Descartes's mathematical thought

How did Descartes grasp ‘mathesis universalis’? We have already discussed its mathematical nature in Chapter 4, § 3. Now we turn to his philosophy of mathematics and attempt to support an argument about how ‘mathesis universalis’ in his youthful work Regulae ad directionem ingenii should be understood philosophically. For this purpose, we consider retrospectively his theory of mathematics there, turning our attention to its philosophical aspect.

The teaching at Descartes' Jesuit college, La Fleche, was based on Saint Thomas, and Descartes continued to consult Thomas throughout his life. With the Index scolastico-cartesien as his instrument of research, Gilson proceeded towork on his commentary onDescartes' Discours de lamethode. Immediately, Roland Dalbiez issued a criticism of the commentary. He pointed out that the Thomist doctrine was disputed by many previous thinkers, and especially Scotists. For Thomists, objective being is only a being of reason; for Scotists, it ismore than a being of reason. Dalbiez also discussed an issue that seemed tangential to the debate between Thomists and Scotists about objective being, but was waged within the Jesuit order itself, between two of its greatest metaphysicians, Suarez and Gabriel Vasquez.Keywords: Dalbiez; Descartes; Gilson; Jesuit order; Saint Thomas; Scotists

It is no pure and simple truism to say that the philosophy of mathematics has always existed in Western culture, at least since philosophy itself came into being. In fact, not only were most of the early Greek philos ophers mathematicians as well, but it is also well known that speculation within the Greek systems of thought was very often based on problems of a mathematical nature. Soon mathematics, besides being a source of philosophical problems and of their solutions, became also a direct object of philosophical enquiry, to such an extent that the early forms of philosophy of science were in fact forms of the philosophy of mathematics. This sort of privileged link between mathematics and philosophy has never been interrupted in Western thought, and even today there are philosophies that are in various ways influenced by mathematical thought (from the philosophy of Russell to that of Husserl, from Wittgenstein to Carnap and logical empiricism), while a large amount of research is being directed to the study of the 'philosophy of mathematics' proper. Underneath this undeniable continuity, however, considerable differ ences emerge between the ancient and modern conceptions of the philos ophy of mathematics, and some problems, once considered of primary importance, seem now to have almost completely lost their value. To mention only a few of them, let us recall certain classical questions of the old philosophy of mathematics: What are numbers? What kind of relationship exists between mathematics and the structure of the world? How can the property of universality and necessity of mathematical truths be explained? In what sense is mathematical infinity to be con ceived? Is mathematics man's invention or man's discovery? By attributing such questions to the past, we do not mean to confine them to ages far distant from our own. Even Dedekind, for example, entitled one of his most celebrated essays: "What are numbers and what must they be?" ; and Frege devoted the whole of his profound logico-math ematical research to the effort of pointing out the essence of the natural number to mention only these two great authors. However, the theories

In this article, I argue that Albertus Magnus and Thomas Aquinas read a certain passage of Aristotle's Metaphysics on the nature of metaphysical curiosity in a way that is inconsistent with the earlier reading of the same passage by Alexander of Aphrodisias. The passage has to do with Aristotle's use of mechanical automata as a metaphor for kinetic mimesis in his metaphysics. The result of the variant reading of the passage in question is that these Scholastic readings emphasize universal causality as a vehicle of “wonder banishment” in metaphysics at the expense of recognizing the key metaphysical principle that Aristotle is suggesting. Such readings actually turn out to be difficult to maintain with the example of mechanical automata that Aristotle employs. I argue that the absence of the availability of Alexander's commentary to Albert and Aquinas contributes to their variant and inconsistent reading. There are three main parts and a conclusion. Part I discusses the passage from Aristotle's Metaphysics in question, which I call the thaumata passage, as well as Alexander's commentary on it. Part II discusses the unavailability of Alexander's commentary to Albert, Aquinas and their predecessors. Part III discusses the variant scholastic readings of the thaumata passage and how these readings, which take Aristotle's mechanical automata as chance occurrences result in an emphasis on wonder banishment through universal causal reasoning that is inconsistent with the example Aristotle uses in the thaumata passage. By way of conclusion I suggest that even had Alexander's commentary been available to Aquinas, he would have understood the passage as more akin to remarks on magic than to metaphysics.

