What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...) Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

In light of recent developments in argumentation theory, we begin by considering the account that Aristotle gives of what he calls sophistical refutations and of the usefulness of being able to recognise various species of them. His diagnosis of one of his examples of the grouping that he labels epomenon is then compared with a very recent account of the matter, which, like Aristotle, calls on us to attribute a mistake or confusion to anyone who uses this kind of argument. (...) From examination of three other examples that Aristotle himself supplies of epomenon, it appears that there are cases of inferences of this kind that we need not, and perhaps cannot, avoid making. The suggestion is made that this is because the whole family of what Peirce calls abductions have important characteristics in common with epomenon. (shrink)

The taxonomy and analysis of fallacies in Aristotle's Sophistical Refutations pre-date the formal logic of his Prior Analytics A4-6. Of the 64 fully described examples of ?sophistical refutations? which are fallacious because they are only apparently valid, 49 have the wrong number of premisses or the wrong form of premiss or conclusion for analysis by the Prior Analytics theory of the categorical syllogism. The rest Aristotle either frames so that they do not look like categorical syllogisms or analyses in a (...) quite different way than by categorical syllogistic. (shrink)

Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct ways; and checking to (...) make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

Concepts are traditionally pictured as discrete containers that bring together objects or qualities based on the possession of shared, uniform properties. This paper focuses on a contrasting notion of the concept which holds that concepts are defined by their capacity to reach out and connect with other concepts. Two theories in recent continental philosophy maintain this view: one from Ricoeur, the other from Deleuze and Guattari. Both are offered as attempts to bring art and philosophy into relation, but they differ (...) over how the process of connection is theorized. With Ricoeur, a concept is only a concept if it is inherently predisposed to connect with others, and open to being misapplied through metaphor, whereas, with Deleuze and Guattari, connection is left as the general notion of each and every concept being mutually consistent with other concepts, with the consistency attributed to the external action of “bridging.” The author demonstrates the impact of this difference on how the philosophers perceive the art–philosophy relation, and argues that Ricoeur is better placed to provide a theory of philosophical discourse that is open to the aesthetic. Ricoeur can show it through metaphor, while Deleuze and Guattari can only assert or state an art–philosophy relation through a series of technical claims. The significance of the showing–saying distinction is that it can demonstrate the depth with which conceptual connectivity is located within the philosophers’ respective ontologies, and can help to reveal the value of conceptual connectivity for that ontology. (shrink)

This study examines the concept of argumentation empirically, to correct the normative conception of argumentation adopted by most scholars since Aristotle. They are not interested in what argumentation is, but in what it ought to be. The pre-Aristotelian approach is preferable, because it recognizes that argumentation, although it includes persuasion, also embraces other eristic techniques in which the speaker does not necessarily seek to persuade, but simply to prevail. This broader descriptive and pragmatic analysis explains the different ways in which (...) discourse actually occurs and particular arguments succeed, leaving in a secondary place the opinion of each author on how they should be. (shrink)

The Middle Included is a systematic exploration of the meanings of logos throughout Aristotle’s work. It claims that the basic meaning is “gathering,” a relation that holds its terms together without isolating them or collapsing one to the other. This meaning also applies to logos in the sense of human language. Aristotle describes how some animals are capable of understanding non-firsthand experience without being able to relay it, while others relay it without understanding. Aygün argues that what distinguishes human language, (...) for Aristotle, is its ability to both understand and relay firsthand and non-firsthand experiences. This ability is key to understanding the human condition: science, history, news media, propaganda, gossip, utopian fiction, and sophistry, as well as philosophy. Ömer Aygün finds Aristotle’s name for this peculiar but crucial human ability of “gathering” both experiences is logos, and this leads to a claim about the specificity of human rationality and language. (shrink)

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The (...) author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce’s own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking. (shrink)

