Medieval logic

This article deals with a brief difficultas in the Tractatus de compositione propositionis mentalis by Fernando de Enzinas: qualiter copule significent tempus et an copule de presenti et preterito sint synonime. A progressive determination of the signification of the copula is analysed: first, Enzinas defines his position about the principal syncategorematic signification of the copula; then, he analyses the sense of the consignification of time traditionally attributed to the copula. The originality of Enzinas’ position is highlighted, given the fact that he gives preference to the question as to how the copulae signify time rather than the question as to which time the copulae signify.
http://www.unav.es/filosofia/pilzarbe1/Enzinassignificatiocopulae_submitted.pdf

Partant du constat que la notion de présupposition n'a donné lieu qu'à de très rares études historiques questionnant ses conditions d'émergence et la stabilité de son contenu conceptuel, cet article examine l'hypothèse selon laquelle la doctrine médiévale des exponibilia aurait joué un rôle déterminant dans la mise en évidence de cette notion. Après avoir explicité la méthode d'analyse des propositions dites exponibles et dressé une typologie de ces propositions grammaticalement simples mais sémantiquement complexes, l'article souligne tout d'abord que toutes les familles d'exponibles ne recèlent pas des présuppositions, si bien que la corrélation établie entre cette doctrine et la mise à jour des présupposés se doit d'être affaiblie. L'examen des exponibles de type exclusif, qui constituent un cas favorable de propositions comportant une présupposition, est ensuite entreprise et cette étude permet de dégager les différents facteurs (absence de hiérarchisation, emploi de la négation, etc.) conduisant à remettre en cause l'idée que les médiévaux jetèrent les fondements d'une conception linguistique de la présupposition. Mais cette analyse, qui met également à jour que la théorie des descriptions définies de Russell pose en matière de présupposition les mêmes problèmes que la théorie médiévale, conduit alors à montrer que les difficultés épistémologiques dont est porteuse l'étude historique de la notion de présupposition proviennent, d’une part, de ce que l'identification des présupposés est tributaire du cadre théorique choisi et, d’autre part, de l’instabilité de la notion même de présupposition qui, à l’heure actuelle, ne fait pas encore l'objet d'un consensus.

This thesis is a detailed examination of the logico-semantic system propounded by the English philosopher and theologian William of Ockham (c.1287 – c.1347). It provides a reinterpretation of Ockham's account of mental content and mental-language semantics, as well as of his theory of consequential goodness. It does so from the standpoint of an inferentialist theory of meaning, in rejection of previous attempts made from the standpoint of internalist and externalist theories of mental content. Chapter 1 ('The Scientific Status of Logic') provides an account of Ockham's understanding of logic as a rational, practical, ostensive science. Chapter 2 ('The Received Interpretation') presents and casts doubt upon the arguments put forward by the defenders of both externalist and internalist construals of Ockham's semantic theory. Chapter 3 ('An Inferentialist Construal') presents the central tenets of a inferentialist theory of meaning. In order to show how Ockham's system can be understood within such a semantic paradigm, we will have to set out at least three things. First, Chapter 4 ('Ockham's Propositionalism') argues that the mature Ockham actually embraced a propositionalist theory of meaning. Second, Chapter 5 ('Obligationes and the Normativity of Asserting') seeks to prove that such a theory of meaning can only be properly understood against the normative background provided by his theory of obligationes. Finally, Chapter 6 ('Consequences') argues that Ockham's theory of consequential goodness is materialist, not formalist. That is to say, that the goodness of a certain kind of consequence ultimately depends upon the meaning of its propositional parts, rather than upon its structure. It is then shown that all remaining kinds of consequences (syllogisms included) are to understood with respect to these material inferences. The main sources of this research are Ockham's Ordinatio, his Summa logicae, and his Quodlibeta septem. As regards the inferentialist theory of meaning, Robert Brandom's Making it Explicit (1994) and Wilfrid Sellars 'Inference andMeaning' (1953) were essential to this research.

Key-words: William of Ockham, logic, semantics, consequence, inference, inferentialism, normativity, obligationes.

This chapter argues that Peter Abelard's theological appropriation of the World Soul should be seen within the larger context of not one, but Platonic triads that were widely available and used in the medieval tradition, the God-Mind-Soul triad and the God-Archetype-Matter triad. It discusses the earliest extant text of Abelard's theological works, the Theologia 'Summi Boni' . The chapter analyses the Augustinian influence upon Abelard's interest in Platonism. Abelard's viewpoint is then positioned among the other significant Platonic interpreters of his day, including Bernard of Chartres, William of Conches, and Thierry of Chartres. Finally, it shows that each of the thinkers differed significantly on four things: how the first triad relates to the Trinity; how the second triad relates to Creation; how both triads together can relate the Trinity to Creation; and how one ought to use language to describe the Divine Nature in the act of Creation. Keywords: Augustine; medieval tradition; Peter Abelard; Platonic triads; Platonism; Theologia 'Summi Boni' ; Trinity

This essay aims to deepen the semantic doctrine of John Buridan, in the light of the first three conclusions that he formulates in the first chapter of his 'Sophismata'. In particular, it is shown how in the thought of the Parisian master the notion of signification is conceived as a transitive attitude, which spreads between the different levels of language and determines their relations of subordination. Particular attention is paid to the 'evidentiae' proposed by the author in support of his theses. These arguments, in fact, turn out to be relevant not only for their theoretical pertinence, but also for their feature of fixing unequivocally the characteristics, as well as the speculative scope of some fundamental notions of scholastic logical doctrine. Eventually, one tries to show how at the basis of Buridan's theories lies the attention he devotes to the cognitive function performed by language, which justifies the passage from signifying ('significare') to conceiving ('concipere'), as soon as the discursive dynamic reaches the mental level.

The assertion candidate expresses a potential logical-linguistic object that can be asserted. It differs from both the act and the product of assertion; it needs not to be actually asserted and differs from the assertion made. We investigate the medieval origins of this notion, which are almost neglected in contemporary logic. Our historical analysis suggests an interpretation of the assertion candidate within the system of logic for pragmatics.

In his use of the notion of impositio as basis for conventional signification, John Buridan puts in perspective the figure of the first impositor nominum in favour of (1) a structure of dialog which at the same time insist on the liberty of the speaker and gives an irreducible place to the recipient of the message ; (2) of the consensus inside a community, either in a restricted or temporal frame, or in the frame of a given language. The first institution, that the usage takes up and modifies, is presented as a convention, commonly accepted, more than as the mythical act of creation of a universal language. So Buridan roots, at least in principle, the object of his analyses in plural language, even if for him, it is about exhibiting its latent conceptual structure
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Dans ses usages de la notion d’imposition comme base de la signification conventionnelle, Jean Buridan relativise la figure du premier instituteur des noms au bénéfice (1) d’une structure de dialogue qui tout à la fois insiste sur la liberté du locuteur et accorde une place irréductible au destinataire ; (2) du consensus au sein d’une communauté, soit dans un cadre restreint ou temporaire, soit dans le cadre d’une langue donnée. L’institution première que l’usage reprend et modifie est présentée comme une convention communément admise, plus que comme l’acte mythique d’instauration d’un langage universel. Buridan ancre ainsi, du moins en principe, l’objet de ses analyses dans un langage pluriel, même s’il s’agit pour lui d’en exhiber la structure conceptuelle latente.

The article is dedicated to the usage of the contemporary formal axiology apparatus, which
was designed by Vladimir O. Lobovikov (b. 1951) on the basis of ideas and work by L. von Wittgenstein,
G. H. von Wright, V. A. Smirnov, to the theory of silence and communication put forward by
the most prominent mundane philosopher of fourteenth-century Byzantium, Theodore Metochites (ca.
1270–1332). Both the authors belong to that philosophical Meta-tradition which has been insisting on
the consistent and hedonistic (but non-utilitarian) character of our knowledge. It was Albert the Great,
Aquinas’s mentor, who represented this Meta-tradition in the Medieval Christian West. In accordance
with the canon of Lobovikov’s and von Wright’s axiology we give special tables of those functions
which are connected with the oral and written communication, as well as with silence, so as to show by
dint of these that a positive speech on something/ somebody coincides with the norms of commnication,
unloike a pejorative or ignominious speech, all this being consistent with G. H. von Wright’s and
N. D. Arutjunova’s general appraisal theory. Besides, both formal axiology and Metochites ascribe a
superior value to silence, thus enabling us to pose a question about their proximity, if only a superficial
one, to the Hesychasts and Wittgenstein. The apparatus in question is instrumental in our trying to
build such a formal hermeneutical model that makes one understand certain discrepancies between
an author’s self-representation in a text, on the one hand, and his appraisals in the consequent
historiography, on the other. This model also elucidates Metochites/ views of the ontological
and epistemological foundations of mathematics.

