told that the slain were a thousand, the saved a hundred; in such case our knowledge becomes adequate and complete. It is in the contemplation of these two quantities thus defined, the continuous by figure, the discrete by number, that we behold them rendered subjects for the two noblest of sciences, the first of them for geometry, the second for arithmetic; from which two, (and not from mere experiments, as some have hastily asserted,) both the knowledge of nature, and the utilities of common life, are in the greatest part derived. It is here we see the rise of those mathematical sciences, arithmetic, geometry, music, &c. which the ancients esteemed so essential to a liberal education. Nor can we believe there is any one now but must acknowledge, that a mind properly tinged with such noble speculations, (supposing there be no want of genius, or of courage,) is qualified to excel in every superior scene of life. Far more honourable they surely are, than the arts of riding a horse, or of wielding a sword, those accomplishments usually assigned to our youth of distinction, and for the sake of which alone they are often sent into distant countries, as if there were nothing to be taught them at home, nor any thing in a gentleman worth cultivating but his body. We would not undervalue these bodily accomplishments, (for perfection of every sort is certainly worth aiming at ;) but we would wish them to be rated as much below the mental, as the body itself is inferior to the mind. There is an elegant account of the sciences above mentioned in the Republic of Plato. Glaucus (one of the persons of the dialogue) takes pains to recommend them from their usefulness in human life: arithmetic for accounts and distributions; geometry for encampments and mensurations; music for solemn festivals in honour of the gods; and astronomy for agriculture, for navigation, and the like. Socrates, on his part, denies not the truth of all this, but still insinuates, that they were capable of answering an end more sublime. "You are pleasant," says he, "in your seeming to fear the multitude, lest you should be thought to enjoin certain sciences that are useless. It is, indeed, no contemptible matter, though a difficult one, to believe, that through these particular sciences the soul has an organ purified and enlightened, which is destroyed and blinded by studies of other kind; an organ better worth saving than a thousand eyes; inasmuch as truth becomes visible through this alone."e These, that we have here mentioned, appear to be the only d See Hermes, p. 218, and note, p. 222. • The above is an attempt to translate the following elegant passage of Plato: Ηδὺς εἶ, ὅτι ἔοικας δεδιότι τοὺς πολλοὺς, μὴ δοκῇς ἄχρηστα μαθήματα προστάττειν Tò d' éσriv où návν paîλov, àλλà xaλenòv πιστεῦσαι, ὅτι ἐν τούτοις τοῖς μαθήμασιν ἑκαστοῖς ὄργανόν τι ψυχῆς ἐκκαθαίρεται, καὶ ἀναζωπυρεῖται, ἀπολλύμενον καὶ τυφ λούμενον ὑπὸ τῶν ἄλλων ἐπιτηδευμάτων, κρεῖττον ὂν σωθῆναι μυρίων ομματων· μόνῳ γὰρ αὐτῷ ἀλήθεια ὁρᾶται. Plat. de Repub. lib. vii. p. 527. edit Serran. Hermes, page 202. species of quantity; inasmuch as other things are called quantities, not from themselves, but with reference to these. Thus we say, that there is much white, because the superficies, which it covers, is much; and that an action was long, because. the time was long during which it was transacted. And hence it is, that, if any one is to explain the quantity of an action, as, for example, the length of the Trojan war, he explains it by the time, saying, it was a war of ten years. So when we give the quantity of any thing white, we define it by the superficies, because, as that is in quantity, so also is the white." We further observe, that quantity continuous and discrete may be said to blend themselves with all things. Thus in substances, let Mount Athos represent the former; the army of Xerxes, the latter. In colours, let us view the former in the uniform blueness of a clear sky; the latter, in the many and diversified tints of a rainbow. In sounds we find quantity discrete belonging to speech or language, it being the essence of articulation, that every syllable should be distinct. The continuous, on the contrary, naturally suggests itself to our ears, when we hear yellings, howlings, and heavy psalmody. In motions, when a grasshopper moves by leaps, we behold quantity discrete; when a ship sails smoothly, we behold quantity continuous. The motion of all animals, that have feet, (whether they leap or not,) by being alternate, is of the discrete kind: but it is fabled of the gods, that, when they moved as gods, it was under one continued progression of their whole frame together; to which Virgil, they say, alludes, in speaking of Venus, Et