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A consideration of platonic theory of universals

Meaning and the Problem of Universals, A Kant-Friesian Approach One of the most durable and intractable issues in the history of philosophy has been the problem of universals.

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.

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.

  • Since images are undoubtedly individual and concrete, this stacks the deck for Nominalism;
  • Because they have tropes that resemble each other;
  • A paradigm as such cannot be a determinable;
  • This method can be applied to any other abstract entity, like whiteness;
  • A universal has to be common to several particulars in its entirety, and not only in part simultaneously, and not in a temporal succession, and it should constitute the substance of its particulars;
  • For example, I can be mistaken if I form in my mind the judgment that a man is running, whereby I conceive a man to be somehow, but if I simply think of a man without attributing either running or not running to him, I certainly cannot make a mistake as to how he is.

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 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 Republictheir 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 a consideration of platonic theory of universals 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.

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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. This word is more familiar to us in its Latin translation: 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. To Aristotle that was the "matter" of the object. Since everything that we can identify about an object, the kind of thing it is, what it is doing, where it is, etc. 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 a consideration of platonic theory of universals 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.

The abstract "form" of an object, the universal in it, Aristotle called "secondary substance.

  1. 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.
  2. Carnap knew that such assertions were metaphysical, which Positivist epistemology precludes. It is neither in space nor in time, neither material nor mental; yet it is something.
  3. She thinks that she can show that Aristotle's criticism are powerful and subtle and fair.

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.

  1. 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. However, obviously, all these questions presuppose that it is at all, namely, that such a universal entity exists.
  2. 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. 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.
  3. Both these opposing philosophies, interesting as they are, result, in my opinion, from an undue attention to one sort of universals, namely the sort represented by adjectives and substantives rather than by verbs and prepositions.

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. Thus the contrast between "substance and accident" or "essence and accident.

A contrast may also be drawn between substance and "attribute. 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. From that we have a principle, still echoed by Kant, that "[primary] substance is that which is always subject, never predicate. Leibniz's principle of the "identity of indiscernibles" thus postulates that individuals which cannot be distinguished from each other, i.

Problem of universals

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.

This brings us to a fundamental conflict in Aristotle's theory, which highlights its drawbacks in relation to Plato's theory.

The Medieval Problem of Universals

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 ": 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.

Payne translation] The Forms are perfect, and the world falls far short of them. This seems to account for important characteristics of reality, that true justice is rarely to be found, and that mathematicians describe the strangest things that have no obvious relation to experience. Aristotle's theory can accommodate this, but only by positing "forms" that are inaccessible to perception and abstraction, which would contradict any original notion in Aristotelian epistemology that knowledge comes from experience.

Universal (metaphysics)

Again, Neoplatonism takes care of this, but only at the cost of an intuitionism that is non-empirical, indeed, mystical, in the extreme, where we certainly do have access to "forms," or the Forms, apart from experience. But if Neoplatonism were correct, then it would be possible for someone to look at an acorn and, unfamiliar with the species, see what the full grown oak would look like. This does not seem to happen on any credible testimony. 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 a consideration of platonic theory of universals calculation. 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 Galileothat modern science got going. 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. 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.

Chapter 9 - The World of Universals

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: Although the debate between the Realists and the Nominalists became the greatest controversy of Mediaeval philosophy, another classic a consideration of platonic theory of universals 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: 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. 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. Hume's argument only works if he really means imagine rather than conceive.

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.

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 a consideration of platonic theory of universals 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]: