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κ′ περὶ ἀριθμοῦ.

[151] Επεὶ δὲ ὁ χρόνος δοκεῖ μὴ ἄνευ ἀριθμοῦ θεωρεῖσθαι,
οὐκ ἂν εἴη ἄτοπον καὶ περὶ ἀριθμοῦ βραχέα διεξελθεῖν. ὅσον μὲν γὰρ ἐπὶ τῇ συνηθείᾳ καὶ ἀδοξάστως ἀριθμεῖν τι φαμὲν καὶ ἀριθμὸν εἶναί τι ἀκούομεν· ἡ δὲ τῶν δογματικῶν περιεργία καὶ τὸν κατὰ τούτου κεκίνηκε λόγον.

¹² 156

[152] αὐτίκα γοῦν οἱ ἀπὸ τοῦ Πυθαγόρου καὶ στοιχεῖα τοῦ κόσμου τοὺς ἀριθμοὺς εἷναι λέγουσιν. φασὶ γοῦν, ὅτι τὰ φαινόμενα ἔκ τινος συνέστηκεν , ἁπλᾶ δὲ εἶναι δεῖ τὰ στοιχεῖα· ἄδηλα ἄρα ἐστὶ τὰ στοιχεῖα. τῶν δὲ ἀδήλων τὰ μέν ἐστι σώματα, ὡς οἱ ἀτμοὶ καὶ οἱ ὄγκοι, τὰ δὲ ἀσώματα,
ματα, ὧς σχήματα καὶ ἰδέαι καὶ ἀριθμοί. ὧν τὰ μὲν σώματά ἐστι σύνθετα, συνεστῶτα ἔκ τε μήκους καὶ πλάτους καὶ βάθους καὶ ἀντιτυπίας ἢ καὶ βάρους (cf. Epic. 276 Us.). οὐ μόνον ἄρα ἄδηλα, ἀλλὰ καὶ ἀσώματά ἐστι τὰ στοιχεῖα.

[153] ἀλλὰ καὶ τῶν ἄσωμάτων ³ ἕκαστον ἐπιθεωρούμενον ἔχει τὸν ἀριθμόν· ἢ
γὰρ ἔν ἐστιν ἢ δύο ἢ πλείω. δι’ ὧν συνάγεται, ὅτι τὰ στοιχεῖα τῶν ὄντων εἰσὶν οἱ ἄδηλοι καὶ ἀσώματοι καὶ πᾶσιν ἐπιθεωρούμενοι ἀριθμοί. καὶ οὐχ ἁπλῶς, ἀλλ’ ἤ τε μονὰς καὶ ἡ κατὰ ἐπισύνθεσιν τῆς μονάδος γινομένη ἀόριστος δυάς, ἧς κατὰ μετουσίαν αἱ κατὰ μέρος γίγνονται
δυάδες δυάδες.

[154] ἐκ τούτων γὰρ καὶ τοὺς ἄλλους γίνεσθαι ἀριθμούς, τούς ἐπιθεωρουμένους τοῖς ἀριθμητοῖς, καὶ τὸν κόσμον κατασκευάζεσθαι λέγουσιν. τὸ μὲν γὰρ
σημεῖον τὸν τῆς μονάδος ἐπέχειν λόγον, τὴν δὲ γραμμὴν τὸν τῆς δυάδος δύο γὰρ σημείων μεταξὺ θεωρεῖσθαι ταύτην), τὴν δὲ ἐπιφάνειαν τὸν τῆς τριάδος ῥύσιν γὰρ εἶναί φασι τῆς γραμμῆς εἰς πλάτος ἐπ’ ἄλλο σημεῖον ἐκ πλαγίου
κείμενον), τὸ δὲ σῶμα τὸν τῆς τετράδος· ἐπανάστασιν γὰρ γίγνεσθαι τῆς ἐπιφανείας ἐπί τι σημεῖον ὑπερκείμενον.

