Author: Mário Santiago de Carvalho
Part of: Conimbricenses Posteriores (coord. by Mário Santiago de Carvalho)
Peer-Reviewed: Yes
Published: January, 5th, 2024
DOI: 10.5281/zenodo.10463708

The latest version of this entry may be cited as follows: Carvalho, Mário Santiago de, “Monteiro, Inácio”, Encyclopedia, Mário Santiago de Carvalho, Simone Guidi (eds.), doi = “10.5281/zenodo.10463708”, URL = “”, latest revision: January, 5th, 2024.

Life and Works

Inácio Monteiro (also spelled Ignacio Monteyro) was born in Lamas (Viseu, Portugal) on January 16, 1724, and died in Ferrara (Italy) in 1812. In the most recent study on Inácio Monteiro, historian Monteiro (2004) divides the life of this Portuguese Jesuit into the following four periods: 1739-1759, the novitiate/professorship; 1759-1761, the exile period; 1761-1789, the pontifical period in Ferrara; and 1789-1796, the revolutionary period. Son of Dionísio Monteiro and Luísa de Almeida, Inácio enters at the age of fifteen the Society of Jesus, on February 8, 1739, at the college of Évora. He begins to study philosophy at the Jesuit University of Évora in 1741, first following the lessons of Francisco Gomes (1705-1771) and after, in the last year’s course, of António de Freitas (1706-1753). The latter was known for his familiarity with some of the works of René Descartes (1596-1650) and Nicolas Malebranche (1638-1715), having read an entire course in Lisbon (1742/45), where the Jesuit library contained several of Descartes’ oeuvres (Gomes 1960: 43, and 49). As will be seen below, Monteiro demonstrates familiarity with a particular trend of “modern philosophy”, but it is likely that the University of Évora was not unfamiliar with the works of “modern philosophers”, as well. Between 1747 and 1748, Inácio Monteiro concludes the master’s degree in philosophy and deepens his skills in mathematics in Évora. The study of mathematics was not uncommon in the major Portuguese Jesuit colleges. Historian Martins (1999: 21) suggests that Monteiro’s orientation towards the study of mathematics was influenced by Manuel Mendes (1716-1782), and Tomás de Campos (?-1766). To the latter’s name could still be added that of João de Borja’s (1711-1767), who surely taught Campos (Borja 1743), and whose mathematical “theses” – namely on speculative geometry, Archimedean theorems, geography and practical geography, trigonometry, astronomy, statics, hydrostatics, optics, catoptrics, gnomic, and the revolution of the circles – have come to our days and. At the end of his studies in Évora, and after a period spent teaching grammar and humanities at the college of Porto (1748/50), Inácio Monteiro is sent to Coimbra to study theology. In 1753-54, Inácio is a third-year student of theology. However, already in 1752 and writing from Coimbra, he expresses his disappointment to Father General Ignacio Visconti (1751-1755, in office) at not being appointed as a mathematics teacher (mathematicae/mathesis magisterio). This is an indication that when Monteiro was sent to Coimbra, he had already anticipated the opportunity to teach a subject matter he did appreciate, as Visconti’s following words might corroborate. In his reply dated December 12, 1752, Visconti acknowledges Monteiro’s inclination towards novelties (inclinari ad amatores novitatum) but justifies the lack of appointment as punishment for not preparing his theology lessons properly (Rosendo 1996: 162, and Silva 1973: 243). Moreover, at that point, Monteiro was subject to the customary accusation of treating some authors disrespectfully (Baldini 2004: 459). The punishment was however brief, and historian Monteiro (2004: 127) gives a psychological account of its context, alluding to Inácio Monteiro’s “nonconformist character” (carácter inconformista). Monteiro is appointed to teach mathematics at the Coimbra College of Jesus in 1753 and holds the position until at least 1756. During this time, he composes his first book in two volumes, Compendio dos Elementos de Mathematica/Compendium of the Elements of Mathematics, published in 1754. The fact that mathematics was the subject of Monteiro’s first book is evidence of the author’s expectations and complains, as well as a testament to the level of his mathematical education in Évora and, finally, the relevance of mathematics in Coimbra (Carvalho 2022). On May 20, 1754, being “the new mathematics teacher” Monteiro requests the general’s “permission to dedicate to him a mathematical work, to keep a precision clock for astronomical observations (the vow of poverty forbade the Jesuits to have clocks), and to have his writings examined by the province censors, not by the Roman ones” (Baldini 2004: 460). If the last request meant that Monteiro had issues concerning Roman math scope or was only merely a matter of hastening things, one does not know. Regardless, on July 9, Visconti denied the first request but granted the others. Six months before the Lisbon earthquake (Rollo 2007), which prompted reflections by Voltaire (1694-1778), Rousseau (1712-1778), Kant (1724-1804) or Alexander Pope (1688-1744), as well as by several Portuguese authors (Carolino 2003: 333), the degree in theology was granted to Inácio Monteiro in Coimbra, in May 1755. A collection of “theses” still extant today, Orbis Theologici Mappam (1755), documents Monteiro’s own conclusions in connection with this academic degree. It is likely he defended these theses in front of his teacher of theology at the college of Jesus, Inácio Borges (dates unknown). This document acknowledges Monteiro’s capacity as a mathematics professor (matheseos professor), but dwells, obviously, on dogmatic, scholastic, and canonical theology. When Monteiro was emerging as a “mathematician” and “physicist”, an equestrian statue of King José I (1750-1777, in office) was being erected in Lisbon, and its erection is to be interpreted as an obvious political statement. To shape a program of “converting the ignorant to the truth” (Tavares 2018: 158), José’s “Republic of Letters” culminates with the brutal acts of power by the Inquisition, such as the horrific persecution and death of Gabriele Malagrida (1689-1761) (see Maxwell 1995: 83) – the adjective “horrific” is used by Voltaire (1878: 397) –, as well as the expulsion of the Society of Jesus of the country in 1759, championed by the Marquis of Pombal (1750-1777, in office). “Republic of Letters” or similar expressions, as it goes without saying, were in fashion among “humanists and savants that emerged in the sixteenth and seventeenth centuries” (Rubiés 2018). It must be said, however, that the two Portuguese kings, João V (1706-1750, in office) and José I, saw themselves at the image of Louis XIV of France (1643-1715, in office), but not at that of Frederick II of Prussia’s (1740-1786, in office) (see Monteiro 2009). During three academic years 1756/1759, Monteiro is at the College of Santarém teaching mathematics, probably, and philosophy, for sure. He was deported from Santarém to the Papal States (1759), as a consequence of the “pogrom” led by Pombal (Romeiras 2019: 23-37, and Monteiro 2004: 198ff). Inácio Monteiro’s personal library in the college of Santarém was seized and catalogued by justice (desembargador) Inocêncio Alves da Silva Freire (Giurgevich & Leitão 2016: 303). In addition to the extraordinary number of books and authors quoted by Monteiro in his books, there were other personal math libraries in the Coimbra college (Giurgevich & Leitão 2016: 298-300, and Golvers, forthcoming). The publication of Monteiro’s second book, the seven volumes entitled Philosophia Libera seu Eclectica/Free or Eclectic Philosophy, occurs in Venice (between 1766-76). This is, of course, justified by Monteiro’s deportation, but the Free or Eclectic Philosophy was entirely composed in Portugal (dum inter vos in Lusitania), as he himself testifies in the Lusitanae Juventuti/Letter to the Portuguese Youth which is the Dedication-Letter (Epistola nuncupatoria) that opens Monteiro’s “magnum opus” (Monteiro 2004: 128). Adopting a nostalgic but grateful tone, Inácio Monteiro does not lose the opportunity to convey his message. Written in Ferrara, the Dedication-Letter recalls Monteiro’s Coimbra companions and years (qui me Conimbricae nostis); its scholar atmosphere, keen on natural science and on contemporary philosophy (scientiam naturalem et nuperam Philosophiam); and emphasizes the utility (non inutile) his book might still have in Portugal. At this point, the names of two Portuguese contemporary authors, Luís António Verney (1713-1792) and António Ribeiro Sanches (1699-1783), could be invoked, for they also wrote letters from abroad aiming at the cultural and educational situation of the country (Verney 1746, Sanches 1759). But whereas Verney and Sanches used mostly the Portuguese language to convey their programs, ideas and criticisms, Monteiro wrote the Letter to the Portuguese Youth in “exquisite Latin” (Freire 1973: 303), a linguistic decision one must take into consideration. Differently from the Free or Eclectic Philosophy, partially written in Portugal – Sommervogel (1894: 1243) says that only its first part was written in Portugal (122 pages, to be precise) –, Monteiro’s subsequent oeuvre was only conceived or planned (mente conceperam) in the country (Silva 2001: 180). Each one of Monteiro’s three future titles deals with logic, metaphysics and ethics. In an abridged English translation (for the complete original titles see below), here are the titles that came out from the Italian Press: Critical Science or Rules for the Direction of the Mind (Venice, 1768; hereafter: Logica); Philosophical Principles of Theology or Natural Religion (Venice, 1770; hereafter: Metaphysica); and Physical and Rational Ethics (Ferrara, 1794; hereafter: Ethica). The extent to which the content of these three titles derives from Monteiro’s Portuguese teaching or has received instead an Italian input, which is more likely, has not been examined and awaits a critical edition of the three books. In the aforementioned Letter, Monteiro refers to other matters (“coisas”) pertaining to his Portuguese period that were lost because of his deportation. Some contents of these Italian publications could be among those matters, but manuscripts on other subjects are also likely to belong to the lost materials. Inácio Monteiro would not leave Italy for the rest of his life. From 1761 on, he resided in Ferrara, preparing his oeuvre for publication and later teaching philosophy in the Society’s college of the city (1767); meanwhile, in 1764, he traveled to Bologna and stayed at the Saint Lucia college for a short time, returning to Ferrara in 1766. Historian Silva (1973: 249) justifies Monteiro’s short stay in Bologna on account of getting the censors authorization to publish his oeuvre. The second collection of “theses” by Monteiro that have reached our days, Theses ex omnibus Philosophiae partibus excerptae, provides evidence of his professorship in Ferrara in 1771. One of his most famous pupils, Antonio Campana (1751-1832), is known. Campana held a few chairs of Experimental Sciences at the Ferrara university for several years (Monteiro 2004: 250) but traces of his teacher have not been detected in Campana’s work. Since the Holy See approved the suppression of the Society of Jesus in 1773, Monteiro was already acting as prefect of studies at the university of Ferrara (Ignatio Monteiro in Pontificia Ferrariensi Universitate Studiorum Praefecto) when his Ethica was finally published in 1794. One unedited formal document related to two former students of Monteiro, dated June 12, 1776, and signed by Monteiro himself, mentions him as former Jesuit (Exjesuita Sig. Ab. Monteiro) and Portuguese priest (sacerdos lusitanus) (Silva 1973: 250-1). In truth, Monteiro was just one of the exiled scholars who came to the university over the course of its history (Pepe 1998: 7). On June 19, and again on June 30, 1797, he was summoned by the city authorities (Cittadino D. Ignazio Monteiro Preffeto de’Studi nella Università) to participate in the reformation of the university (Piano di organizzazione dei Studi). Following the revolutionary period in Northern Italy, Monteiro was dismissed from his professorship on October 9, 1799, only to be reintegrated later by occasion of the restoration of the Cisalpine Republic (1801). Perhaps due to the decline of the university and Monteiro’s advanced age, the university did not benefit from his capacity as Prefect. Two years after Inácio Monteiro’s death (1812), Diosdado Caballero (1814: 36) briefly mentions the respect paid by the Academy in Ferrara to its ancient professor (suo celeberrimo per tot anos Magistro honestissime parentavit), and the Italian city honored him with a portrait (Monteiro 2004: 420).

