Aquinas employs formal abstraction to secure the possibility of mathematics conceived as a theoretical Aristotelian science. Mathematics is a science that investigates real quantity and it grasps its necessary, universal, and changeless properties by means of formal abstraction. In accord with it the paper is divided into two parts. In the first part Aquinas’s conception of (formal) abstraction is explicated against the background of the Aristotelian theory of science and mathematics. In the second part the problems associated with formal abstraction in mathematics are critically assessed.

Famously, Plato argues that the soul pre-exists the body, continues to exist after the body dies, and can come to exist afterwards in another body. Aristotle argues against the transmigration of souls in On Generation and Corruption and for the most part appears not to endorse these Platonic doctrines. But in De Anima III.5 Aristotle also seems to argue that a part of the soul, usually dubbed the nous poiētikos, is separable from the body and eternal. This has presented interpreters of Aristotle with a problem: how can we reconcile Aristotle the naturalist philosopher with the apparently Platonist philosopher of De Anima III.5? Can we understand Aristotle’s position in De Anima III.5 in a way that does not conflict with the anti-Platonism he expresses in texts like On Generation and Corruption? I will argue that we can and offer an interpretation of De Anima III.5 that does not commit Aristotle to the position that the human soul is eternal. Even if Plato is right about the concept of the human soul, about what the human soul is in its own nature, he is wrong on ontological grounds. There are no eternal human souls.

The paper addresses the concept of useful fiction in texts authored by the fourteenth-century nominalists Henry Harclay, William Ockham, John Buridan and Nicholas Oresme. Three fundamental ideas related to fictionalism will be documented. First, the view that statements about fictions are covert conditionals with impossible antecedents. Second, the view that the primary concern with fictions is their practical utility, i.e., applicability in the context of a scientific discipline. Third, the view that it is useful to pretend that fictions of a certain kind can be used uniformly to represent physical reality, such that a natural phenomenon A is pretended to be a B, where Bs themselves are only pretended to be real.

The year 2021 saw the publication of Sven K. Knebel’s new book on Middle Knowledge. It is an exceedingly important research publication which deserves scholarly attention. The book contains a long introduction (consisting of various studies) and an edition of the fourth book of the Irish Jesuit theologian Luke Wadding’s incomplete work on scholastic theology. This present review article first recapitulates the origins and historical significance of the doctrine of Middle Knowledge. Then Knebel’s book as well as the career of Luke Wadding are introduced. I then discuss the place of Wadding’s work in the Jesuit discourse of ‘concordia’ and its relation to Molinism. In the subsequent sections, I investigate various doctrines defended by Wadding. These include his view of disjunctive necessity, his variant of the doctrine known as ‘connectionism’, and his use of various kinds of distinctions in theology. The study concludes with a critical assessment of Knebel’s publication. Despite all praise, I disagree with Knebel’s all too pessimistic view of the research landscape: We will soon be pondering over why Early Modern scholasticism has received so much attention in recent scholarship, rather than why it did not do so in the past.

One of Leonardo da Vinci’s autographed aphorisms states that Aristotle and Alexander were each other’s teachers. Interpreting it in light of those of Leonardo’s readings which instigated him to write it down along with providing him the material he needed to do so, I argue that the aphorism turns against Aristotle as an emblematically boastful, know-it-all man involved in undue occupation of all knowledge throughout history. Leonardo presents Aristotle as if he had been taught by the pernicious conqueror Alexander to act in scholarship in the way the Macedonian king had acted in politics and external affairs. The core of this critique goes back to a traditional anti-Aristotelian point in Antiquity, complies with the 15th- and 16th-century anti-Aristotelianism and goes hand-in-hand with Leonardo’s own view that intelligent men (including himself) are capable of going much further than Aristotle in the direction of discovering the truth. I identify Leonardo’s sources and I argue that Francis Bacon’s repeated bitter remark that the soul of Aristotle was infected by Alexander’s tyrannic character was quite probably based on Leonardo’s aphorism.

Gilbert Harman, in a well-known thought experiment, evokes the intuition that moral value can be perceptually seen. However, Harman dismisses the intuition, contending that moral concepts and judgments are the products of agent psychology and do not map onto mind-independent objects. Robert Audi, attempting to account for moral perception himself, fails to meet Harman’s challenge since his own ontological commitments do not allow for objects that moral concepts can map onto. This paper will offer an alternate theory of moral perception that maps moral concepts onto mind-independent entities, thereby meeting Harman’s challenge. To accomplish this, I offer that moral properties are not supervenient but are relational properties which possess their own non-reducible phenomenology.