One of the most durable and intractable issues in the history of philosophy has been the problem of universals. Closely related to this, and a major subject of debate in 20th century philosophy, has been the problem of the nature of the meaning.
The problem of universals goes back to Plato and Aristotle. The matter at issue is that, on the one hand, the objects of experience are individual, particular, and concrete, while, on the other hand, the objects of thought, or most of the kinds of things that we know even about individuals, are general and abstract, i.e. universals. Thus, a house may be red, but there are many other red things, so redness is a general property, a universal. There are also many houses, and even kinds of houses, so the nature of being a house is general and universal also. Redness can also be conceived in the abstract, separate from any particular thing, but it cannot exist in experience except as a property of some particular thing and it cannot even be imagined except with some other minimal properties, e.g. extension. Abstraction is especially conspicuous in mathematics, where numbers, geometrical shapes, and equations are studied in complete separation from experience. The question that may be asked, then, is how it is that general kinds and properties or abstract objects are related to the world, how they exist in or in relation to individual objects, and how it is that we know them when experience only seems to reveal individual, concrete things.
Plato's answer to this was that universals exist in a separate reality as special objects, distinct in kind, from the things of experience. This is Plato's famous theory of "Forms." Plato himself used the terms idéa, , and eîdos, , in Greek, which could mean the "look" of a thing, its form, or the kind or sort of a thing [Liddell and Scott, An Intermediate Greek-English Lexicon, Oxford, 1889, 1964, pp. 226 & 375]. Since Aristotle used the term eîdos to mean something else and consistently used idéa to refer to Plato's theory, in the history of philosophy we usually see references to Plato's "theory of Ideas."
Although Aristotle said that Socrates had never separated the Forms from the objects of experience, which is probably true, some of Socrates's language suggests the direction of Plato's theory. Thus, in the Euthyphro, Socrates, in asking for a definition of piety, says that he does not want to know about individual pious things, but about the "idea itself," so that he may "look upon it" and, using it "as a model [parádeigma, "paradigm" in English]," judge "that any action of yours or another's that is of that kind is pious, and if it is not that it is not" [6e, G.M.A. Grube trans., Hackett, 1986]. Plato concludes that what we "look upon" as a model, and is not an object of experience, is some other kind of real object, which has an existence elsewhere. That "elsewhere" is the "World of Forms," to which we have only had access, as the Myth of Chariot in the Phaedrus says, before birth, and which we are now only remembering. Later, the Neoplatonists decided that we have access now, immediately and intuitively, to the Forms, but while this produces a rather different kind of theory, both epistemologically and metaphysically, it still posits universals as objects at a higher level of reality than the objects of experience (which partake of matter and evil).
Plato himself realized, as recounted in the Parmenides, that there were some problems and obscurities with his theory. Some of these could be dismissed as misunderstandings; others were more serious. Most important, however, was the nature of the connection between the objects of experience and the Forms. Individual objects "participate" in the Forms and derive their character, even, Plato says in the Republic, their existence, from the Forms, but it is never clear how this is supposed to work if the World of Forms is entirely separate from the world of experience that we have here. In the Timaeus, Plato has a Creator God, the "Demiurge," fashioning the world in the image of the Forms, but this cannot explain the on-going coming-into-being of subsequent objects that will "participate" themselves. Plato's own metaphorical language in describing the relationship, that empirical objects are "shadows" of the Forms, probably suggested the Neoplatonic solution that such objects are attenuated emanations of Being, like dim rays of sunlight at some distance from the source.
Whether we take Plato's theory or the Neoplatonic version, there is no doubt that Plato's kind of theory about universals is one of Realism: Universals have real existence, just as much so, if not more so, than the individual objects of experience.
Aristotle also had a Realistic theory of universals, but he tried to avoid the problems with Plato's theory by not separating the universals, as objects, from the objects of experience. He "immanentized" the Forms. This meant, of course, that there still were Forms; it was just a matter of where they existed. So Aristotle even used one of Plato's terms, eîdos, to mean the abstract universal object within a particular object. This word is more familiar to us in its Latin translation: species. In modern discussion, however, it is usually just called the "form" of the object. The Aristotelian "form" of an object, however, is not just what an object "looks" like. An individual object as an individual object is particular, not universal. The "form" of the object will be the complex of all its abstract features and properties. If the object looks red or looks round or looks ugly, then those features, as abstractions, belong to the "form." The individuality of the object cannot be due to any of those abstractions, which are universals, and so must be due to something else. To Aristotle that was the "matter" of the object. "Matter" confers individuality, "form" universality. Since everything that we can identify about an object, the kind of thing it is, what it is doing, where it is, etc., involves abstract properties, the "form" represents the actuality of an object. By contrast, the "matter" represents the potential or possibility of an object to have other properties.
These uses of "form" and "matter" are now rather different from what is familiar to us. Aristotelian "matter" is not something that we can see, so it is not what we usually mean by matter today. Similarly, Aristotelian "form" is not some superficial appearance of a fundamentally material object: It is the true actuality and existence of the object. This becomes clear when we note Aristotle's term for "actuality," which was enérgeia, , what has become the modern word "energy" -- with modern physics giving us a version of matter as "frozen energy." Similarly, the term for "potential" is familiar: dýnamis, (e.g. "dynamic," "dyne"), which can also mean "power" and "strength."
The continuing dualism of Aristotle's theory emerges when we ask how the "forms" of things are known. An individual object Aristotle called a "primary substance" (where the Greek word for substance, ousía, might better be translated "essence" or "being"). The abstract "form" of an object, the universal in it, Aristotle called "secondary substance." So if what we see are individual things, the primary substances, how do we get to the universals? Aristotle postulated a certain mental function, "abstraction," by which the universal is comprehended or thought in the particular. This is the equivalent of understanding what is perceived, which means that we get to the meaning of the perception. The "form" of the thing becomes its meaning, its concept, in the mind. For Plato, in effect, the meaning of the world was only outside of it.
