Philosophical Reflections XXIV
Part A: Knowing
The mind is our means of survival, via its power to know the facts of reality and by knowing them, adapt them to our purposes. Thus the question of how we know things – how to make the most effective use of our mind – is crucial to our life and happiness. In the earliest Philosophical Reflections we looked briefly at this question. Now we return to analyse it in greater depth.
A Rose is a Rose is a Rose
To know anything, we first need to grasp the fundamental nature of reality. And that is, reality exists. It has an independent existence not under our conscious control: it is what it is and does what it does, whatever our wishes or prejudices. There can be no denying this. You confirm it in your own life in every breath you take, every time you open your eyes to see, every time you eat a piece of bread or drink a glass of water, every time you open a door, go to work, smell a rose or comb your hair. If you wish to deny it, I suggest you try to stop breathing. Your own body will soon tell you that reality exists and is not to be denied, and if you wish to continue fighting it you will soon leave it.
The next thing we can say about the individual things which make up reality is that a thing is itself.This is Aristotle’s law of identity, expressed simply as A is A. It is the recognition that objects in reality have a nature, and behave according to that nature. Again, there can be no denying this: it is demanded in everything you do. You eat food and drink water, but avoid poison, fire and speeding cars, because of the known nature of your body and of food, water, poison, fire and hard objects. If you refuse to drink poison or put your hand in a fire, then you admit the truth of the law of identity. I accept no argument on this point unless you put your hand in a fire first! You cannot go on living without accepting that reality exists, and that the things in it act according to their nature: for without that acceptance, you’d never have any idea what to do. You cannot even put pen to paper or open your mouth to discuss it, without acting upon that assumption. Some philosophers, such as skeptics and Kantians, have gone to great lengths to evade this plain fact, but the proper response to them is simple: if a person manifestly doesn’t believe their own words, nobody else should either. If someone tells you something they won’t live by themselves (because nobody can), then they are liars with a hidden agenda – one which has nothing to do with the truth, with how they live their own life, nor with helping you live your life.
All knowledge comes from the fact that A is A. This is true both epistemologically, because it is the foundation of logic, and in reality, as it is the physical basis of our senses. If things weren’t themselves – if rocks were sometimes snakes and light and sound changed their nature mid-flight – then we could see nothing and know nothing. Indeed, were they not basically reliable, something as complex as our senses could never have evolved. That they did, is itself a result and proof of the law of identity. If you wish to argue that our senses are invalid: see how long you can exist unaided with your eyes blindfolded, your ears blocked and your touch deadened. If your senses did not give you reliable information about the world, you wouldn’t have them. Fish that have lived for generations in darkness are blind.
Because a thing is itself, it cannot contradict its own nature. Its nature might change with time – but only within the constraints of that nature. A rock might erode to sand, or a branch burn to ashes, but neither will turn itself into a rabbit and hop away before your eyes. Contradictions cannot exist in reality: if a thing is itself, it is itself, it has a nature and its nature is what it is. A thing cannot be what it is not, do what it cannot do, nor become that which it cannot become!
Contradictions can exist only in your mind and its understanding of reality. Since they cannot exist in reality, any contradiction in your mind indicates an error in your understanding. This then leads us to the first rule of knowledge: to be called knowledge, all you know must be consistent, without contradiction. Any contradiction means that you have misidentified the nature of something, partially or completely.
A Rose is a Flower is a Plant
In Philosophical Reflections 23: The Little People, briefly described our primary process of learning: concept formation. This is the process of abstracting concepts from the individual things which exist in reality, and the further abstracting of higher concepts from lower ones. For example, we integrate our experience of individual roses into the concept “rose”, and integrate “rose” with other similar concepts such as “carnation” and “tulip” into the more general concept “flower”.