vera incessu patuit dea. Æn. i. 411. The mind, though devoid of corporeal extension, admits what is analogous to these two species of quantity, and recognises their force even within the sacred recesses of itself. For what can be more truly united in perfect continuity, than the terms which compose a self-evident truth? And how is this continuity still further extended, when by the union of two such truths there is produced a third, under the indissoluble connection of a demonstrative syllogism? If there was not this syllogistic continuity, there might indeed be other continuities, but it would never be in our power to prove any thing concerning them. Again, when we consider either many propositions, without reference to a syllogism; or many independent terms, without reference to a proposition; what have we then but quantity discrete? Philosophical arrangements? Treasures, as capable of being numbered, estimated, and recorded, as those which the miser commits to his coffers. 1 Κυρίως δὲ ποσὰ ταῦτα λέγεται μόνα τὰ εἰρημένα, τὰ δὲ ἄλλα πάντα κατὰ συμβεβηκός· εἰς ταῦτα γὰρ ἀποβλέποντες καὶ τὰ ἄλλα ποσὰ λέγομεν· οἷον πολὺ τὸ λευκον λέγεται, τῷγε τὴν ἐπιφάνειαν πολλὴν εἶναι· καὶ ἡ πρᾶξις μακρὰ, τῷγε τὸν χρόνον, κ. τ. λ. Aristot. Præd. p. 32. edit. Sylb. 66 It is, indeed, by the help of an innate power of distinction that we recognise the differences of things, as it is by a contrary power of composition that we recognise their identities." These powers, in some degree, are common to all minds; and as they are the basis of our whole knowledge, (which is, of necessity, either affirmative or negative,) they may be said to constitute what we call common sense.h On the contrary, to possess these powers in a more eminent degree, so as to be able to perceive identity in things widely different, and diversity in things nearly the same; this it is that constitutes what we call genius, that power divine, which through every sort of discipline renders the difference so conspicuous between one learner and another. It was from speculations of this kind, that some of the ancients were induced to consider quantity in a far higher rank than is usual in common speculations. They considered both species under the common character of a bound or measure, and as such to be conspicuous throughout the whole universe; the nature of the continuous, called magnitude, being seen in union and connection; that of the discrete, called multitude, in accumulation and juxtaposition; that by virtue of magnitude, the world or universe was one; was extended and connected everywhere, through its most distant parts; that by virtue of multitude it was diversified with that order and fair arrangement, seen in the amazing variety of stars, of elements, of plants, of animals; of contrarieties on one side, and of similarities on the other; that if these quantities were thus distinguishable in the copy or image, (for such was this world, when compared to its archetype,) much more so were they in those pure and immaterial forms, the invariable and immediate objects of the Supreme Intellect. The whole production of quantity (as of every thing else) they referred with reason to this primary intelligent cause; whose virtual efficacy, as far as it passes through all things without dividing itself or stopping, they supposed to generate continuity and union; as far as it stops in its progress at every particular, and communicates to each a peculiar form of its own, they held to generate distinction and multitude; and as far as it perpetually exerts at once these two distinct and opposite energies, they considered as for ever rendering the universe both many and one; many, through its order and fair variety; one, through its connection and general sympathy."i See p. 221, note d. 1 The authors from whom the preceding sentiments are taken, are Plotinus and Iamblichus, in the commentary of Simplicius upon this predicament of quantity. Ἔτι δὲ ὁ Πλωτίνος—ἰδία γὰρ καὶ φύσις ἑκάστῳ, ὡς καὶ ἐν τῷ παντὶ κόσμῳ θεωρεί ται, τοῦ μὲν συνεχοῦς ἡ φύσις, ἥτις καλεῖ ται μέγεθος, κατὰ ἔνωσιν καὶ ἀλληλουχίαν· τοῦ δὲ διωρισμένου, ἥτις καλεῖται πλῆθος, κατὰ σώρειαν καὶ παράθεσιν· καὶ γὰρ κατὰ μὲν τὴν τοῦ μεγέθους οὐσίαν, εἷς ὁ κόσμος ἐστί τε καὶ νοεῖται, σφαιρικὸς καὶ συμπεφυκώς ἑαυτῷ, διατεταμένος τε καὶ ἀλλη λουχούμενος· κατὰ δὲ τὸ πλῆθος, ἥτε σύνταξις καὶ ἡ διακόσμησις, ἡ ἐκ τοσῶνδε φέρε εἰπεῖν στοιχείων, καὶ ζώων ἢ φυτῶν And so much for the third universal genus, or predicament, that of quantity, its various species, and its peculiar properties.