Monteiro’s Compendium of the Elements of Mathematics (1754)

As was already said, Inácio Monteiro’s mathematical Compendium is a product of the author’s learning and teaching experience in Évora and Coimbra. The Compendium of the Elements of Mathematics Necessary for the Studies of Natural Sciences and the Arts, to be Used by Portuguese Students, and to serve as an Introduction to the Study of Mathematics to the Curious for those sciences is a two-volume manual published by the Press of the college of Arts in Coimbra in 1754 and 1756. The two years coincide with the author’s period of lecturing mathematics and studying theology, as was common practice in Portuguese Jesuit schools. Cardinal Henrique (1512-1580), the founder of the Jesuit university of Évora in 1559 (at that time the second Portuguese university), established the studies not without a scientific outlook. However, during the 17th century, the time and place for strictly scientific topics were significantly reduced there and that explains why a formal chair of mathematical sciences was created there in the first years of the 18th century (Gomes 1960: 46). From its early years, the university of Évora, as well as the college of Jesus in Coimbra, welcomed indipitae as math teachers – that is, foreign Jesuits who stayed in Portugal while waiting for the ship for the Eastern missions. Just to mention one case, in 1655, the English “indipetus” George Brett Keynes (1629-1658) was sent to Évora with the explicit mandate of “teaching mathematics to students of theology and philosophy” (Golvers & Simões 2022: 60). Naturally, Monteiro does not fit in that category. He belongs to a different period in the history of math teaching within the Portuguese province, as will be seen below and as was already suggested when I previously alluded to the fingerprint of Mendes, Campos and Borja in Monteiro. Historians Andrade (1966a: 243-51) and Gomes (1946) praised the Compendium and were the first scholars to pay due attention to it (see afterwards Monteiro 2004: 133ff.). Overall, the Compendium is an introduction to the study of mathematics for high schools, or, one may conjecture, a manual for the Jesuit colleges all over the country, less likely for the other colleges of the Portuguese assistancy. While it may be remembered that in their very beginning Jesuit Constitutions prescribed the teaching of mathematics – albeit within the Society’s goals though (quatenus ad nobis propositum), and alongside the more philosophical matters (Lukács 1965: 283) –, Monteiro’s Compendium differs in two respects from both earlier and later mathematical Portuguese contributions to that field. On the one hand, it differs “a parte ante” because Monteiro was not a foreign teacher (indipetus) and was wholly committed to the teaching of mathematics and, likely, not so keen on theology. It also differs because the formation of helmsmen – notably, thanks to the stress put on Sacrobosco’s Sphaere (Albuquerque 1972) – were no more under Monteiro’s goal, and because math studies were no longer framed by the ancient discussions dependent on Domingo de Soto’s (1494-1560) teaching on falling motion; the discussions had been common ground for 16th century Roman and Portuguese Jesuit schools (Wallace 1995, and 1997: 124; Baldini 1998: 235 ). In a nutshell, Monteiro’s approach to mathematics differed from the older paradigm because, just like what happened with Borja, it was no longer attached to the “mathematical” Aristotelian texts, mostly On Heaven, On Generation, or Physics (Carvalho 2022). This feature is usually mentioned as a distinctive mark to interpret Monteiro’s contributions to philosophy and the studies in general. But, on the other hand, Monteiro’s Compendium might differ also “a parte post”. For instance, a book by the Oratorian José Anastácio da Cunha (1744-1787), Mathematical Principles/Principios Mathematicos (see Cunha 1790), is said to embody “an ambitious project to organize and expound mathematics on solid grounds”, to intertwine purely mathematical assertions with experience, that is, the very root of the physical sciences (Queiró 2004: 501, and 511 respectively). This appears to be crucial even if it is still impossible to determine the exact place of Inácio Monteiro in the history of mathematics in Portugal. Such a goal can only be achieved by considering the contributions of the Jesuits along with the Oratorians, in Lisbon, and the Franciscans, in the Saint Peter Coimbra college of Arts – not to mention the alternative paradigm provided by laymen, exemplified by the Portuguese Engineer by Manuel de Azevedo Fortes (1660-1749), a treatise on fortification, attack and defense of forts, the first volume of which (Fortes 1728) dwells on practical geometry and plane trigonometry (Martins 2017, Saraiva 2008: 3, Garção-Stockler 1819). Whereas amongst the Oratorians, the figure of the mathematician João Baptista (1722-1801) emerges (Andrade 1946: 326-32; Dias 1953), amid the Franciscans, attention should be given to the contributions by Valentim de Alpoim (1623-1696), Joaquim de São José (1707-1755) and Manuel do Cenáculo (1724-1814; see Caeiro 1957). Let us return to Monteiro’s situation in this history. One of the mathematical authorities frequently quoted by Monteiro is Antoine Thomas’ (1644-1709) Sinopsis Mathematica (see Thomas 1685). While praising Thomas’ “good method”, Monteiro considers it strictly philosophical-oriented (apenas dirigido a filosofia) (Golvers 2020). This might lead one to think that Monteiro tried to avoid the criticism directed at Thomas’ limitations, but the necessary study to determine whether this is correct or not has not yet been carried out. Historian Monteiro does not hesitate in characterizing the Portuguese Jesuit mentality as “modern” as regards the goal of mathematics (Monteiro 2004: 152, 379, 407), but a comparative examination of the aforementioned Portuguese contributions remains to be conducted. Furthermore, Inácio Monteiro’s intervention as a “science” teacher and writer must be read in the context of the growing absolutist political atmosphere, with the ambiguities that affected the “enlightened” Republic of Letters, for better or worse (Tavares 2018, Rubiés 2018), and, of course, with the epistemological situation of mathematics within the Portuguese province. In contrast to situation in Portugal, where the university in Coimbra was reorganized having the Society of Jesus as its target (Silva 1767), Maximillian III Joseph, Elector of Bavaria (1727–1777, in office), invited the Jesuits to teach experimental philosophy at the university of Ingolstadt in 1746, a policy later followed in Innsbruck, Freiburg, and Bamberg (Hellyer 2005: 38). Situations abroad are worth recalling because they coeval with Monteiro’s Portuguese efforts. Not without reason, some historians consider the situation of the province as poorer when compared to that of other latitudes. For several times, historian Baldini depicted the epistemological status of mathematics in Jesuit Portuguese schools as lower overall when compared to other European Jesuit schools. He explained this situation by “the different recognition given to mathematics as a profession, not only by the local context but by the mathematicians themselves” (Baldini 2004: 363, and Baldini 2013). In Coimbra, Inácio Monteiro succeeded Filipe de Gamboa (1722-?) who was transferred to Évora “to refine his competences” (Baldini 2004: 459). Baldini suggests that such a transfer could indicate that the quality of mathematics instruction in Évora was superior to that in Coimbra. However, the teacher who was appointed to continue Monteiro’s teaching in Coimbra was Bernardo de Oliveira (1714-1796), a competent mathematician as well. Oliveira had held the chair in 1741, in Coimbra, he had also taught mathematics in Évora, and would continue to do it in Ferrara, after 1759. It is yet too soon to assess the mathematical level of the Jesuit schools at Évora and Coimbra, but I suspect they do not differ that much. What must be stressed out is that Jesuits in Portugal did not know of any enlightened political decisions like those that took place in Roman or German provinces, despite the Portuguese Jesuits’ response to several interventions, such as: Tirso de González’s (1686-1705, in office) call to the increment of mathematics, in 1692; Michelangelo Tamburini’s (1706-1730, in office) letter to the Provincial of the Portuguese Province, on April 11, 1711 (see Baldini 2004: 318-27; Rosendo 1996, and 1998); the 16th General Congregation of the Society (1730/31) which recognized the importance of erudition related with experimental and mathematical physics within Jesuit studies (Rosendo 1998: 348); and lastly, and within national borders, one very important document, the List of Subject-Matters to be Taught by Our Philosophy Masters in this Portuguese Province of the Society of Jesus/Elenchus Questionum, Quae a Nostris Philosophiae Magistris Tractari Debent, in hac Provincia Lusitana Societatis Iesu (Andrade 1973: 295-6, and Andrade 1966b). Arguably, if the first two interventions marked the beginning of a new period in the Jesuit history of mathematics in Portugal due to their appraisal of mathematics as pure scientific research – precisely the topic Monteiro seemed to have criticized in Antoine Thomas’s Synopsis –, Monteiro’s Compendium coincides in time with that List published in 1754, that is, only five years before the Jesuits’ expulsion and in the year of the publication of the first volume of the Compendium. A few more facts evidence the relevance of that year: while the Lisbon newspaper A Gazeta, in its issue of June 13, 1754, announces the philosophical and mathematical vastness of the Jesuit Inácio Soares’ (1712-?) Philosophia Vniversa Eclectica ex cunctis philosophorum sectis methodice selecta ac concinnata in northern Braga, in southern Évora both Sebastião de Abreu (1713-1792) and João Leitão (1715-after 1782) emerge as two top-ranked Jesuits professors of mathematics (see Gomes 2012: 304). As briefly summarized by historian of science Martins (1999), the List aimed at “the study of gravity based on the explanation of Peripatetic, Cartesian and Newtonian opinions, proposing the adoption of the one closer to the truth. It also added that studies of speed and quantity of motion would be based on the laudable method of the