Boaz Faraday Schuman

If you don’t like the conclusion of an argument by reductio, you can rebrand it as a paradox. We did this with Zeno, and more recently McTaggart. But what—if anything—is the principle at play? Is this practice of rebranding justified? Here I argue that sometimes, under certain conditions, it is. The reason why emerges from careful study of paradox and reductio in the distinctively socio-political logic of Abū Naṣr al-Fārābī, the Arabic philosophical tradition’s “Second Teacher” (after Aristotle). As we’ll see, al-Fārābī gives us a roadmap for a direction suggested in passing by Quine.

Suppose we’re at a horserace, and you turn to me and say, ‘Eclipse is at the finish line!’ But by the time you’ve finished saying this—by the time your utterance is complete—Eclipse is already well past the finish line, and what you’ve said is no longer true. But you did say something true. More generally, we can—and often do—say true things about events that take up less time than our utterances themselves. We can also contradict each other about such events—something that takes even more time. How is all this possible? In the twentieth century, this problem was discussed by Arthur Prior. In the 14th, John Buridan treated an older—probably 12th-century—version of it. Buridan’s treatment is more successful than Prior’s, which runs into Zeno’s paradox of the arrow. Buridan avoids the paradox, but faces further puzzles for his account of contradiction. In untangling these, we’ll uncover important latent features of his pragmatics and temporal logic—features that are supported by more recent research in linguistics. Ultimately, our considerations here will turn up new insight into the Gricean Cooperative Principle. In a slogan: to contradict is to cooperate.

Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of massive diagrams (_magnae figurae_) which map out the logical interrelations of two sets of doubly-general forms. These appear in a fourteenth-century MS of John Buridan’s _Summulae de Propositionibus_. In this paper, I present these diagrams, and determine the truth conditions of their different forms. To that end, I have developed a bespoke system of diagrams to display their truth conditions. As we will see, such forms present significant difficulties for an all-encompassing account of the role form plays in logic. Accordingly, they can tell us important things about the role logical form plays in Buridan’s account of logical foundations.

Three claims have dominated contemporary epistemology for the better part of a century: 1. Knowledge is justified true belief; 2. Treating knowledge as justified true belief has been standard in epistemology since Plato; 3. This ancient standard was torpedoed by Gettier’s (1963) paper, “Is Justified True Belief Knowledge?” Taken together, 1–3 form the background of the JTB theory of knowledge (henceforth JTB). According to JTB, a subject S knows a proposition p just in case (i) p is true; (ii) S believes p; and (iii) S’s belief is justified. But in 1963, Edmund Gettier dealt what is generally regarded to be a devastating blow to (iii), and therefore to JTB on the whole. So then, the thinking goes, some new version of JTB must be found, usually by modifying (iii), the J condition. Many many studies have been written on this, with mixed results. But what if the whole JTB enterprise is frustrated precisely because it was wrong-headed from the get-go?

Twelfth-century Paris was without a doubt the leading European intellectual center of its day, and it was so in part because of the logical schools that flourished there. Ambitious youths flocked from all over Europe to attend lectures, and the, mostly independent, masters who ran these schools in turn competed keenly to win scholarly fame and attract students. Particularly in the first half of the century there were a number of charismatic and gifted philosophers, who on the basis of ancient authors, such as Aristotle, Boethius, Porphyry, and Priscian developed highly sophisticated positions on a number of peren- nial problems in the areas of logic, philosophy of language, and metaphysics. Alberic was, according to his own contemporaries, one of the leading figures among these philosophers.

Can God’s foreknowledge change? There are two ways to interpret this question. First, is God capable of knowing future things that God, at present, does not know? Call this addition to divine foreknowledge. Second, is God capable of not knowing the things that God, at present, does know? Call this subtraction from divine foreknowledge. Peter Abelard rejected both possibilities. His rivals, Alberic of Paris and his school (the Albricani), held not only that both were possible, but even that both were true: God comes to know new things, and even comes not to know things formerly known. Accordingly, the Albricani argued that these such alterations in divine knowledge do not entail that there is any alteration in God. Here, I show how they developed their arguments along these lines, anticipating a later debate between Ockham and Robert Holcot, and much later thinking about infinity in David Hilbert. This paper also includes, by way of an appendix, the first ever Latin edition and English translation of key passages from two important 12th-century logical texts associated with Alberic's school: H10 (Bibliothèque de l’Arsenal, 910, fols 163ra–186vb) and H17 (Staatsbibliothek zu Berlin – Stiftung Preußischer Kulturbesitz, lat. fol. 624, fols 87vb–96vb).

Alberic of Paris was one of the leading philosophers of the 12th century. He was the main rival to Peter Abelard and, according to John of Salisbury, “a most fierce opponent of the nominalist school.” But although he was an important figure in his time, Alberic is almost completely unknown today. This collection of essays is the first ever dedicated to exploring and contextualizing the views of Alberic and his followers, the Albricani. It discusses topics such as universals, time, mereology, divine foreknowledge, fallacies, and modal logic, and shows that Alberic was an original thinker in a vibrant intellectual milieu. Contributors are Andrew W. Arlig, Enrico Donato, Sten Ebbesen, Charles Girard, Heine Hansen, Peter King, John Marenbon, Sofia Orsino, Boaz Faraday Schuman, Caterina Tarlazzi, Paul Thom, and Wojciech Wciórka.