This essay (a revised version of my undergraduate honors thesis at Stanford) constructs a theory of analogy as it applies to argumentation and reasoning, especially as used in fields such as philosophy and law. The word analogy has been used in different senses, which the essay defines. The theory developed herein applies to analogia rationis, or analogical reasoning. Building on the framework of situation theory, a type of logical relation called determination is defined. This determination relation solves a puzzle about (...) analogy in the context of logical argument, namely, whether an analogous situation contributes anything logically over and above what could be inferred from the application of prior knowledge to a present situation. Scholars of reasoning have often claimed that analogical arguments are never logically valid, and that they therefore lack cogency. However, when the right type of determination structure exists, it is possible to prove that projecting a conclusion inferred by analogy onto the situation about which one is reasoning is both valid and non-redundant. Various other properties and consequences of the determination relation are also proven. Some analogical arguments are based on principles such as similarity, which are not logically valid. The theory therefore provides us with a way to distinguish between legitimate and illegitimate arguments. It also provides an alternative to procedures based on the assessment of similarity for constructing analogies in artificial intelligence systems. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

In Fallacies and Judgments of Reasonableness, Frans H. van Eemeren, Bart Garssen and Bert Meuffels report on their systematic empirical research of the conventional validity of the pragma-dialectical discussion rules. The experimental studies they carried out during more than ten years start from the pragma-dialectical theory of argumentation developed at the University of Amsterdam, their home university. In these studies they test methodically the intersubjective acceptability of the rules for critical discussion proposed in this theory by confronting ordinary arguers who (...) have not received any special education in argumentation and fallacies with discussion fragments containing both fallacious and non-fallacious argumentative moves. The research covers a wide range of informal fallacies. In this way, the authors create a basis for comparing the theoretical reasonableness conception of pragma-dialectics with the norms for judging argumentative moves prevailing in argumentative practice. Fallacies and Judgments of Reasonableness provides a unique insight into the relationship between theoretical and practical conceptions of reasonableness, supported by extensive empirical material gained by means of sophisticated experimental research. (shrink)

Une analogie entre les aspects épistémologiques et méthodologiques de l'activité des services de renseignement et certaines disciplines scientifiques, en préconisant une approche plus scientifique du processus de collecte et d'analyse de l'information au sein du cycle du renseignement. J'affirme que les aspects théoriques, ontologiques et épistémologiques de l'activité de nombreux services de renseignement sont sous-estimés, ce qui conduit à une compréhension incomplète des phénomènes actuels et à une confusion dans la collaboration interinstitutionnelle. Après une brève Introduction, qui inclut un historique (...) de l'évolution du concept de service de renseignement après la Seconde Guerre mondiale, Renseignement définit les objectifs et l'organisation des services de renseignement, le modèle de base de ces organisations (le cycle du renseignement) et les aspects pertinents de la collection de l'information et l'analyse du renseignement. Dans la section Ontologie, je souligne les aspects ontologiques et les entités qui menacent et qui sont menacés. La section Épistémologie comprend des aspects spécifiques à l'activité de renseignement, avec l'analyse du modèle traditionnel (Singer) utilisé traditionnellement, et j'expose une approche épistémologique possible à travers le concept de connaissance tacite développé par le scientifique Michael Polanyi. La section Méthodologie contient diverses théories méthodologiques mettant l’accent sur les techniques analytiques structurelles ainsi que certaines analogies avec la science, l’archéologie, les affaires et la médecine. L'article se termine par les Conclusions sur la possibilité d'une approche plus scientifique des méthodes de collecte d'information et d'analyse des services de renseignement. SOMMAIRE: Abstract 1. Introduction 1.1. Histoire du renseignement 2. Renseignement 2.1. Organisations 2.2. Cycle du renseignement 2.3. La collecte du renseignement 2.4. Analyse du renseignement 2.5. Contre-espionnage 2.6. Communautés épistémiques 3. Ontologie 4. Épistémologie 4.1. La connaissance tacite (Polanyi) 5. Méthodologies 6. Analogies avec d'autres disciplines 6.1. Science 6.2. Archéologie 6.3. Affaires 6.4. Médecine 7. Conclusions Bibliographie DOI: 10.13140/RG.2.2.35970.22729 . (shrink)