moderns. Regarding the study of elastic bodies, the presentation of the models of Descartes, Gassendi (1592-1655) and Newton (1643-1727) was recommended. ‘Restricted physics’ should deal with the world in general, and the opinions of Aristotle (c.384-c.322), Descartes, Kepler (1571-1630), and Newton should be presented therein. The study of the four elements should acknowledge the Torricelli tube, the Magdeburg spheres, and the opinions of Descartes, Gassendi, and Borelli (1608-1679) on several scientific topics. Overall, these subjects should be followed by the study of magnetism, electricity, and geography, covering topics such as longitude and latitude, zones, climates, the origin of hills, rivers, fountains, thermal springs, mineral waters, salt and color of sea waters, ebb, and flow, etc.” (Martins 1999: 20). Monteiro’s Compendium does not cover all of these topics but does acknowledge some of them, and testifies to its didactic approach to mathematics, in particular, and science, in general, as noted by Garção-Stockler (1819: 161) for the first time. With a different approach, historian Gomes (2012: 77) highlighted two items of importance in the Compendium: the method of study followed therein and the choice of the authors. The combination of both items explains why Monteiro preferred Christian Wolff’s (1679-1754) algebra over Guillaume François Antoine’s (1661-1704) L’Analyse des Infiniment Petis, which he considered unsuitable for beginners (Gomes 2012: 79-80). Arguably, Monteiro followed closely Wolff’s way of presenting mathematics in school texts (Nobre 2005). To put it briefly, the Compendium addresses pragmatic issues such as the shortage of time for studying, the low success rate in studies, the order of the subject matters and the choice of manuals, which are all core teaching issues (Rosendo 1998: 328). It was said provocatively that Inácio Monteiro’s sharp eye to didactics made him leave a few observations that “deserve to be an example to many of the present-day authors of manuals for basic and high schools” throughout the Compendium (Rosendo 1998: 340). This demonstrates a certain continuity with the major didactic objectives of the first Coimbra Jesuit Course (1592-1606), which targeted two types of students: those seeking a deeper knowledge of mathematics and those wishing to approach philosophy with a foundation in physics (Andrade 1973: 297-8). Monteiro’s dual goal appears to align with these same targets, which may explain Verney’s crippled diatribe against Monteiro (see Gomes 1944a, now in Gomes 2012: 97-106, and Monteiro 2004: 409ff). One might even say that the set of surviving tiles reproducing figures from The Elements of Euclid, in the version by André Tacquet (1612-1660), and testifying how quadrivium sciences were methodologically taught at the Coimbra college (Duarte 2020, Leitão 2007), could still be used by Monteiro in his introductory lessons. I wrote “introductory” because although the Compendium opens in a Euclidean key, Monteiro does not consider the Elements to be an entirely suitable instrument for doing geometry, even though he favors the Euclidean synthetic method for teaching and presenting the science. Discussions about the best method to teach mathematics and, consequently, its epistemological horizon must have been crucial at the time. Scholars recognize that by the mid-18th century, “experiment” had become synonymous with natural philosophy for the Jesuits, but this positive attitude toward experiments was mainly found in German colleges (Hellyer 2005), as said above. However, Baldini (2004: 454) is not alone in considering Monteiro as “the most noble scientist in the years immediately preceding 1759”, an honor he is said to share with Jesuit Eusébio da Veiga (1718-1798). Overall, the contents of Monteiro’s Compendium are the following: after a General Introduction, consisted of Definitions, Universal Axioms, and Evident Propositions, the first volume is divided into Arithmetic (further divided into Elementary or Speculative Arithmetic and Algebra), Geometry (divided into Speculative or Elementary and Practical, and which is the largest chapter in the volume, with an appendix on Conical sections), followed by Trigonometry, Algebra, Statics, Mechanics, Hydrostatics, Aerometry, Hydrometry, Hydraulics, and Pyrotechnics. The pure mathematical section of the first volume ends with the chapter on Algebra, after which the physical and mathematical issues are introduced. The second volume of the Compendium begins with the elements of Optics, Catoptrics and Dioptrics, followed by the elements of the Sphere and Astronomy, and ends with the elements of Geography and Chronology. Monteiro does not justify the absence of Gnomic, Perspective and Architecture, but as regards the nature of the light, for instance, he departs from the ancient theory of the Peripatetics (Gomes 2012: 73; but see Bernardo 2009: 535). Throughout the Compendium various illustrations depicting machines, instruments, and experiments enrich the volume, totaling over three-hundred pictures. Some of these also appear in Manuel Pinheiro’s (1718-1776) General Physics at Évora (Gomes 1960:592), and they cover arithmetic, geometry, trigonometry, statics, mechanics, hydrostatics, hydrometrics, aerometric, hydraulics, pyrotechnics, optics, catoptrics, dioptrics, the sphere, astronomy, geography, chronology, and algebra. While this is not the place to delve deeper into the content of the Compendium (see Rosendo 1998), I shall briefly point out some challenging topics or issues therein. Monteiro does not seem to consider irrational numbers, he does not discuss the infinite at length, he is not always consistent when science and religion conflict, and he wavers between the systems of Brahe (1546-1601) and Copernicus (1473-1543). However, he provides interesting insights on mereology, and shows a willingness to embrace the permanent evolution that characterizes science. Without being a “scientist” as one nowadays understands the word, Monteiro must have been a mathematics enthusiast, and a man with strong appetite for the most updated scientific knowledge. His personal library bears witness to his eagerness to acquire recent publications in order to stay updated (Golvers forthcoming). As mentioned earlier, one final feature of Monteiro’s Compendium that deserves attention is that it was written in the Portuguese language. Nicolau Gaspar (dates unknown) used the same procedure before, in 1519, and his Matemáticas Práticas/Practical Mathematics is the first known mathematical treatise in the Portuguese language. Monteiro was not the first Jesuit to use his mother language at the high school level, but he still acknowledged the difficulty of explaining mathematics in Portuguese, instead of Latin (Rosendo 1998: 324). Note that even Pedro Nunes (1502-1578), the greatest mathematician at the university of Coimbra, set an example with his own translations of the Treaty of the Sphere and Ptolemy’s Geography (Nunes 1537: 5, and Leitão 2002). One may recall that in the Aula da Esfera (the Class on the Sphere) at the Lisbon College of Saint Antão/Saint Anthony, mathematics was taught in Portuguese, not in Latin (Gomes 2012: 42-43). This could also be the case in Coimbra as well as in the other Portuguese Jesuit colleges. Furthermore, Monteiro’s Compendium alludes to the Oratorian Teodoro de Almeida’s Philosophical Recreation (1751-1800), and to other Portuguese titles as well, both published and unpublished. In addition, besides João de Borja, mentioned earlier, one could note the Elements of Geometry by Jesuit Manuel de Campos (1681-1758; not to be mistaken with Tomás de Campos, mentioned at the beginning of his article), considered “an excellent preparation for the substitution of the false Aristotelian by the true Newtonian and experimental philosophy” (Andrade 1973: 296, see Campos 1735), and the unpublished Newtonian Chronology in Epitome by Jacob de Castro Sarmento (1690-1762), probably a pupil of Campos in Évora during 1710/11 (see Sarmento 1737). Hence, if Monteiro chose to write in his mother language, given the short books for study, as he admits, one cannot ignore that his initiative was not isolated, and was actually typical among “science professors”. Although experimentation and mathematization never reached the level they did in Italian or German latitudes, the Portuguese circumstance likely favored them more from a didactic perspective. Additionally, the philological interest of this situation has not been yet given proper attention (see Rosendo 1998: 337, regarding Gaspar’s and Monteiro’s terminologies). Castelão-Lawless (2018), Rosendo (1998) and Andrade (1973: 298) agree that Monteiro is an example of the dissemination of modern science in Portugal, made by science popularizers in the 18th century. Optics could be a good example of this situation, despite Monteiro’s hesitation between Cartesian and Newtonian solutions regarding that subject matter (Ribeiro & Bulhões 2014). To the names of Almeida and Sarmento, Castelão-Lawless (2016) adds two pedagogic letters, The True Method of Studying by Verney (1746), and the Letters for the Education of the Youth by Sanches (1759), mentioned above. However, both present concerns, ideal programs, and negative opinions concerning the state of Portuguese studies, which was not the negative target aimed at by Monteiro. It is possible that their goal was not to disseminate science to large audiences, but to educate within the context of schools. Monteiro did not write about the need to reform the educational system, but he wrote his own version of what the system should provide. Among the authors quoted in the Compendium, the following must be mentioned here, mainly for future evaluation of the possible “translations” or adaptations by Monteiro (see e.g. Carvalho 1997b): Copernicus, Kepler, Galileo (1564-1642), Pascal (1623-1662), Bernard Lamy (1640-1715), Wolff, Newton, Nollet (1700-1770), Mariotte (1620-1684), Boyle (1627-1691), Isaac Barrow (1630-1677), and Christiaan Huygens (1629-1695), among many other names registered by Gomes (2012: 84-97), to which should be added the names of John Locke (1632-1704), and Samuel Clark (1675-1729), as noted by Martins (1973: 268). Marginally, it may be said that the Dominicans had Monteiro’s Compendium in their Coimbra Library (Rodrigues 1987: 61).