Η θεωρία της συνέπειας είναι ένας κλάδος της λογικής που μελετά ως ξεχωριστό θέμα τις σχέσεις εξάρτησης μεταξύ προτάσεων. Έτσι, κατά κάποιον τρόπο, η θεωρία της συνέπειας είναι γενικότερη από τη συλλογιστική. Στηρίζεται σε παλιά θεμέλια, αλλά ως ξεχωριστό λογικό πεδίο γεννήθηκε γύρω στο 1300. Η πιο δημιουργική φάση της ήταν το 1320–1340 (Burley, Ockham, Buridan). Μετέπειτα λογικοί την επεξεργάστηκαν και διατηρούσε μια καθιερωμένη θέση στα λογικά βιβλία. Η συνέπεια (στη λατινική γλώσσα consequentia, «επακόλουθο», «αποτέλεσμα») είναι ένα – συχνά υποχρεωτικό, αλλά τουλάχιστον δυνατό – συμπέρασμα. Ανάλογα με το περιβάλλον, είναι πιο συχνές πιο συγκεκριμένες εκφράσεις. “Συνέπεια” σημαίνει επίσης τη αποτελεσματική ορθότητα των ενεργειών ενός ατόμου. Η αντίθετη συμπεριφορά αναφέρεται επομένως ως “ασυνεπής”, για παράδειγμα, εάν παραλειφθεί μια ανακοινωμένη ενέργεια. Μια «συνέπεια» από το προκείμενο (ή τα προκείμενα) σε ένα επακόλουθο μπορεί να θεωρηθεί καλύτερα ως ένα έγκυρο συμπέρασμα. Σύμφωνα με τον τυπικό ορισμό της θεωρίας, μια συνέπεια ισχύει όταν το προκείμενο δεν είναι συμβατό με το αντίθετο του επακόλουθου. Οι λογικοί αναζήτησαν γενικούς κανόνες για τέτοιες σχέσεις. Μερικοί κανόνες ήταν «αποδεικτικοί-θεωρητικοί», δηλαδή, μια συνέπεια ακολουθείται από άλλες συνέπειες. Ορισμένοι κανόνες αφορούσαν την εγκυρότητα ενός τύπου συμπεράσματος. Πολλά από τα θεωρήματα της προτασιακής λογικής αποδείχτηκαν σε αυτό το πλαίσιο και σύντομα προστέθηκαν τροπικές εμπεριστατώσεις.

Premises rhymes with nemesis. The words 'premises' and 'nemesis' are used autonymously above. A word that denotes itself-that is used to mention itself-in a given statement is used autonymously. Autonymy is the phenomenon of autonymous usage. The word premises rhymes with the word nemesis. In the preceding statement, 'premises' and 'nemesis' are used parautonymously-as they are in this statement. A word denoted in a given statement by an expression containing that word is used parautonymously. Parautonymy is parautonymous usage. Autonymy cannot "iterate"; parautonymy can-at least in "semi-ideographic" contexts. 'Plato' begins with pee. ' 'Plato' ' begins with a left quotation mark. Ancient Greek and Medieval Latin writings were usually phonographic-readable aloud. Both languages permitted autonymy and both had phonographic devices for parautonymy. The two-letter Ancient Greek word to-also used for the definite article-marks parautonymy: aristotelês denotes Aristotle, to aristotelês denotes Aristotle's Greek name, the word aristotelês. In Medieval Latin, which lacks articles, the otherwise meaningless two-letter word li marks parautonymy: aristoteles denotes Aristotle, li aristoteles denotes Aristotle's Latin name, the word aristoteles. Autonymy permits ambiguity not present in parautonymy. Socrates is Greek. The name Socrates is Greek. This study-sharpening Corcoran's discussions in this BULLETIN vol. 12 (2006), pp. 219-40-surveys logic-related autonymy and parautonymy (and use-mention distinctions). We discuss previously ignored questions: whether translations should respect the two distinctions of autonymy versus parautonymy and phonography versus ideography.

