There are only two options: objects are infinitely reducible, or there are things that are fundamental and irreducible. — Purple Pond

I think the idea that reality is composed of fundamental and irreducible particles was proven as illogical by Aristotle. But if you allow for dualism, such as Aristotle's proposed dualism between matter and form, there are more than just two options.

reality — Metaphysician Undercover

Do you mean the physical world?

such as Aristotle's proposed dualism between matter and form — Metaphysician Undercover

That's not at all what Aristotle proposed.

it can't have a top or a bottom because then it could be reduced even smaller to the top part and the bottom part — Purple Pond

Aren't quarks irreducible? From what I recall, when one attempts to subdivide a quark, the combined matter and energy result in the creation of two quarks exactly alike the one you are attempting to split.

An atom was uncuttable matter. But it still had a shape or form. It still had a location and so a potential for motion. Relatively speaking, it could have a top and bottom from some point of view.

It depends how you are thinking of top and bottom. Are they actually parts or contextual and holistic properties? Are they parts of the material being or parts of the atom’s form?

How is it possible that a particle has no top nor bottom? — Purple Pond

I suspect you are thinking of the particle as being made of 'stuff' (aka 'substance'). That way lie irresolvable paradoxes that Nagarjuna, amongst others, had great fund drawing out and playing with.

One way to avoid the paradoxes is to think of a particle as a force field. There is no 'stuff' to be seen, measured or split. All there is is certain repelling and attracting properties centred at a certain point in space.

That's not at all what Aristotle proposed. — CuddlyHedgehog

No? What did he propose then?
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One way to avoid the paradoxes is to think of a particle as a force field. There is no 'stuff' to be seen, measured or split. All there is is certain repelling and attracting properties centred at a certain point in space. — andrewk

I don't see how this would avoid the problems. Wouldn't the forces have to act within some kind of substance, like the so-called aether? If there was no such aether what would constitute spatial extension? You have proposed forces, and points of interaction, along with "space", but if there is no substance to space, then all the things we observe are just imaginary, products of our own minds, like forces and points are generally considered to be. So you've just inverted everything, saying that the substance is not the object, it is the space. In other words you describe objects as a property of the substance, space, instead of describing space (via measurements) as a property of objects.

Wouldn't the forces have to act within some kind of substance, like the so-called aether? If there was no such aether what would constitute spatial extension? — Metaphysician Undercover

I see no reason to postulate an aether, nor any reason to postulate something to 'constitute spatial extension'. I see spatial extension as something that is brought to our understanding of the world by the mind, rather than an intrinsic property of the world. But even if that were not the case, I see no need to suppose that space is 'made of substance'.

Wouldn't the forces have to act within some kind of substance, like the so-called aether? — Metaphysician Undercover

I see no reason to postulate an aether, nor any reason to postulate something to 'constitute spatial extension'. — andrewk

Yep MU. That is why physics now talks of excitations in condensates.

You have proposed forces, and points of interaction, along with "space", but if there is no substance to space, then all the things we observe are just imaginary, products of our own minds, like forces and points are generally considered to be. So you've just inverted everything, saying that the substance is not the object, it is the space. In other words you describe objects as a property of the substance, space, instead of describing space (via measurements) as a property of objects. — Metaphysician Undercover

It is more tricky. We can't escaped the necessity of some kind of duality - the usual form vs matter, or whole vs part distinction.

And it doesn't work to try to reduce this duality to a monadic stuff. Atomism tried to do that by imagining causal particles in an a-causal void. That sort of works because it accepts the necessity of a duality of part and whole, but reduces the whole to an inert container or backdrop. It gives us a classical picture of causality. However we know that the classical picture actually breaks down as we approach either the global relativistic bound, or the local quantum bound, of scale. Suddenly the context, the vacuum, the spatiotemporal backdrop, becomes powerfully causal again.

So physics has to instead accept an irreducibly triadic view of things. The parts and the wholes must be involved in the third thing of a mutual relation. They must be fundamentally entangled. The reality must be both particle-like and field-like within the one coherent physical description.

You are arguing that it is a defect that physics can't seem to decide - which rules, the particle or the field conception of reality? But the very fact that we have arrived at an invertible relation (one that is formally a reciprocal, complementary or dichotomous relation) shows we are in the right place. If it is actually a contrast of two mathematically inverse models, then we have a larger model that is in fact relating two opposed limits on being.

Our work is done! We have a reciprocal formula that can flip the parts into wholes and the wholes into parts.

This is why there is all the current fuss over holography and the dualities of string theory. Mathematically, we can demonstrate that our best theories of the small scale can be reflected on to our best theories of the large scale, and vice versa. Like particle vs field, they are two views of the same thing essentially.

As ever, only the details need to be worked out. ;)

My understanding is the the Planck scale is theoretically the smallest scale where the predictions of the Standard Model, QM and GR no longer work. That is the scale of hypothetical strings, which would appear as a point to us - no top or bottom - while the rest of the string ran through other dimensions like a metaphysical iceberg, which perhaps just shifts the problem into speculative multi-dimensional realms.

So, to us, the string would appear as a vibrating point, like irreducible bits (as in bits and bytes) of reality.

I agree with apokrisis that the hardware/software and matter/form dualities seem hard to escape. While it seems logical to think of reality as all one thing that expends far beyond our perceptions in every respect, one can mentally break reality up in numerous ways, and not always just in two.

Our work is done! We have a reciprocal formula that can flip the parts into wholes and the wholes into parts.

This is why there is all the current fuss over holography and the dualities of string theory. Mathematically, we can demonstrate that our best theories of the small scale can be reflected on to our best theories of the large scale, and vice versa. Like particle vs field, they are two views of the same thing essentially.

As ever, only the details need to be worked out. — apokrisis

So all that fuss just concerns minor details? I don't think so. String theory is insufficient. Quantum loop gravity is insufficient. It looks more like the big picture is what is missing, not just minor details.

If a true atom is irreducible and the smallest thing there is it can't have a top or a bottom because then it could be reduced even smaller to the top part and the bottom part. — Purple Pond

I disagree. By 'object', philosophers really do mean intelligible objects. The "top" or "bottom" part of an atom, as you say, is unintelligible. They don't count as objects.

Below explains something else that could help with this problem.

Aren't quarks irreducible? From what I recall, when one attempts to subdivide a quark, the combined matter and energy result in the creation of two quarks exactly alike the one you are attempting to split. — CasKev