Monteiro’s Eclectic/Selective philosophy

Inácio Monteiro’s following works fall under the umbrella of “eclecticism”. By their common title, Free or Eclectic Philosophy, the eight volumes of his Physica clearly evidence this. The two volumes of the Logica are announced as an eclectic manifesto (secundum eclecticae philosophiae leges adornata), and the same goes for the Metaphysica (eclecticae philosophiae regulas pertractata), and the Ethica or moral philosophy (secundum philosophiae eclecticae institutionem pertractata). In the next paragraphs, I shall return to this, but, besides the obvious comparison with the Oratorians, for they were meant to replace the Jesuits, it is worth comparing Monteiro’s eclectic proposals with the solutions followed by the various religious orders that adopted the structure of the university of Coimbra in the wake of Pombal’s reformation (see e.g., Plano 1776a, and 1776b). Before the publication of Monteiro’s philosophical “opus magnum”, the Free or Eclectic Philosophy/Physica, Jesuit João Leitão taught a philosophical course (1754/58) that shared the same eclectic motif, at the university of Évora. Leitão’s Philosophia Analitico-Eclectica in tres partes distributa is accessible in manuscript (BPME: BP cod. CXVIII/1-4, and BGUC: Ms. 2333), and was described by Gomes (1960: 588-9). Unfortunately, Monteiro’s and Leitão’s titles were not subject to a full comparative examination yet. The latter’s three parts – rational, natural, and moral philosophy – do not coincide with Monteiro’s structure. Even though Leitão was the author of a reformed philosophy (philosophia reformata), the way he divides it differs from Monteiro’s proposal. Note that Leitão’s five scales or methods are Aristotle’s method, Galileo’s, Gassendi’s or the Atomists’, Descartes’s and finally the Peripatetic one. As explicitly recognized by Francisco António (1752) or Inácio Soares (1754), both lecturing in the northern city of Braga, a label like “Modern Peripatetic School” was then taken as synonym of “Eclecticism” (Gomes 2012: 27), a way of thinking finally free from pure Aristotle’s inputs. “Eclecticism” had a presence of its own in Portugal, and its influence was even detected in American territories (Rovira Gaspar 1958), except for Monteiro’s works, for obvious political reasons. Experiencing his time as an epoch of crisis, Monteiro sees no merit in Skepticism (scepticismum rigorosum, seu pyrrhonismum neque verum esse esse dogma, neque serio atque sincere ab aliquo teneri propugnarique existimo). According to him, eclecticism should be the response fed by history of philosophy whenever it shows the imperfection of human knowledge. I shall return to the role the history of philosophy had in Monteiro’s philosophy, but, as he himself puts it, even if one truth may be found in every and each author, the whole truth cannot be found in any one of them. There is nothing new here. In the same vein, a course taught at Évora in 1755 by Manuel Pinheiro introduced eclecticism as follows: “a sect of those authors who do not want to swear to the words of a single master, but who embrace what they judge most according to the truth” (Gomes 2012: 28). Surely, this could even apply to Aristotle himself whose authority was still claimed by the Society of Jesus. Incidentally, António de Freitas’ manuscript, Peripateticae Philosophiae Medullam a Mechanicae Philosophiae corpusculis ac faecibus expurgatam (BNL-R. 5138 A), read by Silva (1973: 237-8), despite considering three major Cartesian principles – the universal doubt, the cogito, and the certain or self-evident ideas – attacks Cartesian “mechanics” based on an Aristotelian position. However, due to the extension of the historical frame from Ancient to Modern authors (in Philosophia et Veteres et Recentiores Philosophi observatione), from that time on, Aristotle was just one of the names among various sects present by the history of philosophy and, as such, individually experienced by each philosophy professor, regardless of their religious order. That is why Leitão’s last scale, mentioned above, becomes biographically experienced by Monteiro’s idiosyncratic itinerary, which he depicts as follows: starting with the study of Aristotle, Monteiro moved on to Epicurus, whom he abandoned to address the Atomists, and then “the new Cartesian world, the new philosophy”, which he also abandoned to meet Newton. Some itineraries of these teachers can be said to recall Justin the Martyr’s itinerary in the 2nd century. However, despite being a common experience of several philosophers’ intellectual biographies, they all lack of systematicity. After all these stations, being at a time a Peripatetic, an Atomist, a Cartesian and a Newtonian, Monteiro arrives at the expected conclusion that although each of the mentioned philosophers had tackled some truth, the prudent philosopher should be a free (meaning: independent) one. In short, an eclectic philosopher suited for “a republic of reason”. This implies that eclecticism was pursued as an enlightened motif by Monteiro as well, whose rejection of dogmatism and sectarianism allowed a recent interpreter to classify Monteiro’s philosophical figure under the rubric “freedom of philosophizing”/”Freiheit des philosophierens” (Albrecht (1994: 587). Nevertheless, strange as it may see, the opposition between eclecticism and sectarianism was also one of the key ideas in Diderot’s (1713-1784) important article “Écletisme” for the Encyclopédie (Wolfe 2021). Hence, to put it in clearer words, it was a topic widely spread but differently understood, as can be seen in the works of non-Jesuit thinkers such as the German philosopher and Lutheran priest Johann Christoph Sturm (1635-1703), or the Portuguese-Jewish physician Isaac Cardoso (1615-1680). Inácio Monteiro will remain faithful to Eclecticism, but this still poses a problem because, prior to Victor Cousin’s (1792-1867) theoretical stance, eclecticism could only be either inconsistent or consistent and systematic. Monteiro’s intellectual and philosophical eclectic biography will always require the reader to check the level and coherence of his attachment to e.g., Descartes, Locke, Leibniz, Wolff, or Newton. However, this will not be enough, as a close examination on how and to what extent those authors and their theories are consistent in Monteiro’s reading is also necessary. Overall, to be considered a consistent eclecticism, Monteiro’s entire oeuvre must be accessed through competent exegetical work, ideally based on its urgent critical edition, and framed by a historical-philosophical sound knowledge. And a work as such has yet to be done.