Reviewed by: One and Many in Aristotle's Metaphysics: Books Alpha-Delta Anthony K. Jensen Edward C. Halper . One and Many in Aristotle's Metaphysics: Books Alpha-Delta. Las Vegas-Zurich-Athens: Parmenides Publishing, 2009. Pp. xli + 524. Hardcover, $45.00. Twenty years after the appearance of the first of his three-volume One and Many in Aristotle's Metaphysics, Edward Halper has produced his much anticipated prequel commentary on the opening books of the Metaphysics. Readers of the chronologically prior Central Books will not be disappointed here. The analytic detail, the remarkably comprehensive yet deftly critical attention to the vast history of Aristotle scholarship, the clarity and precision of compositional style—all hallmarks of Halper's earlier work—are here in abundance as he works through his singularly sweeping vision of the unity of Aristotle's book. Halper's central argument is that the problem of the One and the Many is Aristotle's most crucial and pervasive concern in the Metaphysics. While Aristotle himself never declares this—not even in those passages on the Presocratic philosophers where this problem features most prominently—Halper argues convincingly that Aristotle's conviction about the possibility of a science as determined by a necessary degree of unity among the objects it studies must itself assume the solvability of the One and Many problem. As explicated in the Posterior Analytics, any science must be able to fully explain the first principles of the genus it treats if it is a science at all. If metaphysics is a legitimate scientific study, then it follows that its content must evince a suitable degree of unity such that it could be understood under a single scientific heading. Yet there is no single characteristic, as Aristotle himself claims, that all beings share commonly. As such, it seems as if there should not be a single [End Page 237] science that could consider the highest principles of all things, which would mean, in turn, that there should be no science of metaphysics. In this way, the problem of the One and Many is no mere historical curiosity among Presocratic philosophers. Its solution is, in fact, the precondition for the possibility of that same inquiry. Aristotle's metaphysics must, then, determine its own nature by working through the subject matter it treats. And this, Halper explains in a dizzyingly thorough analysis of the text, Aristotle does accomplish provisionally in Book Gamma by introducing the notion of a pros hen genus (299–307). Being turns out to be the unifying nature of all beings rather than a single common characteristic shared by them: "The 'nature' common to every being, that is, being qua being, is simply its having some sort of essence" (480; his italics). Thus, "having an essence" is conceived as the unifying nature of all beings. Accordingly, beings are sufficiently one so as to permit inquiry into their first principles within a single science. Therefore, the conclusion of the "science-he-seeks," which hinged on the solution to the One and Many problem, will of itself justify the possibility of pursuing that same science. Halper's view of unity has important consequences not only for the content of Aristotle's views, but also for our own interpretive strategies. Scholars who overlook the One and Many problem—and most do—have obscured the compositional unity of the book. Excepting notable names like Sachs and Madigan, the great majority of twentieth-century scholars have doubted the coherence of the Metaphysics on the grounds that the oft-noted inconsistencies and repetitions present either a patchwork of notes or else the developing thoughts of an "artist at work" (32–38). Operating within either hermeneutical framework, these scholars have failed to see that the unifying theme of the book is in fact Aristotle's concern about unity itself. The Metaphysics certainly does contain oddities and aporiai, which Halper, rightly, does not dismiss. He insists instead that, when the text as a whole is read with a mind to the problem of One and Many, Aristotle should be interpreted as attempting to resolve those aporiai in a dialectical way. Instead of presenting established conclusions, Aristotle engages in active philosophical thinking by pursuing this single...

This article argues for an emendation in Aristotle's Metaphysics A 10, 993a13–15. The emendation is based on a hitherto overlooked reading preserved in Alexander of Aphrodisias’ commentary on A 7. First, the article problematizes the reading of the Metaphysics manuscripts in terms of syntax, diction and content. Second, it shows that Alexander's reading is free of all three problems. Third, it argues for the originality of Alexander's reading according to the principle utrum in alterum abiturum erat? and based on the fact that the new reading reveals a subtle didactic link between A 7 and A 10 that sheds new light on the argumentative architecture of Metaphysics Book A.

This volume deals with the rapports among the extant Greek commentaries on Aristotle's Metaphysics: Alexander of Aphrodisias, Syrianus, Asclepius, Ps. Alexander. It traces the precise map of these texts and provides a starting point for any future research in the field.