[155] καὶ οὕτω τά τε σώματα καὶ ὅλον τὸν κόσμον ἐνειδωλοποιοῦσιν, ὅντινα καὶ διοικεῖσθαί φασι κατὰ ἁρμονικοὺς λόγους, τόν τε διὰ τεσσάρων, ὅς ἐστιν ἐπίτριτος, ὡς ἔχει
πρὸς τὰ ἕξ τὰ ὀκτώ, καὶ τὸν διὰ πέντε, ὅς ἐστιν ἡμιόλιος, ὧς ἔχει πρὸς τὰ ἕξ τὰ ἐννέα, καὶ τὸν διὰ πασῶν, ὅς ἐστι διπλάσιος, ὧς ἔχει πρὸς τὰ ἕξ τὰ δώδεκα.

[156] ταῦτά τε οὖν ⁴⁵⁶⁷ 157 ὀνειροπολοῦσιν, καὶ ὅτι ἕτερόν τι ἐστὶν ὁ ἀριθμὸς παρὰ τὰ ἀριθμητὰ κατασκευάζουσι, λέγοντες ὅτι εἰ τὸ ζῷον κατὰ τὸν ἑαυτοῦ λόγον ἐστίν, εἰ τύχοι, ἔν, τὸ φυτόν, ἐπεὶ μή ἐστι
ζῷον, οὐκ ἔσται ἕν· ἔστι δὲ καὶ <τὸ> φυτὸν ἔν· οὐκ ἄρα ζῷον, <ὡς ζῷον>, ἔν ἐστιν, ἀλλὰ κατά τι ἕτερον ἐπιθεωρούμενον ἔξωθεν αὐτῷ, οὗ μετέχει ἕκαστον καὶ γίνεται δι’ αὐτὸ ἔν. καὶ εἰ τὰ ἀριθμητά ἐστιν ὁ ἀριθμός, ἐπειδὴ ἄωθρωποί εἰσιν οἱ ἀριθμητοὶ καὶ βόες, εἰ τύχοι, καὶ ἵπποι,
ἄνθρωποι καὶ βόες καὶ ἵπποι ἔσται ὁ ἀριθμός, καὶ λευκὸς ἀριθμὸς καὶ μέλας καὶ γενειήτης, εἰ τύχοιεν τοιοῦτοι ὄντες οἱ μετρούμενοι.

[157] ταῦτα δέ ἐστιν ἄτοπα· οὐκ ἄρα τὰ ἀριθμητά ἐστιν ὁ ἀριθμός, ἀλλ’ ἰδίαν ὑπόστασιν ἔχει παρὰ ταῦτα, καθ’ ἣν καὶ ἐπιθεωρεῖται τοῖς ἀριθμητοῖς καὶ
ἔστι στοιχεῖον.

Oὕτως οὖν ἐκείνων συναγαγόντων , ὅτι ἀριθμὸς οὔκ ἐστι τὰ ἀριθμητά, παρεισῆλθεν ἡ κατὰ τοῦ ἀριθμοῦ ἀπορία. λέγεται γάρ, ὅτι εἰ ἔστιν ἀριθμός, ἤτοι αὐτὰ τὰ ἀριθμητά ἐστιν ὁ ἀριθμὸς ἢ ἕτερόν τι παρὰ ταῦτα ἔξωθεν·
οὔτε δὲ αὐτὰ τὰ ἀριθμητά ἐστιν ὁ ἀριθμός, ὧς ἀπέδειξαν οἱ Πυθαγορικοί, οὔτε ἕτερόν τι παρὰ ταῦτα, ὡς ὑπομνήσομεν· οὐδὲν ἄρα ἐστὶν ὁ ἀριθμός.

