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But in that claim lies a problem. For while dialectic treats things “only with an eye to general opinion,” philosophy must treat them “according to their truth” (Topics 105b30–31). Endoxa, however, are just generally accepted and unobjectionable opinions. Since even such unopposed opinions may nevertheless be false, how can an argument that relies on them be guaranteed to reach the truth? The answer lies in aporematic philosophy’s dialectical capacity to criticize or examine (101b3).

  Because he is a generally educated person, an aporematic philosopher knows what it takes to be a genuine science of whatever sort (On the Parts of Animals 639a1–8). Hence he will know, for example, what level of exactness a science should have, given its subject matter, and what we should and should not seek to have demonstrated (Nicomachean Ethics 1094b23–27, Metaphysics 1006a5–11). Using his dialectical capacity to examine, therefore, a philosopher can, for example, determine whether a person, A, has any sort of mathematical knowledge, or is simply a charlatan. If A passes the examination, the philosopher can use his own knowledge of what a mathematical science must be like to determine whether A’s mathematical knowledge is genuinely scientific. If he finds that it is, he knows that the undemonstrated mathematical first principles A accepts are true. If, in particular, A accepts that magnitudes are divisible without limit, the philosopher knows that this is true.

  When he uses his dialectical skill to draw out the consequences of this principle and of its negation, however, he sees difficulties and supporting arguments based on endoxa on both sides. Since he knows the principle is true, however, his goal will be to resolve the difficulties it faces and undo the arguments that seem to support its negation. If he is successful, he will have refuted all the objections to it, and so will have provided a negative demonstration, or demonstration by refutation, of it (Metaphysics 1006a12). Such a demonstration is aporematic philosophy’s way to a scientific first principle, and constitutes the sufficient proof of it to which Aristotle refers.

  In many texts, Aristotle characterizes problems as knots in our understanding that dialectic enables us to untie, in others, he characterizes dialectic itself as enabling us to make first principles clear. What aporematic philosophy offers us in regard to the first principles of the sciences, then, is no knots—no impediments to clear and exact intuitive grasp. And with such clarity comes scientific knowledge of the most excellent and unqualified sort—knowledge that manifests the virtue of theoretical wisdom (Nicomachean Ethics 1141a16–17).

  The marginal numbers accompanying the text correspond to the page number, column (represented by the letters a and b), and line of the edition of Aristotle’s works published in Berlin by Immanuel Bekker in 1831. Line numbers given in citations are those of the Greek text and correspond only approximately to lines in translations.

  Organon

  CATEGORIAE

  Translated by E. M. Edghill

  CONTENTS

  CHAPTER

  1. Homonyms, synonyms, and derivatives.

  2. (1) Simple and composite expressions.

  (2) Things (a) predicable of a subject, (b) present in a subject, (c) both predicable of, and present in, a subject, (d) neither predicable of, nor present in, a subject.

  3. (1) That which is predicable of the predicate is predicable of the subject.

  (2) The differentiae of species in one genus are not the same as those in another, unless one genus is included in the other.

  4. The eight categories of the objects of thought.

  5. Substance.

  (1) Primary and secondary substance.

  (2) Difference in the relation subsisting between essential and accidental attributes and their subject.

  (3) All that which is not primary substance is either an essential or an accidental attribute of primary substance.

  (4) Of secondary substances, species are more truly substance than genera.

  (5) All species, which are not genera, are substance in the same degree, and all primary substances are substance in the same degree.

  (6) Nothing except species and genera is secondary substance.

  (7) The relation of primary substance to secondary substance and to all other predicates is the same as that of secondary substance to all other predicates.

  (8) Substance is never an accidental attribute.

  (9) The differentiae of species are not accidental attributes.

  (10) Species, genus, and differentiae, as predicates, are ‘univocal’ with their subject.

  (11) Primary substance is individual; secondary substance is the qualification of that which is individual.

  (12) No substance has a contrary.

  (13) No substance can be what it is in varying degrees.

  (14) The particular mark of substance is that contrary qualities can be predicated of it.

  (15) Contrary qualities cannot be predicated of anything other than substances, not even of propositions and judgements.

  6. Quantity.

  (1) Discrete and continuous quantity.

  (2) Division of quantities, i. e. number, the spoken word, the line, the surface, the solid, time, place, into these two classes.

  (3) The parts of some quantities have a relative position, those of others have not. Division of quantities into these two classes.

  (4) Quantitative terms are applied to things other than quantity, in view of their relation to one of the aforesaid quantities.

  (5) Quantities have no contraries.

  (6) Terms such as ‘great’ and ‘small’ are relative, not quantitative, and moreover cannot be contrary to each other.

  (7) That which is most reasonably supposed to contain a contrary is space.

  (8) No quantity can be what it is in varying degrees.

  (9) The peculiar mark of quantity is that equality and inequality can be predicated of it.

  7. Relation.

  (1) First definition of relatives.