A short, early anonymous logical treatise on consequences, translated from the critical edition of N. J. Green-Pedersen (Cahiers de l’Institut du Moyen-Âge Grec et Latin 35 (1980):, pp. 1-28). The ms. also contains Burley’s early treatise on consequences, and is dated by the scribe to 1302.

The question 'whether an utterance (word/term/name) loses its signification with the destruction of things (i.e. things signified)' is raised as a question about the truth-value of assertions with an empty term as a subject, namely as a sub-problem of the sophism 'Whether "omnis homo de necessitate est animal" is true when no man exists (=OHNEA)'. In this paper, I shall introduce the discussions as they are present in Roger Bacon's "De signis" IV.2, Peter John Olivi's "Quaestiones logicales", q. 2–3, Boethius of Dacia's OHNEA, and Anonymus Alani's OHNEA. These texts present us with four different ways of relating the question about signification to OHNEA, and therefore with four different positions regarding the relation between signification and empty reference. I shall use Anonymus Alani as the guiding thread of my analysis, inserting other positions where it is relevant.

In this paper I examine the phenomenon of order-dependence in obligational disputations. I am concerned with two medieval authors, Walter Burley and Richard Kilvington. In Burley’s theory I especially concentrate on two of the ‘useful’ rules of positio, namely “one must pay special attention to the order” and “when a false contingent proposition is posited, one can prove any false proposition that is compossible with it”. I argue that there is an intimate connection between these two rules in that they both express consequences of the notion of relevance inherent in the constitutional rules in connection with a false positum. Closely connected to the concept of order-dependence are the special kinds of incon­sistencies that can be found in Burley’s theory. I call these ‘interdisputational’ incon­sistencies. Kilvington finds these consequences of Burley’s theory unacceptable. According to Kilvington, there should be no inconsistencies and, consequently, no order-dependence. Regretfully, he does not present any explicit revision of the rules for obligational disputation in which his views are incorporated. Finally, I turn to the ‘relativised’ interpretation of Burley’s theory, and more specifically the proposed purpose or meaning of the first useful rule. According to Paul Spade, Burley may be giving advice in saying “one must pay special attention to the order”, referring to some preferred ordering of propositions. On my view, this interpretation is highly problematic. Burley’s own explanation of the rule does not seem to support such an interpretation. Furthermore, the second of the two rules examined in this paper seems difficult to reconcile with the notion of a preferred order. If however, as I propose, the rules are simply seen as consequences of the constitutive rules, Burley’s explanation is no problem and Kilvington’s critique becomes clearly intelligible.

http://dx.doi.org/10.4067/S0718-92732021000200177
En este artículo, busco clarificar algunos aspectos de la teoría del nombre de fray Luis de León contenida al comienzo de De los nombres de Cristo mediante una comparación con obras de lógica escolástica, particularmente las Summulae de Pedro Hispano y el tratado homónimo de Domingo de Soto. Procuraré mostrar que dicha teoría solo puede comprenderse acabadamente desde esta perspectiva, sin negar la relevancia de otras, en una medida mayor que la que hasta ahora han presentado los investigadores. Me ocuparé especialmente de la presencia de los conceptos de "término simple", "suppositio" y "significatio", y del modo en que fray Luis los articula de tal forma que resulten claramente reconocibles en sus detalles por quien está versado en ellos y, al mismo tiempo, pone su sentido filosófico originario al servicio de la intención fundamental de su obra.

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions maintains its validity when some of the terms included in these propositions are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for the truth of propositions like ‘It is possible for my son to be alive’ or ‘it is necessary that all men are animals’ that their subjects’ referents exist. Then, I present the schemata of inferences that Abelard proposes to describe the logical behaviour of de rebus modal propositions. I argue that these systems of relations are valid only as long as all the terms contained in the formulas have an existing referent. I also claim that Abelard was aware of this difficulty (at least in the Logica Ingredientibus), an...