[158] ὅτι δὲ
οὐδὲν ἔξωθέν ἐστι παρὰ τὰ ἀριθμητὰ ὁ ἀριθμός, παραστήσομεν ἐπὶ τῆς μονάδος τὸν λόγον στήσαντες εὐσήμου διδασκαλίας ἕνεκεν. εἰ γὰρ ἔστι τι καθ’ ἑαυτὴν ἡ μονάς, ἧς μετέχον ἕκαστον τῶν μετεχόντων αὐτῆς γίνεται ἔν, ἤτοι
μία ἔσται αὐτὴ ἡ μονὰς ἢ τοσαῦται ὅσα τὰ μετέχοντα αὐτῆς ἐστιν. ἀλλ’ εἰ μὲν μία ἐστίν , πότερον ὅλης αὐτῆς μετέχει ἕκαστον τῶν μετέχειν αὐτῆς λεγομένων ἢ μέρους αὐτῆς; εἰ μὲν γὰρ πᾶσαν ἔχει τὴν μονάδα, εἰ τύχοι, ὁ εἰς ἄνθρωπος , οὐκέτι ἔσται μονὰς ἧς μεθέξει ὁ εἶς ἵππος
⁸⁹¹⁰ 158 ἢ ὁ εἷς κύων ἤ τῶν ἄλλων ἕκαστον ὃ λέγομεν εἶναι ἕν, ὧσπερ καὶ πολλῶν ὑποτεθέντων γυμνῶν ἀνθρώπων,

[159] ἑνὸς δὲ ὄντος ἱματίου καὶ τοῦτο ἑνὸς ἀμφιασαμένου, γυμνοὶ μενοῦσιν οἱ λοιποὶ καὶ χωρὶς ἱματίου. εἰ δὲ μέρους αὐτῆς
μετέχει ἕκαστον, πρῶτον μὲν ἕξει μέρος τι ἡ μονάς, καὶ ἄπειρά γε ἔξει μέρη, εἰς ἃ διαιρεῖται· ὅπερ ὅπερ εἶτα ὡς τὸ μέρος τῆς δεκάδος, οἷον ἡ δυάς, οὔκ ἐστι δεκάς, οὕτως οὐδὲ τὸ μέρος τῆς μονάδος ἔσται μονάς, διὰ δὲ τοῦτο οὐδὲ μεθέξει τι τῆς μονάδος. ὥστε οὔκ ἐστι μία ἡ
μονὰς ἧς μετέχειν λέγεται τὰ κατὰ μέρος.

[160] εἰ δὲ ἰσάριθμοι τοῖς ἀριθμητοῖς, ἐφ’ ὧν λέγεται τὸ ἔν, αἱ μονάδες εἰσίν, ὧν κατὰ μετοχὴν ἕκαστον τῶν κατὰ μέρος λέγεται ἕν, ἄπειροι ἔσονται αἱ μετεχόμεναι μονάδες. καὶ αὗται ἤτοι μετέχουσιν ἔπαωαβεβηκυίας μονάδος ἢ μονάδων ἰσαρίθμων
αὐταῖς καὶ διὰ τοῦτό εἰσι μονάδες) ἢ οὐ μετέχουσιν, ἀλλὰ χωρίς τινος μετοχῆς μονάδες εἰσίν.

[161] <...> εἰ μὲν γὰρ χωρὶς μετοχῆς μονάδες εἶναι δύνανται αὗται, δυνήσεται καὶ τῶν αἰσθητῶν ἕκαστον χωρὶς μονάδος μετοχῆς ‘ὲν εἶναι, καὶ αὐτόθεν περιτρέπεται ἡ καθ’ ἑαυτὴν θεωρεῖσθαι λεγομένη ὁ μονάς. εἰ δὲ ἀπὸ μετοχῆς κἀκεῖναι μονάδες εἰσίν, ἤτοι μιᾶς μετέχουσι πᾶσαι ἢ μία ἑκάστη ἰδίας. καὶ εἰ μὲν πᾶσαι μιᾶς, ἤτοι κατὰ μέρος ἑκάστη ἢ ὅλης λεχθήσεται
μετέχειν, καὶ μένουσιν αἱ ἀρχῆθεν ἀτοπίαι·

