In lieu of an abstract, here is a brief excerpt of the content:There are only three surviving biographical notices regarding Marcus of Orvieto: two as colophons of Vatican manuscripts and a third as an entry in a catalog of the papal library in Avignon where we read: "Item, liber de mortalitatibus septem Martini de Urbevetani Ordinis Minorum." While the spelling of the book title and its author can be attributed to scribal errors or misreadings, the 'seven,' place of origin, and (...) religious order affiliation are accurate. Marcus's Liber de Moralitatibus is indeed divided into seven treatises: On the celestial bodies, On the elements, On the birds, On the fish, On the animals, On trees and plants and On precious gems. The colophons of the two Vatican manuscripts attest to his being a Friar Minor: Ego frater Marcus Urbis Veteris Fratrum Minorum Ordinis pauperculus. The prooemium of the Liber de Moralitatibus attests to the fact that Marcus's patron was Benedict Gaetani cardinal of St. Nicholas in carcere Tulliano,' the future pope Boniface VIII. This would put the time of composition circa 1290. Several allusions in Marcus's work to Paris, viz. the Parisian masters, its patron Ste. Genevieve, indicate that Marcus was at one time a student there and it is conceivable that Benedict commissioned the work while he was a papal legate there. Marcus's opus falls into the category of exempla literature, i.e. a source book for preachers.We offer the English translation of the chapter on pelicans as typical of Marcus's way of proceeding which, generally speaking, is threefold. First a physical description, which was generally copied from Bartholomew of England's 'On the Properties of Things,' secondly its spiritual signification attested to by pertinent passages from Scripture and bolstered by citations from the Fathers and Doctors of the Church, and thirdly examples of persons who exemplify the spiritual lesson either supportively or adversely. The legend of the pelican piercing its breast in order to revivify its dead chicks was familiar in Christian literature and art signifying analogously Christ's salvific blood redeeming the human race from its fallen state. The following is the English translation of Marcus's treatise 3, 'De avibus,' chapter 31.Chapter 31: On the pelicanThe pelican is seen to possess the following conditions or properties according to the doctors.1. First of all, as Isidore says, it is a "bird dwelling in solitude along the banks of the Nile." This signifies preachers and contemplative persons who flee the vanities of the world and occupy themselves with heavenly consolations or delightful and re-creative consolations of Sacred Scripture, Psalm 54, 8-9: Far away I would flee; I would lodge in the wilderness. I would hasten to find shelter from the violent storm and the tempest. Bernard, On the Canticle of Canticles and in his sermons: "Divine consolation is delicate, it is not given to those preoccupied with what is alien to it." Ambrose, On Luke: "Those preoccupied with secular vanities cannot know what is divine."2. Secondly, as Isidore says, whatever it eats, it first dips in water with its foot and having done so, using the foot as a hand as it were, puts it [the morsel] in its mouth. This signifies doctors [i. e. teachers] and preachers who practice what they teach or preach after the example of the Apostle, Romans 15, 18: I will not dare to speak of anything except what Christ has accomplished through me. Jerome, To Nepotian: "Make sure your deeds do not 'confound' your words, lest when you speak in the assembly someone might say to himself: 'Physician, cure yourself'."3. Thirdly, as Isidore says, of all the birds, with the exception of the phylargum, only the pelican uses its foot as a hand. This signifies a devout religious who frequently, motivated by holy desires and affections, prefers holy meditations rather than manual labor. 1Tim. 4: 7-8: Train yourself for devotion, for while physical training is of.. (shrink)

In the process of completing his critical edition of Marcus of Orvieto's Liber de Moralitatibus, Girard J. Etzkorn happened upon a set of questions attributed to Henry of Ghent at the end of Rome's Bibliotheca Angelica codex 750. These questions are edited in this volume under the proviso "attributed to" so that scholars may compare the texts with other works of the Ghentian master known to be authentic. Etzkorn concludes that the ten questions appear to be of (...) two literary genres. Moreover, the ten questions seem to be "selected" questions and were not likely disputed at the same time. Future investigations are essential to find out if the questions may indeed be attributed to Henry himself or whether they were written by one of Henry's disciples who was copying the thoughts and words of the master. (shrink)

