One and Many in Aristotles Metaphysics: The Central Books (One and Many in Aristotles Metaphysics)
Halper argues that Aristotle poses and pursues the problem of the existence of metaphysics as a version of the problem of the one and the many. However, Aristotle resolves this problem by introducing doctrines of being and substance, and it is these latter that he continues to explore in the next portion of the Metaphysics, treated in the second volume, "The Central Books". Hence, the opening books of the Metaphysics show, Halper argues, Aristotle's transformation of metaphysics from a treatment of the problem of the one and the many to a treatment of being and substance.
Many of the details in these well worked books of the Metaphysics are, of course, well known. The converse is not true: numbers are subjects of predication — six is even, seven is prime — but not of change. In the Categories , individual substances a man, a horse were treated as fundamental subjects of predication.
They were also understood, indirectly, as subjects of change.
These are changes in which substances move, or alter, or grow. What the Categories did not explore, however, are changes in which substances are generated or destroyed.
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But the theory of change Aristotle develops in the Physics requires some other subject for changes such as these — a subject of which substance is predicated — and it identifies matter as the fundamental subject of change a Change is seen in the Physics as a process in which matter either takes on or loses form. The concepts of matter and form, as we noted, are absent from the Categories. Individual substances — this man or that horse — apart from their accidental characteristics — the qualities, etc. Although there is metaphysical structure to the fact that, e.
This horse is a primary substance, and horse , the species to which it belongs, is a secondary substance. But there is no predicative complex corresponding to the fact that this is a horse in the way that there is such a complex corresponding to the fact that this horse is white. But from the point of view of the Physics , substantial individuals are seen as predicative complexes cf.
Matthen ; they are hylomorphic compounds — compounds of matter and form — and the subject criterion looks rather different from the hylomorphic perspective. Matter, form, and the compound of matter and form may all be considered subjects, Aristotle tells us, a , but which of them is substance? The subject criterion by itself leads to the answer that the substance of x is an entirely indeterminate matter of which x is composed a For form is predicated of matter as subject, and one can always analyze a hylomorphic compound into its predicates and the subject of which they are predicated.
And when all predicates have been removed in thought , the subject that remains is nothing at all in its own right — an entity all of whose properties are accidental to it a The resulting subject is matter from which all form has been expunged.
So the subject criterion leads to the answer that the substance of x is the formless matter of which it is ultimately composed. Precisely what the requirement amounts to is a matter of considerable scholarly debate, however. A plausible interpretation runs as follows. Being separate has to do with being able to exist independently x is separate from y if x is capable of existing independently of y , and being some this means being a determinate individual.
So a substance must be a determinate individual that is capable of existing on its own. The matter of which a substance is composed may exist independently of that substance think of the wood of which a desk is composed, which existed before the desk was made and may survive the disassembly of the desk , but it is not as such any definite individual — it is just a quantity of a certain kind of matter. Of course, the matter may be construed as constituting a definite individual substance the wood just is , one might say, the particular desk it composes , but it is in that sense not separate from the form or shape that makes it that substance the wood cannot be that particular desk unless it is a desk.
So although matter is in a sense separate and in a sense some this, it cannot be both separate and some this. It thus does not qualify as the substance of the thing whose matter it is. This phrase so boggled his Roman translators that they coined the word essentia to render the entire phrase, and it is from this Latin word that ours derives.
It is important to remember that for Aristotle, one defines things, not words. Aristotle's preliminary answer Z. That is, items in all the categories are definable, so items in all the categories have essences — just as there is an essence of man, there is also an essence of white and an essence of musical. The precise meaning of this claim, as well as the nature and validity of the arguments offered in support of it, are matters of scholarly controversy.
Man is a species, and so there is an essence of man; but pale man is not a species and so, even if there is such a thing as the essence of pale man, it is not, at any rate, a primary essence. At this point there appears to be a close connection between the essence of a substance and its species eidos , and this might tempt one to suppose that Aristotle is identifying the substance of a thing since the substance of a thing is its essence with its species.