[162] εἰ δὲ ἑκάστη ἰδίας, καὶ ἐκείνων τῶν μονάδων ἑκάστῃ μονάδα ἐπιθεωρεῖσθαι δεῖ, καὶ ταῖς ἐπιθεωρουμέναις ἐκείναις ἄλλας, καὶ μέχρις ἀπείρου. εἰ οὖν ἵνα καταλάβωμεν, ὅτι εἰσί τινες
καθ’ ἑαυτὰς μονάδες, ὧν κατὰ μετοχὴν ἕκαστον τῶν ὄντων ἐστὶν ἕν, δεῖ κατειληφέναι ἀπειράκις ἀπείρους νοητὰς μονάδας, ἀδύνατον δὲ καταλαβεῖν ἀπειράκις ἀπείρους μονάδας νοητάς, ἀδύνατον ἄρα ἐστὶν ἀποφήνασθαι, ὅτι εἰσί τινες νοηταὶ μονάδες καὶ ἕκαστον τῶν ὄντων ἐστὶν ‘ὲν
κατὰ μετοχὴν ἰδίας μονάδος γινόμενον ἔν.

[163] ἄτοπον ἄρα τὸ λέγειν, ὅτι τοσαῦταί εἰσιν αἱ μονάδες ὅσα τὰ μετέχοντα ¹¹ 159 αὐτῶν. εἰ δὲ μήτε μία ἐστὶν ἡ καθ’ ἑαυτὴν λεγομένη μονὰς μήτε τοσαῦται ὅσα τὰ μετέχοντα αὐτῆς ἐστιν, οὐδὲ ἔστιν ὅλως μονὰς καθ’ ἑαυτήν. ὁμοίως δὲ οὐδὲ τῶν ἄλλων ἀριθμῶν ἕκαστος καθ’ ἑαυτὸν ἔσται· χρῆσθαι γὰρ ἔνεστιν
ἐπὶ πάντων τῶν ἀριθμῶν τῷ λόγῳ παραδειγματικῶς νῦν ἐπὶ τῆς μονάδος ἠρωτημένῳ. ἀλλ’ εἰ μήτε καθ’ ἑαυτόν ἐστιν ὁ ἀριθμός, ὧς ὑπεμνήσαμεν, μήτε αὐτὰ τὰ ἀριθμητὰ ὁ ἀριθμός ἐστιν, ὧς οἱ ἀπὸ Πυθαγόρου παρέστησαν, παρὰ δὲ ταῦτα οὐδὲν ἔστι, λεκτέον μηδὲ εἷναι
ἀριθμόν.

[164] Πῶς δὲ καὶ γίνεσθαί φασιν ἐκ τῆς μονάδος τὴν δυάδα οἱ ἔξωθέν τι δοκοῦντες εἶναι τὸν ἀριθμὸν παρὰ τὰ ἄρμ’ ὅτε γὰρ συντίθεμεν μονάδα ἑτέρᾳ μονάδι, ἤτοι προστίθεταί τι ταῖς μονάσιν ἔξωθεν, ἢ ἀφαιρεῖταί τι
ἀπ’ αὐτῶν, ἢ οὔτε προστίθεταί τι οὔτε ἀφαιρεῖται. ἀλλ’ εἰ μὲν οὔτε προστίθεταί <τι> οὔτε ἀφαιρεῖται, οὐκ δυάς. οὔτε γὰρ χωρὶς ἀλλήλων οὖσαι αἱ μονάδες εἶχον τὴν δυάδα ἐπιθεωρουμένην αὐταῖς κατὰ τὸν ἴδιον αὐτῶν λόγον, οὔτε νῦν τι αὐταῖς ἔξωθεν προσγέγονεν,

[165] ὥσπερ οὐδὲ
ἀφῄρηται κατὰ τὴν ὑπόθεσιν. ὥστε οὐκ ἔσται δυὰς ἡ σύνθεσις τῆς μονάδος πρὸς τὴν μονάδα, μήτε ἀφαιρέσεως μήτε προσθέσεως ἔξωθέν τινος γινομένης. εἰ δὲ ἀφαίρεσις γίνεται, οὐ μόνον οὐκ ἔσται δυάς, ἀλλὰ καὶ μειωθήσονται
αἱ μονάδες. εἰ δὲ προστίθεται αὐταῖς ἔξωθεν ἡ δυάς, ἴνα ἐκ τῶν μονάδων γένηται δυάς, τὰ δύο δοκοῦντα εἶναι τέσσαρα ἔσται· ὑπόκειται γὰρ μονὰς καὶ ἑτέρα μονάς, αἷς προστιθεμένης ἔξωθεν δυάδος ὁ τέσσαρα ἀριθμὸς
ἀποτελοῖτο ἄν.

