This paper seeks to articulate the relationship between medieval logic and theology. Reviewing modern scholarship, we find that the purpose of medieval logic, when it is even inquired about, has proven difficult to articulate without reference to theology. This prompts reflection on the metaphors of logic as a “tool” and a “game”: a tool is not merely instrumental, insofar as it can have its own intrinsic goods and can shape and be shaped by that which it serves; likewise a game, (...) with its own intrinsic goods, may yet contribute to extrinsic goods as well. After reviewing some distinctive ways in which theology shaped developments of medieval logic, this paper summarizes key examples from the work of Thomas Aquinas where medieval logic shaped the articulation of, and is therefore crucial to a proper understanding of, theological arguments and claims. The conclusion suggests implications for future philosophical and theological work. (shrink)

Augustine famously claims every word is a name. Some readers take Augustine to thereby maintain a purely referentialist semantic account according to which every word is a referential expression whose meaning is its extension. Other readers think that Augustine is no referentialist and is merely claiming that every word has some meaning. In this paper, I clarify Augustine’s arguments to the effect that every word is a name and argue that ‘every word is a name’ amounts to the claim that (...) for any word, there exist tokens of that word which are autonymous nouns. Augustine takes this to be the result of universal lexical ambiguity or equivocity and I clarify how Augustine’s account of metalinguistic discourse, which is one of the most detailed to have survived from antiquity, differs from some ancient and modern theories. (shrink)

Tässä artikkelissa käsittelen Descartesin ikuisten totuuksien välttämättömyyteen liittyvää ongelmaa. Teoksessa Mietiskelyjä ensimmäisestä filosofiasta (1641–1642) Descartes nostaa esiin käsitteen ikuisista totuuksista, käyttäen esimerkkinään kolmiota. Kolmion muuttumattomaan ja ikuiseen luontoon kuuluu esimerkiksi, että sen kolme kulmaa ovat yhteenlaskettuna 180°. Se on totta kolmiosta, vaikka yhtään yksittäistä kolmiota ei olisi koskaan ollutkaan olemassa. Eräät ajattelemieni asioiden piirteet ovat siis Descartesin mukaan ajattelustani riippumattomia. Ikuisia totuuksia ovat ainakin matemaattiset ja geometriset tosiseikat sekä ristiriidan laki. Samoin Descartesin kuuluisa lause “ajattelen, siis olen” lukeutuu ikuisten totuuksien (...) joukkoon. Descartesin ikuiset totuudet olisivatkin siis loogisesti välttämättömiä. Niillä on kyseinen olemus riippumatta ulkoisten kohteiden olemassaolosta tai siitä, ajattelenko niitä lainkaan. Kuitenkin kirjeenvaihdossaan Descartes pitää itsepintaisesti kiinni käsityksestään, että ikuiset totuudet ovat Jumalan vapaasti luomia ja Jumala olisi voinut luoda ne erilailla. Näin ollen luodut ikuiset totuudet eivät tarkkaan ottaen olisikaan välttämättömiä vaan kontingentteja. Ne voisivat olla myös toisella tavalla. Artikkelin alkuun esittelen Descartesin modaalista metafysiikkaa sekä luotujen ikuisten totuuksien kontingenttiudesta seuraavia tulkinnallisia vaikeuksia. Tämän jälkeen pureudun kolmeen erilaiseen ratkaisuyritykseen kommentaarikirjallisuudessa (Frankfurt 1977; Curley 1984 & Bennett 1994) ja osoitan, miksi ne eivät riitä vastaamaan ongelmaan. Lopussa vedän johtopäätöksiä ja luonnostelen mahdollisen ratkaisun. (shrink)

I undertake to examine the practice of Richard, Master of Abstractions, with respect to supposition in his dealing with the fallacy of figure of speech. His practice turns out to support the ‘single theory’ account of the theory of personal supposition, as does his treatment of a functional equivalent of simple supposition, but his practice of proposing additional solutions points to changing attitudes with respect to species as separate entities. Questions having to do with material supposition and the like are (...) completely absent, even in discussions where we might expect to find them. (shrink)

Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin’s formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130–135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an obligatio, two agents, the Opponent and the Respondent, engage in an (...) alternating-move dialogue, where the Respondent’s actions are governed by certain rules, and the goal of the dialogue is establishing the consistency of a proposition. We implement obligationes in the formal dialogue system framework of Prakken (Knowl Eng Rev 21(2):163–188, 2006) using Dynamic Epistemic Logic (van Ditmarsch et al. in Dynamic epistemic logic, Synthese Library Series. Springer, Berlin, 2007). The result is a new type of inter-agent dialogue, for consistency-checking, and analyzing obligationes in this way also sheds light on interpretational and historical questions concerning their use and purpose in medieval academia. (shrink)

This paper advances an approach to presupposition rooted in the concept of commitment, a dialectical notion weaker than truth and belief. It investigates ancient medieval dialectical theories and develops the insights thereof for analyzing how presuppositions are evaluated and why a proposition is presupposed. In particular, at a pragmatic level, presuppositions are reconstructed as the conclusions of implicit arguments from presumptive reasoning, grounded on presumptions of different type and nature. A false (or rather unaccepted) presupposition can be thus represented as (...) the outcome of a conflict of presumptions – the ones used by the Speaker and the ones commonly accepted or backed by evidence. From an interpretative perspective, this defaulted presumptive reasoning can be explained by comparing the available presumptions and repaired by replacing the weaker and unacceptable ones. (shrink)

The focus of the paper is a sophism based on the proposition ‘This is Socrates’ found in a short treatise on obligational casus attributed to William Heytesbury. First, the background to the puzzle in Walter Burley’s traditional account of obligations (the responsio antiqua), and the objections and revisions made by Richard Kilvington and Roger Swyneshed, are presented. All six types of obligations described by Burley are outlined, including sit verum, the type used in the sophism. Kilvington and Swyneshed disliked the (...) dynamic nature of the responsio antiqua, and Kilvington proposed a revision to the rules for irrelevant propositions. This allowed him to use a form of reasoning, the “disputational meta-argument”, which is incompatible with Burley’s rules. Heytesbury explicitly rejected Kilvington’s revision and the associated meta-argument. Swyneshed also revised Burley’s account of obligations, formulating the so-called responsio nova, characterised by the apparently surprising thesis that a conjunction can be denied both of whose conjuncts are granted. On closer inspection, however, his account is found to be less radical than first appears. (shrink)

This thesis addresses three challenges posed by intentionality - the ability of our mental states and language to be about something - to a logician: an apparent reference to non-existent objects, intentional indeterminacy and the failure of substitutivity of coextensive terms in an intentional context. Since intentionality plays an important role in our everyday reasoning, a proper formal account of it is highly desirable, yet it requires a departure from classical logic. One can modify classical logic and adapt the formal (...) apparatus to account for the aforementioned problems (Graham Priest’s logic for intentionality serves as an example of such an approach in this work) or one can make an even more radical shift and seek for inspiration in a different logical tradition like the terminist logic developed in the Late Middle Ages by figures like William of Ockham or John Buridan. The second path is explored here as a modest attempt to show that once we abandon the bias against the history of logic as irrelevant, we can actually get access to firm logical solutions inaccessible from a classical perspective, while still practising logic proper. (shrink)

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...) conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction. (shrink)

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aris... (shrink)

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied . Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss (...) two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments . In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize. Pode-se dizer que, enquanto disciplina, a lógica é caracterizada por dois subprojetos: teorias formais da validade de argumentos, baseadas em um número reduzido de esquemas e padrões formais, e teorias de como reduzir a multiplicidade de argumentos em contextos informais, não lógicos, ao pequeno número de padrões formais cuja validade é estudada de maneira sistemática no âmbito do primeiro subprojeto. O segundo subprojeto corresponde à noção de formalização de argumentos. Infelizmente, a tendência atual é de considerar como sendo a lógica propriamente dita exclusivamente o que se encaixa no primeiro subprojeto, em detrimento do segundo subprojeto, igualmente importante. Neste artigo, duas teorias históricas sobre a formalização de argumentos são analisadas: a teoria da silogística apresentada por Aristóteles nos "Primeiros Analíticos" e teorias medievais da suposição. Ambas ilustram o caráter duplo da lógica, que envolve dois subprojetos distintos, e contêm reflexões sofisticadas sobre como formalizar argumentos. Em ambos os casos, os métodos formais utilizados se diferenciam dos métodos atuais de tradução de um argumento em linguagem vernacular para um simbolismo especialmente formulado, ou seja, uma linguagem formal. Em conclusão, o artigo pode ser visto como a defesa de uma conceitualização mais abrangente do que significa 'formalizar' um argumento. (shrink)

This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.