This volume deals with the rapports among the extant Greek commentaries on Aristotle's Metaphysics: Alexander of Aphrodisias, Syrianus, Asclepius, Ps. Alexander. It traces the precise map of these texts and provides a starting point for any future research in the field.

452 BOOK REVIEWS meant the formal extrinsic cause, the causa exemplaris, but the intrinsic formal cause. To the present reviewer such a teaching seems very like theological pantheism. But Fr. Rahner is not worried by that; nor is he worried by the very formal and explicit teaching of the Council of Trent that the unique formal cause of justification is created grace (Denz. 799). He explains {or perhaps better, explains away) this explicit teaching of the magisterium by saying that " we must remember that the Council only wishes to meet the imputation theory of the Reformers, Seripando and others, but did not wish to determine how created and uncreated (inner!} grace (of which latter it also says precisely 'signans et ungens Spiritu promissionis Sancto . .') are related to each other and together constitute the single grace of justification" (p. 841-842}. In attributing his theory to St. Thomas (p. 888} Fr. Rahner again displays an amazing facility for reading into the words of the Angelic Doctor a meaning which is not to be found there. Examples of this kind could be multiplied almost without end. Let these three, however, suffice to give some idea of Fr. Rahner's theological method and teaching. They will also suffice to explain why we feel ourselves driven to the conclusion that Fr. Rahner, in the process of making theology " vividly alive," has only succeeded in making it less orthodox. Albertinum, Fribourg Switzerland. C. WILLIAMS, 0. P. St. Thorruu Aquinas, Commentary on the Metaphysics of Aristotle, Translated by JoHN P. RowAN, II Volumes; Henry Regnery Co. {1961} {$25.00) One who is requested to write a review of a translation, is given not one but two tasks. Obviously he is expected to record his comments on the merits of the translation. But there is another feature of the work about which he should express an opinion. It is this. Does the original merit a translation? It was with concern for the two tasks that .this reviewer approached the translation of St. Thomas, Commentary on the Metaphysics of Aristotle by John P. Rowan. Did Professor Rowan expend what must have added up to a very large investment of time, patience and scholarly research on a worthwhile project ? Or was his effort analogous to the groaning mountain that brought forth the mouse? M. Etienne Gilson, whose historical studies in Thomism have earned for him the right to be heard with respect, writes of the phil- BOOK .REVIEWS 458 osophical treatises: " Les Commentaries de S. Thomas sur AriStote sont pour nous des documents precieux, dont Ia perte eut ete deplorable." (Le Thomisme, 1948) . Whether one is in complete agreement with Gilson's description of their (happily contrary to fact) loss as "deplorable," or believes such an occurrence should merit a much stronger term, depends ultimately on his acceptance or rejection of Gilson's central thesis on the character of Thomism. · In a sense though Gilson's " deplorable " situation is· not entirely contrary to fact. In a manner of speaking. the Commentaries of St. Thomas on Aristotle are lost, and this in spite of the fact that copies of the same are to be found in full view: on the library shelves of Universities, Colleges and Seminaries. While physically available to anyone who wishes to take and read, they are not in the same measure intellectually available. Their thought remains remote, inaccessible because it lies beneath a language that is today ' deader ' than it was twenty years ago. But some adventurous souls were not content and translations of some of the Commentaries began to appear. For those, however, whose interest in philosophy brought them to Metaphysics, these translations have served to heighten the sense of loss at the remoteness of St. Thomas' Commentary on· the Metaphysics. Nor was the attempt to assuage the feeling of loss by pointing out the availability of Aristotle's text in the vernacular too successful . The fact is that these translations of Aristotle's text offer the student the thought of Aristotle in a language that is familiar but that thougkt remains difficult to grasp. The metaphysical thought of Aristotle, and to a degree the thought of the entire Corp'UIJ A:ristotelicum, demands a...