Concept-formation is the hallmark of a rational consciousness. We share with other advanced animals the acquisition of information about the world via our senses, and the automatic processing of sensory information into percepts: discrete objects. When you – or your cat – look around a room, your consciousness does not struggle through an undifferentiated wash of colour and sound, you see things, discrete objects already picked out for you: here a bottle, there a table, there a cat. This job is done for you by the nerves in your eyes and brain, before ever reaching your consciousness. Where we diverge from other animals is that our mind integrates multiple percepts of similar kinds into single concepts, identified by words, and integrates these further, without limit. While your cat sees a bottle as a discrete object, and might even recogniseits nature in some way, only you think of it with the word and as the concept “bottle”, placing it in a context of related concepts (“glass”, “containers”, “liquid-storage”, “man-made”, etc.) by which you understand its nature, purpose and place in the world.
Many philosophers, from Plato down, have stumbled on the relationship between concepts and reality. Are concepts valid? If so, why? The apparent difficulty is because concepts don’t exist in reality. Only individual things and their properties and actions exist in reality. Concepts are purely mental constructs which unite multiple individual things into one idea. The erroneous interpretations of this fall into two main groups: that concepts do exist “out there” in some supernatural fashion, with individual objects being mere manifestations or shadows of this “ideal”; and a denial of the very validity of concepts, hence human consciousness is fundamentally flawed and unable to grasp “true” reality.
These are opposite faces of the same false belief: that the human way of knowing is defective. The things we see are not the things that are, or the things we think aren’t the things that are. True reality is to be understood by some mystical means, not via our senses which deceive us – or true reality is not to be understood at all, because our very minds deceive us.
If such beliefs were true, then we would indeed be in a bad way. A human being – and for that matter, any rational being living in the real world – is by the nature of reality “limited” to gaining knowledge by applying reason to sensory information to generate valid concepts. That is, knowledge must come via senses, reason, and concepts – for the reasons following.
- Senses: The only way you can obtain information about any other thing is by how some physical entity – itself, or an intermediary which was affected by it – affects you. That is what sensory information is – whatever sense you are referring to, be it sight, hearing, or one we ourselves don’t possess (such as the sonar of a bat or the electric sense of some fish).
- Reason: Your senses show you the surface appearance of things. But to understand what you are seeing requires reason, which means integrating it with everything else you know without contradiction – as there are no contradictions in reality. That is how you tell the difference between a hologram and the object it represents, between an oasis and a mirage, and between a man and his reflection. It is how you know that the desk you can see is made of atoms which you can’t see.
- Concepts: The necessity of a conceptual consciousness is less obvious, but in it lies our greatest power. The benefits of concepts are compression, predictive generalisation, and abstraction. Compression is extremely useful, predictive generalisation is necessary in some form for any higher form of life, and abstraction is essential for thought and civilisation, for knowledge, science and technology:
- Any living thing is finite in capacity, and the more compressed its knowledge (in this case, by grouping a multitude of individual things into one concept), the more it can know. No matter how vast its intellect, to think about a single concept as a proxy for innumerable concrete referents will allow it to think and know much more efficiently than if it had to hold images of all those examples in its consciousness in order to think about them.
- To survive in a world which can easily kill you, you must be able to predict the qualities of new existents based on what you know of other existents: a feat impossible if everything you encounter is a unique surprise, but child’s play if it is just another example of a concept already in your head. (Animals rely on the primitive analogue and precursor of conceptual identification, perceptual recognition with learned or evolved responses).
- The hallmark of intelligent life, capable of understanding the universe, making machines and reaching into outer space, is abstraction. If you can’t integrate things into primary concepts, nor can you integrate primary concepts into higher concepts: and without this power of abstraction, you can never rise above the state of an animal. Without abstraction, without the ability to divine the essential nature of things, any form of science is impossible. Even mathematics is impossible: the notions of counting and number themselves are abstractions from multiple instances of specific concepts, which in the absence of concepts, are just a bunch of different objects (you can’t have three “apples” unless you have the concept apple; nor even three objects without the concept “object”).
Wishing for some kind of mystical knowledge, which just appears in your brain without physical cause or mental effort, won’t make it so. What we have is a conceptual consciousness – and that is all we can have. And it is sufficient to rule the earth, and reach the stars.
Part B: Validating
The validity of concepts can be inferred from the fact that they are how our brains work: and our brains work. Our brains make tons of metal fly us safely around the world, cure diseases that once were scourges of mankind, and send our machines to other planets; they allow us to extend our senses to the scale of atoms and across the universe. But this does not tell us why concepts are valid. Given that the things in reality which we combine into a mental concept are different, in what way does a concept which lumps them together describe reality?