Physica: A Free or Eclectic Philosophy (1766)

Monteiro’s Free or Eclectic Philosophy/Philosophia Libera seu Eclectica was first published in 1766 in Venice, and its content derives from the three-year time that the author spent lecturing in Portugal, likely in Santarém, ten years earlier (although its opening Letter was signed on February 28, 1761). Several matters that had integrated the Compendium reappear in the opening volume of this Physica, which even reproduces a free Latin version of the Compendium made by the author himself. The French journal L’Esprit (1776: 383-5) saluted and described the publication of Monteiro’s Free or Eclectic Philosophy as a “model” of the modern philosophy wholly dedicated to physics. Monteiro outlines his conception of a genuine course in philosophy, meaning, in “natural philosophy” (integrum, absolutumque Philosophiae naturalis cursum), to be completed in three years. During the first year, students would be introduced to geometry, the history of philosophy, and logic, with the latter being dealt with after the former two or mixed with them. Later, in 1788, Monteiro would publish an independent title wholly dedicated to logic. Seeing geometry as a necessary introduction to the study of physics, Monteiro assigns the same role (tyronem philosophiam) to the study of the history of philosophy, considering it suitable for anyone wishing to be well educated (bene cultum). Due to its style and purpose, the Physica has been compared to Almeida’s Philosophical Recreation, written in Portuguese, and focused on physics as well. Castelão-Lawless (2016: 41) suggests that Monteiro wrote the Physica in Latin, probably with the intent of having it adopted by foreign professors at the newly reformed university of Coimbra. Although this suggestion contradicts the historian’s view that Almeida’s and Monteiro’s titles may be considered contemporary examples of science dissemination, studies evaluating the differences between Monteiro and Almeida, one a Jesuit and the other an Oratorian, are still lacking, and one must always take into consideration that Portuguese titles and Latin titles likely had different audiences. Broadly, the publication of the Physica aimed to provide students with the necessary or ideal inception (tyrones) in philosophy. Monteiro consistently sees his intervention under the same didactic goal: to help students overcome limitations imposed by the short period of time during which teachers were constrained within the academic year. This is, at least, the way I read the original: “…ut adolescentes in Philosophia satis instructi evadant, si Philosophicum stadium absolvant, quin aliud menti, et memoriae mandaverint, praeter ea, quae a magistro dictata accceperunt.” According to the syllabus proposed by Monteiro, to which I now return, in the second year of philosophy, students should address the following three items, all of them related to physics in general (physica generalis): (i) the notion, object, method and rules of philosophy, plus physics; (ii) the notion and existence of bodies; (iii) nature, first elements, the principles and composition of bodies. The remaining chapters, such as mechanics, statics, and barycenter physics, would follow. Volumes two and three of the Physica also dwell in the same subject matters. Astronomy occupies the fourth volume, and with it ends the study of physics in general. From the fifth to the eighth volume, Monteiro deals with specific parts of the world, bodies, and the phenomena related to them (physica particularis), such as geography (vol. V), aerometry, pyrotechnics, electricity, sleep, and music (vol. VI). The last two volumes deal with the physics of living beings (physica viventium), which covers subject matters as diverse as plants, animals, their anatomy, the circulation of the blood and respiration, but also lessons on light, and colors (vol. VII), and, of course, the human body and soul, the so-called “homo sentiens” (vol. VIII). Just like Manuel de Góis’ (1543-1597) conception of the Coimbra Jesuit Course, almost two centuries before (1592), Monteiro would have nothing to say against the huge presence of natural philosophy in any exposition of philosophy. The difference lies, however, in the fact that while the former stuck to the Aristotelian text, the latter swims in an eclectic wave. Is that peculiarity sufficient to call Monteiro “the last of the Coimbra Jesuits” (o último Conimbricense), as Silva (2001) does? The answer cannot be straightforward. While it is possible to affirm that Monteiro continues the attention to natural philosophy opened by Góis, it is also possible to sustain that the philosophical program defined by Monteiro antedates an horizon that one would only find in 20th century Portugal, when philosopher Leonardo Coimbra (1883-1936), in his capacity as Minister of Education, designs a scientific-philosophical syllabus to be applied in high schools from scratch (Carvalho 2011a: 482). In the meantime, one could, of course, recall the scientific attention to the “book of nature” embodied in education by the Society of Jesus in Portugal during the second phase of its history (Romeiras 2019). Divided into a systematic part (the study of causes) and an experimental part (the observation and analyses of phenomena), physics is the science of nature or the universe, in its wider philosophical sense, according to Monteiro; or in another words: a science having as its object all the things and bodies that fill the entire world (physica, amplissima philosophiae pars, est scientia naturae seu universi, hoc est, rerum et corporum omnium, quae universum mundum componunt). Considering the vastness of the universe – a world, it may be remembered, that was becoming increasingly wide and studied with rather diverse and different tools –, the place of the earth is reconsidered, and the natural approach is mandatory (Carolino 2003, and Carvalho 1997b). Furthermore, Monteiro discusses the hypothesis of other humans and worlds in “an attentive and updated form” (Conceição 2004: 296ff). In any case, the more promising way to assess Monteiro’s epistemology of physics is to tackle his understanding of experience. Besides insisting upon the new paradigm that natural philosophy had to follow, namely “observation and calculation”, the eclectic approach adopted by Monteiro led him to produce a manual both with success and gaps or weaknesses. Earlier, I mentioned some historians who embraced the idea that Monteiro was a modern scientist in some way. Indeed, he writes after Galileo, Descartes, and Newton, thence his explicit admission that mathematics is crucial to engage in the study of experimental physics. Or, in his picturesque yet clear words, which I shall translate given their interest: “To true physics, precisely the one we are doing nowadays, do not belong the beings of reason, the possibilities, the chimeras of the Ancients, all of them being subtle idleness of the human mind. Nowadays, nature is studied by observation and calculation (…) Wanting to study experimental physics with no knowledge of mathematics is like teaching theology not knowing the catechism. Sir Newton’s teaching has more calculations than conclusions. / A Physica verdadeira, e que nestes tempos se cultiva, naõ saõ os entes de razaõ, as possibilidades, e chymeras dos antigos, ociosas sutilezas do entendimento humano. Estudamos hoje a natureza pela observaçaõ, e pelo calculo (…). Pertender estudar physica experimental sem Mathematica, he, querer ensinar Theologia, ignorãdo o Cathecismo. A doutrina do Cavalleiro Newton tem mais calculos, do que conclusoens.” (Compendio I, Prol.).” Just as with the Compendium, Monteiro’s Physica attends to method and demonstration, as well as to the differences between the analytical/resolution and synthetic/composition methods. “Method” (methodus/ordo), it goes without saying, is a key-notion for the Jesuits, and from the very beginning of the Spiritual Exercises, an itinerary itself, one reads that a better understanding depends on “method and procedure” (Loyola 1992: 21). In its general definition, Logica V states that “method is that particular kind of order by which one dispose one’s ideas, judgments, and reasoning to find or to teach the truth” (Methodus generatim accepta est peculiaris ille ordo, quo nostras ideas, judicia, ratiocinationes ad veritatem aut inveniendam aut docendam disponimus). Despite the Cartesian tone associated with the stress put on ideas (on their evidence, to be precise), despite the relevance of observation and experience (according to Physica II), despite Monteiro’s inflexibility in stating that in physics one should stick to geometrical reasoning (geometrica ratiocinandum), whenever possible, and despite the fact that “analysis” and “synthesis” are two structural dimensions of method, Monteiro, I repeat, follows mostly the principle that analysis is better suited to finding the truth, whereas synthesis is better suited to teaching it (Logica II). This is, among other things, a sensible departure from Descartes’ emphasis on “analysis” in mathematical contexts (see e.g., AT II, 22,30, 82, 337, 394, 400, 438, 637; AT III, 99; AT VI, 17-18, 20; AT X, 373). There is no surprise here, as in his “autobiography” Monteiro ranks Newton before Descartes, even though he never read Kant (KrV, 1781). This does not imply by itself that Cartesian mathematics was surpassed by Newtonian physics because, I insist, Monteiro is not a scientist but rather someone who is attentive to the need of being updated and preoccupied with the dissemination of science for didactic and human reasons. It is true that the Ancient or Aristotelian dichotomy sense/reason (sensus/ratio) is interpreted by the Jesuit as the trichotomy observation/experience/demonstration (observatio/experientia/demonstratio), but I submit that it all indicates that the latter appears mostly at the service of didactic exposition. In the case of Inácio Monteiro, it is arguable that he rarely, if ever, engaged in doing experiments, and, as was already said, the only known instance was his request for having a precision clock for astronomical observations. In short, despite his awareness of the importance of observation and experience as “fundamental phases in the search of a mathematical law and the permanent verification of the conclusions reached, following the path opened by Galileo’s and Descartes” (Rosendo 1998: 326), Monteiro’s “experimental demonstration” mostly consisted of the description of facts, eventually read by a few new instruments, following the attention given to them by updated literature, all this conceived in view of the most efficacious didactic repetition. Finally, regarding the history of philosophy, it is not enough to consider the topics dealt therein by Monteiro, mostly related with the ideological “monsters” of his epoch such as optimism, materialism, atheism, pantheism, Manicheanism, space and place, liberty and fate, providence and divine justice, human mind, the nature of the soul, acts or ideas of the soul, and the human will. While the attention given to the history of philosophy has been traced back to the teachings of António de Freitas (BNL-R. Ms. 5138 A), who was likely the last professor of young Monteiro in 1746 in Évora (Silva 1973: 237), historians are not in agreement on this issue. For instance, although the role of Verney (1746) in that domain is recognized, and the special place occupied therein by Fr Manuel do Cenáculo (1724-1814) is also acknowledged, historian Caeiro attributed the first thesis ever published concerning the history of philosophy to Friar Leonardo da Encarnação (dates unknown), in Coimbra, 1747 (Caeiro 1957: 350, 356). However, Gomes (1960: 654) ascribes this merit to António de Freitas, who presided over a thesis defended by António Álvares Correia (dates unknown) in March 1746. Being this as it may, the credit for recognizing the importance of the history of philosophy in Monteiro’s oeuvre belongs to historian Carvalho (1946), who has drawn attention to two sections of the Free or Eclectic Philosophy‘s first volume, the “Historiae philosophiae sinopsis” and the “Adnotationes historicae”. Monteiro divided the history of philosophy into three parts: the first deals with the beginning, progress, and current state of human opinions, and errors; the second deals with the various schools and their main authors; the third discusses ideas and inventions, especially in sciences. This third part is particularly interesting because the author provides the reader with his thoughts on major or relevant topics such as the Cartesian notion of extension, the world and its primordial elements, the Aristotelian theory of matter and form, human composition, the theory of the elements, space, void, the divisibility of matter, the theory of movement, God and movement (especially in Cartesian theory), the impenetrability of matter, and so on.

