Footnotes

[1.]2 vols. Longmans, 1912.[2.]Institutions Metaphysica, quas Roma, in Pontificia Universitate Gregoriana tradiderat P. Joannes Josephus Urraburu, S.J. Volumen Secundum: Ontologia (Rome, 1891).[3.]French version by Sierp, 4 vols. Paris, Gaume, 1868.[4.]Ontologie, ou Métaphysique Générale, par D. Mercier. Louvain, 3me édit., 1902.[5.]Τὴν ὀνομαζομένην σοφίαν περὶ τὰ πρῶτα αἴτια καὶ τὰς ὑπολαμβάνουσι πάντες.—Aristotle, Metaph., I., 1. “Sapientia [philosophia] est scientia quae considerat primas et universales causas.”—St. Thomas, In Metaph., I., I. 2.[6.]Cf. De Wulf, Scholasticism Old and New, pp. 59-61, 191-4; History of Medieval Philosophy, pp. 311-13; also two articles in the Irish Ecclesiastical Record (March and May, 1906) on Thoughts on Philosophy and Religion, and an article in the Irish Theological Quarterly (October, 1910) on Philosophy and Sectarianism in Belfast University, by the present writer.[7.]Cf. Encyclical Aeterni Patris, on Philosophical Studies, by Pope Leo XIII., August 4,1880.[8.]Introduction, § 1.[9.]As a brief general statement of the matter this is sufficiently accurate and will not be misunderstood. Of course the general standpoint of ultimate causes and reasons admits within itself some variety of aspects. Thus Epistemology and Psychology deal with human thought, but under different aspects; Psychology and Ethics deal with human volition, but under different aspects, etc.[10.]“Theoreticus sive speculativis intellectus, in hoc proprie ab operativo sive practico distinguitur, quod speculativus habet pro fine veritatem quam considerat, practicus autem veritatem consideratam ordinat in operationem tamquam in finem; et ideo differunt ab invicem fine; finis speculativae est veritas, finis operativae sive practicae actio.”—St. Thomas, In lib. Boetii de Trinitate.[11.]Here is St. Thomas' exposition and justification of the doctrine in the text: “Sapientis est ordinare. Cujus ratio est, quia sapientia est potissima perfectio rationis, cujus proprium est cognoscere ordinem.... Ordo autem quadrupliciter ad rationem comparatatur. Est enim quidam ordo quem ratio non facit, sed solum considerat, sicut est ordo rerum naturalium. Alius autem est ordo, quem ratio considerando facit in proprio actu, puta cum ordinat conceptus suos ad invicem, et signa conceptuum, quae sunt voces significativae. Tertius autem est quem ratio considerando facit in operationibus voluntatis. Quartus autem est ordo quem ratio considerando facit in exterioribus rebus, quarum ipsa est causa, sicut in arca et domo. Et quia consideratio rationis per habitum perficitur, secundum hos diversos ordines quos proprie ratio considerat, sunt diversae scientiae. Nam ad philosophiam naturalem pertinet considerare ordinem rerum quem ratio humana considerat sed non facit; ita quod sub naturali philosophia comprehendamus et metaphysicam. Ordo autem quem ratio considerando facit in proprio actu, pertinet ad rationalem philosophiam, cujus est considerare ordinem partium orationis ad invicem et ordinem principiorum ad invicem et ad conclusiones. Ordo autem actionum voluntariarum pertinet ad considerationem moralis philosophiae. Ordo autem quem ratio considerando facit in rebus exterioribus constitutis per rationem humanam, pertinet ad artes mechanicas.”—In X. Ethic. ad Nichom., i., lect. 1.[12.]Cf. Science of Logic, i., Introduction, ch. ii. and iii.[13.]Aristotle and the scholastics distinguished between the domain of the practical (πρᾶσσω, πρᾶξις, agere, agibilia) and the operative or productive (ποιεῖν, ποίησις, facere, factibilia).[14.]Cf. Science of Logic, i., § 8.[15.]“Quædam igitur sunt speculabilium quæ dependent a materia secundum esse, quia non nisi in materia esse possunt, et hæc distinguuntur quia dependent quædam a materia secundum esse et intellectum, sicut illa in quorum definitione ponitur materia sensibilis: unde sine materia sensibili intelligi non possunt; ut in definitione hominis oportet accipere carnem et ossa: et de his est physica sive scientia naturalis. Quædam vero sunt quæ, quamvis dependeant a materia sensibili secundum esse, non tamen secundum intellectum, quia in eorum definitionibus non ponitur materia sensibilis, ut linea et numerus: et de his est mathematica. Quædam vero sunt speculabilia quæ non dependent a materia secundum esse, quia sine materia esse possunt: sive nunquam sint in materia, sicut Deus et angelus, sive in quibusdam sint in materia et in quibusdam non, ut substantia, qualitas, potentia et actus, unum et multa, etc., de quibus omnibus est theologia, id est scientia divina, quia præcipuum cognitorum in ea est Deus. Alio nomine dicitur metaphysica, id est, transphysica, quia post physicam dicenda occurrit nobis, quibus ex sensibilibus competit in insensibilia devenire. Dicitur etiam philosophia prima, in quantum scientiae aliæ ab ea principia sua accipientes eam sequuntur.”