Reviewed by: Aristotle’s Ethics and Medieval Philosophy: Moral Goodness and Practical Wisdom by Anthony Celano Matthew R. McWhorter Aristotle’s Ethics and Medieval Philosophy: Moral Goodness and Practical Wisdom. Anthony Celano. New York: Cambridge University Press, 2016, 272 pp. Anthony Celano’s Aristotle’s Ethics and Medieval Philosophy is a recent collection of studies from a veteran scholar of medieval philosophy who has conducted more than thirty years of research into the ethical doctrine of Aristotle and its reception by thirteenth-century Latin thinkers. Celano observes that Aristotle’s Nicomachean Ethics is the seminal kind of cultural achievement that admits of numerous interpretations and developments (7). At the same time, Celano promotes a central thesis in this volume that underscores that the content of the Ethics must be differentiated from how it was understood by medieval commentators. The hermeneutical key that should be used to understand Aristotle’s original doctrine, Celano contends, is one that recognizes practical wisdom (phronesis) as having a broader scope than that which was admitted by the medieval commentators, a scope that includes the ability to originate moral norms (viii–ix). In contrast, Aristotle’s medieval commentators were influenced in their reading of the Ethics by the natural law doctrine found in Scripture and Patristic thinkers (5) and as found in the works of Cicero and Seneca (238). The medieval commentators, Celano maintains, read Aristotle with an “acceptance of natural law and synderesis” and, due to these presuppositions, subsequently “transform Aristotle’s Ethics from one based upon a human standard into one that depends upon a divine foundation” (viii). The interpretational result is a truncated understanding of practical wisdom that is no longer recognized as able to originate “moral universals,” that is restricted to the prudential ability to apply the “eternal principles of action” (ix). Elsewhere, Celano refers to this as “the evolution from practical reason to prudence” (241). He points to Albert the Great as the primary medieval thinker who significantly restricted the scope of practical wisdom in this regard (169). Celano’s volume is divided into nine chapters. The work includes selections from Aristotle’s Greek and extensive Latin quotations, as well as frequent citation of relevant English and international secondary sources. Celano begins his study by briefly outlining certain moral topics that can affect one’s interpretation of the Nicomachean Ethics. These topics include how one understands the nature of happiness (eudaimonia), the relation of Aristotle’s ethical doctrine to a natural moral law, and the structure of moral acts. Celano then provides a longer treatment of the issue of happiness in connection [End Page 1430] with Aristotle’s doctrine of practical wisdom. The study then shifts and proceeds chronologically through the works of important thirteenth-century thinkers. His third chapter begins this chronological survey by focusing on William of Auxerre and Philip the Chancellor. The fourth chapter examines commentaries on the Ethics authored prior to 1248 (an anonymous commentary, a commentary ascribed to Robert Kilwardby, and the pseudo-Pecham commentary). Celano then dedicates two chapters to Albert the Great and his treatment of Aristotle’s Ethics. This discussion is followed by a chapter focused on Thomas Aquinas and Bonaventure, and then a chapter examining two late-thirteenth-century commentaries, one of which is ascribed to Parisian arts master Radulphus Brito. Celano closes the volume with a short concluding chapter that returns to discuss in part the themes outlined in his first chapter (namely, the issues of natural law and practical wisdom). Celano states that he developed this book out of a desire to understand what he describes as Aristotle’s two different accounts of happiness that are found in separate sections of the Nicomachean Ethics (vii). These distinct accounts, Celano maintains, also indicate different understandings of human goodness (23). He contends that one account, in book 1, describes happiness as resulting from a combination of contemplative and practical activities (2). Reading the Ethics in light of this first account results in what Celano (appropriating terminology from W. F. R. Hardie) calls the “inclusive” interpretation of Aristotle’s doctrine of happiness (2 and 16). In contrast, a second account that Aristotle provides, in book 10, describes happiness as the result...

In a series of texts that Sten Ebbesen has published in the Cahiers de l’Institut du Moyen-Âge Grec et Latin and elsewhere, he has directed the attention of scholars to the presence of sensitive logical and semantical issues in the commentary tradition on Aristotle’s Metaphysics . In this chapter the author continues this line of investigation and focuses on the interconnection between logic and metaphysics. He discusses the contribution that (syllogistic) logic can give to metaphysics. Since the medievals normally read Aristotle’s Metaphysics as a work applying the Posterior Analytics theory of science to the field of metaphysics, (syllogistic) logic is supposed to structure the way of doing investigation in metaphysics. The author deals with Thomas Aquinas’s interpretation of Metaphysics 7.17 , the chapter where, according to some contemporary interpreters, Aristotle extends the Posterior Analytics explanation theory from attributes to substances. Keywords:Aristotle; logical approach; metaphysics; Metaphysics 7.17 ; Posterior Analytics ; Thomas Aquinas

