thinking in theses

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Aristotle’s notion of ἐπαγωγή (induction)

The essential concept of inductive reasoning – the shift from particular circumstance to general principle – was first delineated by Aristotle, in the Posterior Analytics, as the concept of ἐπαγωγή (induction). The major concluding sentence is found at 100b3: δῆλον δὴ ὅτι ἡμῖν τὰ πρῶτα ἐπαγωγῆι γνωρίζειν ἀναγκαῖον· καὶ γὰρ ἡ αἴσθησις οὕτω τὸ καθόλου ἐμποιεῖ. [Thus it is clear that we must get to know the primary premises by induction; for the method by which even sense-perception implants the universal is inductive.]

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See below for the lengthy passage in which Aristotle explains ἐπαγωγή (induction) in detail. It constitutes the better part of chapter 19 of the second (and final) book of the Posterior Analytics.

Roman copy (in marble) of a Greek bronze bust of Aristotle by Lysippos (c.a 330 bc)

Ἀναλυτικὰ ὕστερα. II, 19. 99b-100b. (Posterior Analytics)

Textus: Aristotelis Analytica priora et posteriora. (ed.: William David Ross, Oxonii, Typographeo Clarendoniano, 1964)

(Translation, G. R. G. Mure)

[99b] 32. ἀνάγκη ἄρα ἔχειν μέν τινα δύναμιν, μὴ τοιαύτην δ᾽ ἔχειν ἣ ἔσται τούτων τιμιωτέρα κατ᾽ ἀκρίβειαν.

Therefore we must possess a capacity of some sort, but not such as to rank higher in accuracy than these developed states.

34. φαίνεται δὲ τοῦτό γε πᾶσιν ὑπάρχον τοῖς ζώιοις. ἔχει γὰρ δύναμιν σύμφυτον κριτικήν, ἣν καλοῦσιν αἴσθησιν·

And this at least is an obvious characteristic of all animals, for they possess a congenital discriminative capacity which is called sense-perception.

36. ἐνούσης δ᾽ αἰσθήσεως τοῖς μὲν τῶν ζώιων ἐγγίγνεται μονὴ τοῦ αἰσθήματος, τοῖς δ᾽ οὐκ ἐγγίγνεται.

But though sense-perception is innate in all animals, in some the sense-impression comes to persist, in others it does not.

37. ὅσοις μὲν οὖν μὴ ἐγγίγνεται, ἢ ὅλως ἢ περὶ ἃ μὴ ἐγγίγνεται, οὐκ ἔστι τούτοις γνῶσις ἔξω τοῦ αἰσθάνεσθαι·

So animals in which this persistence does not come to be have either no knowledge at all outside the act of perceiving, or no knowledge of objects of which no impression persists;

39. ἐν οἷς δ᾽ ἔνεστιν αἰσθομένοις ἔχειν ἔτι ἐν τῆι ψυχῆι.

animals in which it does come into being have perception and can continue to retain the sense-impression in the soul:

[100a] 1. πολλῶν δὲ τοιούτων γινομένων ἤδη διαφορά τις γίνεται, ὥστε τοῖς μὲν γίνεσθαι λόγον ἐκ τῆς τῶν τοιούτων μονῆς, τοῖς δὲ μή.

and when such persistence is frequently repeated a further distinction at once arises between those which out of the persistence of such sense-impressions develop a power of systematizing them and those which do not.

3. Ἐκ μὲν οὖν αἰσθήσεως γίνεται μνήμη, ὥσπερ λέγομεν, ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομένης ἐμπειρία· αἱ γὰρ πολλαὶ μνῆμαι τῶι ἀριθμῶι ἐμπειρία μία ἐστίν.

So out of sense-perception comes to be what we call memory, and out of frequently repeated memories of the same thing develops experience; for a number of memories constitute a single experience.

6. ἐκ δ᾽ ἐμπειρίας [–] ἢ ἐκ παντὸς ἠρεμήσαντος τοῦ καθόλου ἐν τῆι ψυχῆι, τοῦ ἑνὸς παρὰ τὰ πολλά, ὁ ἂν ἐν ἅπασιν ἓν ἐνῆι ἐκείνοις τὸ αὐτό, [–] τέχνης ἀρχὴ καὶ ἐπιστήμης, ἐὰν μὲν περὶ γένεσιν, τέχνης, ἐὰν δὲ περὶ τὸ ὄν, ἐπιστήμης.

From experience again – i.e. from the universal now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all – originate the skill of the craftsman and the knowledge of the man of science, skill in the sphere of coming to be and science in the sphere of being.

10. οὔτε δὴ ἐνυπάρχουσιν ἀφωρισμέναι αἱ ἕξεις, οὔτ᾽ ἀπ᾽ ἄλλων ἕξεων γίνονται γνωστικωτέρων, ἀλλ᾽ ἀπὸ αἰσθήσεως, οἷον ἐν μάχηι τροπῆς γενομένης ἑνὸς στάντος ἕτερος ἔστη, εἶθ᾽ ἕτερος, ἕως ἐπὶ ἀρχὴν ἦλθεν.

