In metaphysics, the problem of universals refers to the question of whether properties exist, and if so, what they are. Properties are qualities or relations that two or more entities have in common. The various kinds of properties, such as qualities and relations, are referred to as universals. For instance, one can imagine three cup holders on a table that have in common the quality of being circular or exemplifying circularity, or two daughters that have in common being the female offsprings of Frank. There are many such properties, such as being human, red, male or female, liquid, big or small, taller than, father of, etc.
While philosophers agree that human beings talk and think about properties, they disagree on whether these universals exist in reality or merely in thought and speech.
There are many philosophical positions regarding universals. Taking "beauty" as example, three positions are:
The realist school claims that universals are real—they exist and are distinct from the particulars that instantiate them. There are various forms of realism. Two major forms are Platonic realism (universalia ante res) and Aristotelian realism (universalia in rebus). Platonic realism is the view that universals are real entities and they exist independent of particulars. Aristotelian realism, on the other hand, is the view that universals are real entities, but their existence is dependent on the particulars that exemplify them.
Realists tend to argue that universals must be posited as distinct entities in order to account for various phenomena. For example, a common realist argument, arguably found in Plato, is that universals are required for certain general words to have meaning and for the sentences in which they occur to be true or false. Take the sentence "Djivan Gasparyan is a musician". The realist may claim that this sentence is only meaningful and expresses a truth because there is an individual, Djivan Gasparyan, who possesses a certain quality: musicianship. Thus it is assumed that the property is a universal which is distinct from the particular individual who has the property.
Nominalists assert that only individuals or particulars exist and deny that universals are real (i.e. that they exist as entities or beings; universalia post res). The term "nominalism" comes from the Latin nomen ("name"), since the nominalist philosopher agrees that we predicate the same property of multiple entities but argues that the entities only share a name, not a real quality, in common. There are various forms of nominalism; four major varieties are predicate nominalism, resemblance nominalism, trope nominalism, and conceptualism.
Nominalists often argue for their view by claiming that nominalism can account for all the relevant phenomena, and therefore—by Occam's razor or some sort of principle of simplicity—nominalism is preferable, since it posits fewer entities.
Transcendental idealist philosopher Immanuel Kant posited that universals are not real, but are ideas in the mind of rational beings. Transcendental idealists do not reject universals as arbitrary names; rather, they treat universals as fundamental categories of pure reason (or as secondary concepts derived from those fundamental categories). Universals, in transcendental idealism, are intrinsically tied to the rationality of the subject making the judgment.
Thus, for transcendental idealists, the problem of universals is only tangentially a metaphysical problem; it is more of a problem of psychology and epistemology. Kant's position has been interpreted as a conceptualist one.
Plato believed there to be a sharp distinction between the world of perceivable objects and the world of universals or forms: one can only have mere opinions about the former, but one can have knowledge about the latter. For Plato it was not possible to have knowledge of anything that could change or was particular, since knowledge had to be forever unfailing and general. For that reason, the world of the forms is the real world, like sunlight, while the sensible world is only imperfectly or partially real, like shadows. This Platonic realism, however, in denying that the eternal Forms are mental artifacts, differs sharply with modern forms of idealism.
Plato's student Aristotle disagreed with his tutor. Aristotle transformed Plato's forms into "formal causes", the blueprints or essences of individual things. Whereas Plato idealized geometry, Aristotle emphasized nature and related disciplines and therefore much of his thinking concerns living beings and their properties. The nature of universals in Aristotle's philosophy therefore hinges on his view of natural kinds.
Consider for example a particular oak tree. This is a member of a species and it has much in common with other oak trees, past, present and future. Its universal, its oakness, is a part of it. A biologist can study oak trees and learn about oakness and more generally the intelligible order within the sensible world. Accordingly, Aristotle was more confident than Plato about coming to know the sensible world; he was a prototypical empiricist and a founder of induction. Aristotle was a new, moderate sort of realist about universals.
"I shall omit to speak about genera and species, as to whether they subsist (in the nature of things) or in mere conceptions only; whether also if subsistent, they are bodies or incorporeal, and whether they are separate from, or in, sensibles, and subsist about these, for such a treatise is most profound, and requires another more extensive investigation".
William of Ockham argued strongly that universals are a product of abstract human thought. According to Ockham, universals are just words/names that only exist in the mind and have no real place in the external world.
Realism was argued for by both Thomas Aquinas and Duns Scotus. Aquinas argued that both the essence of a thing and its existence were clearly distinct; in this regard he is close to the teaching of Aristotle. Scotist realism argues that in a thing there is no real distinction between the essence and the existence, instead there is only a Formal distinction. Both of these opinions were denied by Scotus' pupil William of Ockham.