Logica: Critical Science or the Rules for the Direction of the Mind (1768)

Echoing a Cartesian tone (ars critica rationis dirigendae seu philosophiae humanae mentis institutio), Monteiro’s Logic does not ignore Descartes’ contribution, and, to a lesser extent, Locke’s, without however losing touch with Aristotle’s legacy. Logic is nothing less than the prolegomena to all sciences (organum omnium scientiarum) and therefore a critical science in what respects the human mind’s (humanum intellectum) natural effort to reach the truth, to learn, to dispute and to teach (ars critica rationis dirigendae ad veritatem assequendam, ad discendum, disputandum, et docendum a ratione ipsa inventa). The general structure of the five parts of Monteiro’s Logica still betray an Aristotelian outlook: the existing and thinking human mind (de mente humana existente et cogitante), subdivided into the following four lessons: metaphysical and physical positions concerning the soul’s (anima) activities, the origin and notion of “idea”, the ideas in themselves, and in their relationship with the objects. The second part deals with the mind and its process of judging (mente humana judicante); the third, with the reasoning mind (mente humana ratiocinante); the fourth, with the mind’s true and false acts; and finally, the fifth, with the method, or more specifically with the mind before its teaching and learning goals. Immediately after the exposition concerning the analytical and synthetic methods, part V of the Logica presents a “true Ratio Studiorum with the laws for a methodical and proper teaching for a constructive dialogue (disputa)” (Silva 2001: 188). It must be added, however, that the fifth part of the Logica is preceded by the study of the human mind following Descartes’s lead. Some interpreters loosely emphasize the proximity between Monteiro’s and Descartes’s methodology to achieve truth, already in the first part of the Logica (Monteiro 2004: 403-06). Again, an eclectic or selective choice justifies the mix that conjointly (i) discusses the origin of ideas, their notion and object, (ii) analyses judgments and propositions; (iii) gives the laws of reasoning and syllogisms; (iv) distinguishes between truth and false and advances evidence as the ultimate criterion for truth. To objectively dismantle such a curious mix is a task that still awaits. Monteiro’s exposition of the rules for preventing humans from falling into false evidence represents a step further in relation to the brief pages in which he deals with “enthusiasm” and fanaticism (Logica I), but the reader must bear in mind that Monteiro also talks about a “true enthusiasm” as a precise representation of sensible reality (Est igitur enthusiasmus vivida quaedam animi commotio ad exactam naturalem, et perfectam rerum sensibilium repraesentationem, quae et a ratione ipsa in immaginatione clarissime percipitur, et animum nostrum percellit). This fervor or enthusiasm differs from fanaticism (mentis furor) since, contrary to the former, the latter is rooted in confused ideas resulting from a vivid or inflamed imagination (Martins 1973: 286-7), meaning deprived from the order the method should lean on, and, I submit, the consequences of which were experienced by Monteiro and his companions in the aftermath of the banning of the Society from his country.

Metaphysica: The philosophical principles of Theology or Natural Religion (1770)

“Metaphysics” is the popular name (vulgo nuncupata) of the discipline concerned with the principles of philosophical theology or natural religion (principia philosophica theologiae atque religionis naturalis). Divided into two major parts – on natural theology, or the study of God as the first cause of all natural things, and the study of mind, the spirit or the human soul (de Deo, aliisque spiritibus, ac proinde de anima nostra, eiusque natura, cognitionibus, commercio et statu separatu) – Monteiro’s Metaphysics begins, however, with the definitions of the most “general and familiar notions”. Among them, are “being”, “existence”, “real being”, “nothingness”, “possible” and “impossible”, “natural”, “supernatural”, and “preternatural”, “accident”, “mode”, “body”, “spirit”, “principles” and “causes”, “effects”, “actions”, and “sufficient reason”. The book continues with several hypothesis, paragraphs, propositions, conclusions, difficulties, and rules that resemble the geometrical method just like Monteiro understands it, after Wolff. The four lessons of the second part, wholly dedicated to the human mind, dwell on its existence (specifically, its nature, origin, creation, its distinction from the body and from all other bodily qualities), its state within the body, its first capacity (meaning, thinking activity as well as the origin and nature of ideas), and the proprieties and nature of the will. Aristoteles’ Metaphysics, to which every Jesuit was once expected to adhere to, is now disregarded – Monteiro alludes to the empty questions of the old Scholastic authors (inanibus Scholasticorum veterum quaestionibus) –, but this is mostly done in connection with the obvious fact that with the Metaphysics Monteiro expects to address the challenges of the European intellectual landscape of his time specially undermined by skepticism, pyrrhonism, deism, atheism, and materialism, among many other “monsters” (as he put it). In contrast to Thomas Aquinas’ doctrine about metaphysics being epistemologically subjected to theology, metaphysics, now illuminated by reason alone (solo rationis lumine), coincides with rational philosophy (philosophia rationalis) i.e., a true, clear and logical exposition of all metaphysical matters (pura ratione, lumine naturali agere, argumentari, atque philosophari oportet: idearum tantum modo claritate et connexione ducti a veritate ad veritatem progredimur), physical and moral laws included (de Deo, anima humana, rerum intelligibilium notionibus, et primitivis rerum legibus physicis et moralibus), ultimately leading to God. As Monteiro is writing in a new era, his “eclectic metaphysics”, as he understands it, takes into account the English, the French and the German major “metaphysicians” – namely, and respectively, John Locke (1632-1704), Samuel Clarke (75-29) and Ralph Cudworth (1617-1688), Nicolas Malebranche, Gottfried Leibniz (1646-1716) and Christian Wollf (1679-1754). It is symptomatic of his eclecticism that Monteiro puts English philosophers and philosophy, mostly Locke, side by side with the Peripatetics, for their shared empiricist approach, as well as Malebranche and Plato, for their defense of innate ideas. With obvious different actors, this division predates the two systems – “sensualisme”/ “idéalisme” – that, according to Victor Cousin, all other philosophical systems could in fact be reduced to (Cousin 1828: 12).

