Organs and Organisms
At first sight the distinction between organs and organisms looks clear and principled: an organism is an individual animal or plant while an organ is a functional part of an organism. An organ functions on behalf of an organism while an organism functions only on behalf of itself. But this apparent clarity begins to blur once we examine the matter more closely. Consider symbiosis: here one organism uses another as an organ, in effect. If the symbiosis is mutually beneficial, each organism uses the other as an organ, since the other functions as an aid to survival for its partner. It may even be a vital organ, if one organism can’t live without the presence of the other. If the benefit goes only one way, then one organism functions as an organ for the other but not vice versa (e.g. a spider using a plant to anchor its web). Some parasites function as organs inside the host organism, as with those bacteria that aid digestion. If we think ant colonies are organisms in their own right, then each ant is an organ within the whole colony. Why aren’t parent organisms effectively organs that help offspring organisms survive? Why aren’t the trees that birds live in organs of birds? The concept of an organ is functional and many things act functionally to aid the organisms they interact with: there are organs within animal bodies and there are organs outside of them (bird nests, beaver dams, spider webs, etc.). Come to think of it isn’t the whole environment of an organism one of its organs, at least in so far as it affects the survival prospects of the organism? Symbiosis is defined simply as (unlike) living things living together, and this is ubiquitous. Many organisms are simultaneously organs for other organisms. In addition, if we follow selfish gene theory, each organism functions as an organ for the survival of the genes: the organism is a “survival machine” enabling genes to be passed onto the next generation—not different in principle from hearts and kidneys.  And isn’t what we call the self or mind really an organ of the biological body, enabling it to reproduce itself? Persons are organs with respect to reproducing bodies (not only that of course). Being an organ is defined functionally and the concept allows for a very wide extension, including whole organisms. Perhaps every organism is an organ of some other organism (e.g. fleas and lice).
But what about the other way round—are organs also organisms? Not as the terms are customarily used: we don’t normally speak of the heart or kidneys as organisms in their own right. We know that some organs are organisms by the above reasoning, but are all? Are there theoretical reasons that could justify extending the label “organism” to all organs? How, indeed, are organisms to be defined so as not to generate this consequence? Merriam-Webster defines “organism” as follows: “A complex structure of independent and subordinate elements whose relations and properties are largely determined by their function in the whole”. But doesn’t this apply straightforwardly to organs within the body? They too are complex structures made up of functionally interacting parts (think of the heart). We can’t add “and is not an organism” because some organs are organisms. The OEDoffers the rather unhelpful, “An individual animal, plant, or single-celled life form”: this is irredeemably disjunctive and fails completely to say what animals, plants, and single-celled life forms all have in common that makes them organisms. It is instructive that the term “organism” was only introduced in 1774 and is not part of natural language: it is clearly intended to cover and unify a wide variety of cases (“animal” is not general enough). It expresses a cobbled together concept designed to fill a taxonomic gap. It is obviously derived from “organ” and carries some of its sense: an organ is precisely an integrated discrete biological structure that behaves in a unified way. True, organs typically exist inside whole bodies, but this is not a necessary truth and is hardly part of the very definition of an organ. Organs could be organisms in some possible world (as mitochondria in cells were once independent bacteria): the organs constituting bodies could be organisms that have come together to form a more complex organism, perhaps leaving the collective when the time is ripe. Couldn’t it turn out that animal bodies on earth are all composed of organisms that have joined together: they may each have their own pocket of sentience and their own evolutionary agenda. In effect, they function as parasites or symbionts in relation to the rest of the body. But even supposing this not to be the case, there are good theoretical reasons for classifying organs as organisms, i.e. as not fundamentally distinct from what are usually called organisms. For the organism-centered view of biology is really an out-of-date anthropocentric approach to biological phenomena. Natural selection selects primarily for organ-types—that is what the survival of whole animals and plants depends on. The genes have to build good hearts and kidneys and brains, so that their own survival will be ensured: these are the true units of natural selection. These are what compete in the battle for survival. Ultimately this is because traits are the essential entities, and organs have traits.  Natural selection operates over traits of organs, selecting hearts and kidneys that perform their function better than other hearts and kidneys. Organisms survive because their organs are well designed, not because they have properties that somehow go beyond the properties of their organs. We tend to focus on organisms because we are organisms ourselves, with consciousness and intelligence; but nature has no special interest in those traits of (some) organisms. In the case of insentient organisms we have a bundle of organs and the entire process depends on how well they function: they are what survive (or don’t) into the next generation—along with the genes that make them. The evolutionary process is gene-centered and trait-centered, with organs carrying the selective burden; whole organisms are just vehicles for these entities (the true replicators). The organism, as traditionally conceived, is a secondary player; the organs are the elements of the evolutionary mechanism. The species or group is made up of individual animals or plants and has no evolutionary significance apart from that (there is no species or group selection), but the whole animal or plant is made up of its organ parts and has no evolutionary significance apart from this. Thus we may as well homogenize the field and classify organs as organisms, i.e. as the functional units of natural selection. The distinction between them is artificial from the point of view of scientific theory, reflecting as it does an anthropocentric view of the biological world. What we really have are genes, biochemical molecules, cells, organs, and collections of organs (“organisms”): these are the true natural kinds of biology—the entities with objective existence and nomological relevance. Biology need not employ an ontology of organisms at all, as organisms are traditionally conceived. 