—St. Thomas, In lib. Boetii de Trinitate, q. 5, a. 1.[16.]Ἐττιν ἐπιστήμη τις ἤ θεωοεῖ τὸ ὄν και τούτῳ ὑπάρχοντα καθ᾽ ἁυτό.—Metaph. III., i (ed. Didot).[17.]Metaph. X., ch. vii., 5 and 6.[18.]Cf. Science of Logic, ii., §§ 251-5.[19.]When the term “science” is used nowadays in contradistinction to “philosophy,” it usually signifies the knowledge embodied in what are called the special, or positive, or inductive sciences—a knowledge which Aristotle would not regard as strictly or fully scientific.[20.]Aristotle's conception of the close relation between Physics (or the Philosophy of Nature) and those analytic studies which we nowadays describe as the physical sciences, bears witness to the close alliance which he conceived to exist between sense observation on the one hand and rational speculation on the other. This sane view of the continuity of human knowledge, a view to which the Schoolmen of the Middle Ages were ever faithful, was supplanted at the dawn of modern philosophy in the sixteenth and seventeenth centuries by the opposite view, which led to a divorce between physics and metaphysics, and to a series of misunderstandings which still prevail with equal detriment to science and philosophy alike.[21.]Cf. De Wulf, History of Medieval Philosophy, pp. 28-9, 66; Mercier, Ontologie, Introd., p. v., n.[22.]“Dicitur metaphysica [scientia] id est, transphysica, quia post physicam dicenda occurrit nobis, quibus ex sensibilibus competit in insensibilia devenire.”—St. Thomas, In Lib. Boetii de Trinitate, q. 5, a. 1.[23.]This is also the title of the social and ethnological study of the various races of men, their primitive habits, customs, institutions, etc.[24.]Not entirely; for instance, what is perhaps the most comprehensive course of philosophy published in recent times, the Philosophia Lacensis (11 vols., Herder, 1888-1900) apparently follows the arrangement of metaphysics outlined above. The fundamental questions on knowing and being, which usually constitute distinct departments under the respective titles of Epistemology and Ontology, are here treated under the comprehensive title of Institutiones Logicales (3 vols.). However, they are really metaphysical problems, problems of speculative philosophy, wherever they be treated; and the fact that the questions usually treated in Ontology are here treated in a volume apart (vol. iii. of the Institutiones Logicales: under the peculiar title of Logica Realis), and not in the volumes assigned to general metaphysics, shows the necessity and convenience of the more modern arrangement. General metaphysics are dealt with in 2 vols. of Institutiones Philosophiae Naturalis and 3 vols. of Institutiones Psychologicae; special metaphysics in the Institutiones Theodicœae (1 vol.); ethics in 2 vols. of Institutiones Juris Naturae.[25.]Cf. Turner, History of Philosophy, p. 525.[26.]Mercier, Logique, Introd., § 9.[27.]pp. 45, 51.[28.]Cf. Science of Logic, i., § 17.[29.]Cf. ibid. i., Introd., ch. i.[30.]Cajetan, In 2 Post Anal., ch. xiii.[31.]Cf. Mercier, Ontologie, §§ 6-13; Ladd, A Theory of Reality, ch. i.[32.]infra, ch. [viii.]; Cf. Science of Logic, ii., Part IV., ch. iii.-vi.; Part V., ch. i.[33.]p. 18—in which context will be found a masterly analysis and criticism of current prejudices and objections against systematic metaphysics.[34.]ibid. pp. 19-20.[35.]Royce, The Conception of God, p. 207.[36.]Mercier, Logique, Introd., § 14.[37.]Encyclical, Aeterni Patris, on philosophical studies.[38.]Summa Theologica, 1, q. 1, a. 8, ad. 2.[39.]Cf. Mercier, Origines de la psychologie contemporaine, ch. viii.; De Wulf, Scholasticism Old and New (passim).[40.]Cf. Ladd, op. cit., pp. 9, 10.[41.]Eucken, Gesammelte Aufsaetze zur Philosophie und Lebensanschauung, § 157 (Leipzig, 1903).