While the Aristotelian "form" of an object is its substance (the "substantial form") and its essence, not all abstract properties belong to the essence. The "essence" is what makes the thing what it is. Properties that are not essential to the thing are accidental, e.g. the color or the material of a chair. Thus the contrast between "substance and accident" or "essence and accident." Accidents, however, are also universals. A contrast may also be drawn between substance and "attribute." In this distinction, all properties, whether essential or accidental, belong to the substance, the thing that "stands under" (sub-stantia in Latin, hypo-keímenon, "lie under," in Greek) all the properties and, presumably, holds then together. Since the properties of the essence are thought together through the concepts produced by abstraction, the "substance" represents the principle of unity that connects them.
Concepts, or predicates, are always universals, which means that no individual can be defined, as an individual, by concepts. "Socrates," as the name of an individual, although bringing to mind many properties, is not a property; and no matter how many properties we specify, "snub-nosed," "ugly," "clever," "condemned," etc., they conceivably could apply to some other individual. From that we have a principle, still echoed by Kant, that "[primary] substance is that which is always subject, never predicate." On the other hand, a theory that eliminates the equivalent of Aristotelian "matter," like that of Leibniz, must require that individuals as such imply a unique, perhaps infinite, number of properties. Leibniz's principle of the "identity of indiscernibles" thus postulates that individuals which cannot be distinguished from each other, i.e. have all the same discernible properties, must be the same individual.
One result of Aristotle's theory was a powerful explanation for natural growth. The "form" of a thing is not just what it looks like, it is the "final cause," the purpose of the thing, the "entelechy," , the "end within," which is one of the causes of natural growth and change. Before the modern discovery of DNA, this was pretty much the only theory there was to account for the growth of living things from seeds or embryos into full grown forms. Nevertheless, it introduces some difficulties into Aristotle's theory: If the "form" is accessible to understanding by abstraction, then this cannot be the same "form" as the one that contains the adult oak tree in the acorn, since no one unfamiliar with oak trees can look at an acorn and see the full form of the tree. But if the entelechy cannot be perceived and abstracted, then it exists in the object in a way different from the external "form." But Aristotle's metaphysics makes no provision, any more than quantum mechanics, for a "hidden" internal "form." Neoplatonism took care of that by making the internal "form" transcendent, as in Plato, but this is then a fatal compromise with Aristotle's prima facie empiricism and with his move to "immanentize" Plato's Forms.
This brings us to a fundamental conflict in Aristotle's theory, which highlights its drawbacks in relation to Plato's theory. If Aristotle is going to be an empiricist, thinking that knowledge comes from experience, this puts him on a slippery slope to positivism or, more precisely, "judicial positivism": that the actual is good (or, as Hegel puts it, "the Real is Rational"). The continuing virtue of Plato's theory of Forms is that the Forms can be profoundly different from the objects of experience.
Hence arises the fact that everything better struggles through only with difficulty; what is noble and wise very rarely makes its appearance, becomes effective, or meets with a hearing, but the absurd and perverse in the realm of thought, the dull and tasteless in the sphere of art, and the wicked and fraudulent in the sphere of action, really assert a supremacy that is disturbed only by brief interruptions.
Arthur Schopenhauer, The World as Will and Representation, Volume I, §59, p.324 [Dover Publications, 1966, E.F.J. Payne translation]
One significant consequence of Aristotle's point of view was, indeed, a belittlement of mathematics. Without mathematical Realism, we do not have the modern notion that real science is mathematical and that mathematics reveals the fundamental characteristics of nature. Mathematics cannot be thought of as "abstracted" from experience in any ordinary way. If it is not, then mathematics is just internally constructed, out of contact with reality. This seems to be Aristotle's view, a rejection of Pythagorean and Platonic mathematical Realism. Mathematics is no more than a "device for calculation." Thus, although Aristotle is usually thought of as being more "scientific" than Plato, he rejects Plato's geometrical view of the elements for the sake of a completely Presocratic sort of theory of opposites. He is overall nowhere near as interested in mathematics as Plato. Aristotle's approach became accepted, all through the Middle Ages, and it wasn't until the revival of Pythagorean-Platonic ideas about mathematics, in people like Kepler and Galileo, that modern science got going.
The Neoplatonic combination of Plato and Aristotle dominated thought in Late Antiquity and the early Middle Ages. Then, beginning in Islâm and moving into Western Europe, we have a revival of a stricter Aristotelianism, culminating in the massive Summas of St. Thomas Aquinas (1225-1274). It may not be a coincidence that this involved the rejection of the mystical elements in Neoplatonism, since Christianity was institutionally far more unfriendly to mysticism, with its promise of direct communication with God, than were Islâm or Judaism. What was rare or unheard of in Islâm or Judaism, mystics being condemned or even executed for heresy, was a fairly regular occurrence in Western Christianity, especially the Latin Church -- as far as I can tell, the Greek Church didn't burn heretics. However, a stricter empiricism again creates the difficulty that the apparent "form" of an object cannot provide knowledge of an end (an entelechy) that is only implicit in the present object, and so hidden to present knowledge.
