ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by (...) example, varies in different authors. For instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

본 논문의 목적은 아리스토텔레스로부터 시작하여 초기 페리파토스학파를 거쳐 고대후기에 이르기까지 ‘아리스토텔레스 논리학’의 특정 요소가 발전해 가는 과정을 추적하는 것이다. 고대 후기에는 가언삼단논법으로 분류된 4개의 논증형식이 있었다. 긍정적 긍정식(modus ponendo ponens), 부정적 부정식(modus tollendo tollens), 긍정적 부정식(modus ponendo tollens), 부정적 긍정식(modus tollendo ponens)이 그것들이다. 우리가 다루게 될 문제는 다음과 같은 것들이다. 앞에서 제시되었던 4개의 논증형식은 정확하게 어떤 상황에서 생겨났는가? 이 4개의 논증형식이 왜 ‘가언’ 삼단논법이라고 명명되었는가? 어떤 근거에서 이 4개의 논증형식이 타당하게 되는가? 논의를 진행하는 가운데 우리는 이 4개의 논증형식이 『분석론 전서』와 (...) 『토피카』에 보존되어 있는 아리스토텔레스 논리학의 특정 요소들이 오랜 기간에 걸쳐 점진적으로 발전한 결과임을 논증할 것이다.BR 우리의 논의결과는 이렇다. 첫째, 고대 후기에 오늘날의 조건명제와 선언명제가 가언명제로 분류된 이유는 단순히 조건명제와 선언명제에 조건적 요소가 포함되어 있기 때문이었다. 둘째, 고대 후기에 4가지 유형의 가언삼단논법이 ‘가언’ 삼단논법이라고 명명된 이유는 이 4가지 유형의 논증에 귀결관계와 비정합성관계의 조합으로부터 획득되는 가언명제가 적어도 한 개는 포함되어 있기 때문이었다. 셋째, 고대 후기에 4가지 유형의 가언삼단논법이 타당한 것으로 간주된 이유는 그것들 모두가 ‘모두스 포넨스’(modus ponens)유형의 형식을 갖고 있기 때문이었다. (shrink)

ABSTRACT: At the turn of the second century AD there existed two different views on the ordering of the figures of the (wholly) hypothetical syllogisms. One goes back to Theophrastus, whereas the other (adopted e.g. by Alexander of Aphrodisias and Alcinous) seems to have been the result of a later change. This reversal of the order of figures has so far not received a satisfactory explanation. In this paper I show how it came about.

ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysippus wrote numerous books (DL 7.196) are not to be confused with the so-called hypothetical syllogisms" but are the same hypothetical arguments as those mentioned five times in Epictetus (e.g. Diss. 1.25.11-12); and (ii) that these hypothetical arguments are formed by replacing in a non-hypothetical argument one (or more) of the premisses by a Stoic "hypothesis" or supposition. Such "hypotheses" (...) or suppositions differ from propositions in that they have a specific logical form and no truth-value. The reason for the introduction of a distinct class of hypothetical arguments can be found in the context of dialectical argumentation. The paper concludes with the discussion of some evidence for the use of Stoic hypothetical arguments in ancient texts. (shrink)

This paper proposes a classification of economic models into three types: historical, axiomatic and conditional. Historical or empirical models utilize the historical-deductive method, and are generalizations from the economic regularities and tendencies that we find in the real world. Axiomatic models utilize the hypothetical-deductive method; they are syllogisms whose major premise is an axiom – a self-evident truth; they are appropriate for methodological sciences such as mathematics and econometrics. Conditional economic models are likewise syllogisms, but they are (...) suitable for economics because they make for clearer and more precise economic reasoning. The criterion of truth of the substantive sciences is the conformity with reality, of the methodological science, its internal consistency. When a school of economic thought adopts mainly axiomatic models, as is the case with neoclassical economics, it implicitly falls into contradiction because their best representatives believe in the conformity with reality criterion. (shrink)

