Translated with introduction and notes by A.E. Taylor

Conclusion← TOC→Appendix B. The Four Senses of Cause


On the Cognition of Universal Axioms, as a product of Experience. (Cf. Met., A, 1, 980a 27-b29, 9, 992b 25ff.) Analytica Posteriora, 2, 71a 1-16.

All instruction and all processes of intellectual167 learning depend upon the presence of antecedent cognitions. This will become manifest if we consider the various cases seriatim.168 The mathematical sciences and every one of the other arts are acquired in this manner. The same is true of logic, both syllogistic and inductive; in both cases the instruction is derived from antecedent cognitions. In the former premises are assumed, with the implication that their sense is understood; in the latter a universal is established by the manifest truth of the individual instances. Rhetorical arguments, again, produce conviction in the same way, either by means of examples (and this is induction) or by means of enthymemes169 (and this is syllogism). The antecedent cognition necessary may be of two kinds. In some cases we require previous recognition of the truth of a statement, in others, previous understanding of the sense of a term; in others again, both are needed. e.g., in the case of the proposition that "every proposition can either be truly affirmed or truly denied"' we have to presuppose the truth of a statement; in the case of "triangle," the meaning of a term; in the case of "the number 1," both the meaning of the term and the existence of the thing denoted.170

Analytica Posteriora, II, 19, 99b 20-l00b 17.

We have already said that it is impossible to have scientific knowledge as the result of demonstration without cognition of the ultimate axiomatic principles.171 But a difficulty might be raised as to the cognition of these axioms themselves. Is it of the same kind [as the cognition of demonstrated truth. TR.], or of a different kind? Are both the objects of science, or is the one the object of science, the other of a different form of cognition? Also, does the cognition of axioms make its appearance in consciousness, having previously been absent, or is it unconsciously present from the first?172 It is certainly strange if we possess it from the first. For it follows that we possess cognitions which are more accurate than demonstration, and yet are unconscious of the fact. Yet, if we do not at first possess them but afterward acquire them, how come we to apprehend and learn them, except on a basis of antecedent cognition? For that, as was said in speaking of demonstrative proof, is impossible. It is plain, then, that we can neither possess them from the first nor could they appear in consciousness if we were ignorant of them and had no disposition to acquire them. One is thus driven to conclude that we have a certain faculty of acquiring them, but not of such a kind as to rank higher than demonstrated truth in respect of accuracy.173 Now, such a faculty is obviously present in all animals. They have a congenital faculty of discrimination, which is called sense-perception. On the occurrence of sensation there supervenes in some animals retention of the sense-percept, in others not. Where it does not occur universally, or with respect to certain sensations, the animal has no cognition beyond the sensation; where it does occur the animal can, after sensation is over, preserve some result of it in consciousness. When this process is frequently repeated a further distinction makes its appearance; in some animals such retention leads to rational cognition, in others not. Thus, as I say, sense-perception gives rise to memory, and repeated memories of the same object to experience; for the numerically many memories form a single experience. And experience, i. e., any establishment in consciousness of a universal, or one over and above the many, which is a point of identity present in them all,174 leads to the principles of Art and Science; of Art if it is concerned with Production, of Science if it is concerned with Being.

These axiomatic cognitions thus are neither there from the first in a determinate form nor yet are they derived from other cognitions of a higher type,175 but from sense-perception. The process is like what occurs in battle after a rout, when first one man makes a stand, and then a second and a third follow his example, and so at last order is established. The constitution of consciousness is such as to permit of this process.176

Let me repeat an explanation which has already been given, though without due precision. When a conviction has been established about any class of objects which are indistinguishable in kind, we have the earliest universal in consciousness; (for in fact, though the object perceived is an individual thing, sense perception is of the universal; e.g., of man, not of the man Callias). Generalisations are then established among these classes, and so we proceed, until we come to the establishment of the unanalysable universals. E. g., we pass from generalisations about "such and such a species of animal" to generalisations about "animal," and treat that concept in the same way. For even sense-perception in this way gives rise to universal cognitions.177

Thus it is clear that we need to apprehend ultimate axioms by a process of induction.178 And since of the intellectual conditions by which we perceive truth some are always truthful, while others admit of error (e.g., Opinion and Computation, whereas Science and Rational Intuition are always truthful); since, further, Rational Intuition179 is the only type of cognition which is more exact than Science, while the principles of demonstration are "more knowable"180 than the results of demonstration, and all Science involves inference, the cognition of axiomatic principles cannot be Science. Hence, since the only form of cognition which can have a higher truth than Science is Rational Intuition, it must be by Rational Intuition that axiomatic principles are cognized. This result follows, also, from the consideration that since the principles of demonstration are not themselves demonstration, those of Science cannot be themselves Science. So, if we have no type of true cognition except Science, Rational Intuition must be the principle from which Science starts.181

Ethica Nicomachea, vi.-xi., 1143a 35-b5.

It is Rational Intuition which apprehends the ultimates in both directions. For both the first and the last terms of our reasoning are apprehended by Rational Intuition, not by discursive reasoning. In demonstrations this intuition is of the primary and immutable principles, in the study of questions of conduct it is of contingent ultimate facts and minor premises, for these are the starting-point of purposive action, since its universal rules are based on particular cases. Of these cases, then, we must have an immediate perception, and that is Rational Intuition.