We conclude that these states of knowledge are neither innate in a determinate form, nor developed from other higher states of knowledge, but from sense-perception. It is like a rout in battle stopped by first one man making a stand and then another, until the original formation has been restored.

13. ἡ δὲ ψυχὴ ὑπάρχει τοιαύτη οὖσα οἵα δύνασθαι πάσχειν τοῦτο.

The soul is so constituted as to be capable of this process.

14. ὁ δ᾽ ἐλέχθη μὲν πάλαι, οὐ σαφῶς δὲ ἐλέχθη, πάλιν εἴπωμεν.

Let us now restate the account given already, though with insufficient clearness.

15. στάντος γὰρ τῶν ἀδιαφόρων ἑνός, πρῶτον μὲν ἐν τῆι ψυχῆι καθόλου (καὶ γὰρ αἰσθάνεται μὲν τὸ καθ᾽ ἕκαστον, ἡ δ᾽ αἴσθησις τοῦ καθόλου ἐστίν, οἷον ἀνθρώπου, ἀλλ᾽ οὐ Καλλίου ἀνθρώπου)·

When one of a number of logically indiscriminable particulars has made a stand, the earliest universal is present in the soul. (for though the act of sense-perception is of the particular, its content is universal; is man, for example, not the man Callias.)

[100b] 1. πάλιν ἐν τούτοις ἵσταται, ἕως ἂν τὰ ἀμερῆ στῆι καὶ τὰ καθόλου, οἷον τοιονδὶ ζῶιον, ἕως ζῶιον, καὶ ἐν τούτωι ὡσαύτως.

A fresh stand is made among these rudimentary universals, and the process does not cease until the indivisible concepts, the true universals, are established: e.g. such and such a species of animal is a step towards the genus animal, which by the same process is a step towards a further generalization.

3. δῆλον δὴ ὅτι ἡμῖν τὰ πρῶτα ἐπαγωγῆι γνωρίζειν ἀναγκαῖον· καὶ γὰρ ἡ αἴσθησις οὕτω τὸ καθόλου ἐμποιεῖ.

Thus it is clear that we must get to know the primary premises by induction; for the method by which even sense-perception implants the universal is inductive.

5. Ἐπεὶ δὲ τῶν περὶ τὴν διάνοιαν ἕξεων αἷς ἀληθεύομεν αἱ μὲν ἀεὶ ἀληθεῖς εἰσιν, αἱ δὲ ἐπιδέχονται τὸ ψεῦδος, οἷον δόξα καὶ λογισμός, ἀληθῆ δ᾽ ἀεὶ ἐπιστήμη καὶ νοῦς, καὶ οὐδὲν ἐπιστήμης ἀκριβέστερον ἄλλο γένος ἢ νοῦς,

Now of the thinking states by which we grasp truth, some are unfailingly true, others admit of error-opinion, for instance, and calculation, whereas scientific knowing and intuition are always true: further, no other kind of thought except intuition is more accurate than scientific knowledge,

9. αἱ δ᾽ ἀρχαὶ τῶν ἀποδείξεων γνωριμώτεραι, ἐπιστήμη δ᾽ ἅπασα μετὰ λόγου ἐστί,

whereas primary premises are more knowable than demonstrations, and all scientific knowledge is discursive.

10. τῶν ἀρχῶν ἐπιστήμη μὲν οὐκ ἂν εἴη, ἐπεὶ δ᾽ οὐδὲν ἀληθέστερον ἐνδέχεται εἶναι ἐπιστήμης ἢ νοῦν, νοῦς ἂν εἴη τῶν ἀρχῶν,

From these considerations it follows that there will be no scientific knowledge of the primary premises, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premises –

12. ἔκ τε τούτων σκοποῦσι καὶ ὅτι ἀποδείξεως ἀρχὴ οὐκ ἀπόδειξις, ὥστ᾽ οὐδ᾽ ἐπιστήμης ἐπιστήμη.

a result which also follows from the fact that demonstration cannot be the originative source of demonstration, nor, consequently, scientific knowledge of scientific knowledge.

14. εἰ οὖν μηδὲν ἄλλο παρ᾽ ἐπιστήμην γένος ἔχομεν ἀληθές, νοῦς ἂν εἴη ἐπιστήμης ἀρχή.

If, therefore, it is the only other kind of true thinking except scientific knowing, intuition will be the originative source of scientific knowledge.

15. καὶ ἡ μὲν ἀρχὴ τῆς ἀρχῆς εἴη ἄν, ἡ δὲ πᾶσα ὁμοίως ἔχει πρὸς τὸ πᾶν πρᾶγμα.

And the originative source of science grasps the original basic premise, while science as a whole is similarly related as originative source to the whole body of fact.