Curiously, the reaction to this was not immediately a new Platonism or Neoplatonism, but a more extreme empiricism: The Nominalists overcame the Aristotelian difficulty by rejecting Realism altogether. Universals were just "names," nomina, even just "puffs of air." The greatest exponent of this approach was the Englishman William of Ockham (1295-1349). To the Nominalists, the individuality of the objects of experience simply meant that only individuality exists in reality. The abolition of a real abstract structure to the world had a number of consequences for someone like Ockham. The omnipotence of God became absolute and unlimited, unrestricted by the mere abstractions of logic, so that God could even make contradictions real, which was inconceivable and horrifying to Aristotelians or Platonists. Similarly, no things had natures (essences) that made them intrinsically either good or evil. Not even God was intrinsically good or evil: The Good would just be whatever God wills it to be, something else inconceivable to Aristotelians or Platonists -- but actually rather Islâmic in tone, since no human notion about the nature or essence of God can impose a limit on the Will of God.
Although the debate between the Realists and the Nominalists became the greatest controversy of Mediaeval philosophy, another classic expression of Nominalism is to be found in the British Empiricists, from John Locke (1632-1704) to George Berkeley (1685-1753) and David Hume (1711-1776). Locke started the approach by simply defining an "idea" as being an image. Since images are undoubtedly individual and concrete, this stacks the deck for Nominalism. Nevertheless, Locke wished to preserve something like a common sense meaning of "abstraction," which he thought of as taking some characteristic of a particular idea and using it in a general way: "the mind makes the particular ideas received from particular objects to become general." Thus, Locke cannot find any difference between the idea "horse" and the idea "Bucephalus" but "in leaving out something that is peculiar to each individual, and retaining so much of those particular complex ideas of several particular existences as they are found to agree in" [An Essay Concerning Human Understanding, Book II, Chapter XI, §9, & Book III, Chapter III, §9]. Locke even wants to preserve a distinction between "nominal essence," the nature of things that we know about, and "real essence," the real nature of things, which we cannot know about given the limitations of human knowledge [Book III, Chapter VI, §§7-18]. How this distinction could be maintained on any kind of empiricism is mysterious. Real essences and the compromise on abstract ideas were swept away by Berkeley and Hume, who quite consistently and forthrightly argued that there was no such thing as "abstract ideas." Hume said:
Let any man try to conceive a triangle in general, which is neither Isoceles nor Scalenum, nor has any particular length or proportion of sides; and he will soon perceive the absurdity of all the scholastic notions with regard to abstraction and general ideas. [An Enquiry Concerning Human Understanding, Section XII, Part I]
Of course, it is quite easy to conceive a triangle in general, which is neither isoceles nor scalene -- Hume has done so himself. Hume's argument only works if he really means imagine rather than conceive. Hume even said:
No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinite divisibility of extension, with its consequences; as they are pompously displayed by all geometricians and metaphysicians, with a kind of triumph and exultation. [ibid., Part II]
Since infinite divisibility is rather important in geometry, and one of the "consequences ... pompously displayed" is calculus, "geometricians" (like Isaac Newton) would probably be offended to be lumped together with metaphysicians. Hume's only recourse is that there are "general terms" to which multiple concrete "ideas" are attached. This however, fails the Socratic test for the "model" that would enable us to judge unfamiliar objects; and while the "family resemblances" of Ludwig Wittgenstein (1889-1951) can be appealed to by Nominalists for such judgments, the imprecision implied by such a test is wholly contradicted by the practice of mathematics, while that in which a "resemblance" would consist must be, indeed, some abstract feature or collection of such features. But Hume allows for no abstract features, much less the recognition of them.
How far this silliness can go is evident in recent analytic philosophy, which fancies itself in direct succession from Hume. The consequences of the project of reducing the world to objects and words is evident in the following statement by the logician Benson Mates [Elementary Logic, Oxford, 1972, boldface added]:
Another matter deserving explanation is our decision to take sentences as the objects with which logic deals. To some ears it sounds odd to say that sentences are true or false, and throughout the history of the subject there have been proposals to talk instead about statements, propositions, thoughts, or judgments. As described by their advocates, however, these latter items appear on sober consideration to share a rather serious drawback, which, to put it in the most severe manner, is this: they do not exist.
Even if they did, there are number of considerations that would justify our operating with sentences anyway. A sentence, at least in its written form, is an object having a shape accessible to sensory perception, or, at worst, it is a set of such objects. Thus
It is rainingand Es regnet,
though they may indeed be synonymous, are nonetheless a pair of easily distinguishable sentences. And in general we find that as long as we are dealing with sentences many of the properties in which the logician is interested are ascertainable by simple inspection. Only reasonably good eyesight, as contrasted with metaphysical acuity, is required to decide whether a sentence is simple or complex, affirmative or negative, or whether one sentence contains another as a part. [pp. 10-11]
Reasonably good eyesight, however, is not enough to tell that "It is raining" and "Es regnet" are synonymous (and let's add "Il pleuve"). That circumstance is evidently not noticed by Mates. What is needed is not eyesight, but understanding, which is nothing so esoteric as "metaphysical acuity," but instead a very simple and very common kind of thought. The "advocates" of the existence of thoughts are pretty much everyone who uses ordinary language, which probably includes Mates himself [note].
Given Mates's own example, it is very hard to deny that meaning is different from both words and objects. Mates, however, can indulge in a particularly Nominalist theory of meaning, which we see in his discussion of Set Theory:
Each set is uniquely determined by its members; in other works, sets having the same members are identical. [ibid., p. 33]
However, the sets "the present  King of France" and "the present  King of England" both have the same members, namely none, which makes them identical with the Empty Set ("Nothing"). They are therefore in no way "uniquely determined" by their members, if we allow that their meaning, even if not their membership, is different. Thus, an "extensional" theory of meaning, which sees reference to objects as the content of meaning, must either ignore "non-existent objects" or must attribute a reality to non-existent objects greater than that allowed by common sense. Equally serious is the problem of how we would know what all the members of a non-empty set are, without omniscience, in order to be able to use the name of the set in its "uniquely determined" way. If all we know are certain members of the set, i.e. the dogs we actually know about from personal experience, then we are using the name of a subset, not the real set, of dogs.