* We cannot however quit this and the preceding predicament (I mean the predicaments of quality and quantity) without observing that, as they are diffused in a conspicuous manner throughout the universe, so writers both sacred and profane, both poetic and prosaic, appear to have expressed their force, and that often at the same time, as the predicaments themselves often exist so in nature. 66 “O Lord, how manifold are thy works! in wisdom hast thou made them all."! Here [manifold] denotes the quantity of the divine works; [made in wisdom] denotes their quality. Nam et qualis in cujusque rei natura, et quæ forma, quæritur : an immortalis anima, an humana specie deus: et de magnitudine et numero: quantus, sol; an unus, mundus.m Where the critic not only delineates the two great predicaments here mentioned, but divides also quantity into its two capital species, I mean magnitude and number. Cicero goes further in his Tusculan Disputations, not only producing quality and quantity, but substance also, their support; which he places first, according to its proper order. Si quid sit hoc, non vides; at quale sit, vides: si ne id quidem; at quantum sit, profecto vides." Even comic writers have expressed the force of these two predicaments. Quantam et quam veram laudem capiet Parmeno? "How great, and how true praise will Parmeno acquire ?" Terent. Eun. v. 4. 3. Great indicates quantity: true indicates quality; for what quality in praise is more valuable than truth? The poets, who dealt in subjects more exalted than comedy, appear many of them to have employed the same language. θεωρεῖται, καὶ ἐναντιωτήτων ἢ ὁμοιοτήτων τόσων καὶ τόσως· εἰ οὖν ἐν ταῖς εἰκόσιν οὕτω ταῦτα κεχώρισται, πολὺ πρότερον ἐν τοῖς νοουμένοις γένεσι· καὶ πρὸ τούτων, ἐν τοῖς καθ ̓ αὑτὰ ἀΰλοις εἴδεσι διέστηκε, κοινὸν ἔχοντα, ὡς εἴρηται, τὸ μέτρον καὶ τὸ Tépas. Simplic. in Præd. p. 32. B. edit. Basil. 1551. Ὁ δὲ θεῖος Ἰάμβλιχος—ἐπειδὴ γὰρ ἡ τοῦ ἑνὸς δύναμις ἀφ ̓ οὗ πᾶν τὸ ποσὸν ἀπογεννᾶται, διατείνεται δι ̓ ὅλων ᾗ αὐτὴ, καὶ ὁρίζει ἕκαστον προϊοῦσα ἀφ' ἑαυτῆς, ᾗ μὲν δι' ὅλων διήκει παντάπασιν ἀδιαιρέτως, τὸ συνεχὲς ὑφίστησι, καὶ ᾗ τὴν πρόσοδον ποιεῖται μίαν, καὶ ἀδιαίρετον καὶ ἄνευ διωρισμοῦ· ᾗ καὶ προϊοῦσα ἵσταται καθ ̓ ἕκαστον τῶν εἰδῶν, καὶ ᾗ ὁρίζει ἕκαστον, καὶ ἕκαστον ἐν ποιεῖ, ταυτῇ τὸ διωρισμένον παράγει.— ἐπεὶ δὲ ἅμα καὶ μένει καὶ πρόεισι, τὰ δύο ἀπογεννᾷ. περιέχει γὰρ ἡ τῶν νοητῶν μέτρων δύναμις ἅμα ἀμφότερα τὰ μένοντα καὶ προΐοντα ἐν ἑνὶ τῷ αὐτῷ. Simplic. in Præd. p. 34. edit. Basil. 1551. As the above sentiments are expressed in the text, a verbal translation of them is omitted. It may, however, be acceptable to the curious to see them in their originals, and for that reason they have been subjoined. * See before, note s, p. 305. m Quintil. Instit. Orat. 1. vii. c. 4. Æn. v. 641. The same, of Polypheme : Qualis, quantusque cavo Polyphemus in antro. Homer, (whom it is probable the rest all copied,) speaking of Achilles : Ητοι Δαρδανίδης Πρίαμος θαύμας ̓Αχιλήα, Iliad. . 629. These attributes, given by poets to gods and heroes, have been found by Euclid in figures geometrical. He has a problem to teach us how to describe a rectilineal figure, which to one given rectilineal figure shall be similar, to another shall be equal.P Similar is a property of quality; equal, of quantity. But it is time to finish, and proceed to the arrangement next in order. CHAPTER X. CONCERNING RELATIVES'-THEIR SOURCE-RELATIVES APPARENT-REAL -THEIR PROPERTIES, RECIPROCAL-INFERENCE, AND CO-EXISTENCE -FORCE OF RELATION IN ETHICS-IN MATTERS DRAMATIC-IN NATURE, AND THE ORDER OF BEING RELATIONS, AMICABLE AND EVIL-WANT-FRIENDSHIP-STRIFE-RELATION OF ALL TO THE SUPREME CAUSE-EXTENT AND USE OF THIS PREDICAMENT, OR ARRANGEMENT. HOSTILE THROUGH the three universal genera, predicaments, or arrangements, already described, subordinate beings may be said to Pope's Homer, book xxiv. ver. 798. The translation, we see, renders the words oooos and olos by a periphrasis, and it should seem with some propriety, as "the god-like aspect" of Achilles is clearly among his qualities, and his "majestic size" evidently respects his magnitude, that is to say, his quantity. It must be confessed, however, that much of the force of the original will necessarily be lost in the translation, where single words in one language cannot be found corresponding to single words in the other. P Euclid, vi. 25. 4 See before, pages 300, and 305. The title of this arrangement is expressed by a plural, and not a singular, (like quality and quantity,) because all relation is necessarily between two: ǹ dè oxéσis Touλáxiotov év dvol mрáyμaσi Dewpeîтai. Ammon. in Cat. p. 94. B.-tolov yàp Tâs σχέσεως μόνης, τὸ ἐν πολλοῖς ὑφεστάναι μόνως. ὅπερ οὐδεμιᾷ πρόσεστι τῶν ἄλλων karnyopiŵv: “it is a peculiarity of relation only, to have its existence in many, which is the case with no one else of the predicaments." Simpl. in Præd. p. 41. B. edit. Basil. 1551. |