[166] ὁ δὲ αὐτὸς λόγος καὶ ἐπὶ τῶν ἄλλων ἀριθμῶν τῶν κατὰ σύνθεσιν ἀποτελεῖσθαι λεγομένων. εἰ οὖν μήτε κατὰ ἀφαίρεσιν μήτε κατὰ πρόσθεσιν μήτε ἄνευ ἀφαιρέσεως καὶ προσθέσεως γίγνονται οἱ σύνθετοι λεγόμενοι εἶναι ἀριθμοὶ ἐκ τῶν ἐπαναβεβηκότων , ἀσύστατός
ἐστιν ἡ γένεσις τοῦ κατ’ ἰδίαν καὶ παρὰ τὰ ἀριθμητὰ ¹²¹³ 160 εἶναι λεγομένου ἀριθμοῦ. ὅτι δὲ οὐδὲ ἀγένητοι τυγχάνουσιν ὄντες οἱ κατὰ σύνθεσιν ἀριθμοί, δηλοῦσιν αὐτοὶ συντίθεσθαί τε αὐτοὺς καὶ γίγνεσθαι φάσκοντες ἐκ τῶν ἐπαναβεβηκότων,
, οἷον τῆς τε μονάδος καὶ δυάδος τῆς ἀορίστου.

[167] οὐκοῦν οὐχ ὑφέστηκε κατ’ ἰδίαν ὁ ἀριθμός. εἰ δὲ μήτε κατ’ ἰδίαν ὁ ἀριθμὸς θεωρεῖται μήτε ἐν τοῖς ἀριθμητοῖς ἔχει τὴν ὑπόστασιν , οὐδὲ ἔστι τι ὁ ἀριθμὸς ὅσον ἐπὶ ταῖς περιεργίαις ταῖς ὑπὸ τῶν δογματικῶν εἰσενηνεγμέναις.
τοσαῦτα μὲν καὶ περὶ τοῦ φυσικοῦ καλουμένου τῆς φιλοσοφίας μέρους ἀρκούντως ὧς ἐν ὑποτυπώσει λελέχθω.

Pyrrhoniae Hypotyposes. Sextus Empiricus. ed. Hermann Mutschmann. Germany. 2014.

Current edition First1KGreek

Pyrrhoniae Hypotyposes (Greek) (Sextus Empiricus. Sexti Empiricii Opera, Volume 1. Mutschmann, Hermann, editor. Leipzig: Teubner, 1912.)

Translations (1)

Outlines of Pyrrhonism First1KGreek (Sextus Empiricus, Vol. 1. Bury, Robert Gregg, translator. London: William Heinemann Ltd.; New York: G. P. Putnam's Sons, 1933.) — 3.20 focus

Chapter XX.—Concerning Number

[151] Since time, it seems, is not found apart from number, it will not be out of place to discuss number briefly.¹ In the customary way we speak undogmatically² of numbering a thing and hear number talked of as something which exists; but the extreme methods of the Dogmatists have provoked the attack upon number also.

[152] Thus, for example, the School of Pythagoras declare that numbers are also elements of the Universe. They assert, in fact, that phenomena are constructed from something, and that the elements must be simple; therefore the elements are non-evident. But of things non-evident, some are corporeal, like atoms and masses, others incorporeal, like figures³ and forms and numbers. Of these the corporeal are composite, being constructed from length and breadth and depth and solidity, or even weight. The elements, therefore, are not only non- evident but also incorporeal.

[153] Moreover, each of the incorporeals involves the perception of number, for it is either one or two or more. Thus it is inferred that the non-evident and incorporeal numbers which are involved in all perception are the elements of existing things. Yet not simply these numbers, but both the Monad also and the Indefinite Dyad which is generated by the expansion of the Monad, and by participation in which the particular dyads become dyads.⁴

[154] For they say that it is from these that the rest of the numbers are generated—those, that is, which are involved in the perception of numerables—and the Universe is arranged. For the point presents the relation, or character, of the Monad,⁵ and the line that of the Dyad (it being regarded as lying between two points), and the surface that of the Triad (for they describe it as a flowing of the line breadth-wise up to another point placed transversely), and the solid body that of the Tetrad; for Body is formed by an ascension of the surface up to a point placed above.