At the beginning of 20th century logic there was a much more Realistic theory of meaning and universals, that of Gottlob Frege (1848-1925). For Frege, "subject" terms referred to individuals, while "predicates," i.e. abstract properties, referred to "concepts." "Concepts," then, exist as abstract objects. In the subject we have meaning as "sense," which is very different from reference. Thus, in his classic example, the "morning star" and the "evening star" have the same reference, namely the planet Venus, but they have different senses, namely "Venus as seen in the morning" and "Venus as seen in the evening." A crude extensionalism cannot account for this. On the other hand, Frege was no metaphysician; and we have no theory to account for the nature or existence of concepts as objects, let alone to what Frege said was the reference of sentences, namely the "True" and the "False." A philosopher looking for the metaphysics of "concepts" has little to go on beyond Aristotle and Aquinas. Frege's theory of senses, however, recently clarified by Jerrold Katz, does preclude Nominalist (and all naturalistic theories, like Wittgenstein's theory of meaning as "usage") theories that only want to stick to concrete words and individual objects.
The possibility occurs, then, that universals may occur, not in words, and also not in any kind of objects (individuals or Frege's concepts), but in the internal mechanisms of sense. This would be a "middle way" between Realism and Nominalism that has been called Conceptualism. This notion seems to go all the way back to Peter Abelard (1079-1142). The drawback of conceptualism, however, would be that universals would not be knowledge, since the structures of meaning would correspond to nothing of the kind in the world: Universals would have to be the "pragmatic" way that we conceive or organize individuals, avoiding the silliness of a Nominalism like Mates's, but there can be no real differences in the objects that our conceptions are reflecting. Conceptualism is devoid of anything like Frege's "concepts" (or Aristotle's "forms") as abstract objects.
Metaphysically, Conceptualism is therefore no different from Nominalism. It is a psychologistic theory, i.e. it attributes structures that we see in reality to structures imposed by the human psyche. Indeed, some structures in the world are imposed by the human psyche. There is nothing natural about a coffee pot, which is an artifact of human conception and human purposes. A Platonic Form or Aristotelian substance that is the objective existence of the abstract and universal coffee pot would seem to be the reductio ad absurdum of their theories as much as the "reasonably good eyesight" is of Mates's. The conventionality of such concepts provides a powerful argument for Conceptualism, as it would also for Nominalism.
If Conceptualism were merely the argument that there is not always an objective structure to correspond to the difference between essence and accident, this would be quite true. However, it seems to be the case that there is an objective structure corresponding to some essences, since there are natural kinds of things (dogs, feldspars, stars, flowers, etc.) whose identity owes nothing to human convention or purposes. Furthermore, since all attributes (properties) are universals, whether essential or accidental, this argument would be beside the point. Even conventional concepts are based on real characteristics. A coffee pot must hold coffee, and its ability to do so owes nothing to convention but everything to the nature of the materials and even the nature of space. Those cannot be altered, much as many would like to, simply by making some change in the conventions of our conception.
If a Conceptualist allows even a moment when real differences are recognized, then, however conventional the rest of the constructions, a fundamental element of Realism has been accepted into the theory. Thus, however conventional a fundamental unit of measure may be, this does not make all fundamental units somehow the same. A meter really is more than three times as long as a foot, which means they are commensurable, i.e. each can be converted into the other. Commensurability and conversion are only possible because of the independent, objective, and real natures of each. The meter and foot both apply to the same continuum of space.
For a true Conceptualism or Nominalism, incommensurability, both of measure and of meaning, must be possible, which is why we find that Nominialists and deconstructionists are eager to leap on W.V.O. Quine's (1908-2000) arguments for the "indeterminacy of translation." The problem of the metaphysics of universals thus overlaps the epistemological issues and theories examined in "Foundationalism and Hermeneutics." A consistent Conceptualism is going to result in the same skepticism that we see in Hume or the same nihilism that we see played out in deconstruction, all because of the same denial of real universals and meaning that has objective reference. Quine, like the deconstructionist Rorty, offers a muddled Pragmatism that obscures the non-responsiveness and question-begging nature of his thought.
Immanuel Kant can be said to be a Conceptualist because of the manner in which the mind's activity of synthesis puts the concepts of reason into phenomenal objects in the first place. This is definitely a Conceptualist move. However, Kant's theory does not end up being a Conceptualist theory, or any kind of psychologistic theory, if Kant is to be taken seriously when he says that it is a theory of "empirical realism." This is commonly misunderstood. Thus Jerrold Katz says: "Kant's Copernican revolution...makes the existence of objects in the world depend on our cognitive faculties" [Realistic Rationalism, MIT, 1998, p. 7, boldface added]. This is flatly contradicted by Kant himself:
Either the object alone must make the representation possible, or the representation alone must make the object possible.... In the latter case, representation in itself does not produce its object in so far as existence is concerned [ihren Gegenstand dem Dasein nach nicht hervorbringt], for we are not here speaking of its causality by means of will. [Kant's emphasis, Critique of Pure Reason A92, Norman Kemp Smith translation, St. Martin's Press, 1965, p. 125]
If the existence of objects were produced by representation alone, this is what Kant called "intellectual intuition." Only God would have intellectual intuition. Our actual ability to produce the existence of objects is not by means of representation alone, but by means of will, otherwise the existence of objects is "given" to us (a "sensible intuition"). Instead, Kant's theory is that the character of objects is in part determined by the nature of representation. Since this is also the very thing we see in contemporary physics, in quantum mechanics, it becomes very hard to reject Kant as some anti-realist without also a somewhat wishful-thinking rejection of this characteristic of physics.