[42.]Cf. art. Philosophy and the Sciences at Louvain, in the Irish Ecclesiastical Record, May, 1905, reprinted as Appendix in De Wulf's Scholasticism Old and New.[43.]Hence the necessity of equipping the student of philosophy with a knowledge of the main conclusions and theories of the sciences that have an immediate bearing on philosophy: chemistry, physics, geology, astronomy, mechanics, the axioms and postulates of pure and applied mathematics, cellular biology, embryology, the physiology of the nervous system, botany and zoology, political economy, sociology and ethnology. Nowhere is the system of combining the scientific with the philosophical formation of mind more thoroughly carried out at the present time than in the curriculum of the Philosophical Institute at the University of Louvain. In the College of Maynooth not only is the study of philosophy completed by a fuller course of Christian Theology,—both disciplines thus combining to give the student all the essential elements of a complete Philosophy of Life (ii.),—but it is preceded by an elementary training in the physical sciences and accompanied by courses on the history of scientific theories in chemistry, physics, physiology, and general biology.[44.]“We may mention it in passing,” writes Mercier in his general introduction to philosophy (Logique, § 1, p. 6)—“it was this feeling of individual impotence in face of the task confronting the philosopher at the present day, that inspired the foundation of the Philosophical Institute at the University of Louvain”. He had previously outlined the project in his Rapport sur les études philosophiques at the Congress of Mechlin in 1891. Here are a few brief extracts from that memorable document: “Since individual effort feels itself well nigh powerless in the presence of the field of observation which goes on widening day by day, association must make up for the insufficiency of the isolated worker; men of analysis and men of synthesis must come together and form, by their daily intercourse and united action, an atmosphere suited to the harmonious development of science and philosophy alike....” “Man has multiplied his power of vision; he enters the world of the infinitely small; he fixes his scrutinizing gaze upon regions where our most powerful telescopes discern no limits. Physics and Chemistry progress with giant strides in the study of the properties of matter and of the combinations of its elements. Geology and Astronomy reconstruct the history of the origin and formation of our planet. Biology and the natural sciences study the minute structure of living organisms, their distribution in space and succession in time; and Embryology explores their origin. The archæological, philological and social sciences reconstruct the past ages of our history and civilizations. What an inexhaustible mine is here to exploit, what regions to explore and materials to analyse and interpret; finally what pioneers we must engage in the work if we are to have a share in garnering those treasures!”[45.]Grammar of Assent, p. 229.[46.]Lucerna pedibus meis verbum tuum, et lumen semitis meis.—Ps. cxviii., 105.[47.]Tennyson, In Memoriam.[48.]Cf. Logic, i., § 123.[49.]Cf. Logic, i., pp. 204-6.[50.]Cf. Scotus, Summa Theologica, edit. by Montefortino (Rome, 1900), i., p. 106, Ad tertium.[51.]Cf. Logic, i., pp. 119-20.[52.]Cf. Scotus, op. cit., i., pp. 104, 129; also Urraburu, Ontologia, Disp. III., Cap. II., Art. III., p. 155.[53.]Hence St. Thomas calls the things about which a generic or specific concept is predicated “analoga secundum esse et non secundum intentionem” (In 1 Sent., Dist. xix., q. 5, a. 2, ad a am): we bring them under the same notion or “intentio” (e.g. “living being”), but the content of this notion is realized in the various things (e.g. in Socrates, this horse, that rose-tree, etc.) in varying and unequal degrees of perfection. Hence, too, this univocal relation of the genus to its subordinate subjects is sometimes (improperly) called “analogy of inequality”.[54.]Cf. infra, ch. [viii].[55.]Cf. Kleutgen, Philosophie der Vorzeit, §§ 599, 600.