© 2017, American Catholic Philosophical Quarterly, Vol. 91, No. 2 pp. 227–249 doi: 10.5840/acpq2017313114 Sebastian Izquierdo on Universals: A Way Beyond Realism and Nominalism? Daniel D. Novotný1 Abstract. The paper deals with the theory of universals of Sebastian Izquierdo (1601– 1681), a Spanish Jesuit author working in Rome, as he formulated and defended it in Disputation 17 of his major philosophical work The Lighthouse of Sciences (Pharus scientiarum), published in Lyon in 1659. Izquierdo's discussion centers around three questions: What is universality? Is there some intellect-independent universality? What is the nature of the intellect-dependent universality? Izquierdo's approach may be seen as a search for the third way between the (moderate) realism of the Thomists and the Scotists and the (conceptualist) nominalism of some Jesuits such as Pedro Hurtado de Mendoza (1578–1641). I. Introduction. The problem of universals, especially in connection with Plato's theory of forms or ideas, appeared in antiquity and has since then occupied the unceasing interest of Western philosophers.2 The 1This study is a result of the research funded by the Czech Science Foundation as project GA ČR 14-37038G "Between Renaissance and Baroque: Philosophy and Knowledge in the Czech Lands within the Wider European Context." It integrates a translation of my earlier paper: Daniel D. Novotný, "Teorie Obecnin Sebastiana Izquierdo (1601–1681)," in Univerzálie ve Scholastice, Studia Neoaristotelica Supplementum 1, ed. Daniel Heider and David Svoboda (České Budějovice: University of South Bohemia, 2012), 258–77. For help with the translation I am grateful to Světla Hanke Jarošová. I would also like to thank Stuart Nicolson and the editors of ACPQ for proofreading the text and the two anonymous referees for their useful comments on the paper. Needless to say, I alone bear the responsibility for any remaining mistakes and imperfections. Parts of the paper were presented at the international conference "Explorations in Baroque Philosophy" in České Budějovice (November 27th, 2015). 2According to Fung Yu-lan, A History of Chinese Philosophy (Princeton: Princeton University Press, 1934/1952), 205, the problem of universals was discovered and reflected by old Chinese thinkers as well. Fung Yu-lan bases his claim on a short treatise by Kungsun Lung (Gōngsūn Lóng; ca 325–250 BC), who allegedly uses the sign (zhǐ; finger, to point) in the sense of universal, which he opposes to concrete individuals (wù, thing). At present Fung Yu-lan's interpretation is mostly American Catholic Philosophical Quarterly228 source of the problem is the common human experience that some things are similar to one another or agree with one another in some way. According to some, the experience is to be explained by the existence of something unitary (i.e., a universal), which various things can share; according to others, it is not.3 These two basic positions occur in the history of philosophy in assorted modifications and versions.4 This paper focuses on the theory of universals of the important but less well-known Spanish Baroque author Sebastian Izquierdo.5 The main thrust of the paper is exploratory and expository, but it will gradually transpire that I find Izquierdo's theory to be unsatisfactory. We shall see that he attempts to find a way between the two theories of universals dominant at the time (vaguely resembling today's realism and nominalism but here to be understood contextually). While such a project might be praiseworthy as such, given the rejected: see Chris Fraser, "Pointing and Things," http://plato.stanford.edu/entries/school-names/ pointing.html. Even if Fung Yu-lan's claim were correct, the problem of universals has certainly not enjoyed the interest of Chinese philosophers since the ascent of the Han Dynasty (after 206 BC) and has fallen into oblivion. 3Cf., e.g., Michael J. Loux, Metaphysics: A Contemporary Introduction (London and New York: Routledge, 1998, 2002). 4For an introduction to the medieval debate over universals cf., e.g., Andrew W. Arlig, "Universals," in Encylopedia of Medieval Philosophy: Philosophy between 500–1500, ed. Henrik Lagerlund (Dordrecht: Springer, 2011), 1353–9. Post-medieval debates took specific shape; for a detailed pioneering study of a sample of representative Baroque authors see Daniel Heider, Universals in Second Scholasticism: A Comparative Study with Focus on the Theories of Francisco Suárez S.J. (1548–1617), João Poinsot O.P. (1589–1644) and Bartolomeo Mastri da Meldola O.F.M. Conv. (1602–1673)/Bonaventura Belluto O.F.M. Conv. (1600–1676), Bochumer Studien zur Philosophie 54 (Amsterdam: John Benjamins, 2014). 5There is no secondary literature about Izquierdo and his thought in English. For other languages, cf. Bernhard Jansen, Die Pflege der Philosophie im Jesuitenorden während des 17–18 Jahrhunderts (Fulda: Parzeller & Co., 1938), 45–8; Ramón Ceñal, "El P. Sebastián Izquierdo y su Pharus Scientiarum," Revista de filosofía (Chile) 1 (1942): 127–54; Ramón Ceñal, La Combinatoria de Sebastián Izquierdo (Madrid: Instituto de España, 1974); Ester Caruso, Pedro Hurtado de Mendoza e la Rinascita del Nominalismo nella Scolastica del Seicento (Firenze: La Nuova Italia, 1979), 107–10; José Luis Fuertes Herreros, "La Lógica de Sebastián Izquierdo (1601–1681): Un Intento Precursor de la Lógica Moderna en el Siglo XVII," Anuario filosófico 16 (1983): 219–63; Piero di Vona, I Concetti Trascendenti in Sebastián Izquierdo e nella Scolastica del Seicento (Napoli: Loffredo, 1994); Sven K. Knebel, Wille, Würfel und Wahrscheinlichkeit: Das System der moralischen Notwendigkeit in der Jesuitenscholastik 1550–1700 (Hamburg: Meiner, 2000); Jacob Schmutz, "Sebastián Izquierdo: De la Science Divine à l'Ontologie des états de Chose," in Sur la science divine, ed. Jean-Christophe Bardout and Olivier Boulnois (Paris: Presses Universitaires de France, 2002), 412–35; Jacob Schmutz, "Les Innovations Conceptuelles de la Métaphysique Espagnole Post-Suarérzienne: Les Status rerum selon Antonio Pérez et Sebastián Izquierdo," Quaestio 9 (2009): 61–99; Carlos Ortiz de Landázuri, "La Lógica Barroca de Sebastián Izquierdo: A Propósito de la Doble Cuantificación de la Proposición," in El Barroco Iberoamericano y la Modernidad: Actas del VI Simposio International del Instituto de Pensamiento Iberoamericano, ed. Ildefonso Murillo (Salamanca: Publicaciones Universidad Pontificia), 183–95. Cf. also the following footnote. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 229 difficulties associated with each of the theories, his solution appears to involve unclear and/or dubious elements. Unfortunately, it is beyond the possible scope of this paper to substantiate these misgivings of mine and see whether Izquierdo might find resources to respond to them. We will not delve deeper into the intricate network of metaphysical and epistemological issues underlying the theory exposed in this paper. My main aim is to draw the attention of historians of philosophy to Izquierdo (and other Hispanic authors of his time) with the hope that I might return to the topic on another occasion or that other scholars will become interested in exploring Izquierdo's work. Like Baroque art, Baroque philosophy and theology is immensely complex. Nothing may be left unsaid in Baroque works-the main current of thought always overflows into innumerable streamlets and rivulets. It may seem unnecessary to pay attention to these side streams. Unfortunately, only when we have rigorously examined the whole text on a given topic does the doctrine and argumentation of the selected Baroque author become apparent. Under well-known and-among the scholastics-generally accepted claims, terms, and quotations there is often concealed a widely different interpretation of familiar data and, without paying attention to detail, one can miss the main point. This paper is therefore based on a careful reading of the whole of Disputation 17 (De Unitate et Multitudine entium seu Rerum atque adeo Obiectorum Intellectus Humani) of Izquierdo's major philosophical work The Lighthouse of Sciences (Pharus Scientiarum), published in Lyon in 1659. The disputation is devoted-among other topics-to the nature, causes, and division of universals, but I will focus here mainly on Izquierdo's conception of the nature of universals (I will not deal in detail with questions of their causes and division). In the course of our considerations it will turn out that Izquierdo's account of universals uses a number of terms and concepts, such as objective concept, act-potency, suppositive-fictitious, substitute phantasm, etc., of which adequate investigation would require further separate studies since Izquierdo deals with them extensively only in other parts of his work The Lighthouse of Sciences. Given the limited scope of this paper, I leave the other parts of Izquierdo's writings aside and work with the above-mentioned concepts mostly only within the context of Disputation 17. II. Life and Work. Sebastian Izquierdo was born in 1601 in