In his Tractatus de Consequentiis, the 14th century logician John Buridan states a theorem, which reads like a refutation of Aristotelian Syllogistics. Syllogistics in its usual form, indeed, faces problems when propositions about the divine persons are involved, and, in some cases, when past- or future-tense propositions occur. Buridan offers different ways of overcoming some of these obstacles. The first aim of this paper is to analyse these ways, the second aim is to draw some conclusions concerning Buridan’s understanding of (...) logic and its relation to theology. (shrink)

1. This paper addresses the development of mutual relations between two sets of ideas in scholastic logic. First, consider the following statements: (1) It is impossible to encounter a chimera.(2)...

I finished my undergraduate degree at Monash University and joined Charles Hamblin’s seminar at the University of NSW in March, 1968. Phil Staines from the University of Newcastle joined at the same time, and Vic Dudman was an established member. Hamblin’s book Fallacies would be published in 1970, but the seminar discussions rarely concerned fallacies. This may have been because Hamblin had been working for so long and so closely with those ideas that he was now ready to turn elsewhere. (...) But I shall argue that the book was only part of a much broader program, other parts of which occupied us in the seminars. Hamblin never explicitly discussed the writing of Fallacies with me, and what follows is an attempt to explain how the book fitted into his overall project as a logician, drawn from his published works and from what I remember of his contributions to the seminar. (shrink)

Proceedings of the 2016 "one word" colloquium of the The Philosophical Society of Finland. The word was "Possibility".

The present paper is concerned with an exposé of the basic general-semantic theses presented in the tract called “De insolubilibus” written by the 14th century British logician Roger Swyneshed. Swyneshed‘s semantics is analysed as a highly specific theory of truth, correspondence and facts . Swyneshed’s theory revises the correspondence theory of truth and rejects the principle of bivalence, while offering the solution to two different types of paradoxes . As it is usual for theories of this kind, Swyneshed’s semantics has (...) to face the specific forms of revenge-arguments, which lead to a specific conception of truthmaking. (shrink)

Thomas Bradwardine (d. 1349) was an English philosopher, logician, and theologian of some note; but though recent scholarship has revived an interest in much of his work, little attention has been paid to an early treatise he wrote on the topic of future contingents, entitled De futuris contingentibus. In this thesis I aim to address this deficit, arguing in particular that the treatise makes original use of the divine power distinction to resolve the apparent conflict between God’s foreknowledge on the (...) one hand, and human free will on the other. Bradwardine argues that God’s foreknowledge operates in accord with God’s ordained power, and so relative to God’s ordained power, our actions are indeed compelled; however, because of Bradwardine’s appeal to the distinction in power, he is able to maintain that our actions remain free relative to God’s absolute power, and are thus free, absolutely speaking. This solution is, I argue, unique to Bradwardine, although it seems to be abandoned in his later writing. Bradwardine’s approach to the problem is heavily influenced by three figures in particular — Boethius, Anselm of Canterbury, and John Duns Scotus — each of whose solutions I discuss in some detail. Furthermore, Bradwardine explicitly places his own solution in opposition to that of William Ockham, and so I give substantial attention to examining Ockham’s position. But while I agree with Bradwardine’s assessment that Ockham’s position undermines God’s foreknowledge in ways that should be untenable to someone of 14th-century Christian commitments, I argue that Bradwardine’s solution amounts to an equally untenable determinism. An appendix contains excerpts from my own English translation of the De futuris contingentibus (the first into any modern language), in parallel with the original Latin. (shrink)

Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...) I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (shrink)

Resumen 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.In this article, I seek to clarify some features of fray Luis de León ’s theory of names which he presents in a passage at the beginning of De los nombres de Cristo by making a comparison between thatpassage and some scholastic treatises on logic, especially the Summulae by Peter of Spain and the homonymous work by Domingo de Soto. Specifically, I expect to show that the theory can be fully understood only on these grounds. I shall dealparticularly with the concepts of “simple term”, “suppositio” and “significatio”, and the way in which fray Luis articulates them, with the result that the scholastic elements can be clearly recognized by those who are acquainted with them and, at the same time, contribute with their essentialphilosoph- ical meaning to the fundamental objectives of the work. (shrink)