[56.]This, of course, is the proper sort of analogical predication: the predication based upon similarity of proportions or relations. Etymologically, analogy means equality of proportions (Cf. Logic, ii., p. 160). On the whole subject the student may consult with profit Cajetan's Opusculum de Nominum Analogia, published as an appendix to vol. iv. of St. Thomas' Quæstiones Disputatæ in De Maria's edition (1883).[57.]Cf. Kleutgen, op. cit., §§ 40-42.[58.]Cf. Scotus, op. cit., i., pp. 318-22, 125-131, 102-7 (especially p. 128, Ad tertium); p. 131, Ad sextum; p. 321, Ad tertium.[59.]Kleutgen, op. cit., § 599.[60.]ibid., § 600.[61.]Suarez, Metaph., Dist. xxviii., § 3; Dist. xxxii., § 2.[62.]Scotus, op. cit., i., pp. 106-7, 128-9.[63.]ibid., p. 107.[64.]Cf. Kleutgen, La philosophie scolastique (“Die Philosophie der Vorzeit”). Fr. trans. by Sierp (Paris, 1868), vol. i., p. 66, § 35.[65.]The logical copula, which expresses this relation and asserts the truth of the judgment, expresses, of course, a logical entity, an ens rationis. True judgments may be stated about logical entities as well as about realities. But since the former can be conceived only after the manner of the latter, the appropriateness of using the verb which expresses existence or reality, as the logical copula, will be at once apparent. Cf. Logic, i., p. 249, n. 1.[66.]Suarez, Metaph., Dist. 54, § i., 6.[67.]Cf. Logic, i., pp. 28-9.[68.]Cf. Kleutgen, op. cit., §§ 551-2.[69.]Cf. Logic, i., pp. 70-1.[70.]“Esse actum quondam nominat: non enim dicitur esse aliquid ex hoc, quod est in potentia, sed ex hoc, quod est in actu.”—St. Thomas, Contra Gent. i., c. xxii., 4.[71.]Certain medieval philosophers had made the same mistake. St. Thomas points out their error frequently. Cf. Contra Gentes, i., c. xxvi: “Quia id, quod commune est, per additionem specificatur vel individuatur, æstimaverunt, divinum esse, cui nulla fit additio, non esse aliquid proprium, sed esse commune omnium: non considerantes, quod id, quod commune est, vel universale, sine additione esse non potest, sed sine additione consideratur. Non enim animal potest esse absque rationali vel irrationali differentia, quamvis sine his differentiis consideretur; licet enim cogitetur universale absque additione, non tamen absque receptibilitate additionis est. Nam si animali nulla differentia addi posset, genus non esset; et similiter est de omnibus aliis nominibus. Divinum autem esse est absque additione, non solum cogitatione, sed etiam in rerum natura; et non solum absque additione, sed absque receptibilitate additionis. Unde ex hoc ipso quod additionem non recipit, nec recipere potest, magis concludi potest quod Deus non sit esse commune, sed esse proprium. Etenim ex hoc ipso suum esse ab omnibus aliis distinguitur, quia nihil ei addi potest.”[72.]Cf. St. Thomas, QQ. DD. De Potentia, q. i. art. 1, ad. 18.[73.]Aristotle, Metaph., c. iv., v., apud Kleutgen, op. cit., iii., p. 60.[74.]Contra Gentes, II., c. vii.[75.]Cf. Laminne, Cause et Effet—Revue neo-scolastique, February, 1914, p. 38.[76.]St. Thomas uses what is for him strong language when he describes such a view as ridiculous: “Ridiculum est dicere quod ideo corpus non agat, quia accidens non transit de subjecto in subjectum; non enim hoc modo dicitur corpus calidum calefacere, quod idem numero calor, qui est in calefaciente corpore, transeat ad corpus calefactum; sed quia virtute caloris, qui est in calefaciente corpore, alius calor numero fit actu in corpore calefacto, qui prior erat in eo in potentia. Agens enim naturale non est traducens propriam formam in alterum subjectum, sed reducens subjectum quod patitur de potentia in actum.”—Contra Gentes, L. III., c. lxix.[77.]Cf. Zigliara, Ontologia (8), ix., Quintum. Cf. also Aristotle, Metaph. v., St. Thomas, In Metaph., v., § 14, and Contra Gentes, i., c. xvi., where he emphasizes the truth that potential being presupposes actual being: “Quamvis id quod quandoque est in potentia, quandoque in actu, prius sit tempore in potentia quam in actu, tamen simpliciter actus est prior potentia; quia potentia non educit se in actum, sed opportet quod educatur in actum per aliquid quod sit in actu. Omne igitur quod est aliquo modo in potentia, habet aliquid prius se”.[78.]Klimke, Der Monismus und seine philosophischen Grundlagen, p. 185. Cf. Irish Theological Quarterly, vol. vii. (April, 1912), p. 157 sqq., art. Reflections on Some Forms of Monism.[79.]For relations of potentia and actus, cf. Mercier, Ontologie, § 214.