the little town of Alcaraz in the Castilian province of Albacete.6 (Another important Baroque 6I draw Izquierdo's biographical data from a thorough study: José Luis Fuertes Herreros, La Lógica como Fundamentación del Arte General del Saber en Sebastian Izquierdo: Estudio del Pharus Scientiarum (1659) (Salamanca: Ediciones de Universidad de Salamanca, 1981), 45–59. On mathematics at Colegio Imperial, cf. Eduard Recasens Gallart, "Geometrical Studies in 17th American Catholic Philosophical Quarterly230 Jesuit thinker, Antonio Rubio, 1548–1615,7 came from the same province.) At the age of twenty-two he entered the Jesuit order and after studies at the Jesuit college in Alcalá de Henares and the prestigious Colegio Imperial de Madrid, he taught philosophy and theology in both institutions starting in 1641 (and further also in Murcia, which belonged to the same province of Toledo).8 The environment at these colleges was brimming with renewed interest in the work of the Catalonian thinker Ramón Llull (1232–1315) emphasizing mathematics, methodology of science, and distinctive mysticism. At a ripe age, in 1659, Izquierdo published his monumental philosophical work The Lighthouse of Sciences.9 Two years later, he left for Rome in order to attend the eleventh general congregation and stayed there as a representative of the Spanish Jesuits. In Rome he befriended among others the well-known German polymath Athanasius Kircher, SJ (1601–1680). In 1664 he published there the first part of his Opus Theologicum iuxta atque Philosophicum de Deo uno ubi de Essentia et Attributis Divinis ubertim Disseritur, and in 1674 the second part. Izquierdo died in Rome in 1681, several months after Kircher and several months before Caramuel.10 Izquierdo was a versatile thinker, being an author not only of philosophical and Century Spain and their Counterparts in European Mathematics," in The Global and the Local: The History of Science and the Cultural Integration of Europe, ed. M. Kokowski (Proceedings of the 2nd ICESHS, Kraków, 2006). http://www.2iceshs.cyfronet.pl/proceedings.html 7For a basic bio-bibliographic overview cf., e.g., Daniel D. Novotný, "Rubio and Suárez: A Comparative Study on the Nature of Entia rationis," in Bohemia Jesuitica, ed. P. Čemus (Praha: Karolinum), 479–80. 8Among the outstanding professors there were, for example, the Belgian mathematicians and engineers Jean-Charles (Juan Carlos) della Faille, SJ (1597–1654) and André Tacquet, SJ (1612–1660), the French mathematician Claude Richard, SJ (1588–1664) and the Italian scholar Francisco Antonio Camassa, SJ (1588–1646). Other important authors connected with Colegio Imperial were the following Spanish philosophers and essayists: Gaspar Hurtado, SJ (1575–1647), Diego de Alarcón, SJ (1585–1634), Antonio Bernaldo de Quirós, SJ (1613–1668), Juan Martínez de Ripalda, SJ (1594–1648), and the German-Spanish essayist Juan Eusebio Nieremberg, SJ (1595–1658). 9The complete Baroque title: Pharus scientiarum ubi quidquid ad cognitionem humanam humanitus acquisibilem pertinet, ubertim iuxta, atque succinte pertractatur. Scientia de scientia, ob summam universalitatem utilissima, Scientificisque iucundissima scientifica methodo exhibetur, Aristotelis organum iam pene labens restituitur, illustratur, augetur, atque a defectis absolvitur. Ars demum legitima ac prorsus mirabilis sciendi, omnesque Scientias in infinitum propagandi, et methodice digerendi; a nonnullis ex Antiquioribus religiose celata; a multis studiose quaesita; a paucis inventa; a nemine ex propriis principiis haectenus demonstrata, demonstrative, aperte et absque involucris mysteriorum in lucem proditur quo verae Encyclopediae Orbis facile a cunctis circumvolvendus, eximio scientiarum omnium emolumento, manet expositus (Lugduni: Sumpt. Claudii Bourgeat, 1659). I give reference in the form "PS t. 3, d. 17, q. 4" for "Pharus Scientiarum, tractatus 3, disputatio 17, quaestio 4." 10Cf. John Glassie, A Man of Misconceptions: The Life of an Eccentric in an Age of Change (New York: Riverhead, 2012); Petr Dvořák and Jacob Schmutz, eds., Juan Caramuel y Lobkowitz (1606–1682): The Last Scholastic Polymath (Praha: Filosofia, 2006). Izquierdo on Universals: A Way Beyond Realism and Nominalism? 231 theological works, but also spiritual (mystical and ascetic) ones. The scope of his interests, as with the other above-mentioned Baroque authors, was impressive-from Jewish mysticism to mathematics.11 Like Kircher, Izquierdo belongs to the exuberant Renaissance and Baroque tradition, which strived to compose a universal encyclopaedia conserving and methodically developing all human knowledge. Unlike Kircher, however, Izquierdo was a more austere and precise thinker, interested in the scientific and not the magical or fantastical aspects of the combinatorial encyclopaedic tradition.12 A brief glance at the contents of The Lighthouse of Sciences reveals that the work is planned in an original way, quite unlike the plan of, for example, Suárez's Disputationes Metaphysicae and other typical Baroque Cursus Philosophici, which is indicative of substantial difference in doctrine and method.13 Tractatus I: De origine et natura intellectionis humanae (Disputatio 1–2) Tractatus II: De accidentibus intellectionis humanae (Disputatio 3–7) Tractatus III: De obiecto intellectionis humanae (Disputatio 8–17) Tractatus IV: De termino, propositione atque argumentatione. . . . (Disputatio 18–20) Tractatus V: De scientia humana . . . (Disputatio 21–22) Tractatus VI: De instrumentis, regulisque sciendi . . . (Disputatio 23–33) Izquierdo's point of departure is clearly an epistemological one: the focal philosophical topic is the process/product of human cognition, the so-called intellectio.14 As the plan indicates, Izquierdo belongs among those Baroque scholastics 11Historians of mathematics remember him especially in connection with combinatorics, to which he devoted Disputation 29 (De Combinatione). He was the first to discuss the number of k-combinations from a given set of n elements. Cf. Donald Ervin Knuth, The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees: History of Combinatorial Generation (Boston: Addison-Wesley Professional, 2006), 60–1. 12The roots of this heterogeneous tradition can be found in the ars memorativa of the ancient world and the later medieval ars combinatoria. Other Baroque representatives were, for instance, Johann Heindrich Alsted (1588–1638), Jan Ámos Komenský (1592–1670) and Kašpar Knittel, SJ (1644–1702). The tradition was also important for René Descartes (1596–1650), Francis Bacon (1561–1626) and Gottfried Leibniz (1646–1716). Cf. Paolo Rossi, Logic and the Art of Memory: The Quest for a Universal Language, trans. Stephen Clucas (London: Athlone Press, 1983/2000), esp. chs. 5–6. 13Cf. José Luis Fuertes Herreros, "Presentia y Límites de Francis Suárez en el Pharus Scienciarum (1659) de Sebastián Izquierdo," Cuadernos Salmantinos de Filosofía 8 (1981): 175–90. 14More precisely, the common meaning of the word is the cognitive process/product of the human intellect, but in Izquierdo (as in other empiricists) the operation of the intellect is so closely interconnected with the operation of the senses that the two merge. Izquierdo deals American Catholic Philosophical Quarterly232 who were bred in the cultural context of traditional scholastic Aristotelianism, but-like Descartes and Caramuel-were not Aristotelians themselves.15 II.A. What is Universality? Izquierdo first characterizes a universal (universale in Latin) as "one in many" (unum in multis).16 As I have already indicated, universals become the focus of his systematic thought in Disputation 17, questions 4–8 (see also the appendix). The following sections of the present paper are devoted to questions 4 (section II.A), 5 (section II.B), and 6 (section II.C). In these three questions Izquierdo addresses the following fundamental problems: 1. What is universality? 2. Is there some intellect-independent universality? 3. What is the nature of the intellect-dependent universality?17 Apart from the three questions devoted to universals Izquierdo in Disputation 17 refers to several other parts of the The Lighthouse of Sciences, especially to question 3 of Disputation 2 (De Natura Intellectionis Humanae), which deals with the problem of how we cognize things inaccessible to the senses,18 and to Disputation 12 (De Ente Rationis), which is concerned with beings of reason under which universals are traditionally classified.19 Let us now have a closer look at how Izquierdo addresses the first problem, i.e., what is universality? The word "universal" (universale), he points out, is used in four meanings: with the nature of sensory and intellective cognition in the extensive Disputations 1 and 2, the investigation of which is beyond the scope of this paper. 