Despre analogia existentă între aspectele epistemologice şi metodologice ale activităţii serviciilor de informaţii şi unele discipline ştiinţifice, pledând pentru o abordare mai ştiinţifică a procesului de culegere şi analiză de informaţii din cadrul ciclului de informaţii. Afirm că în prezent aspectele teoretice, ontologice şi epistemologice, în activitatea multor servicii de informaţii, sunt subestimate, determinând înţelegere incompletă a fenomenelor actuale şi creând confuzie în colaborarea inter-instituţională. După o scurtă Introducere, care include o istorie a evoluţiei conceptului de serviciu de informaţii după (...) al doilea război mondial, în Activitatea de informaţii definesc obiectivele şi organizarea serviciilor de informaţii, modelul de bază al acestor organizaţii (ciclul informaţional), şi aspectele relevante ale culegerii de informaţii şi analizei de informaţii. În secţiunea Ontologia evidenţiez aspectele ontologice şi entităţile care ameninţă şi sunt ameninţate. Secţiunea Epistemologie include aspecte specifice activităţii de informaţii, cu analiza principalului model (Singer) folosit în mod tradiţional, şi expun o posibilă abordare epistemologică prin prisma conceptului de cunoaştere tacită dezvoltat de omul de ştiinţă Michael Polanyi. În secţiunea Metodologii prezint diverse teorii metodologice cu accent pe tehnicile analitice structurale, şi câteva analogii, cu ştiinţa, arheologia, afacerile şi medicina. Lucrarea se încheie cu Concluziile privind posibilitatea unei abordări mai ştiinţifice a metodelor de culegere şi analiză a informaţiilor din cadrul serviciilor de informaţii. -/- Cuvinte cheie: servicii de informaţii, agenţii de informaţii, informaţii, intelligence -/- CUPRINS -/- Abstract 1. Introducere 1.1. Istorie 2. Activitatea de informaţii 2.1. Organizaţii 2.2. Ciclul informaţional 2.3. Colectarea informaţiilor 2.4. Analiza informaţiilor 2.5. Contrainformatii 2.6. Comunităţi epistemice 3. Ontologia 4. Epistemologia 4.1. Cunoaşterea tacită (Polanyi) 5. Metodologii 6. Analogii cu alte discipline 6.1. Stiinta 6.2. Arheologia 6.3. Afaceri 6.4. Medicina 7. Concluzii Bibliografie -/- ISBN: 978-606-033-160-5 , DOI: 10.58679/TW56764. (shrink)

In his works on argumentation, Aristotle develops three main forms: apodeictical, dialectical, and rhetorical argumentation; dialectic is subdivided into several subspecies. The purpose of this paper is to discuss all of the forms described by Aristotle, to examine their differences and to point out their interrelations. This leads to an examination of the differentiating criteria and their applicability in the case of each argumentation form—and in particular to the question regarding the number of criteria that are necessary to describe each (...) form clearly and unambiguously. It is argued that Aristotle’s works on argumentation contain an implicit system of argumentation forms that is based on no more than three criteria. (shrink)

This paper makes a case for a refined look at the so- called ‘fallacy of hasty generalization’ by arguing that this expression is an umbrella term for two fallacies already distinguished by Aristotle. One is the fallacy of generalizing in an inappropriate way from a particular instance to a universal generalization containing a ‘for all x’ quantification. The other is the secundum quid (‘in a certain respect’) fallacy of moving to a conclusion that is supposed to be a universal generalization (...) containing a ‘for all x‘ quantification while overlooking qualifications that have to be added to the more limited kind of generalization expressed in the premise. It is shown that these two fallacies relate to two different kinds of generalization. (shrink)

Throughout his whole work, Wittgenstein seizes on a distinction between logical and physical possibility, and impossibility. Despite this continuity and although, Wittgenstein brings in this distinction in various contexts and from different vantage points, he often solely brushes over it without elaborating in detail. In the so-called Big Typescript, however, he dedicates himself not only to the distinction between logical and physical possibility but also to the distinction between logical possibility and impossibility in particular investigations. In the course of these (...) investigations, another aspect arises and is tossed and turned repeatedly by Wittgenstein – namely, the place of “imaginability” in these considerations. On the basis of three focussed chapters in the Big Typescript, I argue that “imaginability” as an utterance of the form “being able to imagine ‘what it would be like’” can be allocated the place of a criterion for logical possibility. To this end, I will first outline the chapters 96., 27. and 26. in one section each. Although in these chapters, Wittgenstein only indicates rather than claiming explicitly “imaginability” to be a criterion for logical possibility, I will discuss in the last section how this conclusion can be drawn by combining the results of the previous sections. (shrink)