[80.]Cf. Physics, v., 1; De Anima, i., 3.[81.]Λεγώ δ᾽ ὕλην, ἢ καθ᾽ ἁυτὴν μήτε τὶ, μήτε ποσὸν, μήτε ποίον, μήτε ἄλλο μεδὲν λέγεται οἶς ὤρισται τὸ ὄν.—Metaph. vi., c. iii.[82.]“Decepit antiquos philosophos hanc rationem inducentes, ignorantia formae substantialis. Non enim adhuc tantum profecerant ut intellectus eorum se elevaret ad aliquid quod est supra sensibilia: et ideo illas formas tantum consideraverunt, quæ sunt sensibilia propria vel communia. Hujusmodi autem manifestum est esse accidentia, ut album et nigrum, magnum et parvum, et hujusmodi. Forma autem substantialis non est sensibilis nisi per accidens, et ideo ad ejus cognitionem non bervenerunt, ut scirent ipsam materiam distinguere.”—In Metaph. vii., 2.[83.]“Esse actum quemdam nominat: non enim dicitur esse aliquid, ex hoc quod est in potentia, sed ex hoc quod est in actu.”—St. Thomas, Contra Gentes, i., ch. xxii., 4.[84.]The etymology of Aristotle's description of the essence as τὸ τί ἦν εἶναι is not easy to explain. The expression τὸ εἶναι supposes a dative understood, e.g. τὸ ἀνθρώπῳ εἶναι, the being proper to man. To the question τὶ ἐστι τὸ ἀνθρώπῳ εἶναι; what is the being or essence proper to man? the answer is: that which gives the definition of man, that which explains what he is—τί ἦν. Is the imperfect, τὶ ἦν, an archaic form for the present, τὶ ἐστι; or is it a deliberate suggestion of the profound doctrine that the essence as ideal, or possible, is anterior to its actual, physical realization? Commentators are not agreed. Cf. Matthias Kappes, Aristoteles-Lexicon, p. 25 (Paderborn, 1894); Mercier, Ontologie, p. 30 n.[85.]Essentia est illud per quod res constituitur in proprio genere vel specie, et quod significamus per definitionem indicantem quid est res.—De Ente et Essentia, ch. i.[86.]Aristotle, Metaph., v., 4; St. Thomas, De Potentia Dei, q. ix., art. 1.[87.]Sometimes, however, the expression “metaphysical essence” is used to signify those objective concepts, and those only, without which the thing cannot be conceived, (or sometimes, even the one which is considered most fundamental among these), and therefore as not explicitly involving the concepts of properties which follow necessarily from the former; while the “physical essence” is understood to signify all those real elements without which the thing cannot actually exist, including, therefore, all such necessary properties. Taken in this sense the physical essence of man would include not merely soul and body, but also such properties as the capacity of speech, of laughter, of using tools, of cooking food, etc.[88.]Et ex hoc patet ratio, writes St. Thomas, quare genus et species et differentia se habeant proportionaliter ad materiam, formam et compositum in natura, quamvis non sint idem cum illis; quia neque genus est materia, sed sumitur a materia ut significans totum; nec differentia est forma, sed sumitur a forma ut significans totum. Unde dicimus hominem esse animal rationale, et non ex animali et rationali; sicut dicimus eum esse ex corpore et anima. Ex corpore enim et anima dicitur esse homo, sicut ex duabus rebus quædam tertia res constituta, quæ neutra illarum est: homo enim nec est anima neque corpus; sed si homo aliquo modo ex animali et rationali dicatur esse, non erit sicut res tertia ex duabus rebus sed sicut intellectus [conceptus] tertius ex duobus intellectibus. Intellectus enim animalis est sine determinatione formae specialis naturam exprimens rei, ex eo quod est materiale respectu ultimae perfectionis. Intellectus autem hujus differentiae, rationalis, consistit in determinatione formae specialis: ex quibus duobus intellectibus constituitur intellectus speciei vel definitionis. Et ideo sicut res constituta ex aliquibus non recipit prædicationem earum rerum ex quibus constituitur; ita nec intellectus recipit prædicationem eorum intellectuum ex quibus constituitur; non enim dicimus, quod definitio sit genus vel differentia.—De Ente et Essentia, cap. iii.[89.]Cf. Mercier, Psychologie, vol. ii., § 169 (6th edit., 1903, pp. 24-5).[90.]Cf. Aristotle, Metaph., L. viii., 10; St. Thomas, In viii., Metaph., Lect. iii., par. i.