Ethica: Physical-Rational Free Ethics (1794)

Assuming its natural dimension, moral philosophy (philosophia morum) is nothing but a natural science that deals with human life in connection with the rules of justice to achieve natural happiness (ethica seu philosophia moralis proprie dicta, est naturalis scientia, et ars vitae moralis secundum justitiae regulas ad naturalem felicitatem consequendam). Once again, and in line with the first moral doctrine ever published by the Jesuits in Coimbra (Góis 2020), ethics is considered the fulfillment of the entire philosophy since “physics, logic, metaphysics, or senses, principles, reason, and actions are connected, and they all lead to ethics”. This reflects the initial pages of Góis’ commentary to Ethics originally published in 1593. However, despite being conceived by a Christian and sincere follower of the revealed religion, ethics is now considered wholly philosophical, meaning wholly founded in nature and reason (ex natura hominis ratione naturalis deducta) and, therefore, accessible to the numerous followers of natural religion. Being impossible to attain true happiness in the historical life of a human being, where, according to Monteiro, one may nonetheless attain the triple “peace that restrains the passions” – “peace with God, peace with oneself, and peace with other men” –, ethics sticks to the three main coordinates of human life or human actions, i.e. life (through mechanical and physical causes), truth (by intelligence), and good (thorough the will). Silva (2001: 192-3), whom I have been following regarding the Ethica (but see also Martins 1973), summarizes the domains of Monteiro’s “special or practical” ethics, mostly restricted to law and political science, and enumerates some of the major authorities thereof like Grotius (1583-1645), Wolff, Puffendorf (1632-1694), Cumberland (1631-1718), Montesquieu (1689-1755), Shaftesbury (1671-1713) or Rousseau. It is worth noticing that Monteiro’s ethics could be somehow seen as not too distant from the “new” approach to ethics developed by the reformed (or anti-Jesuit) Coimbra university. Arguably, nineteenth-century Portuguese historiography was much more inclined to see the link between the reform of the university and Luís Verney’s or Teodoro de Almeida’s works (Arriaga 1886: 373), and, as a result, it lost the necessary perspective to appreciate Monteiro’s doctrine on ethics and how it could also be taught within the Republic of Letters. It is sad, to say the least, that scholars still tend to insist on the divide instead of reading Inácio Monteiro’s oeuvre without outdated prejudices such as those. But as is the case with the titles above, Ethics deserves to be read anew, and I submit, that its comparison with the manual in use in the reformed university (Barbosa 1792) will certainly pay off (Carvalho 2011b: 237). Incidentally, it may be recalled that the year the Ethica was published (1794) also witnessed the publication of The Age of Reason by Thomas Paine (1737-1809) and Fichte’s (1762-1814) Grundlage der gesammten Wissenschaftslehre.

Provisional Evaluation

When it comes to unveil Monteiro’s figure, one should refrain from looking for it in any particular doctrine he espouses, but rather in his attitude of inquiry and teaching. The eventual coherence of all his works has not been the object of any study whatsoever yet. Furthermore, it is too soon to say that Monteiro’s work encompasses an entire Enlightenment program, which emphasizes the role of physics in mathematics and enhances it, “in its ramifications, turning it into the indispensable nucleus of knowledge that should interest scholars of all kinds, particularly those engaged in public governance…” (Coxito 1991: 951). There is no reason to overestimate Monteiro’s Physica to the detriment of his subsequent works. If one intends to discern an “enlightenment” design in Monteiro, one must bear in mind that it should be closer to its Spanish (Feijóo) or its German version (Wolff) rather than the English (Locke), not to mention the French ones (Diderot). Other interpreters suggest addressing Monteiro’s profile and contribution between continuity and rupture (Maduro 2016, and Fiolhais & Franco 2016). According to Vaz de Carvalho, his main philosophical features would have been the following: (i) Eclecticism, (ii) Antiperipateticism, Cartesianism, and Moderate skepticism (Carvalho 1997a: 765). Amândio Coxito proposed these very features, explaining each one of them as follows: (i) Eclecticism, meaning that Monteiro is opposed to partisanship, refractory to authority whenever reason is downsized, and a lover of freedom in philosophy; (ii) Antiperipatetic, since he denies the qualitative explanations of the physical and biological phenomena that make use of substantial or accidental forms; (iii) Cartesianism, since he seems to favor Descartes, as well as his doctrine about the evident ideas, theodicy, and rational explanation of the mystery of transubstantiation; and (iv) Moderate skepticism, as he claims that one knows few things, ignores a lot more, and divine revelation cannot become the criterion for our few certainties (Coxito 1991: 951-2). In the end, I suspect Monteiro’s eclecticism is not to be understood as devoid of any kind of inherited or inner systematicity, but the work required to prove it is yet to be done. As Monteiro sticks to the division between theoretical and practical philosophy, the question remains whether that division is still ancient (Aristotle) or not. His division of the whole of philosophy into logic, pneumatic, moral, and physics, is common, but consistent with the new intellectual tide. In order to interpret the coherence of Monteiro’s choice for eclecticism, Gomes (1944b) traces it back to the spirit of independence towards Aristotle shared by Pedro da Fonseca (1528-1599), Manuel de Góis, Francisco Soares Lusitano (1605-1659) and António Cordeiro (1640-1722). However, eclecticism, a specific philosophical feature that would only be in fashion in Portugal during the 18th century, is a step forward that must neither be neglected nor confused with the intention of prioritizing the search for truth above all else. Adopting the words of Jesuit Joan Baptista Gener (1711-1781), who was speaking about a period between 1700 and 1750 and therefore ignored Monteiro’s oeuvre, I submit that the latter’s eclecticism, was mainly an updated Scholasticism, meaning, its most recent and Modern expression (scholastica novissima ad seculi gustum et genium) (Gener 1766: 28). Ultimately, Inácio Monteiro may not have been that different from his fellow companions with regard to the Jesuits’ ambiguous contribution to the Enlightenment, as expressed by Rubiés (2018): he was modern in his efforts to make humanistic disciplines and mathematics accessible to students by creating curricular books; modern in the sense that he tried to intertwine natural reason and empirical research. But he was not radically modern, “rather the opposite, reactionary, if we identify modernity with skepticism”; or with “materialist and neo-Epicurean philosophies, including utilitarian and hedonistic ethics.


Latin Works, and Translations

  • Compendio dos Elementos de Mathematica, Coimbra: Real Collegio das Artes, 2 vols., 1754, 1756.
  • Orbis Theologici Mappam […] in tres partes divisam, 1. De Theologia Scholastica et Dogmatica 2. De Theologia Morali et Dogmatica 3. De Theologia Canonica. Praeside P.M. Ignatio Borges Societ.Iesu Primario Professore/ Publico offert examini P. Ignatius Monteiro Eiusdem Societ. Matheseos Professor/ In aula theologica Regi Artium Collegii Collimbriensis, integra die [5] huius mensis/Disputabitur: Utrum ad virum theologum apte efformandum omnes memoratae partes sint necessariae? [1755].
  • Philosophia Libera seu Eclectica Rationalis, et Mechanica Sensuum ad studiosae juventutis institutionem accomodata, ac per lectiones digesta, 7 vols., Venice: Antonii Zatta, 1766 (1st edition), 1775-1776 (2nd edition, in 8 vols).
  • Ars Critica Rationis Dirigendae, seu Philosophiae Humanae Mentis Institutio, Logica communi usu nuncupata secundum Eclecticae Philosophiae Leges adornata, Venice: Antonii Zatta, 2 vols., 1768 (1st edition), 1777 (2nd edition).
  • Principia Philosophica Theologiae atque Religionis Naturalis, seu Philosophia Rationalis de Deo, Anima Humana, Rerum Intelligibilium notionibus, et primitivis rerum legibus physicis et moralibus, Metaphysica vulgo nuncupata, et eclecticae philosophiae regulas pertractata, Venice: Antonii Zatta, 2 vols., 1770 (1st edition), 1778 (2nd edition).
  • Theses ex omnibus Philosophiae partibus excerptae disputabuntur publice in Templo Ferrariensi PP. Societatis Iesu, anno MDCCLXXI […] Ferrariae: Josepho Rinaldo Tip., 1771.
  • Ethica Physico-Rationalis Libera seu Philosophia Morum ex natura hominis ratione naturalis deducta et secundum Philosophiae Eclecticae Institutionem pertractata, 2 vols., Ferrara: Josephi Rinaldi, 1794.
  • The “Letter to the Portuguese Youth” as well as the “Prologue to the Reader” of the Philosophia Libera have been translated into Portuguese by Freire (1973; 306-317, and 318-322 respectively, the former with the Latin text in front).

