The modern use of the word science implies a univocal meaning that has become widely accepted in the everyday language of our time. Postmediaeval man considers that the paradigm of science should be the genus of knowledge predicated of the physicomathematical disciplines, i. e. the sciences whose task is the study of natural things based on positive experimentation as to their phenomenical manifestations. Therefore when contemporary man wishes to allude to a person who will exemplify the scientist, the names which come quickly to mind are not those of Socrates, Plato or Aristotle, but those of Lavoisier, Einstein or Heisenberg. Furthermore the modern meaning of the noun science seems intended increasingly to exclude as far as pos-sible all reference to philosophy and sacred theology. This conviction permeates the spirit of our civilization to such an extent that the arbitrary univocation of science with physico-mathematics is now virtually a fait accompli.

Many authors have thought that the history of science began in the Seventeenth Century. We often hear its referred to as though the period had witnessed the formal birth of mankind's scientific knowledge, but such a view is not substantiated by a careful study of the history of science. Although nobody would question the incomparable development of physicomathe-matical sciences since that date, it is necessary to affirm both their previous existence and also the ancient and mediaeval recognition of their distinction from the philosophical science of nature⁽¹⁾. This is a factor of capital importance. Few modern men know that the distinction between the philosophy of nature and the physicomathematical sciences was precisely expounded for the first time by Aristotle in Book of his Physics. Aristotle expresses in this work that there is a certain knowledge of natural things which differs from the µ --the classical denomination of the philosophical treatise on material substances⁽²⁾. This alternative science does cover some aspects proper to natural beings, but it consists of a non-philosophical investigation because its proper method does not coincide with the philosopher's apodictical argumentation. Instead the researcher into this non-philosophical discipline makes use of a method which is the result of a combination of natural knowledge and mathematical measuring. So the matter of this science is physical by reason of the things it is concerned with --the natural bodies--, but it is formally mathematical by virtue of the process of quantification of their measurements This non-philosophical science, which has received no special name in Aristotelian epistemology, is a genuine physicomathematical discipline. It is neither a scientia propter quid, as on the contrary is the philosophy of nature itself, nor a branch of mathematics, for the science of the ens quantum does not deal with bodily substances⁽³⁾. Aristotle gives us an eloquent example of this kind of physicomathematical knowledge:

«While geometry investigates physical lines but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical»⁽⁴⁾.

Therefore not only is it inconsistent to attribute to pre-modern culture an ignorance of the distinction between philosophical and physicomathematical sciences, but also it is clear that Aristotle has bequeathed exact proof of the impossibility of confusion between them⁽⁵⁾.

Saint Thomas Aquinas went deeply into the Aristotelian distinction between physicoma-thematics and natural philosophy. He called physicomathematical disciplines by the explicit name of scientiae mediae because they lie halfway between physics or the philosophy of nature and mathematics⁽⁶⁾. St. Thomas said that the scientiae mediae are more mathematical than physical since they have more affinity with the method of the science of quantities than with that of the science of the movable being, so that their epistemic process is quasi materialiter in a physical sense but quasi formaliter in a mathematical one. Moreover Aquinas observed that halfway or intermediate sciences have a particular place in the context of the arbor scientiarum because of the application of mathematical measuring to the quantities predicated of natural bodies, as can be appreciated in the case of musical knowledge. In fact the musician's knowledge deals with the sensitive nature of sounds, but he must organize them by means of an algebraic distribution of their quantitative proportions⁽⁷⁾. Again the key to this epistemological Thomistic theory is to be found in Aristotelian philosophy, where St. Thomas noted the recourse of Aristotle to mathematical applications for research into movable substances whose essences and movements are studied by the physicist. But these mathematical applications to natural things have no reciprocity, as Aristotle saw, because it is impossible any transfer of physical methods to the study of mathematical entities⁽⁸⁾. For instance, I can measure geometrically the quantitative dimensions of a rock of marble, the earth's axis or the distance existing between Buenos Aires and New York, but, on the other hand, mathematical bodies are considered in a way that is independent of all sensitive nature for the natural constitution of physical bodies is entirely indifferent to the interest of geometry, the science of pure extensive quantity⁽⁹⁾.

The Thomistic distinction between physicomathematics and philosophical knowledge induces us to raise the gravest problem of modern epistemology: Is the concept of science unilaterally restricted to the significance of only one genus of intellectual cognition? Our answer to this question must be categorically negative for the notion of science is not limited univocally to any genus of intellectual knowledge. There are intermediate sciences between physics and mathematics not belonging to the philosophical field. There are philosophical and extraphilosophical sciences. There are theoretical or speculative sciences and practical sciences. There are sciences whose principles are evident to man's natural reason which differ from the sacred theology whose principles are derived from our faith in supernatural revelation. There are human sciences and there is an angelic science. There is also a divine science which is the substance of God himself because his intellection is the intellection of his own intellection, according to the masterly statement of Aristotle -- ⁽¹⁰⁾-- which brilliantly anticipates the conception of the ipsum intelligere subsistens of Thomistic metaphysics. Now all these meanings of science cannot be reduced either to an univocal notion or to an equivocal signification. Consequently the meaning of science is predicated analogically of all this diversity of scientific knowledge, a real and undoubted diversity that does not affect the ratio communis implied in themselves.

