Are there really atoms?

By atom I mean the literal denotation of the word: something which has no parts, as conceived by Democritus and Leucipus. Today atoms are strings, or branes, or whatever object that we may fancy as being the end of the line in the decomposition of things into smaller parts.

Kant’s second conflict of the transcendental ideas is formulated in relation to the notion of simple substance, in the sense of a basic form of atom or monad. Let us formulate the antinomy without his Aristotelian semantic operator of substance/accident. I will use two principles which I consider evident:

Principle alpha: A composite object is constituted either by simple or by composite elements.

Principle beta: An object, whether simple or composite, can only be conceived through a defined and finite sequence of mental processes.

A. Every composite object in the world is constituted by simple elements, and nothing can be conceived anywhere but the simple or what is constituted by simple elements.

1. Suppose the contrary: composites are not constituted by simple elements, then by principle alpha, they are constituted by composite elements.

2. Since there are not simple elements by assumption 1, the series of composites keeps going on forever.

3. By principle beta, such object cannot be conceived.

4. Then composites have to be constituted by simple elements.

∴ Our thesis A is valid.

B. No composite object in the world is constituted by simple elements, and nothing simple can be conceived anywhere.

1. Suppose the contrary: There are simple elements and composite objects are constituted by them.

2. A simple element can only have one single property which defines its identity.

3. Simple elements cannot be identical. When we say that A≡B, we are saying that there is one and the same property in both A and B but; but we are saying also that we constitute a property with two things, i.e. that they are not simple but a composite.

4. Simple elements cannot be different. When we say A≢B we are ascribing two properties to A: the property which defines its identity as A, and the property of being different from B. And analogously for B.

5. If simple elements cannot be identical nor different, they cannot be defined.

6. Since they cannot be defined, they cannot be conceived through a sequence of mental processes (principle beta).

7. We cannot conceive simple elements.

∴ Our antithesis B is valid.

It does not make any sense that both thesis and antithesis are valid.

The idea that there are atoms is absurd, and so it is the idea that there are not simple parts in the universe. These ways of thinking express the problems in the application of concepts of ordinary experience (Lebenswelt) such as “simple/composite” beyond ordinary scenarios. Physics steps very easily in metaphysics, in fact, it could not avoid it, for it has to carry intuitions from everyday life (Lebenswelt) into the formalized world of science (Überlebenswelt). Physics needs basic building blocks, objects and relations, to construct its theories, but does not need to reify them and declare them final entities of a universal order. Such attitude implies that as a science has to renounce to the unreasonable ambitions developed in the present as the ultimate kind of knowledge, and embrace a modest but necessary position as our tool to construct concepts for the experience of space-time and matter.