Secondary Literature

Bibliographical References related to Inácio Monteiro

  • Abreu (2012), Adélio Fernando. “Iluminismo e Cristianismo em Portugal. Uma abordagem” Humanística e Teologia 33: 31-61.
  • Albrecht (1994), Michael. Eklektik: eine Begriffsgeschichte mit Hinweisen auf die Philosophie- und Wissenschaftsgeschichte, Stuttgart-Bad Cannstatt: Fromman-Holzboog.
  • Andrade (1946), A. A. Banha de. Verney e a filosofia portuguesa, Braga: Livraria Cruz.
  • Andrade (1966a), A. A. Banha de. Vernei e a cultura do seu tempo, Coimbra: Universidade de Coimbra.
  • Andrade (1973), A. A. Banha de. “Inácio Monteiro e a evolução dos estudos nas aulas dos Jesuítas de Setecentos”, Revista Portuguesa de Filosofia 29: 289-304.
  • Azevedo (2011), Ana. “Entre os ‘Antigos’ e os ‘Modernos’: as querelas sobre o ensino das ciências que antecederam a reforma pombalina da Universidade”, in Congresso Luso-Brasileiro de História das Ciências. Livro de Actas, coordenado por Carlos Fiolhais, Carlota Simões e Décio Martins, Coimbra: Departamento de Física, 119-128.
  • Baldini (2004), Ugo. “The Teaching of Mathematics in the Jesuit Colleges of Portugal, from 1640 to Pombal”, in The Practice of Mathematics in Portugal, edited by Luis Saraiva, and Henrique Leitão, Coimbra: Universidade de Coimbra, 293-465.
  • Bernardo (2009), Luis Miguel. Histórias da Luz e das Cores. Lenda-Superstição-Magia-História-Ciência-Técnica. vol, 1. 2ªed., Porto: Universidade do Porto.
  • Carolino (2003), Luís Miguel. Ciência, Astrologia e Sociedade. A Teoria da Influência Celeste em Portugal (1593-1755), Lisbon: Fundação Calouste Gulbenkian.
  • Carvalho (1946), Joaquim de. “Evolução da historiografia filosófica em Portugal XIX”, Biblos 1, now in: Joaquim de Carvalho. Obra Completa. vol. I: Filosofia e História da Filosofia, Lisbon: Fund. Calouste Gulbenkian, 1981, 121-153.
  • Carvalho (1991), José Vaz de. “Jesuitas portugueses com obras filosóficas publicadas nos séculos XVI-XVIII”, Revista Portuguesa de Filosofia 47: 651-659.
  • Carvalho (2022), Mário Santiago de. “Coimbra Jesuit Mathematicians. A Possible Reasoned Catalog”, Encyclopedia, Mário Santiago de Carvalho, Simone Guidi (eds.), doi = “10.5281/zenodo.7101873”, URL = “”, latest revision: December 9th, 2022.
  • Castelão-Lawless (2018), Teresa. “Not Lagging Behind Enlightned Europe: The Circulation of Natural Philosophy in Portugal”, Agathos: An International Review of the Humanities and Social Sciences 9/1: 61-72.
  • Castelão-Lawless (2016), Teresa. “A Brief History of the Introduction of Modern Science to Portugal During the 18th Century”,  Agathos: An International Review of the Humanities and Social Sciences 7/1: 33-47.
  • Conceição (2004), Joaquim Fernandes da. O imaginário extraterrestre na cultura portuguesa. Do fim da Modernidade até meados do século XIX. PhD Thesis, Porto: Faculdade de Letras.
  • Coxito (1991), Amândio. “Monteiro (Inácio)”, in Logos. Enciclopédia Luso-Brasileira de Filosofia, Lisbon: Ed. Verbo, vol. 3: 950-953.
  • Coxito (2006), Amândio. Estudos sobre Filosofia em Portugal na Época do Iluminismo, Lisbon: Imprensa Nacional – Casa da Moeda.
  • Dias (1953), José Sebastião da Silva. Portugal e a cultura europeia (sécs. XVI a XVIII), Coimbra: Universidade de Coimbra.
  • Diosdado Caballero (1814), Raimundus. Gloria Posthuma Societatis Iesu, Romae: Apud Franciscum Bourilé.
  • L’Esprit (1776) des journaux franc̜ais et étrangers, tome VII, volume 29, juillet 1776: 383-385.
  • Figueiredo (1922), Fidelino de. Para a historia da philosophia em Portugal: subsidio bibliographico, Lisbon: Typ. da Empr. Litteraria e Typographica.
  • Fiolhais & Franco (2016), Carlos & José Eduardo. Os jesuítas em Portugal e a ciência: continuidades e ruturas (séculos XVI-XVIII)”, Brotéria, 183: 9-28.
  • Freire (1973), António. “Textos de Inácio Monteiro”, Revista Portuguesa de Filosofia 29: 303-322.
  • Garção-Stockler (1819), Francisco de Borja. Ensaio historico sobre a origem e progressos das mathematicas em Portugal, Paris: P.N. Rougeron.
  • Giurgevich & Leitão (2016), Luana & Henrique. Clavis Bibliothecarum. Catálogos e Inventários de Livrarias de Instituições Religiosas em Portugal até 1834, Moscavide: Secretariado Nacional para os Bens Culturais da Igreja.
  • Golvers (forthcoming), Noel. “The mathematical books and culture in the Colégio das Artes in Coimbra before the Pombal-reformation (17th-18th cent.)”.
  • Gomes (1944a), João Pereira. “Verney e o Jesuíta Inácio Monteiro”, Brotéria 38:16-25 [now in: Gomes 2012: 97-106].
  • Gomes (1944b), João Pereira. “Perante Novos Sistemas e Novas Descobertas”, Brotéria 39: 378-396 [now in: Gomes 2012: 27-45].
  • Gomes (1946), João Pereira. “A cultura científica de Inácio Monteiro”, Brotéria 43: 268-287 [now in: Gomes 2012: 76-96].
  • Gomes (2012), João Pereira. Jesuítas, Ciência e Cultura no Portugal Moderno. Obra selecta de Pe. João Pereira Gomes, S.J., org. de H Leitão & J. E. Franco, Lisbon.
  • Guimarães (1940), F. Rocha. “Inácio Monteiro e a filosofia do seu tempo”, Brotéria 31: 506-520.
  • Maduro (2016), Carlos. “O Padre Inácio Monteiro, entre a ruptura e a continuidade” Revista de Estudos Culturais 6 (set/out.): 31-45.
  • Martins (1973), António Manuel. “Para uma análise da filosofia de Inácio Monteiro”, Revista Portuguesa de Filosofia 29: 267-288.
  • Martins (1999), Décio Ruivo. “Inácio Monteiro no contexto da cultura científica portuguesa até 1760”, Gazeta de Física 22/1:17-21.
  • Maurício (1935), Domingos. “Os Jesuítas e o ensino das matemáticas em Portugal”, Brotéria 20: 189-205.
  • Maurício (1945), Domingos. “Para a História do Cartesianismo entre os Jesuítas portugueses do século XVIII”, Revista Portuguesa de Filosofia 1: 27-44.
  • Monteiro (2004), Miguel Maria Santos Corrêa. Inácio Monteiro (1724-1812), um jesuíta português na dispersão, Lisbon: Centro de História da Universidade de Lisboa.
  • Monteiro (2009), Miguel Corrêa. “Os Jesuítas e a Ilustração”, in Razão e Liberdade. Homenagem a Manuel José do Carmo Ferreira, Lisbon: CFUL, 779-791.
  • Nobre (2005), Sérgio. “As influências de Christian Wolff sobre a obra matemática do Jesuíta Português Padre Inácio Monteiro”, in Jesuítas, Ensino e Ciência. Séc. XVI-XVIII, coord. by Luís Miguel Carolino & Carlos Ziller Camenietzki, Casal de Cambra: Caleidoscópio, 125-133.
  • Pacheco (1982), Maria Cândida Monteiro. “Filosofia e ciência no pensamento português dos séculos XVII e XVIII” Revista Portuguesa de Filosofia 38: 474-486.
  • Pepe (1998), Luigi. “I gesuiti a Ferrara tra religione e scienza”, in I Gesuiti e i loro libri a Ferrara Frontespizi figurati del Seicento, a cura di L. Pepe, Ferrara: Biblioteca Ariostea, 7-18.
  • Ribeiro & Bulhões (2014), Marília de Azambuja & Arthur Feitosa de. “Os colégios jesuítas de Portugal e a revolução científica: Inácio Monteiro e a recepção das novas teorias da luz em Portugal”, História Unisinos 18/1: 27-34.
  • Rodrigues (1950), Francisco. História da Companhia de Jesus na Assistência de Portugal, tomo 4 (A Província Portuguesa no século XVIII: 1700-1760), vol. 1: Virtude, Letras, Ciências, Porto: Apostolado da Imprensa.
  • Rodrigues (1986), Resina. “Física e Filosofia da Natureza na Obra de Inácio Monteiro”, in História e Desenvolvimento da Ciência em Portugal, Lisbon: Academia das Ciências, vol. 1, 191-242.
  • Rosendo (1998), Ana Isabel. “O ‘Compêndio dos Elementos de Mathemática’ do P. Inácio Monteiro”, Revista Portuguesa de Filosofia, 54: 319-353.
  • Rosendo (1996), Ana Isabel Rodrigues da Silva. Inácio Monteiro e o Ensino da Matemática em Portugal no séc. XVIII. Dissertação de Mestrado/Departamento de Matemática, Braga: Universidade do Minho.
  • Silva (2001), Lúcio Craveiro da. “Um jesuíta no contexto das Luzes: Inácio Monteiro (1724-1812)”, in P. Calafate (dir.), História do Pensamento Português, vol. III: As Luzes, Lisboa: Ed. Caminho, 177-194.
  • Silva (1973), Lúcio Craveiro da. “Inácio Monteiro. Significado da sua vida e da sua obra”, Revista Portuguesa de Filosofia 29: 229-266.
  • Sommervogel (1894), Carlos. Bibliothèque de la Compagnie de Jésus, Tome V, Bruxelles-Paris: O. Schepens-A. Picard.

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