Taylor's Notes

(Taylor's footnotes have been converted to endnotes)


[167]. The qualifying epithet is intended to exclude cognition through immediate sense-perception on the one hand and the immediate intuition of ultimate axioms on the other.

[168]. The argument which follows is a typical Aristotelian "inductive syllogism," i e., a demonstration that a predicate a belongs universally to a genus A by showing that it belongs separately to each of the subordinate species into which A can be exhaustively subdivided. Mathematical and scientific reasoning, λόγοι or philosophic science not aided by sensuous diagrams, rhetorical reasoning, are treated as the three species of the genus "inferential knowledge."

[169]. "Enthymemes" not in the modern but in the Aristotelian sense of "inference from likelihood or presumptive evidence."

[170]. This is meant for a formulation of the law of Excluded Middle.

[171]. τάς πρώτας ἀρχὰς τὰς ἀμέσους. "first and immediate principles," i. e., axioms incapable of being syllogistically deduced, through a middle term, from any more general and ultimate principles.

[172]. The two alternatives, both of which he finds unsatisfactory, are pure Empiricism and the Platonic doctrine of recollection, which he interprets as a theory of "innate ideas." He proceeds to mediate between these alternatives much as Leibniz did between the doctrines of Locke and Descartes.

[173] τούτων, in line 33, I take to mean τῶν ἀποδειξέων. The meaning of the "accuracy" or "exactness" here spoken of will be perceived by reference to Analytica Post., 1., 27, 87a 33, where we are told that a science which deals with universal relations in abstraction is more "exact" than one which considers their application to a special subject-matter (e.g., Arithmetic than Harmonics), and a science which makes few initial postulates than one which makes more (e.g., Arithmetic than Geometry).

[174]. This clause is added to show that by the "one over and above the many" he means merely a subjective "general concept," not a Platonic Idea.

[175]. γνωστικώτερων "naturally more knowable," i. e., logically simpler and therefore more ultimate.

[176]. The point of the comparison lies in the fact that in the rally order and discipline come to be spontaneously re-established without the direct issuing of instructions to that effect by a superior. So, owing to the implicit generalising character of all cognition, axioms come spontaneously to be recognized in consequence of our perception of their validity in special applications, without any process of conscious formal deduction.

[177]. Translation of the highly condensed expressions of this paragraph necessarily involves some amount of interpretative paraphrase, but I have endeavoured to keep as closely as possible to the actual words of the text. The key to its meaning is given by the parenthetical remark about the implicit universality of sense-perception. The spontaneous inductive process which leads from the simplest generalisations about the more obvious classes of sensible objects, through axiomata media--to use Bacon's familiar phrase--to the most universal of axioms, which are quite incapable of adequate representation by sensible illustrations, depends for its possibility upon the principle that though the object cognized in sense-perception itself is always a particular individual (the man Callias), the content of the perception, that which is cognized about the object, is always a universal, or complex of universals. The use of the expression ἀμερῆ "indivisibles" (rendered in the text "unanalysable") for the axioms of highest generality is, I suppose, explained by the fact that in Aristotle's theory of definition by genus and difference, the genus appears as a "part" of the intension of the species. (Metaphysics, Δ 25, 1023b 24: "Hence the genus is also called a part of the species, though in another sense the species is part of the genus.") Thus an "unanalysable" genus is one which cannot be regarded as a species of a higher class, an indefinable summum genus or highest universal.

[178]. Induction, that is, in the Socratic sense; i. e., the general principle of the axiom is made clear to us in consequence of our previous recognition of its validity in particular classes of instances.

[179]. νοῦς, “Mind;" i. e., a cognition which is at once rational and universal, and also like sense-perception at the other end of the series, immediate. See the passage from the Ethics, which immediately follows.

[180]. i. e.. "naturally, in the logical order of concatenation of truths, more knowable;" that is, are simpler and more ultimate universal truths.

[181]. Aristotle's view is thus twofold. The process by which the individual mind, as a fact in its psychological history, comes by the apprehension of the axioms is one of generalising induction from examples. We are individually led up to the recognition of the principle by being familiarised with examples of its truth in concrete cases. But the "induction" in no sense proves the axiom; it merely calls attention to it. (Cf. 91b 33. "He who produces an example does not prove the conclusion, though he does point out something.)" The axiom is, in fact, neither proved nor provable. When the requisite illustrations have been produced, you simply have directly to see what the implied principle is, and, if you do not see it, no proof can make you see. Aristotle's view thus turns out to be simply the Platonic doctrine of "innate ideas" minus its imaginative psychological background of pre-existence. Whether the removal of this background is an improvement is a point on which opinions may possibly differ. The ultimate germ of the whole theory is the treatment of association as a source of suggestion in Phaedo, p. 73 ff.

Created for Peithô's Web from Aristotle on his predecessors; being the first book of his Metaphysics; tr. from the text edition of W. Christ, with introd. and notes by A. E. Taylor. Chicago, Open Court, 1907.Taylor's footnotes have been converted to endnotes. Greek unicode text entered with Peithô's Younicoder.
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