Religious pluralism (the view that all the great world religions are equally true) is largely motivated by the fear that religious exclusivism ( the view that there is just one correct religion) leads to intolerance and oppression of those holding differing religious views. I claim that this suggests a false dichotomy: either be a tolerant pluralist or an intolerant exclusivist. I argue, first, that the seventeenth-century doctrine of toleration supports the claim that exclusivists of differing sects can peacefully coexist and, (...) second, that religious pluralism has harmful consequences. Exclusivism (tempered by toleration) is the best solution to the challenge of religious diversity. (shrink)

Religious pluralism (the view that all the great world religions are equally true) is largely motivated by the fear that religious exclusivism ( the view that there is just one correct religion) leads to intolerance and oppression of those holding differing religious views. I claim that this suggests a false dichotomy: either be a tolerant pluralist or an intolerant exclusivist. I argue, first, that the seventeenth-century doctrine of toleration supports the claim that exclusivists of differing sects can peacefully coexist and, (...) second, that religious pluralism has harmful consequences. Exclusivism (tempered by toleration) is the best solution to the challenge of religious diversity. (shrink)

The expression conditional fallacy identifies a family of arguments deemed to entail odd and false consequences for notions defined in terms of counterfactuals. The antirealist notion of truth is typically defined in terms of what a rational enquirer or a community of rational enquirers would believe if they were suitably informed. This notion is deemed to entail, via the conditional fallacy, odd and false propositions, for example that there necessarily exists a rational enquirer. If these consequences do indeed follow from (...) the antirealist notion of truth, alethic antirealism should probably be rejected. In this paper we analyse the conditional fallacy from a semantic (i.e. model-theoretic) point of view. This allows us to identify with precision the philosophical commitments that ground the validity of this type of argument. We show that the conditional fallacy arguments against alethic antirealism are valid only if controversial metaphysical assumptions are accepted. We suggest that the antirealist is not committed to the conditional fallacy because she is not committed to some of these assumptions. (shrink)

We present a single sequent calculus common to classical, intuitionistic and linear logics. The main novelty is that classical, intuitionistic and linear logics appear as fragments, i.e. as particular classes of formulas and sequents. For instance, a proof of an intuitionistic formula A may use classical or linear lemmas without any restriction: but after cut-elimination the proof of A is wholly intuitionistic, what is superficially achieved by the subformula property and more deeply by a very careful treatment of structural rules. (...) This approach is radically different from the one that consists in “changing the rule of the game” when we want to change logic, e.g. pass from one style of sequent to another: here, there is only one logic, which—depending on its use—may appear classical, intuitionistic or linear. (shrink)

We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...) F the point where the increasing F-sequence terminates. We apply these results to inverse Goodstein sequences, i.e. increasing (1 + Id) (ω) -sequences. We show that the theorem every inverse Goodstein sequence terminates (a combinatorial theorem about ordinal numbers) is not provable in ID 1 . For a general presentation of the results stated in this paper, see [1]. We use notions and results concerning the category ON (ordinal numbers), dilators and bilators, summarized in [2, pp. 25-31]. (shrink)

These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting (...) with Godel's paradox --so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination. Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction, all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way. (shrink)

Ceteris Paribus clauses in reasoning are used to allow for defeaters of norms, rules or laws, such as in von Wright’s example “I prefer my raincoat over my umbrella, everything else being equal”. In earlier work, a logical analysis is offered in which sets of formulas Γ, embedded in modal operators, provide necessary and sufficient conditions for things to be equal in ceteris paribus clauses. For most laws, the set of things allowed to vary is small, often finite, and so (...) Γ is typically infinite. Yet the axiomatisation they provide is restricted to the special and atypical case in which Γ is finite. We address this problem by being more flexible about ceteris paribus conditions, in two ways. The first is to offer an alternative, slightly more general semantics, in which the set of formulas only give necessary but not sufficient conditions. This permits a simple axiomatisation. (shrink)