To be thinking, as often happens, that things-in-themselves in Kant are what are "really" real is to contradict the meaning of "transcendental idealism," which is that transcendent objects are only "ideal," i.e. subjective. Schopenhauer, although leaving out most of the subtlety of Kant's theory, clarifies the metaphysics by ruling out any order of transcendent objects, whose possibility always seems to be hovering in the background for Kant, confusing his realism. Kant, however, is correct in that we inevitably try and conceive of transcendent, which means unconditioned, objects. This generates "dialectical illusion" in the Antinomies of reason. Kant thought that some Antinomies could be resolved as "postulates of practical reason" (God, freedom, and immortality); but the arguments for the postulates are not very strong (except for freedom), and discarding them helps guard against the temptation of critics to interpret Kant in terms of a kind of Cartesian "transcendental realism" (i.e. real objects are "out there," but it is not clear how or that we know them). If phenomenal objects, as individuals, are real, then the abstract structure (fallibly) conceived by us within them is also real. Empirical realism for phenomenal objects means that an initial Kantian Conceputalism turn into a Realism for universals.
Kant's theory, indeed, is not the kind of realism that we see in Descartes, or that was evidently desired by Einstein, where objects exist as such entirely independent of subjects. Instead, phenomenal objects presuppose the subject, and we cannot say whether their properties are "really" objective or "really" subjective -- as examined in "Ontological Undecidability." This is how Kant's theory can be both a form of Conceptualism and a form of Realism at the same time [note]. Thus, if the mind conceives abstract properties, abstract properties will be in objects, because objects are just the other side of the structures found in the mind. But it would be equally true to say that the structures in the mind are just the other side of those in the objects. The Aristotelian function of "abstraction," by which universal forms are taken from objects into the mind, in these terms is less mysterious: Phenomenal objects are already in the mind, so the purely mental operation does not reach out into transcendent (Cartesian) reality to fetch the essences. [note]
While Kant's empirical realism allows for an Aristotelian Realism of universals, it also means that we do not have to accept Aristotle's theory of substantial forms and of essence and accident. There are conventional concepts. Not all concepts therefore correspond to real essences. To think that they do is what Karl Popper called "essentialism" -- a good label for such an error, though the term is now widely used by "post-modern" nihilists to condemn any doctrine of essences or natural kinds. But there are natural kinds and real essences.
Real essences, however, must be due to something; they are not just self-generating. A clue may be found in the modern theory of DNA that has replaced the entelechy of Aristotelian "form." DNA governs the growth and development of organisms through the causal laws of nature. The natural kinds of plants and animals are thus the result of causal necessity. All essences, whether real or conventional, are the result of some form of necessity. The fixity and unchangeability of Plato's original Forms, "immanentized" by Aristotle, are artifacts of a form of necessity itself, the necessity of the perfect aspect, of time which has occurred (the past or the present perfect tenses, the opposite of Aristotle's own "future contingency"). The various modes of necessity are discussed in "A New Kant-Friesian System of Metaphysics" and the nature of the perfect aspect in a note to that essay. Purely conventional concepts rely on the fact of their use, which is a function of perfect necessity, for the fixity of their own conceptual essences. The entelechy of a coffee pot is owing entirely to human purposes, and to no causal necessity, but it is functionally parallel, in human understanding, to natural kinds created by causal laws of nature.
If we distinguish between substance and attribute and identify some attributes as essential, this will mean, not that there is a hidden, underlying substance unifying the essence, but that such a notion of substance can be replaced by the forms of necessity, whether causal for natural kinds or purposive for purely human conceptions. This means that the ghostly skeletons of the Platonic Forms, brought down to earth by Aristotle, and uncomfortably inhabiting the transient individuals that we perceive, can be eliminated. The abstract features we conceive in individual objects are not different in kind from the objects, which are themselves artifacts of necessity (logical, a priore, perfect, and causal), but the living skeleton of the objects, in a phenomenal world where necessity and contingency are the structure of everything.
The fixity of our own concepts collapses all the necessities of reality into the fact of conventional usage, which Plato and Aristotle projected out into the world, even into the transcendent; but it is now possible to correct this. It is not the Concept out among objects, as Frege put it, but mental concepts do refer to some abstract structure grounded in some form of necessity. By the same token we can identify the ground of the "True" and the "False," which Frege saw as the reference of sentences, since the same necessities that unify real or conventional essences also unify predications in sentences. Kant's doctrine of the "primacy of judgment," indeed, subordinates the unity of concepts to the unity of propositions, which enables us to say that even analytic truths are of different kinds, depending on the necessity that unifies the properties in the concepts. "All placental mammals give live birth" is thus analytic of the concept "placental mammal," which is a natural kind based in causal necessity, while "All Hobbits are short" is analytic of the concept "Hobbit," which is a fictional artifact of J.R.R. Tolkien's Lord of the Rings and so dependent on the mere fact of the convention adopted by the imagination of Tolkien.
The modes of necessity are interrelated with the modes of contingency, so that perfect necessity is contingent in relation to a priore necessity, a priore necessity is contingent in relation to logical necessity, and logical necessity is contingent in relation to an "ur-contingency" that would transcend non-contradiction. Each mode of contingency, in turn, represents the possibility of something different from what we see in each subsequent mode of necessity. The very possibility that, in time, we can open the window or make some other alteration in reality is a case where we deal with the contingency of present time and our ability to bring about some new possibility. What this adds up to for universals is that as forms of necessity they represent the rules and guideposts that limit and direct possibility: Universals represent all real possibilities. Thus, what Plato would have called the Form of the Bed, really just means that beds are possible. What would have seemed like a reductio ad absurdum of Plato's theory, that if there is the Form of the Bed, there must also be the Form of the Television also (which is thus not an artifact and an invented object at all, but something that the inventor has just "remembered"), now must mean that the universal represents the possibility of the television, which is a possibility based on various necessities of physics (conditioned necessities) and facts (perfect necessities) of history.