The reason is that different things in reality in fact share essential qualities, and it is those essential qualities, out of all the qualities the objects possess, which we are identifying and using to group them. This is simple to see in the case of fundamental entities such as electrons. Being fundamental (enough for our purposes here), individual electrons are much more alike than more complex entities such as people. While at any time they vary in spin, velocity, position etc., they are completely interchangeable: all electrons in the same state will act the same way under the same conditions. They will all accelerate identically in an electric or magnetic field, they will all bind to an atom in the same ways, they will all excite the phosphors of your TV screen in the same ways.
The same is true of more complex derivatives. Atoms with the same number of protons and neutrons are as interchangeable as the protons, neutrons and electrons they are made of, and chemicals of the same formula are as interchangeable as the atoms they are made of. This reveals something very significant: the validity of concepts is a consequence of the law of identity.Atoms of the same composition must be interchangeable, because their properties derive from the properties of subatomic particles, which themselves obey the law of identity: and so on up the chain of causation and complexity.
This remains true up to the highest levels. A living thing is made of atoms and chemicals, as is a star, a galaxy or the entire universe. The properties of matter and energy cause the birth of stars, the formation of solar systems and the evolution of life. Everything a star does and everything a living organism does are consequences of the laws of physics and chemistry: laws which are consequences of the natures of the fundamental constituents of everything in the universe.
When considering the validity of concepts, it is worth paying special attention to the most complex entities: living things. Unlike electrons, which are all interchangeable, the entities subsumed by the concept “dog” are not. They vary in many qualities, such as size, colour, speed, behaviour and personality. Indeed, like humans no two dogs are absolutely identical. In what way, and why, are concepts that unite these disparate creatures valid?
Consider the highest abstraction here: life itself. All living things share essential qualities, determined by the nature of reality. The fundamental quality of living things is that they are self-organising, self-reproducing chemical systems (no non-chemical forms of life are known, so we can ignore that possibility here; similar constraints would apply even to them). To do that, they must counteract one of the fundamental laws of the universe: entropy, the tendency of systems to become more disordered with time. The only way for them to achieve that is by the directed use of energy.
To be directed, an organism needs to contain within itself a set of instructions. To use energy, it must acquire it from the environment. Because both the usable energy and the efficiency with which the organism fights entropy are limited (especially for primitive life), the creature is mortal, and for life to continue it must make copies of itself, both using and transmitting its set of instructions. Furthermore, in order to flourish – in order to cope with changes in the environment and to exploit new environments – the instructions must be mutable. Even if it was possible to have immutable instructions in chemically based life, the world would be overrun by the descendants of those who lacked that restriction on their adaptability.
You can see that the qualities of life which we see around us on earth are not an accident. The details of life on earth – DNA-based genes, the colour of chlorophyll, the organelles that make our cells work – might be unique. But all natural life must share with us the core things which make life what it is: a means to acquire energy, a set of instructions, machinery to translate those instructions into the appropriate actions, machinery to make copies of the organism, and the ability to evolve in order to adapt to and exploit its environment.
Thus for all their variability – a variability inherent in their nature as life – living things will share essential qualities, and therefore concepts based on those essential qualities will be valid. Dogs are dogs because they all possess a similar instruction set, a DNA code so similar that they can interbreed, a DNA code which makes a dog grow into a dog and not into a cat, a mouse or a man. The concept “dog” is valid, because the animals it refers to are all variants of the same kind of creature, with the same basic anatomy and means of survival – because all are descended in a variable, shuffled, yet unbroken living chain of copies from common ancestors in their past.
Recall the hierarchy of concepts: the grouping of lower concepts into increasingly generalised ones. It should be clear by now why this is valid – which means, why it reflects the nature of things in reality.