[91.]Cf. Mercier, Ontologie, pp. 42-3. How do we know that not only water (H2O) is a possible essence but also hydrogen di-oxide (H2O2)? Because the latter substance has been actually formed by chemists (Cf. Roscoe, Elementary Chemistry, Lesson VI.). Is hydrogen tri-oxyde (H2O3) a possible substance? We may ask chemists,—and they may not be able to tell us with any certainty whether it is or not.[92.]The actual existence of a thinking mind is of course a necessary condition, in the actual order, for the apprehension of objects in this abstract way. But such existence is no part of the apprehended object. That the human mind, which is itself finite, contingent, allied with matter, and dependent on the activity of corporeal sense organs for the objects of its knowledge, should nevertheless have the power to apprehend contingent realities apart from their contingent actual existence in time and space,—is a fact of the greatest significance as regards the nature of the mind itself. But if we try to prove the existence of God from a consideration of the nature and powers of the human mind, our argument proceeds from the actual, and is distinct from any argument based exclusively on the nature and properties of possible essences as such. St. Augustine's argument assumes as a fact that the human mind represents to itself possible essences as having reality independently both of its own thought and of any actual existence of such essences (Cf. De Munnynck, Praelectiones de Dei Existentia, p. 23). But is this a fact? This is the really debatable point.[93.]Among others Henry of Ghent († 1293; Cf. De Wulf, History of Medieval Philosophy, pp. 364-6; Kleutgen, Philosophie der Vorzeit, Dissert, vi., cap. ii., 2 §§ 581-5), Capreolus (1380-1444), certain Scotists, and certain theosophists of the thirteenth and fourteenth centuries, are credited with this peculiar view. For numerous references, Cf. Urraburu, Ontologia, Disp. iii., cap. ii., art. v. pp. 650-63.[94.]Cf. Urraburu, op. cit., pp. 652-3, for references; among others, to St. Thomas, De Potentia, q. 3, art. 1, ad 2um; art. 7, ad 10um; art. 5, argum. 2o; ibid., ad 2um. Summa Theol., i., q. 14, art. 9; q. 45, art. 1; ibid. , art. 2, ad 2um; q. 61, art. 2, corp.[95.]Among others, Balmes (Fundamental Philosophy, bk. iv., ch. xxvi.), Lepidi (Ontologia, quoted by De Munynck, Praelectiones de Dei Existentia, Louvain, 1904, p. 19); De Munynck (ibid., pp. 19-23, 46-7, 75); Hickey (Theologia Naturalis, pp. 31-4); Driscoll (God, pp. 72 sqq.); Lacordaire (God, p. 21); Kleutgen, Philosophie der Vorzeit, Dissert. iv., § 476.[96.]Truth is not the work of any human intelligence, says St. Augustine, nor can any one arrogate to himself the right to say “my truth,” or “thy truth,” but all must say simply “the truth”: “Quapropter, nullo modo negaveris esse incommutabilem veritatem, haec omnia, quae incommutabiliter vera sunt, continentem, quam non possis dicere vel tuam vel meam, vel cujuscumque hominis, sed omnibus incommutabilia vera cernentibus, tamquam miris modis secretum et publicum lumen, praesto esse ac se praebere communiter: omne autem quod communiter omnibus ratiocinantibus atque intelligentibus praesto est, ad ullius eorum proprie naturam pertinere quis dixerit?”—De Libero Arbitrio, lib. ii., ch. xii. Cf. his striking expression of the same thought in his Commentary, Super Genesim ad Litteram, lib. ii., cap. vii.: “We may conceive the heavens and the earth, that were created in six days, ceasing to exist; but can we conceive the number ‘six’ ceasing to be the sum of six units?”: “Facilius coelum et terra transire possunt, quae secundum numerum senarium fabricata sunt, quam effici possit ut senarius numerus suis partibus non compleatur” (apud Mercier, Ontologie, pp. 35-6).[97.]

Cf. Balmes (Fundamental Philosophy, bk. iv., ch. xxvi.), who, analysing the truth of the proposition “Two circles of equal diameters are equal,” as an example of the necessary, eternal, immutable characteristics of possible essences, goes so far as to write (italics ours): “What would happen, if, withdrawing all bodies, all sensible representations, and even all intelligences, we should imagine absolute and universal nothing? We see the truth of the proposition even on this supposition: for it is impossible for us to hold it to be false. On every supposition, our understanding sees a connection which it cannot destroy: the condition once established, the result will infallibly follow.