Authors: Richard Mckeon
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
1–8). 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 (
5–11). 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 (
12). 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 (
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.
Homonyms, synonyms, and derivatives.
(1) Simple and composite expressions.
(2) Things (
) predicable of a subject, (
) present in a subject, (
) both predicable of, and present in, a subject, (
) neither predicable of, nor present in, a subject.
(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.
The eight categories of the objects of thought.
(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.
(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.
(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.
(1) Definition of qualities.
(2) Different kinds of quality:
) habits and dispositions;
) affective qualities [Distinction between affective qualities and affections.]
) 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.
Action and affection and the other categories described.
Four classes of ‘opposites’.
) Contraries. [Some contraries have an intermediate, and some have not.]
) Positives and privatives.
The terms expressing possession and privation are not the positive and privative, though the former are opposed each to each in 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.
) 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.]
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.
The word ‘prior’ is applicable:
) to that which is previous in time;
) to that on which something else depends, but which is not itself dependent on it;
) to that which is prior in arrangement;
) to that which is better or more honourable;
) to that one of two interdependent things which is the cause of the other.
The word ‘simultaneous’ is used:
) of those things which come into being at the same time;
) of those things which are interdependent, but neither of which is the cause of the other.
) of the different species of the same genus.
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.
The meanings of the term ‘to have’.
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.
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,
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’,
and the courageous man from the word ‘courage’.
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,
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,
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.
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.
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.