15That holds, I believe, despite Izquierdo's intention to defend Aristotle, expressed in the full title of The Lighthouse of the Sciences, cf. n. 9, and also in Izquierdo's argument against nominalism from Aristotle's authority, cf. n. 49. It is interesting to note that in the introduction Izquierdo makes a laudatory mention of Instauratio Magna and Novum Organon (1620) by Francis Bacon (1561–1626), one of the founders of the modern anti-scholastic tradition, though with a reproach of incompleteness: "Denique, Franciscus de Varulamio Anglus, in opere, cuius titulus Instauratio magna, praesertim in secunda eius parte dicta, Organum novum multa de universali sciendi methodo scripsit seu potius scribere caepit. Opus enim delineatum et inchoactum dumtaxat reliquisse videtur," PS Praef. 16PS t. 3, d. 17, Intr., n. 1. 17"Quaestio 4: Quid sit universale? Quaestio 5: Utrum independenter ab operatione intellectus detur a parte rei universale, aut aliqua unitas multis communis, atque adeo minor unitate numerica, qua unum est in se quodvis singulare? Quaestio 6: Qualis sit unitas ab intellectu oriunda, qua constituitur universale? Qualis item aptitudo eius ad essendum in pluribus et ad praedicandum de illis?" PS t. 3, d. 17, q. 4–6. 18PS t. 1, d. 2, q. 3. 19In this paper I do not take these further texts into adequate consideration-they would deserve a separate study of at least the same extent as the present one. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 233 1. With respect to causal operation, i.e., of God, the heavens and the planets; 2. With respect to signification, i.e., of words (vox) such as "man" and "animal"; 3. With respect to representation, i.e., of universal acts of cognition signified by universal words; and 4. With respect to predication/existence, i.e., of "an objective concept cognized by a universal cognitive act."20 We speak of universals in the proper sense of the word only in the last case, i.e., with respect to predication/existence. The fact that Izquierdo mentions objective concept indicates that he does not espouse the radical position of Baroque thinkers such as Pedro Hurtado de Mendoza (1578–1641), Rodrigo de Arriaga (1592–1667), and Francisco de Oviedo (1602–1651), who refused to posit objective concepts formed by objective precision (see below). What are objective concepts and objective precision? In brief: Baroque authors had different views on that, although we can say that the standard conception of the objective concept at the time was that it is an object as conceived by the intellect and contrasted with the formal concept conceived as an act (= form) of the intellect. Objective precision means an intentional "cutting off" or "cutting out" of one metaphysical part of an individual from another part. For instance, human and animal are metaphysical parts of Peter, which our intellect can conceive in an intentional "cutting off," i.e., in precision, from Peter, Mary, and other individual humans.21 Izquierdo cites several passages from Aristotle,22 from which scholastic authors "generally deduce . . . the following two definitions . . . of universal": 20"Quatuor potissimum modis solet vox universale usurpar Primo pro universali in causando, quale est causa aut ad omnes aut ad plerosque effectus concurrens, ut Deus, coeli, planetae et ceterae huiusmodi. Secundo pro universali in significando, quale est vox ad plura significanda se extendes, uti istae, vivens, animal, homo, et ceterae similes. Tertio pro universali in repraesentando, quale est cognitio humana voci universali respondens et eadem plura, quae talis vox significat . . . Quarto denique pro universali in praedicando aut etiam in essendo, quale est conceptus obiectivus per cognitionem universalem cognitus, per vocemque universalem significatus. Ergo in praesenti de universali hoc quarto modo usurpato nobis sermo est," PS t. 3, d. 17, n. 4. 21As with any scholastic term much more would need to be said to avoid oversimplification. For some recent discussions of conceptus obiectivus with further references, cf., e.g., Wouter Goris, Tranzendentale Einheit (Leiden: Brill, 2015), 412 ff; Claus A. Andersen, Metaphysik im Barockscotismus: Untersuchungen zum Metaphysikwerk des Bartholomeus Mastrius, mit Dokumentation der Metaphysik in der scotistischen Tradition ca. 1620–1750 (Amsterdam: John Benjamins, 2016), 268 ff. 22Metaphysics VII (textus 45): "Hoc enim dicitur universale, quod pluribus inesse natum est," and Perihermeneias (cap. 5): "Dico autem universale, quod de pluribus natum est praedicari." American Catholic Philosophical Quarterly234 [D1] A universal is that which can exist in many. [D2] A universal is that which can be predicated of many. A universal must firstly be capable of being in the many or belonging to the many, and only then to be capable of being predicated of the many: hence the first definition, called the essential, expresses the essence of a universal; the second, called the descriptive, expresses the proper attribute.23 By introducing these definitions Izquierdo has accomplished the task of addressing the introductory problem of the question. He then proceeds by briefly characterizing his conception of how a universal relates to individuals: "A universal is one belonging to many in such a way that formally or logically it is found in individuals as the same, but really or physically it is found in them as distinct and multiplied. That is the obvious meaning, supported both by Aristotle's words and by experience."24 More specifically, if we take the universal animal as an example: "[A] Animal abstracted from man and beast claims the same objective concept in our mind and is therefore signified by the same word . . . [B] Nevertheless the animal of man and the animal of beast, taken as such, really differ both from each other and from the common animal. There will be more on this later."25So far, there is nothing distinctive in what Izquierdo says. The claim that a universal is "to be formally or logically found in individuals as the same, but really or physically found in them as distinct and multiplied" is acceptable to all participants in the scholastic debate. In question six (see section II.C), however, he explains more clearly what he means, which makes his views controversial. At the close of question four Izquierdo briefly mentions reasons why aggregates, physical compounds, and the divine essence are not part of the extension of the concept universal. Since the discussion of this issue is not crucial to the main point of this paper, I will merely report Izquierdo's reasons for the sake of completeness, without attempting to explain and evaluate them: 23"Ex quibus has duas definitiones universalis desumunt Authores communiter. Universale est unum potens esse in pluribus. Universale est unum potens praedicari de pluribus. Quarum primam essentialem, secundam descriptivam dicunt, quia prius est in natura universali posse esse in pluribus sive eis convenire, quam posse praedicari de pluribus; atque ita primum essentia, secundum vero proprietas universalis reputatur," PS t. 3, d. 17, n. 40. 24"Igitur universale ita est unum conveniens pluribus ut formaliter seu logice idem reperiatur in singulis; tametsi realiter seu physice distinctum in singulis, multiplicativumve inveniatur. Hoc enim prae se ferunt verba Aristotelis et experientia manifestat," PS t. 3, d. 17, n. 41, emphasis added. 25"Eundem quippe conceptum obiectivum vendicat sibi in mente nostra, tandemque subinde voce significatur animal abstractum ab homine et bruto . . . ; tametsi animal hominis et animal bruti sumpta seorsim tum ab se invicem, tum ab animali communi utrique realiter distincta sint. De quo plura in sequentibus," PS t. 3, d. 17, q. 5, n. 41. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 235 □ An aggregate is not a universal, even though it can be in the many, because it lacks unity: it is represented by several concepts; □ A physical compound is not a universal, even though it is one and can be in the many, because it is not formally or logically identical in them; □ The divine essence is not a universal because it is not multiplied: even though it belongs to the three divine persons, it remains the same in them.26 Concerning what Izquierdo has said so far in question four, there is allegedly full agreement among almost all the scholastics of the time and no one-not even the so-called nominalists-took the nominalist position, according to which universals are merely words (for being a nominalist in the Baroque era meant maintaining a number of various philosophical and theological theses, not only those concerning universals).27 II.B. Is There Some Intellect-Independent Universality? Having defined universals, Izquierdo asks in question five whether universality is found in reality, independently of the operation of the intellect.28 There are allegedly four main answers to the question. Aristotle ascribes (as Izquierdo stresses) the first position to Plato: T1. (Aristotle's Plato) A universal is a nature, which exists as separate from individuals; it is common to the individuals, which exist by participating in it.29 26"Itaque defectu unitatis aggregatum plurium entium cum distinctione conceptorum non est universale, etsi in plura ipsa divisibile seu multiplicabile sit. Defectu autem identitatis in singulis compositum physicum non est universale, quia licet sit unum et multiplicabile in plura, nimirum in partes, ex quibus constat; non tamen ita ut maneat idem in singulis formaliter seu logice. Defectu denique multiplicationis in plura essentia divina non est universalis, tametsi una sit et conveniens pluribus, nempe tribus personis, eademque manens in singulis," PS t. 3, d. 17, q. 5, n. 41. 