  (2) Some relatives have contraries.

  (3) Some relatives are what they are in varying degrees.

  (4) A relative term has always its correlative, and the two are interdependent.

  (5) The correlative is only clear when the relative is given its proper name, and in some cases words must be coined for this purpose.

  (6) Most relatives come into existence simultaneously; but the objects of knowledge and perception are prior to knowledge and perception.

  (7) No primary substance or part of a primary substance is relative.

  (8) Revised definition of relatives, excluding secondary substances.

  (9) It is impossible to know that a thing is relative, unless we know that to which it is relative.

  8. Quality.

  (1) Definition of qualities.

  (2) Different kinds of quality:

  (a) habits and dispositions;

  (b) capacities;

  (c) affective qualities [Distinction between affective qualities and affections.]

  (d) shape, &c. [Rarity, density, &c., are not qualities.]

  (3) Adjectives are generally formed derivatively from the names of the corresponding qualities.

  (4) Most qualities have contraries.

  (5) If of two contraries one is a quality, the other is also a quality.

  (6) A quality can in most cases be what it is in varying degrees, and subjects can possess most qualities in varying degrees. Qualities of shape are an exception to this rule.

  (7) The peculiar mark of quality is that likeness and unlikeness is predicable of things in respect of it.

  (8) Habits and dispositions as genera are relative; as individual, qualitative.

  9. Action and affection and the other categories described.

  10. Four classes of ‘opposites’.

  (a) Correlatives.

  (b) Contraries. [Some contraries have an intermediate, and some have not.]

  (c) Positives and privatives.

  The terms expressing possession and privation are not the positive and privative, though the former are opposed each to each i
n the same sense as the latter.

  Similarly the facts which form the basis of an affirmation or a denial are opposed each to each in the same sense as the affirmation and denial themselves.

  Positives and privatives are not opposed in the sense in which correlatives are opposed.

  Positives and privatives are not opposed in the same sense in which contraries are opposed.

  For (i) they are not of the class which has no intermediate, nor of the class which has intermediates.

  (ii) There can be no change from one state (privation) to its opposite.

  (d) Affirmation and negation. These are distinguished from other contraries by the fact that one is always false and the other true. [Opposite affirmations seem to possess this mark, but they do not.]

  11. Contraries further discussed.

  Evil is generally the contrary of good, but sometimes two evils are contrary.

  When one contrary exists, the other need not exist.

  Contrary attributes are applicable within the same species or genus.

  Contraries must themselves be within the same genus, or within opposite genera, or be themselves genera.

  12. The word ‘prior’ is applicable:

  (a) to that which is previous in time;

  (b) to that on which something else depends, but which is not itself dependent on it;

  (c) to that which is prior in arrangement;

  (d) to that which is better or more honourable;

  (e) to that one of two interdependent things which is the cause of the other.

  13. The word ‘simultaneous’ is used:

  (a) of those things which come into being at the same time;

  (b) of those things which are interdependent, but neither of which is the cause of the other.

  (c) of the different species of the same genus.

  14. Motion is of six kinds.

  Alteration is distinct from other kinds of motion.

  Definition of the contrary of motion and of the various kinds of motion.

  15. The meanings of the term ‘to have’.

  CATEGORIAE

  (Categories)

  1 [1a] Things are said to be named ‘equivocally’ when, though they have a common name, the definition corresponding with the name differs for each. Thus, a real man and a figure in a picture can both lay claim to the name ‘animal’; yet these are equivocally so named, for, though they have a common name, the definition corresponding with the name differs for each. For should any one define in what sense each is an animal, his definition in the one case will be appropriate to that case only. (5)

  On the other hand, things are said to be named ‘univocally’ which have both the name and the definition answering to the name in common. A man and an ox are both ‘animal’, and these are univocally so named, inasmuch as not only the name, but also the definition, is the same in both cases: for if a man should state in what sense each is an animal, (10) the statement in the one case would be identical with that in the other.

  Things are said to be named ‘derivatively’, which derive their name from some other name, but differ from it in termination. Thus the grammarian derives his name from the word ‘grammar’, (15) and the courageous man from the word ‘courage’.

  2 Forms of speech are either simple or composite. Examples of the latter are such expressions as ‘the man runs’, ‘the man wins’; of the former ‘man’, ‘ox’, ‘runs’, ‘wins’.

  Of things themselves some are predicable of a subject, (20) and are never present in a subject. Thus ‘man’ is predicable of the individual man, and is never present in a subject.

  By being ‘present in a subject’ I do not mean present as parts are present in a whole, but being incapable of existence apart from the said subject.

  Some things, again, are present in a subject, but are never predicable of a subject. For instance, a certain point of grammatical knowledge is present in the mind, (25) but is not predicable of any subject; or again, a certain whiteness may be present in the body (for colour requires a material basis), yet it is never predicable of anything.

  Other things, again, are both predicable of a subject and present in a subject. [1b] Thus while knowledge is present in the human mind, it is predicable of grammar.