[155] It is in this way that they image forth both the bodies and the whole Universe, which also they declare to be arranged according to harmonic ratios⁶—namely, that of the ‟By-Fours,” which is ‟epitrite,” as is the ratio of 8 to 6; and that of the “ By-Fives,” which is one and a half times, as is the ratio of 9 to 6; and that of the ‟By-Alls,” which is double, as is the ratio of 12 to 6.

[156] These are the fictions they imagine; and they also make out that number is something else apart from numerables, arguing that if ‟animal” according to its proper definition⁷ is (say) one, the plant, since it is not an animal, will not be one; but the plant is one; therefore the animal is not one qua animal but in virtue of some other attribute perceived outside itself, whereof each animal partakes and because of which it becomes one. And if number is the numerables, since the numerables are men (say) and oxen and horses, number will be men and oxen and horses—and number will be white and black and bearded, if the objects counted should happen to be such.

[157] But these things are absurd; therefore number is not the numerables, but it has a reality of its own apart from them whereby it is involved in the perception of the numerables and is an element.

So when they had thus concluded that number is not the numerables, there arose in consequence the difficulty about number. For it is argued that if number exists, number is either the actual numerables or something else apart from them; but number is neither the actual numerables, as the Pythagoreans have proved, nor something else apart from them, as we shall show; number, therefore, is nothing.

[158] That number is nothing apart from the numerables we shall demonstrate by basing our argument on the Monad, for the sake of lucidity of exposition.⁸ If the Monad, by partaking in which each of its participants becomes one, is in itself a real object, this Monad will be either one or as many as are its participants. But if it is one, does each of the things said to partake thereof partake of all of it or of a part of it? For if the one man (say) takes all the Monad, there will no longer exist a monad for the one horse to partake of, or the one dog or any one of all the other things which we declare to be one

[159] —just as, supposing there are a number of naked men, who possess only one garment amongst them, which one man had put on, all the rest will remain naked and without a garment. And if each thing partakes of a part of it, then, in the first place, the Monad will have a part. and parts, too, infinite in number into which it is divided; which is absurd. And further, just as the part of the Decad, such as the Dyad, is not a Decad, so neither will the part of the Monad be a Monad, and for this reason nothing will partake of the Monad. Hence the Monad whereof the particular objects are said to partake is not one.

[160] But if the monads, by participation in which each of the particular objects is called one, are equal in number to the numerables to which the term ‟one” is applied, the monads partaken of will be infinite in number. And these either partake of a superior⁹ monad or of monads equal in number to themselves, or else they do not so partake but are monads apart from any participation.

[161] Yet if these can be monads without participation, each of the sensibles also will be able to be one without participation in a monad, and so at once the monad said to be perceived as real in itself is overthrown. Whereas, if those monads are monads by participation, either they all partake of one monad, or each partakes of a monad of its own. And if all partake of one, each will be said to partake either of a part or of the whole, and the original difficulties will still remain;

[162] but if each partakes of its own monad, we must posit a new monad for each of those monads, and others again for the former, and so on ad infinitum. If then, in order to apprehend that there are certain self-sub-sistent monads by participation in which each existing thing is one, it is necessary to apprehend an infinite infinity of intelligible monads, and to apprehend an infinite infinity of intelligible monads is a thing impossible, then it is impossible to show that there are certain intelligible monads and that each existing thing is one through becoming one by participation in its own monad.

[163] It is absurd, therefore, to say that the monads are as numerous as the things which partake of them. But if the so-called self-subsistent monad is neither one nor as many as its participants, a self-subsistent monad does not exist at all. So likewise none of the other numbers will be self-subsistent; for one may apply to all the numbers the argument which has now been employed in the typical case of the monad. But if number is neither self-subsistent, as we have shown, nor consists in the actual numerables, as the Pythagoreans have demonstrated, and beyond these there is no other alternative, then we must declare that number does not exist.

