In Knowledge and facts we met Alfred Tarski’s Condition T, “ ‘Snow is white’ is true if and only if snow is white.” Thus, Tarski defined ‘fact’ in the formal sense, as a proposition or sentence in object language – ‘Snow is white’ –, of which the truth value could be checked against snow being actually white or not. However, there are many caveats. “Ravens are black” is only partly true. “Farmers in the Middle Ages were poor” is relative. “JFK died in Dallas” is incomplete. “This line is straight” is an idealization. “Two plus two is four” is about nothing concrete. Yet all of the above statements may play a satisfactory role in narratives where further specifications seem unimportant.
If further specification is necessary, power over narratives becomes important, see Truth and power, but even in open discourse, the truth value of imprecise propositions may be at stake.
‘Identity’ goes back to the Latin ‘idem’, meaning ‘the same’. Identity is an association between two things: a being and its representation, e.g. in language, be it a proper name – John F. Kennedy –, a generic term – president of the United States – or a specific description – who was shot in Dallas, Texas in November 1963. Identity is here defined as the most extensive factual representation of concrete beings. Thus, identity is a cluster of formal facts: representations, expressed in propositions or sentences. Identity does not exist mind-independently; it is given by humans. In the ideal situation, it is everything that is known about a being. This brings up the questions of how to discern between beings and how to identify them.
Leibniz’s Law famously speaks of the “identity of indiscernibles”: according to Leibniz, no two concrete beings can be exactly identical. Even if they are intrinsically the same, they will still differ because of relations with other beings and because of existence in different places or at different times. If they are indiscernible in all of these respects, they are one and the same thing. In the French original of his Discours de Metaphysique (1686), Leibniz used “identité” in the meaning of identicality, which might offer a more comprehensible naming of the law in modern English: “(numerical) identicality of indiscernibles”. Since Wittgenstein’s 1921 Tractatus the dominant view is that reality consists of facts or ‘states of affairs’, not of objects and their properties. Thus, beings are beings by their own unique complex of facts as ascribed to them, i.e. their identity.
All beings exist in physical interaction with the rest of the world. Identity, like all knowledge, is necessarily incomplete, because much may never be known, least of all the precise future. The identity of a being includes all intrinsic as well as spatiotemporal and relational facts about it, structured by the processes leading to its present existence. These processes comprise everything physical, including all actions of living beings. In principle, identity also extends into the future insofar as we know it, see Truth and time.
Only a few parts of a being’s identity are necessary for a being’s identification as being. Identification is based on membership of categories. Immanuel Kant used ‘category’ in the meaning of “one of the a priori conceptions applied by the mind to sense-impressions.” This means that according to Kant, categories, classes, sets and the like are not ‘given’ by reality as such: they are human concepts meant to organize knowledge. A classic example is Dmitri Mendeleev’s periodic table, where chemical elements are divided over various intersecting categories, depending on the main physical or chemical feature of that category. The periodic table shows that human categorizing is influenced by physical features. If not so, we would have nothing to go on in terms of recognizing patterns.
To identify beings, it will in many cases be sufficient to point out their membership of only a few categories. Silicon is in period 3 and group 14 of the periodic table. Although their identity is far more complex, for living beings, identification works exactly the same way. There has been only one of the John F. Kennedy’s who became president of the United States: membership of only two categories is sufficient to identify him.
There’s a lot missing from this identification: that his wife’s name was Jacky, that he had a son bearing the same name as he, that he delivered a speech in Berlin just after they built the Wall, that he withstood Khrushchev in the Cuba crisis, that he was shot in Dallas, Texas in November 1963 – and quite a lot more. The proper name “John F. Kennedy, president of the United States” identifies a particular human being – its referent, but it does not constitute his identity. Identification is based on any small number of categories a being belongs to, the crossword principle: “President during the Cuba crisis”, “Jacky Onassis’ first husband”, “Crystalline metalloid used in electronics”, “Marsupial feeding on termites”.
Which facts from a being’s identity we use for identification depends on the narrative that links that being’s existence to other beings. The essence of a being is not definable by absolute criteria: it is defined by a being’s role in the actual narrative.
JFK’s identity is essentially a story, a narrative, just like the whole of history is essentially a narrative on identities, see Truth and history. The whole of knowledge and how we came to know it is a narrative, the totality of formal facts about all beings. Although our sources of knowledge about identities are essentially historical, also everything we know about a being’s future is part of its identity, see Truth and time. As an identity contains all that is known about a particular being, we can conceive the idea of narrative just as easily for the identity of objects as for living beings. Objects change over time because of all kinds of physical and chemical processes. They swell, shrink, change places, wear down, fall apart, or end up in relations with other beings. All these changes are part of that being’s identity, constituting its entire history insofar as known. This includes all asserted causal chains leading to its existence from the beginnings of the universe.