Biology seems to present local and transitory regularities rather than immutable laws. To account for these historically constituted regularities and to distinguish them from mathematical invariants, Montévil and Mossio (Journal of Theoretical Biology 372:179–191, 2015) have proposed to speak of constraints. In this article we analyse the causal power of these constraints in the evolution of biodiversity, i.e., their positivity, but also the modality of their action on the directions taken by evolution. We argue that to fully account for the (...) causal power of these constraints on evolution, they must be thought of in terms of normativity. In this way, we want to highlight two characteristics of the evolutionary constraints. The first, already emphasised as reported by Gould (The structure of evolutionary theory, Harvard University Press, 2002), is that these constraints are both produced by and producing biological evolution and that this circular causation creates true novelties. The second is that this specific causality, which generates unpredictability in evolution, stems not only from the historicity of biological constraints, but also from their internalisation through the practices of living beings. (shrink)

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of (...) explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)

This paper undertakes a re-examination of Sir William Hamilton’s doctrine of the quantification of the predicate . Hamilton’s doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit existential quantifiers, so that, for example, All p is q is to be understood as All p is some q . Second, these implicit quantifiers can be meaningfully dualized to yield novel sentence-forms, such as, for example, All p is all q . Hamilton attempted to provide a deductive system (...) for his language, along the lines of the classical syllogisms. We show, using techniques unavailable to Hamilton, that such a system does exist, though with qualifications that distinguish it from its classical counterpart. (shrink)

Some Carrollian posthumous manuscripts reveal, in addition to his famous ‘logical diagrams’, two mysterious ‘logical charts’. The first chart, a strange network making out of fourteen logical sentences a large 2D ‘triangle’ containing three smaller ones, has been shown equivalent—modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture—to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape—slightly deformed—has been (...) rediscovered, independently from Carroll and much later, by a logician , a mathematician and a linguist studying the geometry of the ‘opposition relations’, that is, the mathematical generalisations of the ‘logical square’. We show that inside what is called equivalently ‘n-opposition theory’, ‘oppositional geometry’ or ‘logical geometry’, Carroll's first chart corresponds exactly, duly reshap.. (shrink)

Stasis is a process of classical rhetoric that identifies the core issue in a trial or a similar debate. Hermagoras of Temnos included the first comprehensive analysis of stasis in his second-century BCE treatise on rhetoric, now lost. Modern scholars tend to echo George Kennedy, who maintains that Hermagoras’ inspiration for the hierarchical structure of stasis is indeterminate. This article, however, employs scholarship in legal semiotics, including the work of Miklós Könczöl and Bernard S. Jackson, to argue that Hermagoras based (...) stasiastic structure on Aristotle’s first-figure syllogism. Ideally, knowledge of that structure can enhance modern applications of stasis. (shrink)

This paper takes issue with Derek Sankey's: ‘Minds, Brains, and Differences in Personal Understanding’, Educational Philosophy and Theory, 39 (2007), pp. 543–558 on the questions of the post-pedagogical classroom and the forms of knowledge. I then try to show that a theory of meaning framed in terms of normative pragmatics is better able than the brain science Sankey relies on to account for the concept of a person or self; the central educational concept of personal understanding; the relation between being (...) a person and membership of the species Homo sapiens; the role of mental images in meaningfulness; the functioning of figurative language; and the Gadamerian notion of understanding as constitutive of the self. It is necessary on the way to answer Sankey's criticisms of correctness, a concept on which any normative theory must rely. (shrink)

In this paper a dialogical account of begging the question is applied to various contexts which are not obviously dialogues: - reading prose, working through a deductive system, presenting a legal case, and thinking to oneself. The account is then compared with that in chapter eight of D. Walton'sBegging the Question (New York; Greenwood, 1991).