Aristotle's account of place in terms of an innermost limit of a containing body was to generate serious discussion and controversy among Aristotle's later commentators, especially when it was applied to the cosmos as a whole. The problem was that since there is nothing outside of the cosmos that could contain it, the cosmos apparently could not have a place according to Aristotle's definition; however, if the cosmos does not have a place, then it is not clear that it could move, but it was thought to move, namely, in its daily revolution, which was viewed as a kind of natural locomotion and so required the cosmos to have a place. The study briefly outlines Aristotle's account of place and then considers its fate, particularly with respect to the cosmos and its motion, at the hands of later commentators. To this end, it begins with Theophrastus' puzzles concerning Aristotle's account of place, and how later Greek commentators, such as Alexander of Aphrodisias, Themistius and others, attempted to address these problems in what can only be described as ad hoc ways. It then considers Philoponus' exploitation of these problems as a means to replace Aristotle's account of place with his own account of place understood in terms of extension. The study concludes with the Arabic Neoplatonizing Aristotelian Avicenna and his novel introduction of a new category of motion, namely, motion in the category of position. Briefly, Avicenna denies that the cosmos has a place, and so claims that it moves not with respect to place, but with respect to position.

Reviewed by: Knowledge and Faıth in Thomas Aquinas by John I. Jenkins E.J. Ashworth John I. Jenkins. Knowledge and Faıth in Thomas Aquinas. Cambridge: Cambridge University Press, 1997. Pp. xv + 267. Cloth, $59.95. There is a strong tension in the thought of Thomas Aquinas. On the one hand, he is strongly naturalist. He insists that our cognition is rooted in sense-perception and that [End Page 673] it is normally reliable. He insists that our moral life is grounded in our nature both as physical beings, able to feel pain and pleasure, and as social beings, depending on each other for our welfare. But he is also strongly supernaturalist. Human nature by virtue of its cognitive orientation toward the physical is not able through its own powers to know God. Still less is human nature able to achieve moral virtue by its own powers. This is not just because we are cut off from God by original sin; rather, there is a primal lack that was there even before the Fall. To achieve our true end, both cognitive and moral, we depend on God’s free gift of grace which elevates our nature and renders it able both to know God through the beatific vision in Heaven and to respond to God through loving, virtuous action. The gift of faith becomes central to human nature and destiny in a way that was to worry later thinkers such as Duns Scotus, who pertinently asked how our intellect can have the ultimate end of knowing God if it has to be made a different intellect before it achieves that end. Jenkins does not worry about the point raised by Scotus. Instead, he sets out to give an interpretation of the Summa theologiae which will help us understand more deeply the interplay between the natural and the supernatural in Aquinas. He begins by taking advantage of new readings of Aristode’s Posterior Analytics which present Aristode’s account of the demonstration which moves from cause to effect, not just as a pedagogic device for presenting material obtained by moving from effect to cause, but as a recipe for cognitive restructuring. Certainly we have to begin with mere observation, and with the piecemeal discovery of causes, but to achieve true scıentia (to use the medieval Latin term for organized, necessary knowledge) we need to acquire a new vision of how reality is structured and to see how effects flow necessarily from their causes. True demonstration is an expression of this new vision. Jenkins applies this reading of Aristotle to Aquinas. He takes with absolute seriousness Aquinas’s claim at the beginning of the Summa theologıae that theology too is an Aristotelian scientıa, and he sees the work as presenting a recipe for the cognitive restructuring of apprentice theologians (those to whom the work is addressed). The scientıa of the Summa theologiae differs from the scientia of the Posterior Analytics in two ways. First, Aquinas allows the term scientia to have an extended sense, so that God too can have scientia, even though he does not move from principles to conclusions by a process of syllogistic demonstration, but instead grasps all that is knowable in one simple act. Second, the basic principles which are the foundation of theological demonstration are the articles of faith, especially those of the creeds, which cannot be known by us in any naturalistic way. It is through God’s infused light that we assent to these articles as divinely revealed. After a lengthy examination of the role of faith in Aquinas’s account, Jenkins describes the epistemology involved as supernatural externalism. Although Jenkins’s presentation of the relationship between scientıa and faith in the Summa is carefully and lucidly argued, there are two aspects of the book that I would question. First, while it is true that Aquinas does present theology as an Aristotelian scientia, I doubt that this single fact “determines the purpose and structure of the Summa theologiae” (15) in any very detailed way. Jenkins further claims that the structure of the Summa is determined by the structure of God’s knowledge (220), but if God is truly [End...