MSS/ 10124 in the Biblioteca Nacional, Madrid, is a luxurious Italian manuscript that was housed at the Marquis of Santillana's library in the fifteenth century and that preserves two older texts related to the Aristotelian tradition, namely, Alderotti's Etica in volgare, and an Italian compendium of logic. The paper will present the main features of this Compendio di Logica as a sample of fifteenth-century vernacular Humanism and as an evidence of the fact that Aristotelianism might have had a more important role in fifteenth-century thought than usually considered. One of the peculiarities of the Compendio is the replacement of induction by division as one of the three basic methods of knowledge acquisition, following in the footsteps of thirteenth-century Aristotelianism and being witness to the sway of Medieval philosophy in vernacular Humanism. How did an Italian manuscript come to be in fifteenth-century Castile? During the fifteenth century, classical translations were resumed due to the necessity to find new models of morality, and to revise the style and contents of Medieval versions, so that humanists could work on them and take advantage of them. MSS/ 10124 in the Biblioteca Nacional, Madrid, shows how humanists, in a broad sense, reshaped and translated old scholastic texts to adapt them to lay readers' necessities. The focus of the revival in the study of classical texts in the Quattrocento was Florence, Italy, where Castilian bibliophiles traveled to acquire new manuscripts to mitigate the shortage of classical texts in Castile. Some of these bibliophiles were sent to Florence by the Marquis of Santillana (1398–1458), the owner of the manuscript that we are now examining.

Aristotle's system of direct and indirect deductions is discussed by Smiley and other recent authors. Aristotle's system of direct and indirect reductions is discussed in older works by Mill, De Morgan, Łukasiewicz, and many others. Although the distinction between them is clear in Aristotle's work, the two seem not to have been contrasted by commentators. A deduction of a conclusion from a premise set is a sentence-sequence constructed by chaining simple inferences to show that the conclusion is implied by the premise set. A reduction is an argument-sequence wherein each argument after the first is constructed from the previous one by " weakening " the premise set, by " strengthening " the conclusion, or by " contraposition " , i.e. by replacing one premise with the contradictory opposite of the conclusion and taking as the new conclusion the contradictory opposite of the replaced premise. " Weakening " here means replacing a sentence by its Aristotelian converse and " strengthening " is the reverse. The initial argument is thereby " reduced to " the final argument. Some valid arguments reduce to invalid: Aab, Abc/ Iac reduces to Aab, Icb/ Iac and to Aab, Abc/ Aca. However, as Aristotle noticed, invalid arguments reduce only to invalid, and thus any reduction ending with an obviously valid argument must have started with a valid argument, thus providing a mark of validity. Exaggeration or misapplication of this point seems to have led to a confusion of deduction with reduction and to mistaking the role of reduction with that of deduction. This paper shows, to the contrary, (1) that Aristotle held to a sharp separation between the two processes (discussing now one, now the other, and also implicitly contrasting them by mentioning both together) and (2) that reduction is not a method of inference but rather a process for studying relationships among syllogisms (cf. 29b26), an almost totally separate enterprise. Although reading certain reductions backward suggests a deduction system, the system thus suggested is a Gentzen-sequent natural deduction system (with arguments as lines) rather than a Jaskowski-supposition natural deduction system (with sentences as lines) as attributed to Aristotle by recent authors. Taking arguments to be conditional sentences leads to transformation of a Gentzen-sequent system into an axiomatic system of the sort proposed by Łukasiewicz. END

Aquinas divides knowledge into two types: certain and probable. Broadly construed, certain knowledge (scientia) is of what is either necessary or true for the most part. Necessity pertains to axiomatic systems, indemonstrable principles of demonstration and perhaps certain natural phenomena such as eclipses. Statistical natural phenomena are the subject of knowledge that is true for the most part. Probabilistic knowledge, on the other hand, comprises a variety of epistemic attitudes that correlate with degrees of assent that fall short of certainty, ranging from low (mere fancy) to high (belief). Scientia is the product of a syllogism that either (1) demonstrates the inherence of a property in a subject by a middle term that immediately designates the essence of the subject, or (2) demonstrates a necessary connection between an essence and a state of affairs by a middle term that indirectly designates the essence.