The purpose of this paper is to analyze the structure and the defeasibility conditions of argument from analogy, addressing the issues of determining the nature of the comparison underlying the analogy and the types of inferences justifying the conclusion. In the dialectical tradition, different forms of similarity were distinguished and related to the possible inferences that can be drawn from them. The kinds of similarity can be divided into four categories, depending on whether they represent fundamental semantic features of the (...) terms of the comparison or non-semantic ones, indicating possible characteristics of the referents. Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus is abstracted. Depending on the nature of the abstracted common feature, different rules of inference will apply, guaranteeing the attribution of the analogical predicate to the genus and to the primary subject. This analysis of similarity and the relationship thereof with the rules of inference allows a deeper investigation of the defeasibility conditions. (shrink)

In his commentary on Plato’sCratylus, Proclus interprets the dialogue not as a mere work on logic or linguistics, but as having a full psychological and theological import.Late ancient Platonists had already proposed a similar reading for another Platonic dialogue,i.e.theParmenides. In that case too they rejected the logical interpretation, and aimed to find in the text the description of the hierarchy of reality, particularly of the highest beings. As a result, theParmenideswas seen as the accomplished expression of Plato’s theology.Proclus too draws (...) a comparison between theCratylusand theParmenidesin order to stress their theological significance. He also contrasts Plato’s dialectic with Aristotle’s dialectic. Proclus’ interpretation of dialectic is best understood if it is compared to the doctrines of his master Syrianus and of one of his co-disciples,i.e.Hermeias, at the Platonic school of Athens in the 5th centuryad.Contrary to what is sometimes assumed, in this milieu Platonists were not always committed to the task of reconciling the philosophies of Plato and Aristotle. As it happens, they could strongly disagree with and even attack Aristotle, and side with Plato. In particular, they greatly valued Plato’s dialectic, which they viewed as the correct form of reasoning and at the same time as a theory of the utmost theological significance. On the other hand, Aristotle’s dialectic was considered as “bare” logic,i.e.as a mere set of logical rules and arguments with no specific contents.On the basis of a problematicCratylus’passage Proclus defends a theory of truth according to which not only propositions, but also names can be true or false. This allows him to view names as substitutes of propositions. This is particularly the case in the application of the four dialectical methods of definition, division, demonstration and analysis. Proclus’ approach arguably provides a basis—to pagan as well as Christian tradition—for the study of divine names as a part of theology, for the name of a god is held to reveal its attributes. (shrink)

In this article, the author studies some central concepts in Avicenna's and sī's modal logics as presented in Avicenna's Al-Ish r t wa'l Tan īh t ( Pointers and Reminders ) and in sī's commentary. In this work, Avicenna introduces some remarkable distinctions in order to interpret Aristotle's modal syllogistic in the Prior Analytics . The author outlines a new interpretation of absolute sentences as temporally indefinite sentences and argues on the basis of this that Avicenna seems to subscribe to (...) the Principle of Plenitude. He also shows that he has no valid proof of the modal conversion rules and that he uses some rather ad hoc distinctions to show that Aristotle's modal syllogistic is correct. The author also notes some interesting differences between Avicenna's and sī's approaches to modal logic. (shrink)

The aim of this paper is to look at the arguments advanced by three Parisian arts masters about how to understand Prior Analytics II 4 and the more general discussion that medieval authors situate...

Used informally, the Reductio ad Absurdum (RAA) consists in reasoning appealing to the logically implied, absurd consequences of a hypothetical proposition, in order to refute it. This kind of reasoning resembles the Argument from Consequences, which appeals to causally induced consequences. These types of argument are sometimes confused, since it is not worked out how these different kinds of consequences should be distinguished. In this article it is argued that the logical consequences in RAA-argumentation can take different appearances and that (...) it therefore must be concluded that RAA cannot be characterised by a specific content, but must instead be characterised as an argument form. Furthermore, clues are provided to distinguish RAA reasoning from the Argument from Consequences. (shrink)

Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. The claim (...) of the Master Argument that Chrysippus rejects, then, is stronger ihan usually supposed. (shrink)