27Izquierdo writes: "Manifeste apparet praeter voces communes pluribus conceptus obiectivos universales per voces ipsas significativos et rebus indistinctos necessario asserendos esse, ut perspicue docet Aristoteles . . . et cum eo S. Thomas caeterique omnes Scholastici contra quosdam paucos Nominales ponentes universalitatem dumtaxat in vocibus, in quorum sententia refellenda non immoror, utpote, quae iam ab omnibus etiam Nominalibus, seu Nominalium quoad alia sectatoribus despecta prorsus est. Videantur Conimbricenses In Praef. Porf. q1a2," PS t. 3, d. 17, q. 5, n. 41. The self-conception of Baroque philosophical and theological schools is one of many interesting topics that would deserve extended investigation. 28Izquierdo asks the question by means of the concept of the "lesser than numerical unity": "Utrum independenter ab operatione intellectus detur a parte rei universale, aut aliqua unitas multis communis, atque adeo minor unitate numerica, qua unum est in se quodvis singulare?" 29"Aristoteles . . . et alii Scholastici, Platoni adscribit quamdam sententiam asserentem dari re ipsa ante intellectus operationem naturas universales . . . separatas a singularibus, et eis communes, American Catholic Philosophical Quarterly236 The second position was, "according to many Thomists" as Izquierdo points out, espoused by Duns Scotus: T2. (Thomistic Scotus) A universal is a nature, which is common to individuals, in which it is formally ( formaliter) and really (ex natura rei) distinct from individual differentiae, and is one in itself independently of the intellect.30 The third position, which was alleged by Izquierdo to have been taken by Cajetan and influenced by Duns Scotus: T3. (Scotified Cajetan) A universal is a nature which is common to individuals only in the intellect, because only in the intellect is it positively one. The nature can also be negatively one, independently of the intellect; such unity, however, is neither universal nor singular.31 The fourth position is, according to Izquierdo, the one taken by Aquinas and espoused by "all other scholastic philosophers and theologians": T4 (Aquinas and everyone): A universal is a nature (natura), which is common to individuals only in the intellect and has no other "lesser than numerical unity" independent of it.32 According to Izquierdo, T1 is an "absurd doctrine, unworthy of such a philosopher as Plato." Izquierdo labels the kind of universal ascribed to Plato as "chimaeric" (by which he means "self-contradictory") and presents two arguments against it: (1) according to T1 universals are on the one hand separate from individuals, but on the other hand they are common to them, therefore identical with them, and therefore inseparable. That is a contradiction. And (2) universals are either uncreated or created. If uncreated, they are part of God utpote a quarum participatione ipsa singularia habent esse. Tametsi ab hac sententia tanquam absurda tantoque Philosopho indigna, multi conantur variis modis vindicare Platonem, ut sunt Iamblichus . . . S. Augustinus et alii," PS t. 3, d. 17, q. 5, n. 45. Cf., e.g., Aristotle's Metaphysics I.6 (987a29–988a17) and Aquinas's Commentary on the Metaphysics I.10. 30"Secunda sententia, quam multi Thomistae attribuunt Scoto . . . naturam pluribus communem formaliter ex natura rei esse distinctam a differentiis eorum, formaliterque subinde ex natura rei esse in se unam ante intellectus operationem. Quo nihil videtur desiderari quominus a parte rei independenter ab intellectu detur universale," PS t. 3, d. 17, q. 5, n. 46. 31"Sed vero Cajetan . . . sequitur Scotum . . . , cum quo etiam sentiunt Scotistae . . . Dicunt itaque naturam specificam in signo ante contractionem per differentias numericas unitatem quamdam negativam habere ante omnem intellectus operationem, in eo omnino consistentem, quod talis natura pro tunc non est singularis; verum non esse universalem, quia ad universalitatem requiritur unitas positiva," PS t. 3, d. 17, q. 5, n. 47. Izquierdo's interpretation of Cajetan is probably mistaken. 32"Reliqui tamen omnes Doctores tam Theologi quam Philosophi unanimiter asseverant cum sancto Thoma ST Iq29a7 [sic] et q85a11. Saepeque alibi; ante operationem intellectus nullatenus dari universale, aut unitatem aliquam multis communem minorem unitate numerica," PS t. 3, d. 17, q. 5, n. 45–8. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 237 and God is therefore universal and capable of being contracted by other beings. That is "ridiculous." If universals are created, they are created by individual acts, as are individuals. That is for Izquierdo also unacceptable.33 Izquierdo rejects T2 on the grounds that it is not possible for a nature to retain a unity independently of the intellect if it is to be common to many. Izquierdo labels the alleged weaker unity of nature, designated by Scotists as "formal," and "chimaeric" as well, and for detailed argumentation against this kind of unity he refers the reader to question five of Disputation 13 (De identitate et distinctione entium seu rerum atque adeo obiectorum intellectus humani).34 In this paper we leave this question aside, only taking note of its title: "Whether really identical formalities [metaphysical parts] of a being . . . are or can be . . . distinct prior to cognition and therefore independently of it"35 Izquierdo's words "are or can be" may indicate that Izquierdo implicitly rejects not only the Scotistic theory of formal distinction, which claims that the metaphysical parts of an individual are actually distinct prior to the operation of the intellect, but also the Thomistic theory of virtual distinction, according to which these parts are distinct only potentially.36 But in Disputation 17 Izquierdo does not speak of the virtual distinction explicitly; he expressly rejects only the formal distinction, or, as we can see from the formulation of T4, any "lesser than numerical distinction" independent of the intellect. Izquierdo does not agree with T3 either, because negative unity independent of the intellect is allegedly impossible. Izquierdo criticizes T3 for assuming a formal distinction between the nature and the individual differentiae; however, he had already rejected this type of alleged distinction in connection with T2.37 33"Propositio 1: Universale illud Platoni adscriptum . . . omnino chimericum est. [1] Primo, quia natura realiter a singularibus separata . . . ex una parte debet realiter esse ab illis distincta, . . . ex alia vero indistincta, quia ponitur communicabilis ipsis, siquidem vero natura specifica non aliter quam per identitatem communicatur individuis. Quae duo contradictoria sunt. . . . [2] Secundo, aut illa natura realiter a singularibus separata est quidem increatum aut quid creatum? Si quid increatum erit Deus et consequenter Deus erit quid universale per caetera entia contrahabile. Quod est ridiculum. Si vero creatum, id nequit non quid singulare per singularem actionem factum, ut caetera entia creata," PS t. 3, d. 17, q. 5, n. 49–50. 34"Propositio 2: Natura specifica in nullo signo potest habere ex natura rei unitatem, qua reddatur una communis pluribus, atque adeo [non est] universalis ante intellectus operationem. . . . chymericam omnino esse distinctionem ex natura rei formalem, quam ipsi [sc. Scotistae] ponunt inter formalitates identificatas realiter," PS t. 3, d. 17, q. 5, n. 51. 35"Utrum formalitates eiusdem entis, sive increati sive creati, realiter identificatae formaliter ex natura rei sint, aut esse possint distincta ante omnem sui intellectionem, atque adeo independenter ab illa?" PS t. 3, d. 13, q. 5. 36The interpretation I present here is not quite certain-its verification would require a careful study of Izquierdo's doctrine of distinctions. 