The acceptance of the analogical diversity of the sciences is the conditio sine qua non for a full understanding of the nonsensical restriction of epistemic knowledge to the human science and, of course, even less to the fields of physicomathematics. We must recognize this analogical diversity of sciences if we wish to find a coherent explanation of the existence and order of the universe. The existence and the order of this world are prior assumptions to the subject of physicomathematical investigation since they are taken for granted as the starting point of every piece of research on natural bodies and phenomena, but physicomathematical examination of material things cannot grasp either their first intrinsec principles and causes or their first extrinsec ones. Moreover the universe's existence and order allow and attract human scientific exploration, but this is so because a preceding non human science produced all things from nothingness, ex nihilo, and, besides this, endowed them with an orderly disposition and a knowability proportionate to our sensitive and intellective powers. In this respect physicoma-thematical attempts at discussing creation and the first cause of our world, such as Stephen W. Hawking has undertaken, are irremediably fruitless because the original emanation of caused things is a non-experimentable act, and even more it is also an act which escapes all mathematical measurement⁽¹¹⁾.

It cannot be demonstrated if there is a creative cause by means of physicomathematical experimentation and mathematical calculus. Hawking aims at the solution of the problem of God's place in a fully complete and self-contained universe, but he transpolates the cosmological conjecture as to a such an universe with a scientific proof of its original source; hence his inappropriate juxtaposition of a very human worry --what is the first cause of our world?-- with a question that discloses the powerlessness of physicomathematics to answer it⁽¹²⁾. It is known that several decades ago Sir Arthur Stanley Eddington made this mistake common to so many contemporary physicomathematicians⁽¹³⁾, but accurately noted their deceptive digressions⁽¹⁴⁾. Very far from these vain cosmological efforts so clearly identified by Eddington, the formal demonstration of creation belongs to the realm of metaphysics or primary philosophy, the science of being qua being and of first principles and causes of every effect. But we must be aware of an observation made by St. Thomas with regard to the human intelligence of creation, that is to say that man's natural reason is faced with severe limitations when he endeavours to understand the mystery involved in itself, for this mystery, as Aquinas now says speaking as a theologian, needs to be focused in the light of the Christian faith on the mystery of the Holy Trinity⁽¹⁵⁾.

The analogical predication of the notion of science also imposes the absolute primacy of theoretical over practical knowledge. Due to the fact that the object of the intellect is truth, as St. Thomas repeatedly said⁽¹⁶⁾, our soul's intellective capacity is primarily directed towards the act of apprehending an intelligible thing as such. For something to be the object of an intel-lectually directed operation, as is the case with all practical action exercised by spiritual substances, this is possible only after its intellectual apprehension. In suscribing to Aristotle's theory of man's speculative intellect which makes itself practical per extensionem⁽¹⁷⁾, Aquinas held unswervingly to this doctrine⁽¹⁸⁾. Even more, St. Thomas affirmed that the proper condition of the work carried out by the practical intellect of men must be a good perceived before by them as something true⁽¹⁹⁾. That is why in his commentary on the Aristotelian Nicomachean Ethics the Common Doctor declared that, although there is a practical truth, the good of the practical mind is not the absolute truth, nor the truth as such, but merely a truth relative to our right appetite⁽²⁰⁾. From this it follows that the genus of the practical sciences is predicated analogically as scientific knowledge, but the speculative or theoretical science remains the principal analogate of the concept of science.

It is obvious that human science, in the light of the analogical conception of epistemic knowledge, is an intellectual virtue of man's soul sealed by finitude. Our science is not an omniscience. Even though our intellect is potentially infinite because the mind's common object is being qua being, an object which comprises all that is or can be, we cannot know an infinite object in act. Aristotle said in his Physics that no infinite object can be perceived by ourselves⁽²¹⁾. St. Thomas insisted on the same view, but he added that the unknowability of an infinite object ought to be affirmed both by actual and by habitual intelligence because a finite potency is unable to become naturally actual by itself⁽²²⁾.

