Everything is made of the atoms that make everything else. That means everything has the potential to be broken down and turned into everything else. For instance, a "table" can be broken down. The left-over materials can be turned into a "chair". What does that mean for the categories themselves? If everything has the potential to be everything else, what makes them what they are categorized as? Going back to my "chair" and "table" examples, why doesn't the potentiality of the "table" to be turned into a "chair" mean the "table" is "chair" and vice versa?
The answer depends on your metaphysical presupposition. In naive realism, objects exist independently of the mind. In subjective idealism, objects do not exist independently and are constructed by the mind. A good middle-ground philosophy would be transcendental idealism which strikes a position that things are independent, but cannot be known by the mind, roughly.
What you are asking after is a very old philosophical question around which no consensus necessarily exists, though some views are more popular than others. For a very long time, the dominant view in Western philosophy was that there were natural kinds (SEP):
To say that a kind is natural is to say that it corresponds to a grouping that reflects the structure of the natural world rather than the interests and actions of human beings. We tend to assume that science is often successful in revealing these kinds; it is a corollary of scientific realism that when all goes well the classifications and taxonomies employed by science correspond to the real kinds in nature.
It is also a question related to mereology (SEP) which attempts to systematize thinking regarding how parts and wholes relate. In one extreme view, mereological nihilism, just atoms exist and everything else is essentially a product of the mind:
[M]ereological nihilism says that mereological simples, or objects without any proper parts, are the only material objects that exist... Mereological nihilism is distinct from ordinary nihilism insofar as ordinary nihilism typically focuses on the nonexistence of common metaphysical assumptions such as ethical truths and objective meaning, rather than the nonexistence of composite objects.
Immanual Kant in the 18th century put forth a comprehensive philosophy in which he claimed that the human mind was capable of detecting what are known as Kantian forms. From Britannica's entry "form":
For the 18th-century German philosopher Immanuel Kant, form was a property of mind; he held that form is derived from experience, or, in other words, that it is imposed by the individual on the material object. In his Kritik der reinen Vernunft (1781, 1787; Critique of Pure Reason) Kant identified space and time as the two forms of sensibility, reasoning that, though humans do not experience space and time as such, they cannot experience anything except in space and time. Kant further delimited 12 basic categories that act as structural elements for human understanding.
Central to this philosophy is the notion of Das Ding-an-sich, which is a real object that is ultimately unknowable. While I won't respond in detail regarding the various philosophical positions, it bears worth that this very debate still is firmly planted in the debate among contemporary scientists who see themselves aligned in a spectrum with scientific realism on one end, and instrumentalism on the other. Scientific realism probably reached it's zenith with the logical positivists who attempted to show the universe was objective by initially trying to show that observational statements could support confirmationalism and put a rigorous footing to the sciences; ultimately, theory ladenness emerged as a response and the logical positivists conceded their program of radical scientific realism had failed.
Today, philosophers are all over the board, but many in the analytic circles have embraced a naturalized epistemology which accepts the detente between scientific realism and instrumentalism. The linguist George Lakoff has put forth a position known as embodied realism, a type of embodied cognition that looks to show how the public and physical world we share as humans is colored by the physical and conceptual experiences we have as codified by our language:
In philosophy, embodied cognition holds that an agent's cognition, rather than being the product of mere (innate) abstract representations of the world, is strongly influenced by aspects of an agent's body beyond the brain itself.1 An embodied model of cognition opposes the disembodied Cartesian model, according to which all mental phenomena are non-physical and, therefore, not influenced by the body.
Here's a graph from that article:
John Searle talks about this a lot. His ontology is there are objects which are mind-dependent and objects which are mind-independent. To understand why this is his ontology, the Chinese Room thought experiment exemplifies how these two categories of objects exist and their implications for the mind and computation.
I would like to pause for a moment to ponder why we should accept anybody’s theory of mind in light of Descartes. It seems like an impossible task, yet some have to take it up if we are to make any kind of progress. Enter Searle who does not claim this is an ironclad ontology, but a better answer than competitors to going beyond Descartes. It is a way forward among few.
His two categories of objects is not a dualism like Descartes. Rather a mind or observer must have a perspective, and we call all perspectival information and objects mind-dependent. Language, syntax, information, qualia, etc are mind-dependent and tables and mountains are mind-independent.
Importantly, mind-independent stuff exists regardless of an observer. That mountain existed before any biological and observer-life has no bearing on its existence. Othello, language, syntax, etc do no exist without there being a mind/observer.
Why this is not a full blown dualism like Descartes is that Searle believes physics/biology can eventually explain how minds and mind-dependent objects are made from physics, just like mountains and tables.
No matter how minds emerge physically though, it seems obvious that certain objects can’t exist without them. These are the mind-dependent. (And this is why computation is mind-dependent to Searle and why computation alone can’t produce intelligence but that is another topic).