Scholastic philosophers sometimes told jokes. Some of these have been preserved in the texts. (And some are even funny!). But beyond the general human interest in having fun, these thinkers had good theoretical reasons to value humor as well. This is because Aristotle himself claims that ready wit (eutrapelia) is a virtue. I published a paper on this in 2022 (“Scholastic Humor”), and since then colleagues have brought further examples to my attention. (Thanks, everyone!) Here, I aim to do three things: (i) catalog and present these jokes in Latin and facing English translation, (ii) give credit where it’s due, and (iii) expand the collection by encouraging researchers on Scholastic philosophy to find and submit examples of jokes from the texts. The text is open access, and will be updated on a rolling basis. So if you do find any such jokes, please email me at boaz [dot] schuman [at] kuleuven [dot] be

Spoken sentences have parts. Therefore they take time to speak. For instance, when you say, “Socrates is running”, you begin by uttering the subject term ("Socrates"), before carrying on to the predicate. But are the corresponding predications in thought also composite? And are such thoughts extended across time, like their spoken counterparts? Peter Abelard gave an affirmative response to both questions. Alberic of Paris denied the first and, as a corollary, denied the second. Here, I first set out Abelard’s account. I then present a series of arguments against Abelard, reconstructed from (sometimes fragmentary) manuscripts associated with Alberic’s school. I conclude with an observation about present philosophy of language: this twelfth-century debate points to some undefended (and largely unstated) assumptions common to our latest thinking about propositions. I highlight this by presenting recent accounts of two philosophers with radically different outlooks: Jeffrey King and Peter Hanks. Both their accounts take many of the same things for granted, as the Alberican criticisms make plain.

It may come as a surprise to readers familiar with the life and work of the Arts Master that he discusses the Eucharist at all. As he likes to remind us, theological topics are generally out of his wheelhouse. Even so, in his Questions on the “Metaphysics” of Aristotle (QM) 4.6, Buridan takes the sacrament of the Eucharist as a key data point in his discussion of Aristotle’s categories. In the Eucharist, the accidents of the bread and wine—their color, texture, and so on—remain intact, but the underlying substance is transubstantiated into the body and blood of Christ. Accordingly, God can preserve accidents independent of their underlying substance. Therefore, for our part we can use abstract accidental terms, like whiteness, without connoting any substances, like communion bread. Moreover, it follows that, contrary to Aristotle, substance and the accidental categories are not the most general genera. Instead, being (ens) is, as Buridan concludes. Here, I trace Buridan’s thought on the metaphysical and semantic matters of substance in light of the Eucharist. The Eucharist is for him not only a theological truth, but a metaphysical and semantic datum as well. I conclude by asking why Buridan did not take any and all questions about the Eucharist to be out of his ken. What does this tell us about his attitude toward theology?This paper also includes, as an appendix, the first ever English translation of the question under discussion (QM 4.6): “Does the term being [ens] signify substances and accidents by one single concept or notion?”

If an argument is valid, it is impossible for its premises to be true, and its conclusion false. But how should we understand these notions of truth and impossibility? Here, I present the answers given by John Buridan (ca. 1300-60), showing (i) how he understands truth in his anti-realist metaphysics, and (ii) how he understands modality in connection with causal powers. In short: if an argument exists and is valid, there does not exist a power capable of making the premises true and, at the same time, making the conclusion false.

Many things can be other than they are. Many other things cannot. We talk about such things all the time. But what is this talk about? One answer, presently dominant in analytical philosophy, is that we are speaking of possible worlds: if something can be other than it is, then it actually is that way in some (other) world. If something cannot be otherwise, it is not otherwise in any world whatsoever. But what are these worlds? David Lewis famously claims that every world exists, just like ours does. In contrast, the medieval thinker John Buridan understands modal logic in terms of objects and causal powers: if something can be other than it is, then there is a causal power that can make it that way. If it cannot, then no causal power—not even God—can make it otherwise. As we’ll see, (i) the Lewisian plurality is not possible on Buridan’s account, and accordingly (ii) a basic tenet of classical theism is untenable on Lewis’s metaphysics. In short, either the Lewisian plurality is incoherent, or a core monotheistic tenet is impossible.

Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of massive logical diagrams (magnae figurae) which map out the logical interrelations of two sets of doubly-general forms. These appear in a fourteenth-century MS of John Buridan’s Summulae de Propositionibus. In this paper, I present these diagrams, and determine the truth conditions of their different forms. To that end, I have developed a bespoke system of diagrams to display their truth conditions. As we will see, such forms present significant difficulties for an all-encompassing account of the role form plays in logic. Accordingly, they can tell us important things about the role logical form plays in Buridan’s account of logical foundations.

What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical discussions as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself

Scholastic philosophers can be quite funny. What’s more, they have good reason to be: Aristotle himself lists ready wit (eutrapelia) among the virtues, as a mean between excessive humor and its defect. Here, I assess Scholastic discussions of humor in theory, before turning to examples of it in practice. The last and finest of these is a joke, hitherto unacknowledged, which Aquinas makes in his famous Five Ways. Along the way, we’ll see (i) that the history of philosophy is not so hostile to humor as is commonly supposed; and (ii) that the competing theories of humor like the Incongruity Theory and the Release Theory are not altogether incompatible. We’ll also see at least one example of an apparent attempt by modern translators to excise humor from a medieval text. Our considerations will open a window into what oral discussion and debate at medieval universities was actually like, and how we should understand the relationship between the texts we have now and the exchanges that actually occurred then.

What does success in online teaching look like? There are two ways to answer this question. The first defines success in terms of replacement of educational means: for example, how closely does an online lecture approximate its offline counterpart? The second defines success in terms of educational goals: for example, how well does an online lecture facilitate learning, compared with its offline counterpart? The first is a trap: it commits us to an endless online game of catch-up with offline models of teaching. Instead, we should adopt a goal-oriented approach, mindful of obstacles to online teaching. As a case study, I present practices developed using this approach to teach philosophy online in 2020. An important upshot is that this approach leaves us open to ways in which online teaching is actually better than its offline counterpart. I conclude with some examples of these, and discuss their future implementation.