Where the power of possibility comes from is a factor unaddressed by Plato. In Aristotle it is represented by matter, which is power and potential; but then matter is so intrinsically amorphous, merely the passive recipient of actualizing "form," that the Neoplatonists identified it with Not-Being (and evil) -- quite apt when Prime Matter, or pure potential, is not actual at all and so in fact doesn't exist -- and both Aristotle and the Neoplatonists eliminated any material component to God (or the One). Rather awkwardly, this left Aristotle's God literally "powerless": He is already perfectly actual, which means that He cannot do anything that He is not already doing. This could be argued theologically, that it would be an insult to God's foreknowledge and wisdom if anything has been left undone that He is going to have to take care of in the future, but at the same time it does seem like an insult to His Omnipotence and Freedom that He cannot just decide to do something new.
The failure of Aristotle's theory is that necessity and possibility are interrelated, actualization does not "use up" possibility, and that what is truly actual, namely phenomenal objects in the world, consists of contingent individuals and not the necessary universals of the "form." In Spinoza's metaphysics, individuals as natura naturata ("nature natured") are the visible products of coming-into-being, but the creativity of Spinoza's God is limited by a determinism that makes every event a complete product of necessity, with no contingency, and so no radical possibility, at all.
Combining necessity and possibility means that actual individuals are always the result of both, always necessary in some ways and contingent in others. Universals exist precisely where possibilities exist: In the future, in one sense, in the imperfect aspect, in another. There is also now a physical meaning for this. The sum of all possibilities before a particular event actualizes one of them, is the square of the wave function in quantum mechanics. The possibilities summed in the wave function are limited by the laws of physics, but not completely limited. There are various possible and probable events. It is the act of observation that "collapses" the wave function and produces definite states of the system. As discussed in "Kantian Quantum Mechanics," this is like nothing so much in physics or philosophy as the act of synthesis that produces consciousness in Kant. For the purpose here, however, it need give us no more than a dimension to reality where the individuality and contingency of phenomenal objects does not yet exist, but possibility and necessity do. That makes it simultaneously Plato's World of Forms and Aristotle's Prime Matter, the place of universals as real possibilities with the power of coming into existence.
The theory of universals also gives us the theory of meaning, since meaning consists of abstract properties, so that meaning is also an artifact of the forms of necessity, both the meaning of words and the meaning of things -- of life and the world. The complete theory thus has required some distinctive elements of Kant-Friesian doctrine, including Kantian empirical realism and transcendental idealism, restated as ontological undecidability, and a Friesian theory of the modes of necessity. Deeper issues of meaning, both for the ultimate significance of matters of value and for religious questions, concern other aspects of Friesian metaphysics and epistemology.
The theory of meaning is now called "Semantics." Unfortunately, the word is heavily tainted with baggage derived from its history, which is shot through with the fallacies of Logical Positivism. In that school of philosophy, strongly associated with Vienna in the 1930's, terms and statements are not meaningful unless they can be empirically verified by science. This is "verificationism," and it founders catastrophically on something of which few Positivists were ignorant, namely the Problem of Induction. The very people who demanded verification for meaningfulness were typically aware of Hume's argument that induction does not verify anything. This was why Hume was a Skeptic, i.e. did not believe that knowledge in the traditional sense existed. The Positivists, nevertheless, rather than resolving the Problem of Induction, seem to have forthrightly determined not to worry about it -- especially since Logical Positivism itself stood no chance of being verified by science, and consequently was meaningless ("literal nonsense") on its own terms. They also didn't worry about the paradox that to know whether a proposition could be verified nor not, one would need to know what it means. Meanwhile, Karl Popper showed that reasoning in the history of science has functioned in terms of falsification rather than verification.
Logical Positivism was also the source of the evil tradition, as we have seen in Benson Mates, of believing that symbolic logic was an ideal language, superior to all natural languages. Since symbolic logic is only the fragment of a functionally and sematically sufficient language, this was a tradition headed for nowhere. Nevertheless, its influence for a long time was immense, lingering even today.
In 1933 Alfred Korzybski (1879-1950) published a book, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. "General Semantics" was not, strictly speaking, part of a discipline of semantics in philosophy, logic, or linguistics. It was a kind of self-help, pop psychology, or pedagogical program, which Korzybski had already been calling "human engineering" and "humanology." As such, it was more in line with projects like that of L. Ron Hubbard, who published Dianetics (a form of pop psychoanalysis) in 1950 and claimed "General Semantics," to the mortification of its supporters, as an influence.
But all the radical innovative ideas of "General Semantics" were along the lines of the verificationism, scientism, empiricism, and Nominalism of Logical Positivism. Influenced by Korzybski, S.I. Hayakawa (1906-1992), who was at first an English professor, became a representative and promoter of the new Semantics, making palpably false prouncements such as, "The way we talk determines the way we think," which reflects, not just Nominalism, but a Behavioristic view of language. This still was supposed to have a edifying purpose as part of education in communications and, presumably, philosophy of science and epistemology. It has had more influence in Linguistics than it should have, but then sensible theories of meaning have long been thin on the ground.