37"Propositio 3: Unitas negativa, quam Caietan et alii ponunt in natura specifica ante intellectus operationem etiam est impossibilis. Quia supponit distinctionem formalem ex natura rei American Catholic Philosophical Quarterly238 What is left is position T4, which Izquierdo himself advocates. He devotes the whole of question six to various versions of it, as well as a defence of his own version. II.C. What is the Nature of the Intellect-Dependent Universality? Status quaestionis. According to T4, which Izquierdo espouses, a universal is a nature which is common to individuals only in the intellect, and there is no "lesser" unity independent of the intellect. Now we can ask: What kind of unity does this universal (generated by the intellect) have? What is the disposition (in the sense of susceptibility or propensity) of the universal for existence-in-many and predicability-of-many?38 Izquierdo presents two main ways of approaching the question: The first opinion is the one of nominalists and modernists who do not admit objective precision; they believe that a universal is generated by the intellect, when it cognizes and grasps many objects at once by a single act of cognition confusedly, without discerning the plurality. By such an act of cognition the many objects appear to be one, not because a unity deriving from them is represented, but because the plurality is represented confusedly, the confusion being fully on the part of the act of cognition. From this the conclusion is drawn that universal unity is in no way something cognized . . . , derived from the object, but the act of cognition itself, by which many confusedly cognized objects are externally designated as one. This position is, together with nominalists whom they report, taken by Hurtado, . . . Arriaga . . . [and] Oviedo.39 Hurtado, Arriaga, and Oviedo (also nominalists) therefore answer the question of what kind of unity a universal has by saying that a universal is one in so far as the act of the intellect that generates it is one. The intellect does not generate inter naturam specificam et differentias singularium, cum quibus est idem, quam distinctionem chymericam statuimus. In quo amplius non oportet immorari," PS t. 3, d. 17, q. 5, n. 52. 38"Quaestio 6: Qualis sit unitas ab intellectu oriunda, qua constituitur universale? Qualis item aptitudo eius ad essendum in pluribus et ad praedicandum in illis?" PS t. 3, d. 17, q. 6, n. 54. 39"Prima sententia est Nominalium et Recentiorum non praescindentium obiective; qui censent tunc ab intellectu nostro effici universale, quando ille unica cognitione plura simul cognoscit atque complectitur obiecta, adeo tamen confuse ut eorum non discernat pluralitatem: perinde enim apparere ea plura per talem cognitionem ac si essent unum, non quidem, quod unitas alia ex parte eorum repraesentetur, sed quod ipsa eorum pluralitas repraesentatur confuse, tota confusione se habente ex parte cognitionis. Unde concludunt: unitatem universalis neutiquam esse quid cognitum . . . ex parte obiecti se habens, sed esse cognitionem ipsam a qua dumtaxat plura illa confuse cognita extrinsece denominat unum. Ita cum nominalibus a se relatis Hurtado . . . Arriaga . . . Oviedo," PS t. 3, d. 17, q. 6, n. 55. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 239 an objective concept; universality applies only to the act of cognition, i.e., the formal concept. The nominalists' answer to the question of what the disposition of the universal to existence-in-many and predicability-of-many is follows from the former:40 "[Hurtado, Arriaga, and Oviedo] therefore believe that a universal is one, common to many, capable of existing in many and capable of being predicated of many by the same single act of cognition."41 Izquierdo criticizes the position later on in connection with proposition P1 (see below). The second approach is according to Izquierdo represented by Thomists and other thinkers who admit objective precision: "The opinion of Thomists and other authors who advocate objective precision or take it as unquestionable is more common: a universal is generated by an act of cognition by which many are represented as one by means of a unity of reason which is derived from the object cognized by the act."42 The authors representing the second approach therefore answer the question of the nature of the unity of the universal by saying that it is a unity of reason. As we will see, Izquierdo addresses the problem in detail later on in connection with proposition P3. However, the authors representing the second approach are not consonant on the question of the disposition of the universal to existence-in-many and predicability-of-many. The specific controversial questions Izquierdo asks in this context concern [A] whether the unity of reason proper to universals is fictitious or not, [B] whether a universal can be generated only by negative abstraction or also by positive one, and [C] what the ability (aptitudo)43 of a universal to exist in many and be predicated of many consists in.44 Izquierdo outlines the basic features of his own version of T4 in four propositions: 40An anonymous referee posed a question here: "What does talk of 'existing in many' mean for nominalists?" I would also like to know the answer to this. 41"Qui consequener arbitrantur ab eadem cognitione, a qua universale habet esse unum, habere quoque esse commune pluribus, atque adeo aptum inesse illis ac praedicari de illis," PS t. 3, d. 17, q. 6, n. 55. 42"Communior tamen tum Thomistarum tum caeterorum, qui praecisiones obiectivas aut expresse defendunt aut indubitate supponunt, sententia est, universale per cognitionem fieri repraesentantem plura ut unum unitate quadam rationis ex parte obiecti se habente, per ipsamque cognitionem cognitam," PS t. 3, d. 17, q. 6, n. 56. 43As far as I can say, this is what elsewhere Izquierdo calls dispositio. 44"[A] Plerique tamen censent, aut certe supponunt, huiusmodi unitatem rationis, qua universale constituitur, fictitiam esse, sicut sunt in sententia eorum omnia entia rationis. [B] Plerique item arbitrantur eiusmodi cognitionem repraesentantem plura ut unum eo ipso esse abstractivam seu praecisivam conceptus obiectivi adunati a differentiis singulorum quibus ille convenit; quasi nequeant plura sub unico conceptu adunati nisi per cognitionem abstrahentem seu praescindentem conceptum ipsum a differentiis singulorum. Quam abstractionem debere esse negativam nonnulli censent. Alii positivam etiam admittunt, ut non minus idoneam ad universalem efficiendum. [C] Iam vero aptitudo, quam universale habet, ut sit in multis et praedicetur de illis, ab omnibus paene Doctoribus huius factionis ponitur in respectu quodam rationis ipsius American Catholic Philosophical Quarterly240 P1. A universal is not constituted by a confused act of cognition.45 P2. A universal has an objective unity generated by means of a substitute phantasm.46 P3. Universal unity is a suppositive unity of reason, not a fictitious one.47 P4. The disposition of the universal to existence-in-many and predicability-of-many can be the subject of further "philosophizing."48 P1 is directed against the nominalists, P2 addresses the question of the nature of universal unity and how we can cognize universals when there are none in reality, P3 is concerned with question [A] above and P4 with question [C]. Izquierdo had not forgotten about question [B], for he deals with it in the socalled Consequences (Confectaria), namely in Consequence 3. Let us now examine the individual propositions P1–P4 more closely. P1: A Universal is Not Constituted by a Confused Act of Cognition. Against the nominalist claim that universals consist in (or are) a confused act of cognition, Izquierdo presents six arguments. The fourth of these arguments charges the nominalist conception of universal with being incompatible with Aristotelianism.49 The sixth argument against nominalism is in Izquierdo's discussion of the substitute phantasm (see below).50 Let me now report on his other arguments. The first argument can be summarized as follows: In order for a universal to arise, it is necessary for many objects to appear as one; the individuality of the act of cognition itself is not enough to unite them. (Even the nominalists universalis ad sua inferiora facto per cognitionem alteram comparativam. De quibus omnibus singillatim dicemus," PS t. 3, d. 17, q. 6, n. 56. 45"Universale nullatenus constitui potest per cognitionem attingentem plura confuse absque alia unitate per ipsam cognitam et ex parte obiecti se habente, prout cum Nominalibus putant Recentiores nuper relati," PS t. 3, d. 17, q. 6, n. 57. 46"Unitas constituens universale obiectiva est, ea nimirum, quam sortiuntur plura cognita, ut unum ab uno phantasmate substituto, in quo ita cognoscuntur a nobis," PS t. 3, d. 17, q. 6, n. 64. 47"Unitas constituens universale est unitas rationis non ficta, sed suppositiva, iuxta doctrinam supra statutam disp. 1 q. 3 confect. 7," PS t. 3, d. 17, q. 6, n. 71. For detail Izquierdo refers to his Disputation 12. 48"De potentia, quam universale habet ad essendum in multis et ad praedicandum de illis, perinde ac de aliis potentiis philosophandum est," PS t. 3, d. 17, q. 6, n. 74. 49"Quarto; universale ita debet esse unum commune pluribus, ut idem formaliter seu logice reperiatur in singulis . . . sed hoc cum sententia Adversariorum constare non potest, quia neque plura confuse cognita reperiuntur in singulis, neque eadem cognitio confusa plurium potest ad singula terminari. Ergo cum sententia Adversariorum universale Aristotelicum et verum non potest constare," PS t. 3, d. 17, q. 6, n. 62. 50"Sexto. Ex dicendis circa sequentem haec propositio confirmabitur," PS t. 3, d. 17, q. 6, n. 63. