LESSON 4

The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. Transferred Usages of "Element" and Their Common Basis

Chapter 3: 1014a 25-1014b 15

             411. The inherent principle of which a thing is first composed and which is not divisible into another species is called an element. For example, the elements of a word are the parts of which a word is composed and into which it is ultimately divided and which are not further divided into other words specifically different from them. But if they are divided, their parts are alike, as the parts of water are water; but this is not true of the syllable. Similarly, people who speak of the elements of bodies mean the component parts into which bodies are ultimately divided and which are not divided into other bodies specifically different. And whether such parts are one or many, they call them elements. And similarly the parts of diagrams are called elements, and in general the parts of demonstrations; for the primary demonstrations which are contained in many other demonstrations are called the elements of demonstrations; and such are the primary syllogisms which are composed of three terms and proceed through one middle term.

             412. People also use the term element in a transferred sense of anything which is one and small and useful for many purposes; and for this reason anything which is small and simple and indivisible is called an element. Hence it follows that the most universal things are elements, because each of them, being one and simple, is found in many things, either in all or in most of them. And to some the unit and the point seem to be principles. Therefore, since what are called genera are universal and indivisible (for their formal character is one), some men call the genera elements, and these more than a difference, since a genus is more universal. For where the difference is present the genus also follows, but the difference is not always present where the genus is. And in all these cases it is common for the element of each thing to be the primary component of each thing.

COMMENTARY

             795. Here he distinguishes the different senses of the term element, and in regard to this he does two things. First (411:C 795), he gives the different senses in which the term element is used. Second (412:C 807), he indicates what all of them have in common ("And in all these").

             In regard to the first he does two things. First, he explains how the term element is used in its proper sense; and second (412:C 802), how it is used in transferred senses ("People also use").

             First (411), he gives a sort of description of an element, and from this one can gather the four notes contained in its definition. The first is that an element is a cause in the sense of that from which a thing comes to be; and from this it is clear that an element is placed in the class of material cause.

             796. The second is that an element is the principle from which something first comes to be. For copper is that from which a statue comes to be, but it is still not an element because it has some matter from which it comes to be.

             797. The third is that an element is inherent or intrinsic; and for this reason it differs from everything of a transitory nature from which a thing comes to be, whether it be a privation or a contrary or the matter subject to contrariety and privation, which is transitory; for example, when we say that a musical man comes from a non-musical man, or that the musical comes from the non-musical. For elements must remain in the things of which they are the elements.

             798. The fourth is that an element has a species which is not divisible into different species; and thus an element differs from first matter, which has no species, and also from every sort of matter which is capable of being divided into different species, as blood and things of this kind.

             Hence he says, as the first note, that an element is that of which a thing is composed; as the second, that it is that of which a thing is "first" composed; as the third, that it is "an inherent principle"; and as the fourth, that it is "not divisible into another species."

             799. He illustrates this definition of element in four cases in which we use the term element. For we say that letters are the elements of a word because every word is composed of them, and of them primarily. This is evident from the fact that all words are divided into letters as ultimate things; for what is last in the process of dissolution must be first in the process of composition. But letters are not further divided into other words which are specifically different. Yet if they should be divided in any way, the parts in which the division results would be "alike," i.e., specifically the same, just as all parts of water are water. Now letters are divided according to the amount of time required to pronounce them, inasmuch as a long letter is said to require two periods of time, and a short letter one. But while the parts into which letters are so divided do not differ as the species of words do, this is not the case with a syllable; for its parts are specifically different, since the sounds which a vowel and a consonant make, of which a syllable is composed, are specifically different.

             800. He gives as a second example natural bodies, certain of which we also call the elements of certain others. For those things into which all compounds are ultimately dissolved are called their elements; and therefore they are the things of which bodies of this kind are composed. But those bodies which are called elements are not divisible into other bodies which are specifically different, but into like parts, as any part of water is water. And all those who held for one such body into which every body is dissolved and which is itself incapable of being further divided, said that there is one element. Some said that it is water, some air, and some fire. But those who posited many such bodies also said there are many elements. Now it should be borne in mind that when it is set down in the definition of an element that an element is not divisible into different species, this should not be understood of the parts into which a thing is divided in a quantitative division (for wood would then be an element, since any part of wood is wood), but in a division made by alteration, as compounds are dissolved into simple bodies.