Boethius' treatise De Hypotheticis Syllogismis provided twelfth-century philosophers with an introduction to the logic of conditional and disjunctive sentences but this work is the only part of the logica vetus which is no longer studied in the twelfth century. In this paper I investigate why interest in Boethius acount of hypothetical syllogisms fell off so quickly. I argue that Boethius' account of compound sentences is not an account of propositions and once a proper notion of propositionality is available (...) the argument forms accepted by Boethius are seen to be incoherent. It was Peter Abaelard who first understood the nature of propositionality and propositional connectives and used this to criticise Boethius' claims in De Hypothetics Syllogismis. In place Boethius' confusion Abaelard offered a simple and correct account of the hypothetical syllogism. (shrink)

In this paper I present the text, a translation, and a commentary of a long anonymous scholium to Aristotle’s Analytics which is a Greek parallel to Boethius’ De Hypotheticis Syllogismis, but has so far not been recognized as such. The scholium discusses hypothetical syllogisms of the types modus ponens and modus tollens and hypothetical syllogisms constructed from three conditionals (‘wholly hypothetical syllogisms’). It is Peripatetic, and not Stoic, in its theoretical approach as well as (...) its terminology. There are several elements of early Peripatetic hypothetical syllogistic preserved in it, and there is a large number of close parallels to Boethius’ De Hypotheticis Syllogismis which we find in no other source. It is very likely that there was a Greek source from which both the scholium and large parts of Boethius’ De Hypotheticis Syllogismis are ultimately derived. (shrink)

In late antiquity, logic developed into what Ebbesen calls the LAS, the Late Ancient Standard. This paper discusses the Neoplatonic use of LAS, as informed by epistemological and metaphysical concerns. It demonstrates this through an analysis of the late ancient debate about hypothetical and categorical logic as manifest in the practice of syllogizing Platonic dialogues. After an introduction of the Middle Platonist view on Platonic syllogistic as present in Alcinous, this paper presents an overview of its application in the (...) syllogizing practice of Proclus and others. That overview shows that the two types were considered two sides of the same coin, to be used for the appropriate occasions, and both relying on the methods of dialectic as revealing the structure of knowledge and reality. Pragmatics, dialectic, and didactic choices determine which type or combination is selected in syllogizing Plato. So even though there is no specific Neoplatonic logic, there is a specific Neoplatonic use of LAS. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he (...) call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

In this paper, we discuss the syllogisms from both fronts : Aristotle and Boethius. We mainly focus on the differences with respect to categorical and hypothetical syllogisms in Aristotle and Boethius. Regarding Aristotle’s works on logic, it is not unusual to claim that Aristotle extensively worked on categorical syllogisms. In Prior Analytics, Aristotle gave proofs for many valid moods. However we cannot find a similar treatment for hypothetical syllogism in his works. Thus, it might be (...) a reason for his students to improve Aristotle’s theory of syllogisms by filling the gaps in hypothetical syllogisms. As Boethius already emphasized in the Book I of De Hypotheticis Syllogismis, the Peripatetic School only initiated the start. The remaining and detailed treatise was due to Boethius himself. The impression we got from Boethius’s and Aristotle’s works on syllogisms is that the categorical syllogism is almost entirely developed by Aristotle himself, whereas the extensive and the detailed study of the hypothetical syllogism was carried out by Boethius, although he was not the first figure in the history who gave concise expositions on hypothetical syllogism. Boethius’s translations of syllogisms in medieval era were the primer resource and textbook for Aristotelian logic during the early Medieval ages. Therefore, the scholars of those times had no other chance but to work from Boethius’s commentaries. So, the evident properties of Aristotelian figures were not then visible. Boethius wrote several textbooks in logic. A detailed investigation might yield significant information on Boethius’s logic compared with the influence of Aristotle on Boethius. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 (...) Forerunners of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

This work provides some interesting new results on the notion of the topos and the theory of hypothetical syllogisms in Aristotle based on an incisive interpretation of Aristotle's _Topics_ and certain passages of the _Analytics_.