Reviewed by: Long Commentary on theDe Anima of Aristotle Kara Richardson Averroes (Ibn Rushd) of Cordoba. Long Commentary on the De Animaof Aristotle. Translated with an introduction and notes by Richard C. Taylor, with Thérèse-Anne Druart, sub-editor. Yale Library of Medieval Philosophy. New Haven-London: Yale University Press, 2009. Pp. cix + 498. Cloth, $85.00. The Andalusian philosopher Ibn Rushd (d. 1198) had two names in the medieval Latin West: 'the Commentator', and 'Averroes'. The first of these underscores his importance as an interpreter of Aristotle ('the Philosopher'). The second was modified at least once by the adjective 'accursed' (in Duns Scotus's Ordinatio, bk. 4, d. 43, q. 2). 'That accursed Averroes' refers to the person who held that there exists only one human intellect. Averroes defends this view—typically called the unicity doctrine—in his Long Commentary on Aristotle'sDe Anima. Richard C. Taylor's translation of the Long Commentaryis based on Crawford's 1953 edition of the medieval Latin text (the original Arabic text is extant only in fragments). Brief portions of this commentary, which relate directly to the controversial and influential unicity doctrine, have previously been translated into English. Taylor's complete translation makes available in English for the first time the whole account of the soul and its powers, of which the unicity doctrine is a part. The translation will benefit graduate or advanced undergraduate students of the history of philosophy, as well as non-specialist scholars who want to understand what all the fuss was about. Taylor also provides extensive notes, which contain, among other things, Averroes' sources, extant Arabic fragments corresponding to the Latin, and explanations of technical terms and dense argumentation. For these reasons alone, Taylor's work must be considered a significant contribution to scholarship in the history of philosophy. There is also a lengthy introduction that presents the state of research on Averroes' psychology. Readers of Aristotle are familiar with his distinction, in De Anima3.5, between intellect in its passive role as a receiver of intelligibles and intellect in its active role as a maker of intelligibles. Averroes' unicity doctrine is remarkable as an interpretation of the passiveintellect, which is called the "material intellect" by analogy with prime matter (like prime matter, the material intellect can, in its own way, receive any form). To advocate the unicity of the activeintellect is not so remarkable. The latter view was standard in the Arabic tradition, which inherited it from Greek commentators on Aristotle. Those who affirm the unicity of the active intellect may hold the material intellect to be a power for receiving intelligibles [End Page 398]that is ultimately brain-based. Or they may hold the material intellect to be the supreme cognitive power of incorporeal human souls, which are multiplied in accordance with the number of human bodies. Averroes' defense of the unicity of the material intellect in the Long Commentaryinvolves a principled rejection of each of these alternative views, as well as a novel account of the role of intellect in human cognition. Taylor's introduction treats the development of Averroes' unicity doctrine and adjudicates a dispute about the dating of his Middleand Longcommentaries on the De Anima. Based in part on a comparison of portions of the Long Commentaryidentical to portions of the Middle Commentary, Taylor argues that the Long Commentaryis most likely the later work. These passages are identified in the notes to the translation. The introduction also provides a brief exegesis of the Long Commentary. This section explains the reasons behind the unicity doctrine, but misses the opportunity to highlight other points of interest in Averroes' psychology. Moreover, it leaves unaddressed certain questions likely to be pressing for newcomers to the text. For example, the unicity doctrine entails the denial that intellect is the seat of individual consciousness; so how would Averroes explain individual consciousness? What role, if any, does consciousness play in his account of cognition? Finally, Taylor's introduction includes a useful survey of Averroes' sources and a brief account of the influence of the Long Commentary, especially in the Latin West, which puts to rest the...

This paper surveys Bolzano's Beytrage zu einer begrundeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later.