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 241 themselves admit this, since if any individual act cognizing many objects as such generated a universal, then God and other spiritual beings would only cognize universals, which is "absurd.") For many objects to appear as one, it is necessary to cognize their unity. But we can only cognize their unity if there is some unity on the part of the objects. In other words, universal unity does not consist in a (confused) act of cognition but derives from the objects; QED. The nominalists can defend their position as follows: For many objects to appear as one, it is enough to cognize them by a confused act of cognition, which does not distinguish among them. Izquierdo responds: The confusedness of this act of cognition is either caused by the fact that many appear as one or not. If the former holds, then the unity derives from the very object of this act of cognition. If the latter holds, then many do not in fact appear as one, since without unity nothing can appear as one.51 Izquierdo concludes that in order for a universal to be generated, some unity on the part of the objects is necessary. Universal unity cannot consist solely in the unity of the act of cognition, as the nominalists claim. Izquierdo's second argument: If universals consist in (are constituted by) an act of cognition, they are generated by any individual act-i.e., whenever we think of something that is many in reality. It cannot matter whether it is a clear act or a confused one, since clarity and confusedness add nothing to unity. That, however, is an absurd consequence. Universals therefore cannot be reduced to acts of cognition, not even confused ones; QED.52 The third argument: Just as an intentional distinction cannot be based on a real distinction (but only on real identity), the intentional unity of a universal cannot be based on the real unity of an act of cognition, as nominalists believe; QED.53 51"Probatur primo. Quia nisi plura appareant unum cognoscenti, non sit universale, quantumvis ea per unicam cognitionem tangantur, ut Adversarii ipsi fatentur (Alioquin Deus et alii intuentes per unicam cognitionem plura ut plura tangentes, universale compingeret, quod est absurdum). Sed impossibile est plura apparere unum, nulla ipsorum apparente unitate, siquidem unum ex suo conceptu per unitatem constituitur, ut notum est: ergo ut fiat universale, alia unitas plurium debet ex parte obiecti se habere distincta a cognitione. . . . Dicunt: ut plura appareant unum satis esse, quod attingantur per cognitionem confusam non discernentem differentias. Sed contra. Aut ista confusio cognitionis in causa est, ut plura cum unitate appareat, aut secus. Si primum, ergo ex parte obiecti talis cognitionis est unitas. Si secundum, ergo plura non apparent per illam unum, quia nequeunt apparere unum sine unitate," PS t. 3, d. 17, q. 6, n. 58. 52"Secundo; si constituitur unice universale per unitatem cognitionis . . . quoties per unicam cognitionem quantumvis claram plura attingantur, efficietur universale, siquidem nec claritas detrahit, nec confusio addit aliquid unitatis. Quod tamen contra omnes est absurdum," PS t. 3, d. 17, q. 6, n. 60. 53"Tertio; distinctio rationis, qua ab intellectu distinguuntur, quae realiter sunt indistincta, nullatenus potest consistere in distinctione reali . . . Ergo neque unitas rationis, qua ab intellectu American Catholic Philosophical Quarterly242 The final argument: The (real) foundation on the basis of which our intellect generates a universal is similarity. We either form specific universals out of similar individuals or generic universals out of similar species. According to nominalist doctrine, generic universals could not be formed, because if we cognize Peter and Mary confusedly, the result is the human, not the rational animal, and if we cognize Buddy and Max confusedly, the result is the dog, not the irrational animal. The similarity of two different genera will therefore not be evident, and it will not be possible to abstract a genus.54 So much for Izquierdo's explicit criticism of what he calls nominalism. Now we shall examine his positive doctrine contained in the remaining three propositions. Izquierdo devotes less space to the exposition and defence of his conception than he does to the criticism of the doctrine he rejects. That is probably because he had already presented elements of his position in other parts of his The Lighthouse of Sciences (e.g., in Disputations 2 and 12). P2: A Universal has an Objective Unity Generated by Means of a Substitute Phantasm. According to Izquierdo, a universal has an objective unity due to the substitute phantasm. What does that mean? The concept of substitute phantasm is laid out in question 3 of Disputation 2. The main point of the question is that we cognize everything that our intellect cognizes by means of alien species (species alienas) as sensible things (e.g., an angel as a boy).55 These alien species are therefore substitute phantasms, which we need in order to cognize something not directly accessible to the senses. For example, from the vital functions of our adunatur, quae realiter sunt distincta, in unitate reali cognitionis . . . potest ullo modo consistere," PS t. 3, d. 17, q. 6, n. 61. 54"Quinto. Fundamentum necessarium, ut intellectus noster faciat universale per adunationem plurium a sua cognitione oriundam eorumdem plurium exacta similitudo est, uti fatentur omnes et experientia manifestat . . . Ob id enim a pluribus, quae inter se dissimilia apparent . . . conceptum eisdem communem, atque adeo universalem neutiquam abstrahere possumus . . . Ergo cum Adversarorum sententia neutiquam possunt componi universalia saltem generica. Probo consequentiam. Nam in Adversariorum sententia ea plura, ex quibus erat abstrahendum seu compingendum universale genericum neutiquam possunt nobis apparere exacte similia, quandoquidem neque apparent nobis praecisa sive distincta obiective a suis differentiis . . . Itaque in Adversariorum sententia animal hominis idem conceptus est obiectivus ac rationale et animal bruti idem ac irrationale; homoque integer individuum, ut est in se est in mente nostra obiective pariterque integrum brutum. Ergo eadem dissimilitudinem habent in mente nostra obiective animal hominis et animal bruti quam habent rationale et irrationale. Quamque re ipsa inter se habent homo et brutum. Ergo in sententia Adversariorum nequaquam possumus defectu similitudinis requisitae formare conceptum universalem atque genericum animalis communem homini et bruto. Quod erat probandum," PS t. 3, d. 17, q. 6, n. 63. 55"Deinde suppono, ut apud omnes etiam certum ex dictis disp. 1 q. 3 . . . Quaecumque intellectus noster concipit per species alienas, consequenter concipere ad instar rerum sensibilium, quarum tales species sunt propriae; atque ita, dum quidpiam insensatum intelligit, non posse non eum tangere simul aliquod phantasma sensibile," PS t. 1, d. 2, q. 3, n. 69. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 243 body we infer that there is the soul. Since the soul is inaccessible to the senses, we imagine it as a subtle wisp or glow which permeates the body. Another example: those who have never been to Rome represent the city by their own phantasm of it. Izquierdo stresses that these substitute phantasms do not prevent us from making true statements about real things, because we apply the predicates to the real things substituted by the phantasms, not to the phantasms themselves.56 To support thesis P3, i.e., that substitute phantasms constitute the objective unity of universals, Izquierdo presents three arguments in Disputation 17. The first argument claims that the theory of substitute phantasms solves the problem of the knowability of beings of reason, to which universals belong. Beings of reason should allegedly not be knowable, because knowability is a proper attribute of real beings. The solution to the problem consists in that universals (as genera of beings of reason) are knowable by means of substitute phantasms, not as they are in themselves.57 The second argument seems to develop a similar idea.58 Finally, the third argument is cumulatively-inductive, or perhaps let us 56The origin of the theory is not clear to me. Izquierdo does not mention Ockham or any other well-known medieval nominalist in this context. 57"Hoc enim ipso, quod cuncta cognita a nobis per species alienas, non in se ipsis, sed in phantasmatibus sensibilibus, ut in quibusdam substitutis repraesentantur . . . ut ea, quae re ipsa sunt unum, cognita in pluribus phantasmatibus multiplicata nobis apparent, atque adeo inter se distincta vel praecisa obiective; ita, quae re ipsa sunt plura, cognita in unico phantasmate adunata nobis apparent, atque adeo obiective, quod est universale," PS t. 3, d. 17, q. 6, n. 6. Cf. John P. Doyle's observation: if all universal cognition takes place by means of "alien species" (species alienas) we do not cognize anything as it is in itself: "Particularly in the case of impossible objects-since having no being in themselves they could not generate their proper species-intelligibility was extrinsic also inasmuch as it required alien species. . . . [Note 166:] Impossible objects could be known, that is, not from anything in themselves but only in a secondary way through the species of other things which presumably could be known in themselves. . . . [Note 167:] . . . see in this connection a reported opinion of Izquierdo, the implications of which are immense: "Supponit quarto: Animal rationale hominis earum rerum esse quae cognoscuntur per species alienas, atque adeo non in se, sed in phantasmatibus substitutis"; Peynado [Ignacio Francisco Peynado. SJ, 1633–1696], Disputationes in universam Aristotelis Logicam, tr. 2, disp. 2, sec. 1, n. 6; for Izquierdo himself, see especially, "Intellectus noster pro hoc statu sine usu speciei alienae, atque adeo sine phantasmate substituto nihil omnino iudicare valet"; Pharus scientiarum, disp. 2, q. 3, prop. 2, 1. See also John P. Doyle, "Between Transcendental and Transcendental: the missing link?" Review of Metaphysics 50 (1997): 783–815. 