Human reason is open to the infinite. We cannot know any actual infinite in our wordly pilgrimage, but the potential infinitude of man's intellect promotes the acquisition of a broad scientific knowledge whose perfect archetype is not physicomathematics. The variety and hierarchy of the human sciences testify to the fact that their archetype, because of its perfection, is the genus of speculative philosophy and mainly metaphysics, the science of first principles and causes of all things caused as effects of the uncaused cause. This does not meant that metaphysics should be conceived as a scientia generalissima or as an omnicomprehensive discipline which should embrace all particular sciences as its parts. On the contrary, it means that metaphysics is the most perfect rational imitation of the antonomastical archetype of scientific knowledge: Gods's wisdom. God is wise in the most perfect significance of this term because his intellection is the same intellection of his own intellection, which is the pure act of his eternal substance and the uncaused creative cause of all caused beings, whereas metaphysics is a wisdom which participates analogically in the divine supreme science, given that man's intelligence is neither a subsistent act nor the essence ot his entity.

Many scientists reject that the notion of science can be predicated of any intellectual knowledge distinct from purely physicomathematical one. For them human science would be restricted to physicomathematics. Nevertheless this is a weak argument. Strictly speaking, it is an opinion divorced from the true scientific spirit. Physicomathematicians can offer us authoritative statements on the appearances of material things inasmuch as they are quantitative measurable bodies, but as physicomathematicians --inquantum huiusmodi, St. Thomas would say-- they cannot judge the intentional structure of science which informs human possible intellect in its condition as an intelligent in act. The formal consideration of this subject is reserved to logical and metaphysical speculation. But other great scientists inversely think to-day that physicomathematical sciences are not only compatible with phi-losophy and sacred theology, but are also a complement of our knowledge of the universe with regard to an integral fulfilment of human wisdom. However it will not be straightforward for our civilization to discover the genuine scope of human science unless men return to the magnificent Aquinas' epistemological principles. St. Thomas taught that the crowning of man's science is not the knowledge of our material and imperfect world, but the intelligence of the ipsum esse subsistens, the very essence of God, just as the saints of heaven obtain the highest wisdom from seeing Him face-to-face in their imperishable blessedness. Thus we can para-phrase St. Thomas by saying that the end of science is the everlasting happiness⁽²³⁾.

1. Fernand Van Steenberghen held this opinion among Neo-Scholastic philosophers in emphasizing «the ignorance of the distinction between philosophy and sciences» (F. Van Steenberghen, Épistémologie, 4th ed. [Louvain-Paris: Publications Universitaires-B. Nauwelaerts, 1965], p. 255. My translation). As we will see henceforth Van Steenberghen's view is untenable.

2. Cf. H. Bonitz, Index aristotelicus, s. v. , new ed. by O. Gigon, in Aristotelis opera, ed. by I. Bekker (Ber-lin: W. De Gruyter, 1971), vol. v: 835 a 28 - b 22.

3. Cf. Aristotle, Phys. 2: 193 b 22 - 194 a 7.

4. Phys. 2: 194 a 9-12, transl. by R. P. Hardie and R. K. Gaye, 5th rpt., in The Works of Aristotle Translated into English, under the Editorship of W. D. Ross (Oxford: Clarendon Press, 1970), vol. ii, ad locum.

5. Cf. J. A. Casaubon, «Sobre las relaciones entre la filosofía y las ciencias positivas»: Vniversitas (Buenos Aires) i (1967) Nº 1, 48-53; Id., «Las relaciones entre la ciencia y la filosofía»: Sapientia xxiv (1969) 89-122; and M. E. Sac-chi, «El pseudoconflicto entre las ciencias positivas y el saber filosófico»: Doctor Communis xliv (1991) 68-86.

6. «Et inde est quod de rebus naturalibus et mathematicis tres ordines scientiarum inveniuntur. Quaedam enim sunt pure naturales, quae considerant proprietates rerum naturalium, in quantum huiusmodi, sicut physica et agri-cultura et huiusmodi. Quaedam vero sunt pure mathematicae, quae determinant de quantitatibus absolute, sicut ge-ometria de magnitudine et arithmetica de numero. Quaedam vero sunt mediae, quae principia mathematica ad res naturales applicant, ut musica, astrologia et huiusmodi» (In Boeth. De Trinit. q. 5 a. 3 ad 6um, ed. by B. Decker, rpt. [Leiden: E. J. Brill, 1965], p. 188).

7. «Quae tamen [=scientiae mediae] magis sunt affines mathematicis, quia in earum consideratione id quod est physicum est quasi materiale, quod autem est mathematicum est quasi formale; sicut musica considerat sonos, non in quantum sunt soni, sed in quantum sunt secundum numeros proportionabiles, et similiter est in aliis. Et propter hoc demonstrat conclusiones suas circa res naturales, sed per media mathematica; et ideo nihil prohibet, si in quan-tum cum naturali communicant, materiam sensibilem respiciunt. In quantum enim cum mathematica communicant, abstractae sunt» (In Boeth. De Trinit., loc. cit., cit. ed., pp. 188-189). Cf. op. cit., ad 5um et 7um, ibid.