[164] In what way, too, is the Dyad said to be generated from the Monad by those who believe that number is something else apart from the numerables? For when we combine a monad with another monad either something external is added to the monads, or something is subtracted from them, or nothing is either added or subtracted. But if nothing is either added or subtracted, there will not be a Dyad. For neither did the monads, when existing apart from each other, contain the Dyad as involved in the perception of them, according to their own definition, nor has any addition now been made to them from without, just as, by hypothesis, nothing has been subtracted.

[165] Hence the combination of the monad with the monad will not be a dyad, as no addition or subtraction from without takes place. But if subtraction does take place, not only will there not be a dyad but the monads will even be diminished. And if the dyad is added to them from without, so that a dyad may be generated from the monads, the things which appear to be two will be four; for there exists already a monad and a second monad, and when an outside dyad is added to these the result will be the number four.

[166] And the same argument applies to all the other numbers which are said to be formed as a result of combination.

If, then, the numbers which are said to be compounded from the superior¹⁰ numbers are formed neither by subtraction nor by addition nor without subtraction and addition, the formation of the number which is said to be independent and apart from the numerables is non-composite. But they themselves make it clear that the numbers formed by combination are not ungenerated by asserting that they are compounded and generated from the superior numbers —from the monad, for example, and the Indefinite Dyad.¹¹

[167] So then number does not subsist of itself. But if number neither is conceived as self-existent, nor subsists in the numerables, then, to judge from the subtleties introduced by the Dogmatists, number is nothing.

Let this, then, suffice as an account in outline of what is called the Physical section of philosophy.

Notes on the current edition

Pyrrhoniae hypotyposes

1. §§ 149–150 ~ adv. dogm. IV 206—211.

2. 29 αὐτῷ Bekk. : ᾧ G 32 οὐδὲ Stephanus: οὔτε G 7 μήτε alt. Gen.: μηδὲ G

3. 24α

4. § 153 cf. adv. dogm. I 104.

5. § 154 ~ adv. dogm. I 99—100 adv. math. IV 4—5.

6. § 155 ~ adv. dogm. I 95—97 IV 283.

7. 15 τοῦ Πυθ. Bekk. : τῶν ΙΙυθ. G 19 αἱ ἄτομοι coll. p. 527, 7 28 ἄρα ML: γὰρ EAB 29 ἀόριστος Fabr.: ἄριστοςG: om. Stephanus 30 δυάδες alt. om. M 5 τριάδος EAB

8. § 156 ~ adv. dogm, IV 285—287. adv. math. IV 11—13.

9. §§ 158—162 ~ adv. dogm. IV 293—298.

10. 16 τὸ add. Rüstow 17 lac, quam stat. Gen. κατὰ τὸν ἑαυτοῦ λόγον Gen.: καθὸ ζῷόν ἐστιν Bekk. 20 οἱ del. Kayser 21 ὁ EAB: om. ML 22 ἀριθμὸς om. M (fors. recte) || τύχοιεν Gen.: τυχοῖσαν G 23 ὄντες scr. Sexti variandi studium respiciens coll. p. 102,3. 160,12: τυγχάνοντες G 29 εἰ om. EAB 6 αὐτὴ Gen.: αὕτη G

11. 14 μενοῦσιν scr.: μένουσιν G 15 μέρος τι ML: τι μέρος EAB 18 μονάδος Stephanus: δεκάδος G 26 excidit ὅπερ ἀδύνατον vel simile quid || γὰρ G: οὖν Bekk. dubit. 2 ἑκάστῃ Bekk.: ἑκάστην G

12. §§ 164—165 ~ adv. math. IV 21—22 (e Platonis Phaedone 96 E sqq. sumpta.)

13. 27 τι add. Bekk. 29 δυάδα Kayser: μονάδα G 30 ὥσπερ ὥστε G ἐκ τῶν LEAB: αὐτῶν M 11 παρὰ Bekk.: περὶ G

Sextus Empiricus Pyrrhoniae Hypotyposes 3.20

ed. Hermann Mutschmann

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Chapter XX.—Concerning Number

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