58"Quia nimirum, quae in se cognoscuntur et non in substituto alieno, non possunt non esse apud cognoscentem, sine in eius mente obiective id, quod re ipsa sunt in se, atque ita non possunt esse obiective in mente cognoscentis plura, quae in se realiter sunt unum, neque unum, quae in se sunt plura. Ex quibus patet idcirco nobis plura apparere in se ipsis, sed in uno substituto phantasmate cognoscuntur ac proinde unitatem, qua universale a nobis factum in esse talis constituitur aliam non esse ab ea, quam plura ipsa ab ipso phantasmate uno, in quo nobis apparent, obiective in mente nostra fortiuntur, ut dicimus in propositione," PS t. 3, d. 17. q. 6, n. 66. American Catholic Philosophical Quarterly244 say phenomenological. It consists in the claim that both authority and experience support P2. Izquierdo discusses the argument from experience at length.59 P3: A Universal Unity is a Suppositive Unity of Reason, not a Fictitious One. In Disputation 17, Izquierdo discusses only briefly whether the thesis that the universal unity is a suppositive unity of reason, not a fictitious one. For a proper explanation and defence of the thesis he refers to other parts of his Lighthouse, in particular Disputation 2, question 3, and Disputation 12, question 1.60 The distinction between the suppositive and the fictitious unity is illustrated there by the distinction between the suppositive and fictitious being of reason. Roughly speaking, a suppositive being of reason is the one that takes what-is to be otherwise-than-it-is, whereas the fictitious being of reason takes what-is-not to be (something). Perhaps we might call the suppositive unity "as-if unity."61 In the short text devoted to P3 in Disputation 17, Izquierdo stresses against anonymous adversaries that the substitute phantasm in his theory is not the universal itself; it is only the foundation for the formation of the universal objective concept.62 By this defensive comment Izquierdo inadvertently reveals the weak point of his theory-if we accept his claim that the substitute phantasm and the objective concept are somehow distinct, there remains the question, what exactly is an objective concept? Disputation 17, where one would expect an explication, does not make this clear. We shall briefly return to this point in the conclusion. 59"Quae tandem inde tertio probatur, quia cum doctrina eius bene cohaerent quaecumque de natura universalis tum Aristoteles, tum alii plerique Philosophi, duce experientia, conceperunt," PS t. 3, d. 17, q. 6, n. 67. 60"Nam ut constat ex propositione praecedenti . . . unitas constituens universale alia non est ab unitate, quam plura cognita a nobis in uno phantasmate substituto ab unitate ipsius phantasmatis sortiri in mente nostra dicuntur, quatenus in illo nobis unum apparent, atque ita in mente nostra obiective unum quid sunt, tametsi in re ipsa sint plura. Huiusmodi autem unitatem . . . rationis . . . non fictitia sit, sed suppositia, ex doctrina illius confectarii 7 [disp. 2, q. 3] latius exposita disp. 12 constat," PS t. 3, d. 17, q. 6, pr. 3, n. 71. 61"Fictum est, quod cum in se non habeat esse . . . in mente obiective illud habet . . . Supposititium autem est, quod in mente obiective aliud esse habet ab eo, quod habet in se," PS t. 3, d. 12, q. 1, n. 5. 62"Hinc collige universale non consistere in illo phantasmate sensibili, seu spectro, seu idolo praecise sumpto, quod intellectus noster subrogat pro pluribus a se cognoscendis, quando facit universale, uti nonnulli male intelligentes sententiam nostram supponunt, quia huiuscemodi substitutum phantasma . . . absolute praedicari . . . de pluribus . . . non potest. . . . Consistit ergo universale in conceptu illo obiectivo: qui ex pluribus cognitis ut unum obiective in mente nostra compingitur, dum plura ipsa in uno substituto phantasmate a nobis cognoscuntur. De quo conceptu obiectivo simpliciter et absolute venit dicendum esse unum quid commune pluribus et praedicabile de illis, atque adeo universale," PS t. 3, d. 17, q. 6, pr. 3, n. 72. Izquierdo on Universals: A Way Beyond Realism and Nominalism? 245 P4: The Disposition of the Universal to Existence-in-Many and Predicabilityof-Many is to Be the Subject of Further "Philosophizing." So far, Izquierdo has not utilized the act-potency distinction, omnipresent in the thinking of Thomists and Scotists. Now he approaches a topic which compels him to talk about it. Izquierdo does not say much, and what he says is shorthand and skeptical: The potency of the universal to existence-in-many and predicabilityof-many, just as other potencies, ought to be subjected to further philosophising. However, one can say that if we consider these potencies materially or so to speak physically, they differ in no way from their foundations . . . if we consider them formally or logically, they are suppositive relations of reason, not fictitious ones.63 What a suppositive relation of reason is, is further clarified by means of the example of the potency of fire to burning: only the fire and the possibility (possibilitas) of burning is real, but "logically," by means of a substitute phantasm, we can understand (concipere), that the fire is related to the burning, and in this sense there "is" in the fire a potency to burning. As we can see, Izquierdo rejects real potencies and reduces them to (logical) possibility. An interesting point to note is that Izquierdo labels this relationship of fire to burning "semi-external," i.e., partly derived from the fire itself, partly from something external to it.64 Izquierdo verbally admits the standard distinction between a logical universal (universale logicum) and a metaphysical universal (universale metaphysicum), but it is of little importance to him (see below, consequences C6 and C7).65 63"De potentia, quam universale habet ad essendum in multis, et ad praedicandum de illis, perinde ac de aliis potentiis, philosophandum est. Atque ita dicendum cum sumptam materialiter et quasi physice nihil prorsus differte [sic] a fundamentis . . . sumptam vero formaliter seu logice respectum quemdam rationis esse non fictum sed suppositivum," PS t. 3, d. 17, pr. 4, n. 74. 64"Pro cuius intelligentia notandum est plerasque potentias denominationes quasdam semiextrinsecas esse identificatas realiter partim cum subiecto, quod potens dicitur, partim cum possibilitate actus, partim cum aliis quae fundant eiusmodi denominationes. Quae proinde sumptae physicae seu materialiter ab aggregato suorum fundamentorum non distinguuntur. Sumptae vero logicae seu formaliter actus quidam primi ex conceptu suo, atque adeo respectus quidam inter subiectum et terminum . . . Sic potentia ignis ad comburendum realiter ab entitate ignis et a possibilitate combustionis non differt. Formaliter tamen actus quidam primus est, quo ignis ad combustionis referri concipitur, eo quod phantasma substitutum pro fundamentis talis actus e genere respectivorum est. Quocirca respectus huiusmodi respectus rationis est non fictus, sed suppositivus," PS t. 3, d. 17, pr. 4, n. 74. 65"Superest notandum duplex a multis dialecticis distingui hic universale . . . metaphysicum scilicet et logicum. Universale metaphysicum dicunt natura abstractam a differentiis inferiorum . . . universale autem logicum addere insuper potentiam formalem, qua expresse ea natura adunata concipitur potens inesse multis aut etiam praedicari de illis. Caeterum his appelationibus non multum est haerendum," PS t. 3, d. 17, pr. 4, n. 79. American Catholic Philosophical Quarterly246 Consequences. Izquierdo infers the following consequences from his theory of universals: C1. When contracted to an individual, the universal does not retain the same kind of universality which it has in the state of abstraction.66 C2. Universals are not vague concepts, but determinate ones, which encompass many individuals in a determinate manner.67 C3. Universals can be formed by both negative and positive abstraction.68 C4. When universals are contracted to individuals, two results generally occur: [first] the multiplication of objects which before seemed to be one, and [second] the objective conjoining of these objects with their differentiae . . . Sometimes the former occurs without the latter.69 C5. A nature abstracted from one individual . . . is not universal and does not even have a medium unity between universal unity and individual unity. But if it is abstracted from many [beings] . . . , even though some of them are impossible, it is universal.70 C6. The so-called metaphysical universal, despite the unification of nature, . . . is multiple in reality. The so-called logical universal is further 66"In actuali cognitione, qua universale contrahitur ad sua inferiora . . . non retinet eamdem universalitatem, quam antea in suo statu abstractionis sive aduantionis habeat. Sententia est communis et satis constat ex dictis," PS t. 3, d. 17, con. 1, n. 81. 