The Basic Works of Aristotle (Modern Library Classics) (30 page)

34
      Quick wit is a faculty of hitting upon the middle term instantaneously.
(10)
It would be exemplified by a man who saw that the moon has her bright side always turned towards the sun, and quickly grasped the cause of this, namely that she borrows her light from him; or observed somebody in conversation with a man of wealth and divined that he was borrowing money, or that the friendship of these people sprang from a common enmity. In all these instances he has seen the major and minor terms and then grasped the causes,
(15)
the middle terms.

Let
A
represent ‘bright side turned sunward’,
B
‘lighted from the sun’,
C
the moon. Then
B,
‘lighted from the sun’, is predicable of
C,
the moon, and
A,
‘having her bright side towards the source of her light’,
(20)
is predicable of
B.
So
A
is predicable of
C
through
B.

¹
Plato,
Meno,
80 E.

²
Cf.
An. Pr.
ii, ch. 21.

³
Cf. the following chapter and more particularly ii, ch. 19.

⁴
An. Pr.
i, ch. 25.

⁵
Ibid.
ii, ch. 5.

⁶
Ibid.
ii, cc. 5 and 6.

⁷
Plato,
Euthydemus,
277
B
.

⁸
Cf.
Met.
1039
^a
9.

⁹
Cf. i, cc. 9 and 13.

¹⁰
sc.
axioms.

¹¹
Cf. Plato,
Theaetetus,
189
E
ff.

¹²
Lit. ‘even if the middle is itself and also what is not itself’; i. e. you may pass from the middle term man to include not-man without affecting the conclusion.

¹³
Cf. 75
^a
42 ff. and 76
^b
13.

¹⁴
An. Pr.
i. 1. The ‘opposite facts’ are those which would be expressed in the alternatively possible answers to the dialectical question, the dialectician’s aim being to refute his interlocutor whether the latter answers the question put to him affirmatively or in the negative.

¹⁵
i. e. a premiss put in the form of a question.

¹⁶
sc.
‘which require two sciences for their proof’. Cf. 78
^b
35.

¹⁷
i. e. in Celarent.

¹⁸
i. e. in Cesare or Camestres.

¹⁹
Cf. 80
^a
29.

²⁰
Cf. 80
^b
17–26.

²¹
Cf. 80
^b
26–32.

²²
sc.
a predicate above which is no wider universal.

²³
sc.
‘that no
C
is
B’.

²⁴
i. e. each of the successive prosyllogisms required to prove the negative minors contains an affirmative major in which the middle is affirmed of a subject successively ‘higher’ or more universal than the subject of the first syllogism. Thus:

Syllogism:		All B is D
		No C is D
		No C is B

Proyllogisms:		All D is E		All E is F
		No C is E		No C is F
		No C is D		No C is E

B, D, E,
&c., are successively more universal subjects; and the series of affirmative majors containing them must
ex hypothesi
terminate.

²⁵
Since the series of affirmative majors terminates and since an affirmative major is required for each prosyllogism, we shall eventually reach a minor incapable of proof and therefore immediate.

²⁶
If the attributes in a series of predication such as we are discussing are substantial, they must be finite in number, because they are then the elements constituting the definition of a substance.

²⁷
The first of three statements preliminary to a proof that predicates which are accidental—other than substantial—cannot be unlimited in number: Accidental is to be distinguished from essential or natural predication [cf. i, ch. 4, 73
^b
5 ff. and
An. Pr.
i, ch. 25, 43
^a
25–6]. The former is alien to demonstration: hence, provided that a single attribute is predicated of a single subject, all genuine predicates fall either under the category of substance or under one of the adjectival categories.

²⁸
Second preliminary statement: The precise distinction of substantive from adjectival predication makes clear (implicitly) the two distinctions, (
a
) that between natural and accidental predication, (
b
) that between substantival and adjectival predication, which falls within natural predication. This enables us to reject the Platonic Forms.

²⁹
Third preliminary statement merging into the beginning of the proof proper: Reciprocal predication cannot produce an indefinite regress because it is not natural predication.

³⁰
Expansion of third preliminary statement: Reciprocals
A
and
B
might be predicated of one another (
a
) substantially; but it has been proved already that because a definition cannot contain an infinity of elements substantial predication cannot generate infinity; and it would disturb the relation of genus and species: (
b
) as
qualia
or
quanta
&c; but this would be unnatural predication, because all such predicates are adjectival, i. e. accidents, or coincidents, of substances.