A great deal of what seems like the influence of Logical Positivism in some science fiction of the era, including Robert Heinlein, evidently was mediated by enthuasism for "General Semantics." The strict Positivism faded in Heinlein's work, but even as late as Time Enough for Love , he was still thinking that the sort of unambiguous ideal language imagined by the Positivists was possible and that the ambiguity of words in English was some sort of historical accident or careless oversight -- rather than something that happens spontaneously as soon as a language is used. Other science fiction more overtly referenced "General Semantics," articularly a novel published in 1948 by A.E. van Vogt, The World of Null-A. "Null-A" is supposed to mean "Non-Aristotelian," as in part of the subtitle of Science and Sanity. The idea that somehow Western philosophy was in the deadly grip of Aristotle and then was freed by Alfred Korzybski gives us a clue that the whole business doesn't involve much awareness of the history of philosophy, where in the 17th century René Descartes, was already drawn treading on volumes of Aristotle -- as, in effect, he was. Indeed, Descartes was the sort of a great mathematician already far beyond the reckoning of any Aristotelian Scholastic and deeply involved in the early development of modern science. But I never understood how the science fiction of A.E. van Vogt represented any philosophical doctrine or viewpoint.
Sense, Reference, and Philosophy, Jerrold J. Katz, Oxford, 2004
Meaning and Naming in Michael Devitt and Kim Sterelny's Language and Reality, MIT Press, 1999
History of Philosophy
Since Mates accepts Frege's distinction between sense and reference, he is left with some explaining to do. Senses are not empirical individuals. Frege also held that truth values were the referents of propositions (since sense covered the semantic content of all the terms in a proposition), to which Mates refers in the following:
In view of the doubts earlier expressed about the existence of such things as propositions -- and the same doubts apply almost as well to truth-values -- the reader may wonder how we dare to invoke these entities in the present context. The answer is that the essentials of Frege's view can be stated without any metaphysical assumptions about the existence of such things as propositions. For instance, it is possible to rephrase principle b) [i.e. "...the sense of a complex expression is a function of the sense of its parts"] as follows: if expressons S and T are synonymous and expressions U and V are alike except that U contains an occurrence of S where V contains an occurrence of T, then U is synonymous with V. Since the non-existence of propositions and the various other nonentities in no way requires us to deny that there are indeed pairs of synonymous expressions, we can accept most of Frege's semantics without agreeing to his metaphysics. The same charitable reading may of course be extended to the use of 'proposition' by other authors, insofar as such use is eliminable in like manner.) [ibid. p.23]
If we are asked what the toll is for the Golden Gate Bridge, and we answer, "A positive integer in dollars," our answer may be true, but it rather misses the point and is non-responsive to the practical sense of the question. What is not really "eliminable" in Mates' treatment is the question of what senses are such that we can recognize them and such that they account for the synonymity of expressions. Mates apparently thinks that rendering a formula so abstract and so formalistic (in the tortured renderings favored by Analytic philosophers) as to eliminate the term means that the question and the problem disappear also.
Well, if he doesn't want to think about it, that is his business. But if he thinks that he has proven something, he is very much mistaken. Nevertheless, the basic logical objection to his exercise in this passage is that it involves a circular definition; for he has not eliminated the term "synonymous." Since "synonymous" means "has the same sense," Mates can only beg the question by using the term at all -- especially in a sentence of the form "If X is synonymous, then Y is synonymous." This answers no question about what sense is as meaning, as opposed to reference as meaning (the reductionistic thesis of Mates's Nominalistic extentionalism). It is a philosophical know-nothing-ism, and the overtone of contempt by Mates for metaphysical "nonentities" does not leave a good impression of him as a philosopher.
The "charitable" reading of all this is that Mates as a logician (and I taught his book both at the University of Texas around 1978 and at LA Valley College from 1988 to 2009) doesn't have to care about the metaphysics. But if he thinks that the need for the metaphysics is "eliminable," then he is deeply out of his reckoning. Why such strategies are appealing is probably due to the "Sin of Galileo." While the standard "Sin" is the idea that if the math works, this explains what is going on, the form exhibited by Mates would be that if we make something sufficiently abstract, and the concept that we don't want to explain drops out, then we don't need to explain it. You'll find out the toll at the Golden Gate Bridge when you get to it. This is almost worse than when it is done with the mathematics, since it is easier to believe that the math represents something mysterious and profound, while Mates' unnatural reformulation just looks silly and evasive, a kind of shell game.
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The "Axiomatics of Universals" chart is similar to many devised by Leonard Nelson.
Other premises and conclusions might be used to differentiate Realism, Nominalism, Conceptualism, and the Kant-Friesian theory from each other, but the given propositions are sufficient for the task.
A likely objection from Aristotelians (cf. Jonathan Jacobs & John Zeis, "Form and Cognition: How to Go Out of Your Mind," The Monist, vol. 80, no. 4, October, 1997, pp. 539-557) to the characterization of Realism as "Universals exist only objectively" would be that universals, or Aristotelian "forms," also exist intentionally, and so subjectively, in the mind, after abstraction from individual objects. Fair enough. This is indeed on the right track, as liberal use is made here of much the same notion of intentionality.
However, Aristotelians cannot mean "subjectively" in the same way. The external form is fundamental to them, and it is then instantiated into the mind through abstraction (from perception), or through the mysterious "formal causation" of Jacobs and Zeis, by which the "form" of the object is causally conveyed into the mind. However, a causal theory must be a scientific theory, and Jacobs and Zeis have neglected to mention what part of science employs "formal causation." Actually, it is none. Causation can only be a specific kind of causation, specified by a particular scientific theory. The causal principle of Hume or Kant is simply the form of a law of nature. Aristotelian causation, whether formal or efficient or otherwise, is a theory proposed in the absence of a modern scientific understanding of the laws of nature. The billiard balls of the classical Empiricists are a function of the mechanics of velocity and mass, 17th century physics, while atom bombs are a function of Relativity and other aspects of 20th century physics. "Formal causation" thus requires a formal physical theory, of which there is no such thing. Aristotelians may well be so busy noting the inadequacies of the Aristotelian theory of "efficient causation" that they fail to notice that modern causation in physics is not the Aristotelian theory.