67"Universale proprie dictum non est conceptus vagus complectens multa vage seu disiunctive (hoc est unum, vel aliud, vel aliud, sub disiunctione) sed determinatus complectens multa determinate. Hoc confectarium contra Petr. Hurt. est," PS t. 3, d. 17, con. 2, n. 84. 68"Universale tum per abstractionem negativam, tum etiam per positivam effici potest. Abstractio sive praecisio negativa appelatur, qua cognoscitur una rei formalitas, ignotis aliis cum quibus illa est idem. Abstractio vero positiva dicitur, qua cognoscitur una rei formalitas ut condistincta ab alia, vel aliis simul cognitis, cum quibus illa idem est. Ergo prior pars confectarii apud omnes est in consentio, qui praecisiones obiectivas admittunt. . . . Secunda vero pars confectarii non adeo est communis," PS t. 3, d. 17, con. 3, n. 85–6. 69"In contractione universalis ad sua inferiora duo regulariter interveniunt; nempe et multiplicatio obiectiva eorum, quae prius apparebant unum; et coniunctio obiectiva eorumdem cum differentiis ipsorum inferiorum, cum aliisve formalitatibus in illis repertis; interdum tamen primum invenitur sine secundo," PS t. 3, d. 17, con. 4, n. 88. 70"Natura abstracta ab uno individuo . . . non est universalis, neque unitatem habet mediam inter unitatem universalis et unitatem singularis. Si autem abstrahatur a multis . . . quamvis sint eorum aliqua impossibilia, universalis erit. Prima pars est contra Petr. Hurt. . . . et Smiglecium," (PS t3d17con5n89). "Iam secunda pars confectarii alias communis," (PS t. 3, d. 17, con. 5, n. 95). "Denique tertia pars confectarii contra Petr. Hurt," (PS t. 3, d. 17, con. 5, n. 97). Izquierdo on Universals: A Way Beyond Realism and Nominalism? 247 . . . conceived as capable of existence-in-many and predicability-ofmany.71 C7. The disposition to existence-in-many, which is said to constitute the logical universal, is a property of the metaphysical universal, just as predicability [is] . . . a property of the logical universal. With respect to the metaphysical universal, predicability is therefore a mediated property.72 C8. Similarly, it is a property of the metaphysical universal to become the subject of the [predicates] which can be predicated of it; [its property] is therefore also being a "preliminary potency" which underlies the [given predicates] as their subject.73 C9. The universality of negations or privations is to be philosophized about . . . as is the universality of things themselves.74 The consequences do not seem to contribute any fundamentally new information: they are concerned with details of Izquierdo's theory, which would only become relevant if the fundamental axioms and theorems of Izquierdo's theory were true and to be elaborated upon. III. Conclusion. Let us now summarize the principal theses of Izquierdo's theory of universals, or more specifically of the part of the theory which concerns their "nature." Izquierdo answers the question "What is the unity characteristic of universals?" as follows: I 1. The essence of universals is to be one which can exist in many. 71"Universale, quod metaphysicum appellant, per adunationem naturae re ipsa multiplicis seu abstractivam seu non abstractivam sit. Universale autem logicum insuper per comparationem, qua natura adunata potens concipitur inesse multis aut etiam praedicari de illis. Utraque pars communis est," PS t. 3, d. 17, con. 6, n. 100. 72"Potentia ad essendum in multis, qua universale logicum constitui dicitur, proprietas quaedam est universalis metaphysici, quemadmodum praedicabilitas, sive potentia ut praedicetur de multis, proprietas universalis logici dici solet. Quae subinde proprietas mediata erit universalis metaphysici," PS t. 3, d. 17, con. 7, n. 103. 73"Eodem iure dicendum est proprietatem universalis metaphysici esse subiicibilitatem respectu eorum, quae de ipso possunt praedicari; atque adeo etiam praeviam potentiam, ut subsit illis tanquam subiectum praedicato," PS t. 3, d. 17, con. 8, n. 104. 74"De universalitate negationum, seu carentiarum rerum perinde philosophandum est sua proportione servata, et per quandam aequivalentiam ac de universalitate rerum ipsarum," PS t. 3, d. 17, con. 9, n. 105. American Catholic Philosophical Quarterly248 I 2. The proper attribute of universals is to be one which can be predicated of many. I 3. Universals are "objective concepts cognized by universal acts of cognition." At first sight theses I 1–I 3 appear to be standard Scotistic-Thomistic Aristotelianism. However, this impression is soon dispelled when Izquierdo answers the question "Is there some universality independent of the operation of the intellect?" with a resolute "No": I 4. A universal is a nature (natura) which is common to individuals only in the intellect; it has no other "lesser than numerical unity" independent of the intellect. Izquierdo answers the last question "What is the nature of the universal unity generated by the intellect?" as follows: I 5. A universal is generated by an act of cognition which represents many as one by means of a unity of reason which is derived from the object cognized by the given act (against the nominalist identification with a confused act of cognition). I 6. A universal has objective unity formed by means of a substitute phantasm (with which it, however, cannot be identified). I 7. Universal unity is a suppositive unity of reason, not a fictitious one (i.e., "as-if unity," not "self-contradictory unity"). Izquierdo's theory of universals is surprising in several respects. On the one hand, with his epistemic plan and blurred distinction between sensory and intellectual cognition, Izquierdo is close to modern empiricism. On the other hand, he closely follows the scholastic philosophy of his time both in methodology and selection of authorities. Izquierdo's project may be interpreted as a search for the way between moderate Scotistic-Thomistic realism and the nominalism of Hurtado, Arriaga, and Oviedo. Izquierdo rejects all extra-mental unity of the common nature, thereby distancing himself from moderate realism, but on the other hand he also rejects nominalism by postulating objective concepts. Izquierdo's endeavour to find a way between moderate realism and nominalism probably derives from the fact that on the one hand he rejects the fundamental Aristotelian distinction of real being to act-potency, but on the other hand he is aware of the many problems nominalism brings. The rejection of the reality of the act-potency distinction has serious consequences, observable also in contemporary metaphysics and philosophy of mathematics, where there seems to be Izquierdo on Universals: A Way Beyond Realism and Nominalism? 249 no middle way between nominalism and Platonism.75 Without the act-potency distinction, the idea of objective concept is rendered meaningless and objective precision cannot be grounded in the metaphysical structure of reality. Izquierdo's deviation from moderate Scotistic-Thomistic Aristotelianism is further accentuated by his representationalist doctrine, according to which we cognize that which is inaccessible to the senses by means of "substitute phantasms," which are strikingly similar to the empiricist ideas.76 Therefore, Izquierdo's search for a third way appears to have failed. University of South Bohemia České Budějovice, Czech Republic 75Cf. Dale Jacquette, "Toward a Neoaristotelian Inherence Philosophy of Mathematical Entities," Studia Neoaristotelica 11 (2014): 159–204; James Franklin, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure (New York: Palgrave Macmillan, 2014); Peter Forrest, "Review of James Franklin's Aristotelian Realist Philosophy of Mathematics," Studia Neoaristotelica 12 (2015): 105–9. 76Further research into the precise character of Izquierdo's espitemology, as well as into his intellectual influence on early modern non-scholastic philosophy (or vice versa), is needed. It is often claimed that "Locke's monumental An Essay Concerning Human Understanding (1689) is one of the first great defenses of empiricism and concerns itself with determining the limits of human understanding in respect to a wide spectrum of topics." Uzgalis, William, "John Locke," The Stanford Encyclopedia of Philosophy (Spring 2016 Edition, first published in the Fall 2001 Edition); ed. Edward N. Zalta, , https://plato.stanford.edu/archives/spr2016/entries/locke/. If it turns out that we may classify Izquierdo as an empiricist, Locke's priority is jeopardized.