Just like all other knowledge, narratives about beings are necessarily incomplete. JFK may have had a genetic predisposition for Alzheimer’s disease, but we shall never know. Something may have happened to him as a child, but it may not have been recorded. Of most objects, we don’t know exactly when they came into existence. Many objects as well as living beings do not even have their own particular, separate identities. They are only known through simplified narratives, or generalizations, e.g. “Numbats feed on termites.” This proposition is sufficiently verified, but it does not imply that numbats share an identity. All of them are different, metaphysically because of Leibniz’s Law and also physically, however little. Rather should we say that what we know of Myrmecobius fasciatus fasciatus is not exemplified in individual numbats: it is what all numbats are known to have in common: evolutionary background, looks, physiognomy, behavior, etc. Part of these can be used to identify them as numbats, but they do not ‘constitute’ their identity. Ever smaller complexes of facts enable us to identify numbats as marsupials, as mammals, as vertebrates, as animals, as living beings. It depends on the subject of a narrative which complexes of facts we use to build our story from. Therefore:
Every attempt to know the world either from transcendental categories – like Plato’s Forms, Plotinus’ One, Thomas Aquinas’ God – are bound to fail. We structure the world through our – limited – observational and intellectual capacities.
According to many philosophers, sets, classes, categories and the like exist mind-independently, either in a transcendental realm or in the real world. Philosophers all give their own account of the one-many relation: how can we reduce the ‘manyness’ of the world to patterns, principles, or even to a One? But as I showed above, sets or classes of concrete beings are intellectual constructs, only definable a posteriori, from shared physical histories, the overlapping parts of their unique identities. However strong the empirical evidence for the relatedness of certain groups of beings, reality does not offer a structure, apart from the physical laws that govern it. In my opinion, abstract objects are relicts of a period in the history of philosophy, when they were needed to substitute scientific knowledge of the physical world. Trying to save them is a rearguard action.
To give a critique of the classic ontology of overlapping identities, I use the traditional example: color. “The roses in my garden are red” Are they all equally red? Does their redness change over time? Is their redness a unique redness or a redness they share with all other red objects? Is redness existentially different from scarletness or crimsonness? Much of this discussion stems from days when people had no idea of the physical nature of color. Nonetheless, philosophers keep gnawing on it up to the present, in spite of the fact that everybody who has a rose garden knows the answer: there are as many reds as there are red roses. To call ‘redness’ a category is to unnecessarily create an abstract object that isn’t even sharply definable.
How can we ever know abstract objects? They don’t make sensory impressions the way red roses do. This objection is equally fatal to universalism and trope theory. Universalists will typically hold that ‘redness’ is a universally existing property, that is instantiated – made actual – by several beings at several moments in time. Trope theorists will say that every red rose – or any other red being – has its own unique, particular redness at some particular point in time, which they call a trope – a state at time t – although trope theories do differ. Trope theorists thus avoid the universalist’s problem to explain why shades of red are nonetheless instantiations of one universal redness, but tropes add nothing to explain the one-many relation: how are all of these shades of red related?
A naturalist way to ask that question is: why do red objects go under the name of ‘red’? Calling objects red is based on resemblance. To be precise: they do not resemble each other because they are red, but we call them red because they resemble each other. Seeing resemblance is caused by one of the main heuristic functionalities of the human brain: systemic thinking, see Coincidence, determinism and free will. We generalize sensory perceptions: colors are patterns. We ourselves do the categorizing, but the borders of these categories are not fixed; we may argue over the color of a rose: Red? Scarlet? Crimson? Texts from the Middle Ages show far less names of different colors than modern texts, and some physically very pure colors – e.g. magenta, the exact balance between red and blue – never got their own name until much later. Besides this, not all humans are equally capable of discerning between colors. Color experts will see far more shades of red than the rest of us. So, color just doesn’t come nicely categorized.
Does this all mean that color only exists in the eye of the beholder? Is it possible that we all see colors differently? Already in the 1920’s, colorimetricians succeeded to quantify and measure color spectra as seen by human vision. Objects have colors because from daylight, they absorb all color, except for the part that they reflect. Which part they reflect depends on the physical nature of the object’s surface. Chlorophyll in plants absorbs all colors but green, carotenoids do the same with all colors but orange, cobalt molecules with all but blue and so on, mixtures will produce shades of colors. The way we perceive these colors is determined by the structure of the human retina. Primates see color better than most other mammals, but butterflies and bees see ultraviolet colors unperceivable by the human eye, that guide them to the hearts of the flowers they visit. So, color exists in reality, and there is not the slightest reason to see colors as metaphysical categories such as universals or tropes.
Returning to numbats: they are not a species because we humans think that its members look or behave alike. Biological categories, like species, families and orders have overlapping evolutionary histories. However, also these histories are representations of reality, formalized into facts, that serve as basis for narration. The same can be said of lifeless objects. Consider very similar rock formations far apart from each other. They will be built from more or less the same chemical material by more or less the same physical processes. Nonetheless, each formation will have its unique extension, precise chemical structure, location, causal timetable, identity. These rock formations can only be a class because their histories resemble each other. Even if a supposed class of physical objects shares its origin, such as the objects of our solar system, discussion continues about classifying them as planets, dwarf planets, planetoids, asteroids, meteoroids, and so on.