We have seen why concepts with direct referents are valid. At the simple end of the scale, all electrons are essentially the same, and all oxygen-16 atoms are the same. But a more general concept than “oxygen atom” is “atom”, which includes not only oxygen but hydrogen, iron, gold etc. These are all different: you can’t breathe gold or make jewellery out of hydrogen. But they all share the same basic structure. All have a nucleus of protons (and usually neutrons) surrounded by electrons, in equal number to the protons. Their chemistries and physical qualities are different: but all determined by the arrangement and nature of their nuclei and electrons. That is, they are different, yet share essential similarities. It is these essential similarities which our higher-level concepts identify. “Atom” is not merely a semantic convenience. It identifies a fact of reality: that all types of atoms share the same kind of structure, a structure which makes them all act in comparable ways (entering into chemical reactions via interactions of their outer electrons) yet different ways (the types of chemical bonds they form). Their fundamental nature and that of their component parts determine both their similarities and their differences.
It is similar at the other end of the scale. As we generalise from poodles, to dogs, to dog-like animals (e.g. foxes, coyotes), to related carnivores (e.g. seals, bears), to mammals, to vertebrates, to animals: we are reflecting the actual history of life on earth, the actual degree of similarity in their DNA codes and resulting structures and solutions to the problems of staying alive. As we generalise our concepts, they identify a broader and broader essence: but that essence is reflected in the nature of the things we are identifying. As we have seen, this remains true all the way to the broadest abstraction of life itself: while you and a bacterium might differ enormously, and have nothing in common in anatomy or lifestyle, you still share the core qualities that define life – the core qualities that your disparate anatomy and lifestyle serve.
From why concepts in general are valid, follows how we can tell if a particular concept is valid or not.
At the most fundamental level, a concept is an abstraction derived from observed reality. We see ten objects that share certain features, group them together as a concept; and group that concept with others into higher concepts. You cannot omit that first step and have a valid concept.
This is plainly true of the lowest level of concepts, those with direct referents in reality. If I tell you that blopples are sentient rocks roaming the Australian plains, “blopple” is an invalid or fictional concept: it refers to nothing that exists. Perhaps there are sentient rocks roaming the plains of some distant planet: but that remains an arbitrary claim – hence an invalid concept – until and unless there is evidence for it.
Critically, this is also true of the most abstract concepts. You cannot make up a concept because you feel like it and validly claim it is knowledge. The only valid concept is one which is abstracted from objects in reality, either directly or by an unbroken chain of abstractions that ultimately rest on real things. A low-level concept is valid only if the objects it refers to exist; the validity of all higher-level concepts rests on that of the concepts from which they are abstracted. If you allege a concept which can not be traced to its roots in observable reality, then by definition you made it up: it is a work of fiction which nobody has any cause to believe, which therefore nobody shouldbelieve.
The other point to note is that concepts are valid because they identify essential qualities held in common by their members, whether those members are things or other concepts. Since this is the key which validates the abstraction of a single mental construct from multiple different things, they are only valid if this is how they are constructed. A concept which ties things together by inessential similarities is invalid, simply because the tie does not reflect reality. For example, to group horses more closely to chairs than to people by choosing “things with four legs” as their fundamental nature, is wrong. That coincidence is less essential than the many qualities that group us and horses as both being mammals and quite distant from chairs in the actual hierarchy of being.
This of course raises the question of how do you know what features are essential? Since we have already established that the way we integrate sensory information into knowledge is reason– reason being the art of identifying what is – that is our answer. To identify the essential similarities (uniting concepts) and differences (separating them from other concepts) that exist, we apply reason, and the touchstone is explanatory power.
As we have seen in investigating what makes concepts valid, concepts are a consequence of the law of identity, in which is implicit cause and effect. That things are what they are and act according to that nature, implies that they affect each other according to their respective natures. This implies that things happen for a reason, a cause grounded in the nature of the entities involved. So the question, “What is essential here?” means, “What are the causes? What makesthese items similar to each but different from these other things? Why should I think a cat is more similar to a dog than a teddy bear?” Thus, the essential is what explains, which means causes,the salient similarities and differences.
The reason this process works is that it is grounded in reality. As we have seen, things do share essential similarities. We are not trying to make them up when we are forming our concepts, but to identify them. And as with all things, it is the task of our reasoning mind to do this identification, by divining a non-contradictory hierarchy of concepts. It is the task of our integrity and honesty to ensure that our purpose is identification, not fabrication – those virtues serving our recognition that reality is what it is not what we might want, that our lives therefore depend on truth not self-deception.