³¹
The ascent of predicates is also finite; because all predicates fall under one or other of the categories, and (
a
) the series of predicates under each category terminates when the category is reached, and (
b
) the number of the categories is limited. [(
a
) seems to mean that an attribute as well as a substance is definable by genus and differentia, and the elements in its definition must terminate in an upward direction at the category, and can therefore no more form an infinite series than can the elements constituting the definition of a substance.]

³²
To reinforce this brief proof that descent and ascent are both finite we may repeat the premisses on which it depends. These are (1) the assumption that predication means the predication of one attribute of one subject, and (2) our proof that accidents cannot be reciprocally predicated of one another, because that would be unnatural predication. It follows from these premisses that both ascent and descent are finite. [Actually (2) only reinforces the proof that the
descent
terminates.]

³³
To repeat again the proof that both ascent and descent are finite: The subjects cannot be more in number than the constituents of a definable form, and these, we know, are not infinite in number: hence the descent is finite. The series regarded as an ascent contains subjects and ever more universal accidents, and neither subjects nor accidents are infinite in number.

³⁴
Formal restatement of the last conclusion. [This is obscure: apparently Aristotle here contemplates a hybrid series: category, accident, further specified accident … substantial genus, subgenus … 
infima species,
individual substance.

If this interpretation of the first portion of the chapter is at all correct, Aristotle’s first proof that the first two questions of ch. 19 must be answered in the negative is roughly as follows: The ultimate subject of all judgement is an individual substance, a concrete singular. Of such concrete singulars you can predicate substantially only the elements constituting their
infima species.
These are limited in number because they form an intelligible synthesis. So far, then, as substantial predicates are concerned, the questions are answered. But these elements are also the subjects of which accidents, or coincidents, are predicated, and therefore as regards accidental predicates, at any rate, the descending series of subjects terminates. The ascending series of attributes also terminates, (1) because each higher attribute in the series can only be a higher genus of the accident predicated of the ultimate subject of its genus, and therefore an element in the accident’s definition; (2) because the number of the categories is limited.

We may note that the first argument seems to envisage a series which, viewed as an ascent, starts with a concrete individual of which the elements of its definition are predicated successively, specific differentia being followed by proximate genus, which latter is the starting-point of a succession of ever more universal attributes terminating in a category; and that the second argument extends the scope of the dispute to the sum total of all the trains of accidental predication which one concrete singular substance can beget. It is, as so often in Aristotle, difficult to be sure whether he is regarding the
infima species
or the concrete singular as the ultimate subject of judgement. I have assumed that he means the latter.]

³⁵
The former proof was dialectical. So is that which follows in this paragraph. If a predicate inheres in a subject but is subordinate to a higher predicate also predicable of that subject [i. e. not to a wider predicate but to a middle term giving logically prior premisses and in that sense higher], then the inherence can be known by demonstration and only by demonstration. But that means that it is known as the consequent of an antecedent. Therefore, if demonstration gives genuine knowledge, the series must terminate; i. e. every predicate is demonstrable and known only as a consequent and therefore hypothetically, unless an antecedent known
per se
is reached.

³⁶
As regards type (2) [the opening of the chapter has disposed of type (1)]: in any series of such predicates any given term will contain in its definition all the lower terms, and the series will therefore terminate at the bottom in the ultimate subject. But since every term down to and including the ultimate subject is contained in the definition of any given term, if the series ascend infinitely there must be a term containing an infinity of terms in its definition. But this is impossible, and therefore the ascent terminates.

³⁷
Note too that either type of essential attribute must be commensurate with its subject, because the first defines, the second is defined by, its subject; and consequently no subject can possess an infinite number of essential predicates of either type, or definition would be impossible. Hence if the attributes predicated are all essential, the series terminates in both directions. [This passage merely displays the ground underlying the previous argument that the ascent of attributes of type (2) is finite, and notes in passing its more obvious and already stated application to attributes of type (1).]

³⁸
It follows that the intermediates between a given subject and a given attribute must also be limited in number.

³⁹
Corollary: (
a
) demonstrations necessarily involve basic truths, and therefore (
b
) not all truths, as we saw [84
^a
32] that some maintain, are demonstrable [cf. 72
^b
6]. If either (
a
) or (
b
) were not a fact, since conclusions are demonstrated by the interposition of a middle and not by the apposition of an extreme term [cf. note on 78
^a
15], no premiss would be an immediate indivisible interval. This closes the analytic argument.