  There is, lastly, a class of things which are neither present in a subject nor predicable of a subject, such as the individual man or the individual horse. (5) But, to speak more generally, that which is individual and has the character of a unit is never predicable of a subject. Yet in some cases there is nothing to prevent such being present in a subject. Thus a certain point of grammatical knowledge is present in a subject.

  3 When one thing is predicated of another, (10) all that which is predicable of the predicate will be predicable also of the subject. Thus, ‘man’ is predicated of the individual man; but ‘animal’ is predicated of ‘man’; it will, therefore, be predicable of the individual man also: for the individual man is both ‘man’ and ‘animal’. (15)

  If genera are different and co-ordinate, their differentiae are themselves different in kind. Take as an instance the genus ‘animal’ and the genus ‘knowledge’. ‘With feet’, ‘two-footed’, ‘winged’, ‘aquatic’, are differentiae of ‘animal’; the species of knowledge are not distinguished by the same differentiae. One species of knowledge does not differ from another in being ‘two-footed’.

  But where one genus is subordinate to another, (20) there is nothing to prevent their having the same differentiae: for the greater class is predicated of the lesser, so that all the differentiae of the predicate will be differentiae also of the subject.

  4 Expressions which are in no way composite signify substance, (25) quantity, quality, relation, place, time, position, state, action, or affection. To sketch my meaning roughly, examples of substance are ‘man’ or ‘the horse’, of quantity, such terms as ‘two cubits long’ or ‘three cubits long’, of quality, such attributes as ‘white’, ‘grammatical’. ‘Double’, ‘half’, ‘greater’, fall under the category of relation; ‘in the market place’, ‘in the Lyceum’, under that of place; ‘yesterday’, ‘last year’, under that of time. [2a] ‘Lying’, ‘sitting’, are terms indicating position; ‘shod’, ‘armed’, state; ‘to lance’, ‘to cauterize’, action; ‘to be lanced’, ‘to be cauterized’, affection.

  No one of these terms, in and by itself, involves an affirmation; it is by the combination of such terms that positive or negative statements arise. (5) For every assertion must, as is admitted, be either true or false, whereas expressions which are not in any way composite, such as ‘man’, (10) ‘white’, ‘runs’, ‘wins’, cannot be either true or false.

  5 Substance, in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse. But in a secondary sense those things are called substances within which, (15) as species, the primary substances are included; also those which, as genera, include the species. For instance, the individual man is included in the species ‘man’, and the genus to which the species belongs is ‘animal’; these, therefore—that is to say, the species ‘man’ and the genus ‘animal’—are termed secondary substances.

  It is plain from what has been said that both the name and the definition of the predicate must be predicable of the subject.(20) For instance, ‘man’ is predicated of the individual man. Now in this case the name of the species ‘man’ is applied to the individual, for we use the term ‘man’ in describing the individual; and the definition of ‘man’ will also be predicated of the individual man, for the individual man is both man and animal. Thus, both the name and the definition of the species are predicable of the individual. (25)

  With regard, on the other hand, to those things which are present in a subject, it is generally the case that neither their name nor their definition is predicable of that in which they are present. Though, however, the definition is never predicable, (30) there is nothin
g in certain cases to prevent the name being used. For instance, ‘white’ being present in a body is predicated of that in which it is present, for a body is called white: the definition, however, of the color ‘white’ is never predicable of the body.

  Everything except primary substances is either predicable of a primary substance or present in a primary substance. This becomes evident by reference to particular instances which occur. (35) ‘Animal’ is predicated of the species ‘man’, therefore of the individual man, for if there were no individual man of whom it could be predicated, it could not be predicated of the species ‘man’ at all. [2b] Again, colour is present in body, therefore in individual bodies, for if there were no individual body in which it was present, it could not be present in body at all. Thus everything except primary substances is either predicated of primary substances, or is present in them, (5) and if these last did not exist, it would be impossible for anything else to exist.

  Of secondary substances, the species is more truly substance than the genus, being more nearly related to primary substance. For if any one should render an account of what a primary substance is, he would render a more instructive account, and one more proper to the subject, by stating the species than by stating the genus. (10) Thus, he would give a more instructive account of an individual man by stating that he was man than by stating that he was animal, for the former description is peculiar to the individual in a greater degree, while the latter is too general. Again, the man who gives an account of the nature of an individual tree will give a more instructive account by mentioning the species ‘tree’ than by mentioning the genus ‘plant’.

  Moreover, primary substances are most properly called substances in virtue of the fact that they are the entities which underlie everything else, (15) and that everything else is either predicated of them or present in them. Now the same relation which subsists between primary substance and everything else subsists also between the species and the genus: for the species is to the genus as subject is to predicate, (20) since the genus is predicated of the species, whereas the species cannot be predicated of the genus. Thus we have a second ground for asserting that the species is more truly substance than the genus.