Ignoring the above principles leads to various fallacies, identified by Ayn Rand. If you cannot trace a concept to roots in perceived reality, it is a floating abstraction: so called because it is not tied to actual existence. For example, mystical claims are floating abstractions by their own admission (being claims to knowledge by ineffable means). A related fallacy is the stolen concept: using a genuine concept while explicitly denying the roots from which it derives, thereby turning it into a floating abstraction within your own mind. For example, using the concept “error” (which depends for its meaning on prior identification of the concept “truth”) while denying that anything can be true, or using words to dispute that words have any meaning.
Even more insidious is package-dealing: uniting things into one concept on the basis of inessential similarities while ignoring fundamental differences which should keep them apart: “treating together, as parts of a single conceptual whole or ‘package’, elements which differ essentially in nature, truth-status, importance or value” (editor’s footnote in Rand’s Philosophy: Who Needs It). A classic example is equating economic and political power, ignoring their opposite fundamental nature: the former being based on voluntary choices and the exchange of values, the latter on physical force and threats of punishment. (While one might be used to gain the other, their essential nature and means of perpetuation are quite different.) Because the power and utility of concepts stems from their mental use as single units, package deals are the Trojan horses of thinking, giving bad ideas the halo of good ones, or poisoning good ideas by a false linkage to bad ones.
Part C: Defining
Size Doesn’t Matter
Concepts combine things in reality which are different. Even electrons vary in their speed, spin etc. Implicit in this is the knowledge that the things to which our concepts apply have many qualities which vary from one to the other, often including the degree of their defining characteristic(s). Thus, implicit in the nature of concepts is the recognition that each referent of a concept differs quantitatively from the others. That is, implicit in grouping things into concepts is the recognition that those things have various qualities in some quantity, but we ignore the actualquantities (except in so far as we define a range of possible values). For example, all men have some height, but it can be anything from around 4 to 7-odd feet.
This idea of measurement omission is a central part of the Objectivist theory of concepts (see especially, Ayn Rand’s Introduction to Objectivist Epistemology, from which the quotes in this section are taken). Rand defined concepts as “a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.” This identifies how we can unite different things by their essential similarities, even if those essentials – and their other qualities – are not quantitatively identical. It is not that the measurements don’t exist: “The principle is: the relevant measurements must exist in somequantity, but may exist in any quantity”. Rand intriguingly compared this to algebraic variables, which similarly have some value which could be “anything”.
Rand further expanded on the relationship of measurements and concepts:
Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics(i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit.
Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables – i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted.
… When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.
Similarity is grasped perceptually;in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philosophy and of science to identify that fact.
Note again the fundamental link between senses and reason: we perceive via our senses, and understand via our reason. We form concepts based on perceived reality: and the perceived similarities must be validated by reason. Our knowledge cannot proceed from either mindless perception or rationalistic ponderings divorced from perception: only the mind applied to perception is the path to truth.
The importance of Rand’s theory of concepts is its profound and original break with the standard errors of mysticism, skepticism and subjectivism:
None of [the traditional theories of concepts] regards concepts as objective, i.e., as neither revealed nor invented, but as produced by man’s consciousness in accordance with the facts of reality, as mental integrations of factual data computed by man – as the products of a cognitive method of classification whose processes must be performed by man, but whose content is dictated by reality.
This is the key to a valid epistemology (theory of knowledge). The duality of reality and consciousness is not a flaw or an impediment, but merely determines a method of cognition – a method which is both valid and necessary, because it derives from the nature of that duality. We are conscious beings living in reality, and our knowledge can only proceed from the application of the former to the latter. Objectivity as the result of the application of consciousness (via reason) to reality (via senses) is the fundamental key to how we know, and thus the only proper basis of epistemology.
Earlier I mentioned that we identify concepts using words. This deserves more detailed treatment.
A word is a label for a concept. As such words serve a dual purpose. Primarily, they are how we use concepts in the privacy of our own minds. When I am thinking conceptually, I use words. Secondarily, they are how we communicate conceptual knowledge. That is what you are reading now.