The 19th-century British philosophy John Stuart Mill discussed the problem of universals in the course of a book that eviscerated the philosophy of Sir William Hamilton. Mill wrote, "The formation of a concept does not consist in separating the attributes which are said to compose it from all other attributes of the same object and enabling us to conceive those attributes, disjoined from any others. We neither conceive them, nor think them, nor cognize them in any way, as a thing apart, but solely as forming, in combination with numerous other attributes, the idea of an individual object".
However, he then proceeds to state that Berkeley's position is factually wrong by stating the following:
But, though meaning them only as part of a larger agglomeration, we have the power of fixing our attention on them, to the neglect of the other attributes with which we think them combined. While the concentration of attention lasts, if it is sufficiently intense, we may be temporarily unconscious of any of the other attributes and may really, for a brief interval, have nothing present to our mind but the attributes constituent of the concept.— as quoted in William James, The Principles of Psychology (1890)
In other words, we may be "temporarily unconscious" of whether an image is white, black or yellow and concentrate our attention on the fact that it is a man and on just those attributes necessary to identify it as a man (but not as any particular one). It may then have the significance of a universal of manhood.
The 19th-century American logician Charles Sanders Peirce, known as the father of pragmatism, developed his own views on the problem of universals in the course of a review of an edition of the writings of George Berkeley. Peirce begins with the observation that "Berkeley's metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop". He includes among these paradoxical doctrines Berkeley's denial of "the possibility of forming the simplest general conception". He wrote that if there is some mental fact that works in practice the way that a universal would, that fact is a universal. "If I have learned a formula in gibberish which in any way jogs my memory so as to enable me in each single case to act as though I had a general idea, what possible utility is there in distinguishing between such a gibberish... and an idea?" Peirce also held as a matter of ontology that what he called "thirdness", the more general facts about the world, are extra-mental realities.
William James learned pragmatism, this way of understanding an idea by its practical effects, from his friend Peirce, but he gave it new significance. (Which was not to Peirce's taste - he came to complain that James had "kidnapped" the term and eventually to call himself a "pragmaticist" instead.) Although James certainly agreed with Peirce and against Berkeley that general ideas exist as a psychological fact, he was a nominalist in his ontology:
From every point of view, the overwhelming and portentous character ascribed to universal conceptions is surprising. Why, from Plato and Aristotle, philosophers should have vied with each other in scorn of the knowledge of the particular and in adoration of that of the general, is hard to understand, seeing that the more adorable knowledge ought to be that of the more adorable things and that the things of worth are all concretes and singulars. The only value of universal characters is that they help us, by reasoning, to know new truths about individual things.— William James, The Principles of Psychology (1890)
There are at least three ways in which a realist might try to answer James' challenge of explaining the reason why universal conceptions are more lofty than those of particulars: the moral/political answer, the mathematical/scientific answer, and the anti-paradoxical answer. Each has contemporary or near-contemporary advocates.
The moral or political response is given by the conservative philosopher Richard M. Weaver in Ideas Have Consequences (1948), where he describes how the acceptance of "the fateful doctrine of nominalism" was "the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence".
Nino Cocchiarella put forward the idea that realism is the best response to certain logical paradoxes to which nominalism leads ("Nominalism and Conceptualism as Predicative Second Order Theories of Predication", Notre Dame Journal of Formal Logic, vol. 21 (1980)). It is noted that in a sense Cocchiarella has adopted Platonism for anti-Platonic reasons. Plato, as seen in the dialogue Parmenides, was willing to accept a certain amount of paradox with his forms. Cocchiarella adopts the forms to avoid paradox.
The Australian philosopher David Malet Armstrong has been one of the leading realists in the twentieth century, and has used a concept of universals to build a naturalistic and scientifically realist ontology. In both Universals and Scientific Realism (1978) and Universals: An Opinionated Introduction (1989), Armstrong describes the relative merits of a number of nominalist theories which appeal either to "natural classes" (a view he ascribes to Anthony Quinton), concepts, resemblance relations or predicates, and also discusses non-realist "trope" accounts (which he describes in the Universals and Scientific Realism volumes as "particularism"). He gives a number of reasons to reject all of these, but also dismisses a number of realist accounts.
Roger Penrose contends that the foundations of mathematics can't be understood absent the Platonic view that "mathematical truth is absolute, external and eternal, and not based on man-made criteria ... mathematical objects have a timeless existence of their own..."
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