In fact, Aristotelians are transcendental realists, cannot avoid the Cartesian paradoxes, and cannot accept that their intentional, subjective forms exist on the same ontological level as the "forms" in the objects. Thus, the characterization of Realism as "Universals exist only objectively" means that subjectivity is only epiphenomenal, ontologically subordinate to objectivity. It is the denial of Kantian transcendental idealism and of the equivalent ontological undecidability. For Realists, real existence, ontologically independent existence, is external, which is the kind of real existence that universals have for them.
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To Conceptualists like Ayn Rand (who explicitly rejected Aristotle's Realism) and her recent supporters, Kant represents merely another brand of scepticism. Thus, a recent issue of the Institute for Objectivist Studies newsletter, the "Navigator" [Volume 2 Number 6, February 1999], included an interview with Stephen Hicks, a Ph.D. from Indiana University and now professor of philosophy at Rockford College in Rockford, Illinois (and sometime collaborator with the Institute's President, David Kelley), about various philosophers, including Kant.
To Hicks, Kant has a "skeptical argument" that "leads him to reject the real world... ...[O]ur cognitive operations are by their very natures precluded from putting us in contact with reality" [p. 8]. Kant is thus judged against a standard of transcendental realism, and his doctrine of empirical realism, which is in no way sceptical, is ignored. Hicks also claims that Kant rejects a correspondence theory of truth. That is not true, since Kant retains a realistic sense of the relationship between knowledge and its objects. (A coherence theory of truth, Hick's "internal consistency," must wait for Hegel.) It is just that the objects are not transcendently real and absolutely outside the subject as Hicks requires. Even if we stipulate, for the sake of argument, that Kant's transcendental idealism is a form of scepticism, Hicks must also overlook the transcendent basis that Kant gives to morality and the "postulates of practical reason." As noted above, this is the kind of thing that appears to compromise Kant's empirical realism and leads to the kind of misinterpretations under consideration. However, Hicks cannot both ignore the transcendent basis of morality and allow it to compromise the realism of phenomenal objects.
With a Kantian alternative rejected, people like Rand, Hicks, and Kelley are left with a Conceptualism that logically reduces to Nominalism and a kind of metaphysical realism that will generate all the usual Cartesian paradoxes. This is better than the rampant nihilism of the modern academy, but it does not represent progress in philosophy.
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Leonard Nelson's axiomatic diagrams are usually of a similar logical form. One much like the diagram on universals above may be seen in "The Foundations of Value, Part II, Epistemological Issues: Justification (quid juris) and Non-Intuitive Immediate Knowledge." The one at right gives a basic logical form for such diagrams.
From four possible premises there are four possible conclusions. Three of the premises are actually true, and three of the conclusions actually false. The key is the single false premise, which usually embodies some traditional philosophical preconception that is false (a "false disjunction," Nelson says). The three false conclusions are then usually the traditional philosophical alternatives, as in Intuitionism (Mysticism, to Nelson), Speculative Constructivism (Logical Dogmatism, to Nelson), and Empiricism in epistemology, or Realism, Conceptualism, and Nominalism in metaphysics. The Kantian Critical conclusion, reached in Kant or in Friesian theory, is then the contradiction of the key traditional premise. At right, this is given both as a conjunction of the three true premises and as the logically equivalent denial of the original false premise. Each conclusion, indeed, is contradicted by the premise that it does not use. The Critical conclusion in epistemology is the Friesian theory of non-intuitive immediate knowledge, while in metaphysics it is Kantian transcendental idealism or ontological undecidability.
An example of one of Nelson's diagrams is below left. This is from Nelson's great Critique of Practical Reason [Kritik der praktishen Vernunft, 1917]. A translation of that book was commissioned by the Leonard Nelson Foundation in 1957. This should have followed the publication of Socratic Method and Critical Philosophy  and the System of Ethics  at Yale University Press, but evidently there had not been sufficient interest in the others, and the book was never published. The Foundation, however, made the manuscript translation available later in photocopied (and bound) form.
The logical structure of this diagram is now familiar (the negations are just distributed with one difference). What it deals with is the notion that moral obligation is the result of someone's will. This would be either my will or another's will. The pious often believe it is their obligation to do God's will. Politicians, the police, and judges often believe it is the obligation of citizens to do what they are told. On the other hand, others (Nietzscheans, Randites) think it is their obligation to do their own will (Existentialist "authenticity," or moralistic egoism), or that they have no obligation at all (moral aestheticism and egoistic aestheticism). The descriptions of these outcomes, "Authoritarianism," "Egoism," and "Nihilism," are not Nelson's terms but are suitable for the fallacies involved.
Examining Nelson's diagrams, one might notice that they have twelve lines and eight points where the lines come together. With this in mind, we might ask what solid figure has twelve edges and eight vertices. The simple answer is, a cube. Nelson's diagrams are thus versions of the logical square of opposition, expanding the square into a cube, as I have already done elsewhere to coordinate conceptions of rights.
Thus, at right I have mapped the logic of Nelson's diagrams onto a cube. As it happens, the lines of the diagrams are not simply the edges of the cube. Four are; but the other eight are diagonals on the vertical faces of the cube. One interesting effect here is that all the premises are at the corners of the upper surface, while all the conclusions are at the corners of the base.
A nice logical property of the cube is that contradictories are at opposite corners along the diagonals that pass through the cube. This is comparable to the property of the square of opposition that contradictories are at opposite ends of diagonals through the square. In general, it is not necessarily the case that a false premise makes for a false conclusion. That is the case here, however, where the true conclusion actually contradicts all the other possible conclusions. This happens just because the conjunction of the true premises (which constitutes the true conclusion) simply is the contradictory of the false premise. This is a tighter logical structure than is always the case with the versions of the square of opposition otherwise found in these pages.
Return to note on "Form and Cognition"
History of Philosophy