(Imagery has its own purposes, for example in creative invention or to illustrate complex relationships and networks – where the linear nature of words is a limitation. However, even then any explanation and validation relies on words. For example, one draws a diagram – and explains it by pointing to and describing its parts: with words.)
Because words are labels for concepts, they are not arbitrary. They have the same bearing on reality as the concepts they label. This is another area where subjectivist philosophers have run aground – oddly, communicating their nonsense by means of words, which proves my point quite adequately. Of course the actual sound of a word or its shape on paper are usually “arbitrary” in the sense that they have no necessary link with what they describe. But while the link between the concept and its word is arbitrary in that sense, and agreed upon socially for the sake of communication, the meaning of words is not arbitrary, but grounded in reality.
The link between a word – a sequence of sounds – and a concept – the reality it labels – is its definition. If you think about the hierarchy of concepts, it is clear that there are two complementary types of definition.
First is its “top-down” deductive definition, which places it in the proper context of knowledge. This is its “genus and species” definition, which names the next higher concept (its “genus”) and identifies what distinguishes it from the other concepts or things in its genus. The classic example is the definition of “man” as a “rational animal”: which notes that we are an animal – with all that implies – while identifying the quality which most fundamentally and causally distinguishes us from other animals – our power of reason.
Second is its “bottom-up” ostensive (“pointing out”) definition, which reflects the inductive process through which concepts are originally formed. Thus to define “star”, one needs merely point at the stars in the sky; to define “dog”, at members of that species.
It is clear that all valid deductive definitions ultimately must rest on ostensive definitions, because all valid concepts are grounded in observable reality. While this is plainly true of visible things such as dogs, it is also true of invisible entities such as electrons, whose existence is inferred more indirectly – but still inferred from observable reality.
A Defining Moment
The nature of valid definitions derives from that of valid concepts.
Why, for example, is “a rational animal” a good definition of “man”, whereas “a farming animal” isn’t? Man is the only animal who farms, after all. The answer is that a correctly formed concept identifies essential or fundamental distinguishing traits, and therefore so must the definition of the concept’s word. Yes, man is the only animal who farms – but that is because he is the only animal which is rational, rationality being a precondition for farming. Indeed, rationality is the precondition for everything concrete which we have and animals don’t: things such as complex language, advanced tool-making, road-building and writing.
Note however that there may be more than one valid definition, depending on the context in which you are working. Defining man as a rational animal is correct philosophically, but is of little use to a palaeontologist studying our fossil forebears. The palaeontologist is forced to deal with a limited part of a human being, and so to identify what are and are not human remains, must choose a definition based on what is available. Usually this is related to rationality, in fact: things related to brain size and function, or bipedalism (which in man is closely linked to the emergence of intelligence). On the other hand, a comparative zoologist might consider man to be “an intelligent ape”, “animal” being too broad a genus for his purposes.
However, such specialist or contextual definitions merely complement the primary definition. Man is a rational animal and even a palaeontologist needs to know that – when dealing with other people as people, as opposed to dealing with old bones.
Part D: Classifying
Broadly, concepts refer to things in reality, to existents. What things?
We can easily identify four classes of concepts: those pertaining to objects (“chair”, “ocean”, “star”), phenomena (“climate”, “gravity”, “time”), qualities (“blue”, “hot”, “fast”) and actions (“flying”, “burning”, “asking”). Not coincidentally, these correspond to the major types of words: objects and phenomena to nouns, qualities to adjectives and adverbs, and actions to verbs. The direct experiences of consciousness, such as “emotion”, “pain”, “giddiness” and “consciousness” itself, are phenomena.
Even these broad classes of concepts have a hierarchy, in which objects are primary. This is because there is no such thing as a “disembodied” phenomenon, quality or action: any such notion is just a floating abstraction. In reality, every concept pertaining to these derives from the observation of objects possessing, causing, doing or affected by them. There is no “gravity” independent of material objects, no “fast” in the absence of things moving rapidly. All phenomena are caused by and/or emergent properties of something, all qualities are of something, and all actions are by something.