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A consequence of this idea would be that Aristotle is radically altering his conception of the importance of the species, which in the Categories he called a secondary substance, that is, a substance only in a secondary sense. But such an identification would be a mistake, for two reasons. First, Aristotle's point at a11 is not that a species is an essence, but that an essence of the primary kind corresponds to a species e.
Since individual substances are seen as hylomorphic compounds, the role of matter and form in their generation must be accounted for. Whether we are thinking of natural objects, such as plants and animals, or artifacts, such as houses, the requirements for generation are the same.
We do not produce the matter to suppose that we do leads to an infinite regress nor do we produce the form what could we make it out of? Both the matter and the form must pre-exist Z. But in either case, the form pre-exists and is not produced b As for what is produced in such hylomorphic productions, it is correctly described by the name of its form, not by that of its matter. What is produced is a house or a man, not bricks or flesh.
For if gold is the matter out of which a statue is made, there was gold present at the start, and so it was not gold that came into being.
It was a statue that came into being, and although the statue is golden — i. The essence of such a hylomorphic compound is evidently its form, not its matter. It is the form of a substance that makes it the kind of thing that it is, and hence it is form that satisfies the condition initially required for being the substance of something. The substance of a thing is its form. The main question these chapters consider is whether the definition of x ever includes a reference to the matter of x. If some definitions include a reference to matter, then the link between essence and form would seem to be weakened.
That is, if y is a part of a definable thing x , then the definition of x will include as a part something z that corresponds to y. Indeed, z must stand to y in the same relation that the definition of x stands in to x ; that is, z is the definition of y. So, according to this principle, the definition of a thing will include the definitions of its parts. In a way, this consequence of the principle seems very plausible, given Aristotle's idea that it is universals that are definable Z.
Consider as a definiendum a universal, such as man , and its definiens, rational animal. The parts of this definiens are the universals rational and animal.
Aristotle's Metaphysics (Stanford Encyclopedia of Philosophy/Summer Edition)
If these parts are, in turn, definable, then each should be replaced, in the definition of man , with its own definition, and so on. In this way the complete and adequate definition of a universal such as man will contain no parts that are further definable. All proper, or completely analyzed, definitions are ultimately composed of simple terms that are not further definable. But the implication of this idea for the definitions of hylomorphic compounds is obvious: since matter appears to be a part of such a compound, the definition of the compound will include, as a part, the definitions of its material components.
And this consequence seems implausible to Aristotle. A circle, for example, seems to be composed of two semicircles for it obviously may be divided into two semicircles , but the definition of circle cannot be composed of the definitions of its two semicircular parts. For, as Aristotle points out b9 , semicircle is defined in terms of circle , and not the other way around.
His point is well taken, for if circles were defined in terms of semicircles, then presumably semicircles would be defined in terms of the quarter-circles of which they are composed, and so on, ad infinitum. Aristotle flirts with the idea of distinguishing between different senses in which one thing can be a part of another b33 , but instead proposes a different solution: to specify carefully the whole of which the matter is allegedly a part.
For more detail on this topic, see Section 3 of the entry on Aristotle's psychology. His point seems to be that whereas bronze may be a part of a particular statue, neither that particular batch of bronze nor even bronze in general enters into the essence of statue, since being made of bronze is no part of what it is to be a statue. But that is only because statues, although they must be made of some kind of matter, do not require any particular kind of matter. But what about kinds of substances that do require particular kinds of matter?
Aristotle's distinction between form and compound cannot be used in such cases to isolate essence from matter. Thus there may after all be reasons for thinking that reference to matter will have to intrude into at least some definitions. The point is not just that each particular man must be made of matter, but that each one must be made of matter of a particular kind — flesh and bones, etc. Perhaps his point is that whenever it is essential to a substance that it be made of a certain kind of matter e. A kind of matter, after all, can itself be analyzed hylomorphically — bronze, for example, is a mixture of copper and tin according to a certain ratio or formula logos , which is in turn predicated of some more generic underlying subject.
The reference to matter in a definition will thus always be to a certain kind of matter, and hence to a predicate, rather than a subject.