I think clarity is served by instituting another terminological revision (dated 2021): let us introduce the neologism “biocule”, based on the familiar “molecule”. Cells, organs, and organisms are all biocules—life forms of various types, biological entities. The evolutionary process operates over biocules, these being the true natural kinds of biology. We can certainly carry on speaking of cats and cabbages, hearts and kidneys, but we retire the organ-organism distinction, save as a vernacular convenience. Clarity is served by collapsing that distinction, thus rating organisms as organs and organs as organisms, so far as biological science is concerned. The official designation is “biocule” construed as a more general and abstract type of biological entity. The term “organism” has outlived its theoretical usefulness, and it was always rickety (what about viruses?). It really is, as the OED concedes, a disjunctive concept with no unitary overarching meaning. Animals and plants and single-celled life forms are really very different, and using “organism” for all of them is misleading in suggesting a common essence. Up to 1774 people got by with more restrictive nouns like “animal” and “plant”, which are perfectly kosher; the neologism “organism” came from a craving for generality (Wittgenstein’s phrase) that has no real basis in nature. Now that we are used to identifying other entities as the units of natural selection (notably genes) we can move away from the focus on individual organisms. Organs and organisms are not importantly distinct from the point of view of biological science, and hence from an accurate vision of how nature is objectively organized. 
Let me end with a fun thought experiment designed to nudge intuition in the direction I am recommending. Suppose some entrepreneurs decide to market internal organs as pets. They detach the organs and put them in tanks, still alive, still glistening. Hearts still pump, kidneys still filter, brains still think (or send nerve impulses around). Customers keep these organs in tanks like fish and give them pet names. They grow fond of them. They put decorative plants next to them. Wouldn’t they come to regard them as like whole organisms? After all, they are composed of living biological tissue and have a definite structure, just like regular pets. The organs have become organisms—units of life with their own separate existence. It’s only because we don’t normally see organs that we refuse to see them as organism-like; once we get to know them we might shift our attitudes towards them. Surely the brain is very like a typical organism in that it houses sentience—a whole species might just consist of brains floating in vats!  The deep similarities between organs and the bodies in which they are located are sufficient to warrant a classificatory scheme in which no deep distinction between them is recognized. We just have biocules at different scales: from cells (and their constituents) to organs (and their parts) to organ systems to totalities of organ systems (organisms). The organ-organism distinction is really an untenable dualism. We may keep it for pragmatic reasons, but it is no part of a properly scientific conception of biological reality. 
 Does biology need to worry about whether caterpillars and butterflies are identical organisms? Does it matter to biology whether organisms exist over time? Does biology need to distinguish organisms from ensembles of traits?
 I haven’t discussed whether genes are also organisms. The question brings up the issue of whether genes are living things. I am inclined to say yes, because of their role in the generation of life and their propensity to replicate. They function symbiotically in relation to the body, coexisting with it to their mutual benefit. Are they also organs? Some might say they are organs of the organism, enabling it to reproduce itself in offspring; but this is really the wrong way round—it is more that animal bodies are organs of the genes, enabling them to reproduce themselves. Questions of taxonomy are theory-dependent, so taxonomic labels may have to be altered when theory changes. We are now at the point at which genes, organs, animals, and plants are all rightly grouped together as biocules, with the notion of organism used promiscuously or not at all.
 Is the mind an organism? The brain is, given that bodily organs are. The idea is not outrageous, ordinary speech notwithstanding: it is a biological organ like other biological organs and has many biological properties (hereditary, functional, vulnerable to sickness and accident). It’s an organic unity, a biocule, a chunk of biological real estate (among other things).
 We make a distinction between tables and chairs but that distinction is no part of physics: its natural kinds don’t coincide with the kinds distinguished in ordinary discourse. Similarly for “organ” and “organism”.