A concept subsumes all examples of it, and therefore all qualities of those examples, not only the uniting and distinguishing qualities which define the concept. Concepts are identified by similarity and defined by essentials, but the things in reality have many qualities and are not identical. Thus it is in the nature of concepts that there will be grey areas and exceptions.
“Grey areas” are cases in which it is hard to tell which of two similar concepts a given thing belongs to. “Exceptions” are things which seem to belong to a concept, but which don’t fit the deductive definition – such as a human being with severe brain damage or insanity, who therefore lacks the power of reason.
However, these do not weaken the power or validity of concepts. Indeed, the very meaning of “exception” implies that the concept is valid in general (else “exception” is a stolen concept!)
A particular case might indeed imply an error or incompleteness in our concepts. Perhaps there is a grey area because we need a new concept to cover it. Perhaps the exception indicates an error in our definition – or in our identification of the thing as an instance of the concept.
On the other hand, there might be a grey area simply because in reality there is a continuous scale. While we identify “orange” as the colour between red and yellow, where does orange end and red begin? The same applies – even more so – to living species, which can vary enormously over space or time as they evolve from one form into another (where did “reptile” end and “bird” begin, for example?) The decision of what do do in such cases is a matter of importance and context. Eskimos have many words for snow and ice, reflecting their needs in the environment in which they live, and artists and printers distinguish many named shades of colour. This is an origin of professional jargon: specialists often find a need for much finer identifications than laymen.
Similarly, an exception may simply be a consequence of that same variability (a variability recognised and reflected in measurement-omission itself). For example, when is intelligence so low that “rationality” is no longer possible? But fundamentally, exceptions derive from the fact that we can have different criteria for our concepts depending on context. For example, that a person is human in the biological sense – being born of another human – does not mean that they must be human in the philosophical or functional sense – possessing the power of thought. Such exceptions simply mean that the thing fits a concept by one definition but not by another. Which definition we should use depends on the context involved.
The nature of concepts includes the recognition that things in reality are different. It recognises that fundamentally a thing is itself, defined by what it is, not by what similar things are. It recognises that concepts are valid because things do have fundamental qualities in common: but that the things in reality vary, sometimes along a continuum, and vary in all their qualities likewise. Because they vary in all their qualities, a particular thing may fit a concept by one set of qualities, but not others.
What to do about exceptions and grey areas is, as usual, the task of reason to decide. Which means, we must work out what the exception means: is it proof that our concept is invalid, or just a reflection of the variability of the natural world, which we must be aware of, but which doesn’t affect the general applicability of our concept? For example, that some biological humans have no power of reason does not alter the fact that the survival of human beings in general – including those ones! – depends on rationality, and therefore on allowing the reasoning mind to function.
As proof that exceptions do not invalidate concepts: we have a conceptual consciousness, yet we handle exceptions quite well! When faced with an exception, our brains don’t collapse into “sheer blank system error”. If we are rational, we follow the process above, work out what it means, and integrate this new knowledge without contradiction into all the rest of our knowledge. This is reflected in how science progresses, for example: exceptions to current theories are studied and the theories improved or replaced so as to fit known reality.
At the base of all our knowledge is concept-formation: mental abstractions from things in reality, which unite multiple things into single concepts based on essential similarities. This is a recursive process – concepts can be formed from other concepts – allowing any level of abstraction.
Concept-formation is necessary for rationality per se, as any thought beyond the perceptual level requires abstraction. Concept-formation is valid, because it reflects the nature of reality: things do in fact share fundamental qualities. Ultimately, concepts are valid because of the law of identity.
Because concepts are mental constructs, they can be in error. Since the validity of concepts rests on the actual fundamental similarities of things in reality, to be valid a concept must ultimately be derived from reality and correctly identify essential qualities. Valid concepts are neither intrinsic (known by some kind of mystical revelation) nor subjective (arbitrary): they are objective, arising from the process of reason applied to the perceptions of our senses.
Our ancestors lived in jungles and caves, at the mercy of the random events of nature. The power of recursive abstraction of concepts derived objectively from reality is what has raised us to mastery of the earth and the beginnings of travel to other worlds. There is no limit to this nor to the potential improvements in human life and happiness – so long as the mind is left free to think and men are left free to achieve.