This volume provides the first critical edition of Abbo of Fleurys "De Syllogismis Hypotheticis," together with a German translation, an introduction and an extensive commentary. Abbo of Fleury (940/45-1004) was the first medieval author to write on hypothetical syllogisms. He relies mostly on Boethius, but he must have had at his disposal a further source which has since been lost.

This study presents the way in which Proclus structures some aspects of his Epistemology on the basis of his metaphysical Ontology. All those that we discuss – relying on his comments on Parmenides (Εἰς τὸν Πλάτωνος Παρμενίδην) (816.11– 819.29) –, take into account the following: a) his theory on the universal Intellect and the individual intellects, b) his theory on the universal Soul and the individual souls, c) some approaches of his in Plato’s theory of Ideas. Combining the above, our (...) purpose is also to show in what way some specific manifestations of the metaphysical world are connected with the natural world. The Neoplatonist philosopher explains the relevant theories by following a clearly defined method and that is why his analyses compose a cohesive system or a coherent Epistemology. He follows the principles that he has established on the basis of a clear ontological realism, which is based on his views about how the similarities and the differences between the two worlds appear. By elaborating these principles, we come to the conclusion that the methodological tools used by him are the principle of analogy, analytical thinking and hypothetical syllogisms. (shrink)

An argument for the eponymous conclusion is given through a series of hypothetical syllogisms, the most basic of which is as follows: morality is necessary for self-respect; self-respect is necessary for happiness; therefore, morality is necessary for happiness. Some of the most obvious objections are entertained and rejected.

ABSTRACT: This paper collects the evidence in Ammonius' surviving works for elements of a propositional logic, coming to the conclusion that Ammonius had a theory of hypothetical syllogisms in the tradition of Aristotle and the Peripatetics, with Platonic elements mixed in, and using some Stoic elements, but not a propositional logic in the narrower sense as we find it in Stoic logic.

Radulphus Brito's Quaestiones super Priora analytica Aristotelis is a major work written in the early 1300s which treated Aristotle's text devoted to the theory of the syllogism. Brito, one of the most influential of the group of medieval thinkers known as the Modistae, examines both categorical and hypothetical syllogisms. In the text offered here, based on six known manuscripts which are complete or nearly complete, Brito was critical of many of the theories of his contemporary, Simon of Faversham. (...) Brito edited his work several times; there are at least two versions which indicate Brito returned to this material during his long career at the university in Paris. This volume is the first critical text edition of Brito's Quaestiones super Priora analytica Aristotelis and will therefore be of great interest to those studying the history of logic and its development during the medieval period. (shrink)

Dialectic is a standard and important part of the logica vetus (or old logic) in medieval philosophy. It has its ultimate origins in Aristotle's Topics,its fundamental source in Boethius's De topicis differentiis,and its flowering in its absorption into fourteenth-century theories of consequences or conditional inferences. The chapter on Topics in Garlandus Compotista's logic book is the oldest scholastic work on dialectic still extant. In this paper I show the differences between Boethius's Theory of Topics and Garlandus's in order to illustrate (...) the role of Topics in early scholastic logic. I argue that for Garlandus Topics are warrants for the inference from the antecedent to the consequent in a conditional proposition and that he is interested in Topics because of his overriding interest in hypothetical syllogisms. I conclude by discussing briefly the relationship between Garlandus's use of Topics and twelfth-century accounts. (shrink)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

Discusses Boethius's logical monographs: his treatises on division, on categorical syllogisms, and most importantly, his works on the theory of topical argument and on hypothetical syllogisms. The theory of topics, as developed in late antiquity and known almost entirely through Boethius, concerns the devising of arguments that rest on obvious general principles but are not, in their basic formulation, formally valid deductions. In his work on hypothetical syllogisms, Boethius seems to take account of Stoic propositional (...) logic, but in fact, he does not properly grasp its principles. This chapter shows how Boethius's logical mongraphs fit with the Aristotelianizing approach of his commentaries. (shrink)