This paper starts with the presentation of an Aristotelian theory of negative properties. Against this backdrop, it then asks whether there could be objects that have solely negative properties, i.e., completely negative objects. This possibility is entertained by Wittgenstein in his Tractatus Logico-Philosophicus. The notion of a completely negative object is compared to the concepts of a nonexistent object, a nonconcrete object, and a nonactual object. Ultimately, it is argued that there can be no completely negative objects, because all negative (...) properties entail some positive properties. (shrink)

Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on (...) analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well. (shrink)

In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (contrary and contradictory) studied (...) by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _!, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature. (shrink)

An eleventh-century Greek text, in which a fourth-century patristic text is discussed, gives an outline of a solution to the Liar Paradox. The eleventh-century text is probably the first medieval treatment of the Liar. Long passages from both texts are translated in this article. The solution to the Liar Paradox, which they entail, is analysed and compared with the results of modern scholarship on several Latin solutions to this paradox. It is found to be a solution, which bears some analogies (...) to contemporary game semantics. Further, an overview of other Byzantine scholia on the Liar Paradox is provided. The findings and the originality of the discussed solution to the Liar Paradox suggest a change in the way in which Byzantine Logic is traditionally regarded in contemporary scholarship. (shrink)

In his famous essay "The Ethics of Belief," William K. Clifford claimed "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." ). One might claim that a corollary to Clifford's Law is that it is wrong, always, everywhere, and for anyone, to withhold belief when faced with sufficient evidence. Seeming to operate on this principle, many religious philosophers—from St. Anselm to Alvin Plantinga—have claimed that non-believers are psychologically or cognitively deficient if they refuse to believe (...) in the existence of God, when presented with evidence for His existence in the form of relevant experience or religious arguments that are prima facie unassailable. Similarly, many atheists fail to see how believers can confront the problem of evil and still assert their belief in a benevolent, omnipotent, and omniscient Creator. In this paper, I propose to explain why religious arguments so often fail to persuade . In doing so, I first offer an account of persuasion and then apply it to religious arguments. I go on to argue that at least some religious arguments commit a form of question-begging, which I call "begging the doxastic question." An argument begs the doxastic question, on my account, when a subject would find the argument persuasive only if she antecedently believes the argument's conclusion. This form of question begging is not, strictly speaking, a case of circularity and thus, is not a fallacy; rather, it would explain why one coming to the argument would fail to be persuaded by it unless he already accepted its conclusion. This has the effect, when applied to religious argumentation, that religious arguments are rarely persuasive, which raises the further question: what good are religious arguments? I end by suggesting some non-persuasive functions of religious argument. Finally, I suggest that a full understanding of religious argumentation should give evidentialists pause, for religious beliefs look less like belief states that are sensitive to evidentiary states and more like framework principles or fundamental commitments. (shrink)

The rule of contraposition has been investigated thoroughly by Arabic logicians. In this paper, we study the work done by Fārābā and Avicenna, the fathers of Arabic logic. Fārābā studied contraposition of universal affirmatives, discussed its four forms, and discovered a relation between one form and the conversion of negative universals. Although Fārābā and logicians before him have used contraposition only for conditionals, as well as for indefinite and universal affirmative categorical propositions, Avicenna generalized the rule to all the four (...) Aristotelian quantified categorical propositions. However, many of his ideas on contraposition were opposed by his 12th and 13th century followers, which are to be investigated later. (shrink)

Argument from analogy is a common and formidable form of reasoning in law and in everyday conversation. Although there is substantial literature on the subject, according to a recent survey ( Juthe 2005) there is little fundamental agreement on what form the argument should take, or on how it should be evaluated. Th e lack of conformity, no doubt, stems from the complexity and multiplicity of forms taken by arguments that fall under the umbrella of analogical reasoning in argumentation, dialectical (...) studies, and law. Modeling arguments with argumentation schemes has proven useful in attempts to refine the analyst’s understanding of not only the logical structures that shape the backbone of the argument itself, but also the logical underpinning of strategies for evaluating it, strategies based on the semantic categories of genus and relevance. By clarifying the distinction between argument from example and argument from analogy, it is possible to advance a useful proposal for the treatment of argument from analogy in law. (shrink)