8. «Vt Philosophus docet in ii Physicorum, quaedam scientiae sunt pure mathematicae, quae omnino abstrahunt secundum rationem a materia sensibili, ut geometria et arithmetica: quaedam autem scientiae sunt mediae, quae sci-licet principia mathematica applicant ad materiam sensibilem, sicut perspectiva applicat principia geometriae ad line-am visualem, et harmonica, idest musica, applicat principia arithmeticae ad sonos sensibiles» (In I Post. analyt., lect. 41, n. 358, 2nd ed. by R. M. Spiazzi O. P. [Turin-Rome: Marietti, 1964], p. 299a). Cf. Aristotle's texts quoted above in notes 3 and 4.

9. «Principia mathematicae sunt applicabilia naturalibus rebus, non autem e converso, propter quod physica est ex suppositione mathematicae, sed non e converso, ut patet in iii Caeli et mundi» (In Boeth. De Trinit. q. 5 a. 3 ad 6um, p. 188). See Aristotle, De caelo 1: 299 a 13-17.

10. Aristotle, Metaphys. 9: 1074 b 33-34.

11. Cf. S. W. Hawking, A Brief History of Time: From the Big Bang to Black Holes, rpt. (New York-Toronto-London-Sydney-Auckland 1990), pp. 7, 9, 116, 141, 174, and passim.

12. «So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simple be. What place, then, for a creator?» (S. W. Hawking, A Brief History of Time, pp. 140-141).

13. «We are uneasy that there should be an apparently self-contained world in which God becomes an unnecessary hypothesis» (A. S. Eddington, The Nature of the Physical World [Ann Arbor: The University of Michigan Press, 1958], p. 281).

14. «We should suspect an intention to reduce God to a system of differential equations, like the other agents which at various times have been introduced to restore order in the physical scheme. That fiasco at any rate is avoided» (A. S. Eddington, The Nature of Physical World, p. 282).

15. «Cognitio divinarum Personarum fuit necessaria [...] ad recte sentiendum de creatione rerum» (Summ. theol. i q. 32 a. 1 ad 3um).

16. «Obiectum intellectus est universale verum» (Summ. theol. i-ii q. 2 a. 8 resp.). «Proprium autem obiectum in-tellectus est verum» (Summ. theol. i-ii q. 3 a. 7 resp.). Cf. Summ. theol. i q. 54 a. 2 resp., and ii-ii q. 25 a. 2 resp.

17. «[Mind practical] differs from mind speculative in the character of its end» (Aristotle, De anima 10: 433 a 14-15, transl. by J. A. Smith, 4th rpt., 1968, in The Works of Aristotle Translated into English, cit. ed., vol. iii, ad lo-cum).

18. «Secundum hoc autem differunt intellectus speculativus et practicus. Nam intellectus speculativus est, qui quod apprehendit, non ordinat ad opus, sed ad solam veritatis considerationem: practicus vero intellectus dicitur, qui hoc quod apprehendit, ordinat ad opus» (Summ. theol. i q. 79 a. 11 resp.). Cf. In III Sent. dist. 23 q. 2 a. 3 qla. 2a resp.; De verit. q. 3 a. 3 per totam; In VI Ethic., lect. 2, nn. 1124-1141; In III De anima, lect. 15, n. 820.

19. «Obiectum intellectus practici est bonum ordinabile ad opus, sub ratione veri» (Summ. theo.l i q. 79 a. 11 ad 2um).

20. «Bonum practici intellectus non est veritas absoluta, sed veritas "confesse se habens", idest concorditer ad ap-petitum rectum [...], quod sic virtutes morales concordant» (In VI Ethic., lect. 2, n. 1130, ed. by R. M. Spiazzi O. P. [Turin-Rome: Marietti, 1949], p. 310b). Cf. Aristotle, Ethic. Nicom. 2: 1139 a 26-31.

21. «Now the infinite qua infinite is unknowable, so that what is infinite in multitude or size is unknowable in quantity, and what is infinite in variety of kind is unknowable in quality» (Phys. 4: 187 a 7-9, cit. transl., ad lo-cum).

22. «Nec actu nec habitu intellectus noster potest cognoscere infinita, sed in potentia tantum» (Summ. theol. i q. 86 a. 2 resp.). Cf. op. cit., loc.cit., ad 4um; and Comp. theol. i 133.

23. «Vltima et perfecta beatitudo non potest esse nisi in visione divinae essentiae» (Summ. theol. i-ii q. 3 a. 8 resp.). See the commentary on this question of the Summa composed by I. M. Ramírez O. P., De hominis beatitudine. Tractatus theologicus ad Primam Secundae Summae theologiae (Qq. 1-5) S. Thomae Aquinatis concinnatus (Madrid: Consejo Superior de Investigaciones Científicas, 1947), t. iii: «De essentia metaphysica beatitudinis formalis».