             801. As a third example he gives the order of demonstrations, in which we also employ the word element; for example, we speak of Euclid's Book of Elements. And he says that, in a way similar and close to those mentioned, those things which "are parts of diagrams," i.e., the constituents of geometrical figures, are called elements. This can be said not only of the demonstrations in geometry but universally of all demonstrations. For those demonstrations which have only three terms are called the elements of other demonstrations, because the others are composed of them and resolved into them. This is shown as follows: a second demonstration takes as its starting point the conclusion of a first demonstration, whose terms are understood to contain the middle term which was the starting point of the first demonstration. Thus the second demonstration will proceed from four terms, the first from three only, the third from five, and the fourth from six; so that each demonstration adds one term. Thus it is clear that first demonstrations are included in subsequent ones, as when this first demonstration--every B is A, every C is B, therefore every C is A--is included in this demonstration--every C is A, every D is C, therefore every D is A; and this again is included in the demonstration whose conclusion is that every E is A, so that for this final conclusion there seems to be one syllogism composed of several syllogisms having several middle terms. This may be expressed thus: every B is A, every C is B, every D is C, every E is D, therefore every E is A. Hence a first demonstration, which has one middle term and only three terms, is simple and not reducible to another demonstration, whereas all other demonstrations are reducible to it. Hence first syllogisms, which come from three terms by way of one middle term, are called elements.

             802. People also use (412).

             Here he shows how the term element is used in a transferred sense. He says that some men, on the basis of the foregoing notion or meaning of element, have used the term in a transferred sense to signify anything that is one and small and useful for many purposes. For from the fact that an element is indivisible they understood that it is one; and from the fact that it is first they understood that it is simple; and from the fact that other things are composed of elements they understood that an element is useful for many purposes. Hence they set up this definition of an element in order that they might say that everything which is smallest in quantity and simple (inasmuch as it is not composed of other things) and incapable of division into different species, is an element.

             803. But when they had set up this definition of element, it turned out that by using it in a transferred sense they had invented two senses of element. First, they called the most universal things elements; for a universal is one in definition and is simple (because its definition is not composed of different parts) and is found in many things, and thus is useful for many purposes, whether it be found in all things, as unity and being are, or in most things, as the other genera. And by the same reasoning it came about, second, that they called points and units principles or elements because each of them is one simple thing and useful for many purposes.

             804. But in this respect they fell short of the true notion of a principle, because universals are not the matter of which particular things are composed but predicate their very substance. And similarly points are not the matter of a line, for a line is not composed of points.

             805. Now with this transferred notion of element established, the solution to a question disputed in Book III (228-31:C 431-36) becomes clear, i.e., whether a genus or a species is more an element, and whether a genus or a difference is more an element; for it clearly follows that genera are elements to a greater degree because genera are more universal and indivisible. For there is no concept or definition of them which must be composed of genera and differences, but it is species which are properly defined. And if a genus is defined, it is not defined insofar as it is a genus but insofar as it is a species. Hence a species is divided into different parts and thus does not have the character of an element. But a genus is not divisible into different parts, and therefore they said that genera are elements more than species. Another translation reads, "For their formal character is one," that is, indivisible, because even though genera do not have a definition, still what is signified by the term genus is a simple conception of the intellect which can be called a definition.

             806. And just as a genus is more an element than a species is because it is simpler, in a similar way it is more an element than a difference is, even though a difference is simple, because a genus is more universal. This is clear from the fact that anything which has a difference has a genus, since essential differences do not transcend a genus; but not everything which has a genus necessarily has a difference.

             807. Last of all he says that all of the foregoing senses of element have this note in common, that an element is the primary component of each being, as has been stated.