The purpose of this paper is to give an account and a rational reconstruction of the heuristic advice provided by Aristotle in the Topics and Prior Analytics in regard to the difficulty or ease of strategic planning in the context of a dialectical dialogue. The general idea is that a Questioner can foresee what his refutational syllogism would have to look like given the character of the thesis defended by the Answerer, and therefore plan accordingly. A rational reconstruction of this (...) advice will be attempted from three perspectives: strategic planning based on the acceptability of Answerer’s thesis, strategic planning based on the predicational form of the thesis, strategic planning based on the logical form of the thesis. In addition, we will provide an illustration of the potential of this heuristic advice as we apply it to the interpretation of a fragment from Plato, presuming that, in a similar way, a reading of this kind might be more generally applicable in the interpretation of the Platonic dialogues. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and (...) developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. Chapter Three explores how Aristotle’s syllogistic fits within Aristotle’s philosophy of science and demonstration, particularly within the context of the Posterior Analytics. Consideration is given to the Aristotelian understanding of the relationship among necessity, explanation, definition, and essence. Chapter Four applies Aristotelian modal logic in contemporary contexts. I contrast Aristotelian modality and essentialism with contemporary modalism based upon the semantics of possible worlds, e.g. Kripke and Putnam. I also develop an account of how Aristotelian modal logic can ground a sortal dependent theory of identity, as discussed by Wiggins. (shrink)

Gender greatly impacts access to opportunities, potential, and success in corporate leadership roles. We begin with a general presentation of why such discussion is necessary for basic considerations of justice and fairness in gender equality and how the issues we raise must impact any ethical perspective on gender in the corporate workplace. We continue with a breakdown of the central categories affecting the success of women in corporate leadership roles. The first of these includes gender-influenced behavioral factors, such as the (...) requirements and expectations of gendered verbal and nonverbal communication styles as well as appearance. We move on to address the impact of family on corporate leadership opportunities and success, discussing the asymmetrical evaluation of an individual’s potential, authority, and competence based on gender stereotypes of familial obligations and expectations. Finally, we address how gender impacts access to networking and sponsorship opportunities and the long-term effects of systematic limitations on women’s inclusion in the upper echelons of corporate leadership. We conclude with a summary of the questions and issues raised by our discussion and direct individuals to consider how different ethical systems and moral requirements might influence their interpretations of gender and leadership in the corporate workplace. (shrink)

The dissertation examines the nature and epistemic implications of epistemic source circularity. An argument exhibits this type of circularity when at least one of the premises is produced by a belief source the conclusion says is legitimate, e.g. a track record argument for the legitimacy of sense perception that uses premises produced by sense perception. In chapter one I examine this and several other types of circularity, identifying relevant similarities and differences between them. In chapter two I discuss the differences (...) between internalist and externalist analyses of justification. I examine in detail foundationalist and non-foundationalist versions of internalism, and go on to consider how one might characterize externalism: either negatively, by denying particular internalist theses, or positively, in terms of a theory offering different conditions for justification. I discuss the views of reliabilist foundationalists at length. In chapter three I present the internalist objection to externalism that the latter mistakenly permit one to be justified in believing the conclusion of an epistemic source circular inference. I explain the externalists' response that it is not in virtue of their externalism that they permit epistemic source circularity but rather their foundationalism; thus, internalist foundationalists must permit epistemic source circularity as well. I evaluate the positions of several internalists, most of them explicitly foundationalists, and argue that they too cannot avoid permitting epistemic source circularity. In the final chapter I consider whether such circularity is vicious, even though both internalist and externalist foundationalists permit it. I argue that one can sustain an objection to epistemic source circularity by imposing a non-question-begging requirement on justification and explain how respecting this requirement leads one to a non-foundationalist view. I conclude by considering the objection that question-begging leads to a certain arbitrariness in belief formation that should give the foundationalist pause when it comes to determining, at the beginning of inquiry, which beliefs are justified and which are not. The dissertation is primarily concerned with making clear the possible skeptical and non-skeptical positions one can take towards epistemic source circularity. I do not argue for the truth of a particular metaepistemology. (shrink)