The influence of Cajetan’s De Nominum Analogia is due largely to its first three chapters, which introduce Cajetan’s three modes of analogy: analogy of inequality, analogy of attribution, and analogy of proportionality. Interpreters typically ignore the final eight chapters, which describe further features of analogy of proportionality. This article explains this neglect as a symptom of a failure to appreciate Cajetan’s particular semantic concerns, taken independently from the question of systematizing the thought of Aquinas. After an exegesis of the neglected chapters, which describe the semantics of analogy through the three levels of cognition (simple apprehension, composition and division, and discursive reasoning), the article concludes with observations about the relationship between Cajetan and Aquinas and the philosophical and historical significance of Cajetan’s approach to the semantics of analogy.

spent his formative years untying logical knots at Oxford. The knottiest of those knots were to be found in semantic paradoxes like that of the well-known liar who says, " I am lying to you right now. " In order to unweave these tangled threads, Bradwardine made use of an unloved instrument from the medieval logicians' toolkit: the ut nunc consequence. 1 Often translated as 'matter of fact' consequence, this logical maneuver involved the supposition of a contingent premise which may not hold 'absolutely' (simpliciter) or in every case. Bradwardine embraced the ut nunc consequence as central to his understanding of how the truth of propositions may be judged in relation to their contingent premises. By relating insolubles like the Liar's Paradox back to contingent, material states of affairs, he was able to push past the limits of paradox and ground truth anew in an apprehension of the facts of the matter—at least, as of now (ut nunc). While Bradwardine's idiosyncratic reliance upon the ut nunc has already been established, there remains work to be done on how this dependence of logic on temporality relates to the theological account of time we meet in his De Causa Dei contra Pelagianos. One central claim there is that human matters can perhaps be understood in terms of temporal instants, whereas God must not be so measured, dwelling as He does in the simultaneity of a " super-instantaneous presentiality, " which Bradwardine dubs the " envy [simultas] of the temporal instant. " 2 The goal of this paper is to unearth Bradwardine's underlying philosophy of

This course picks up where medieval logic I: medieval contributions to the logica vetus left off, albeit without presupposing a knowledge of its contents. Where the former course examined medieval accounts of predicables, categories and propositions grounded in the texts available throughout the medieval period in the Latin west – Porphyry's Isagoge and Aristotle's Categories and On Interpretation – this course looks primarily at the developments of the 13th and 14th century, grounded in the reemergence of two 'new' texts of Aristotle's logic – the Topics and On Sophistical Refutations. This course examines the medieval theories of fallacies and topical inference, along with their influence on the development of theories of consequences. We begin with an earlier Boethian text, along with some material on supposition to provide some needed background for the treatment of fallacies and consequences. From here, we jump into developments concerning these latter topics.

La "Margarita Philosophica" es una enciclopedia del saber redactada en Friburgo de Brisgovia a finales del s. XV por Gregorius Reisch. Este trabajo analiza el libro segundo, dedicado a la lógica, según la edición de 1517, que fue la octava y última, siguiendo el ejemplar que se conserva en la Universidad de Salamanca. De ahí se desprende que la lógica de Reisch sigue el modelo de la doctrina medieval de la "consequentia", sin quedar afectada por el desplazamiento hacia la retórica propio del Renacimiento. Se detectan lugares comunes como la confusión en torno a la cuarta figura del silogismo, presente también en las súmulas de Pedro Hispano, o la ejemplificación del "exemplum" que delata el lugar de composición. Se ofrece un recorrido reflexivo por los ocho tratados del libro: "De predicabilibus", "De predicamentis", "De propositione", "De argumentatione et syllogismo simpliciter dicto", "De syllogismo dialectico", "De syllogismo demonstrativo", "De syllogismo sophistico" y "De passionibus terminorum quas parva logicalia dicunt".

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 , 189–218] or else it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 ; Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 , 58–78]. Against , I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity.

Mathematical examples in Ibn Sina’s logic.
In the paper we argue that the mathematical examples accompanying Ibn Sina’s outlines of his logical ideas do not only serve as illustrations to the provisions of his logical doctrine, but also point to the special circumstances of verification judgments dictated by the ontological status of objects considered in them, as well as the characteristics of their study.