupied by B and the region occupied by C, and no region distinct from those. But if spacetime is dense, and an extended thing is the mereological sum of fundamental particles, and those particles are point-sized, then any extended thing must contain infinitely many fundamental particles (continuum many if spacetime is real). I guess we should reject the premiss that physical things are mereological sums of things that lie within their spacetime region. For even if we ignore the issue of indivisibles, there is a lot of void within the spacetime region of this table. And yet the table fully occupies the region. We can't count the void as part of the table because the void doesn't exist. Since it would be very odd to claim that a thing is not the mereological sum of all its parts we should perhaps count the empty spacetime itself as part. At any rate, the above argument breaks down: There are things, such as the table, which fully occupy an extended region of spacetime even though there are subregions of that region not occupied by any thing which is part of the big thing. The case of extended atoms is of course still somewhat stranger. Here we'd have an extended thing fully occupying a region even though no subregion of that region is occupied by any part of the thing.
Third: Are any of the particles currently postulated by physics point-sized?
Magdalena says one shouldn't take physicists seriously when they say so. She also showed me a book, according to which (on an account called 'classical') the diameter of electrons is 2.8e-15 m. (Does 'classical' in physics mean 'not quite right'?)