The purpose of this paper is to outline an alternative approach to introductory logic courses. Traditional logic courses usually focus on the method of natural deduction or introduce predicate calculus as a system. These approaches complicate the process of learning different techniques for dealing with categorical and hypothetical syllogisms such as alternate notations or alternate forms of analyzing syllogisms. The author's approach takes up observations made by Dijkstrata and assimilates them into a reasoning process based on modified (...) notations. The author's model adopts a notation that addresses the essentials of a problem while remaining easily manipulated to serve other analytic frameworks. The author also discusses the pedagogical benefits of incorporating the model into introductory logic classes for topics ranging from syllogisms to predicate calculus. Since this method emphasizes the development of a clear and manipulable notation, students can worry less about issues of translation, can spend more energy solving problems in the terms in which they are expressed, and are better able to think in abstract terms. (shrink)

This work provides some interesting new results on the notion of the topos and the theory of hypothetical syllogisms in Aristotle based on an incisive interpretation of Aristotle's Topics and certain passages of the Analytics .

In this paper I examine Avicenna’s conception of the consequence relation. I will consider in particular his categorical and hypothetical logics. I will first analyse his definition of the implication and will show that this relation is not a consequence relation in his frame. Unlike the medieval logicians, he does not distinguish explicitly between material and formal consequences. The arguments discussed in al-Qiyās, where the conclusion is true only in some matters, and would seem close to a material consequence (...) for that reason, are rejected explicitly as not syllogistic. He also rejects the ‘enthymemes’ unless they are complemented by their missing premise and the superfluous premises which, according to him, should promptly be ruled out. It seems then that the consequence relation in his theory is formal. It can be characterized as being ‘productivity in all matters’ or ‘necessary truth preserving’. It is illustrated by some single premise arguments, and above all by all kinds of syllogisms which, in his theory, are more numerous and various than in Aristotle’s one. The syllogism may contain two or more premises, including disjunctive ones. When it is hypothetical, it may lead to several conclusions. The premises may be in conflict, but then, the conclusion is false. He thus rejects the principle according to which ‘anything follows from a contradiction’. But, unlike what some scholars say, he does not admit any connexive principle. In the compound syllogisms, the conclusion follows by steps, each step taking two premises at once. (shrink)

The main idea animating the present paper is that the general aim of debates, such as the one involving the notorious case of the Master Argument, is the ponderation of logical principles by confronting them with some set of assertions and other endorsed principles on the meaning explanation of connectives, quantifiers and modality. As suggested by Seel (2017), the point of the specific case of the MA is about examining Aristotle’s notion of possibility – as implemented by the Possibility Principle (...) (i.e., If it is necessary that if A then B, then B is possible if A is) and the Possibility Rule (i.e., If A is possible, and if B follows from the assumption of A, then B is is possible) in the context of a dialectical debate where it has been asserted that a given proposition is possible, even it is neither true now nor it will ever be, and where at the same time the irrevocability of the past has been endorsed. This suggests to study the MA debate in a setting based on Marion’s (2020) reconstruction of Aristotle’s Dialectical Bouts, adapted to propositions affected by modalities. The setting of Dialectical Bouts for the MA proposed includes•Propositions affected by Reichenbach’s (1948, § 5) three-folded temporal reference, namely: the point of speech S, the point of reference R and the point of the event E. This constitutes our take on Vuillemin’s (1977, 1979, 1984, 1996) suggestion of a “double indexation”.•The dialogical meaning explanation for modalities understood as involving hypotheticals. •The dialogical rules that settle the commitments undertaken when endorsing Aristotle’s Possibility Principle. In fact, in relation to the notion of possibility at work in Vuillemin’s (1996) reconstruction we explored different formulations of the Possibility Rule. Still, there remains a dearth of researches confronting the different formulations of the Possibility Rule with the texts studied by Crubellier (2010) and Rosen and Malink (2012). More generally and coming back to my remarks above, one of the most fruitful insights that can be gained from Vuillemin’s writings on the MA, is that such kind of debates provide an instance of a general pattern for reasoning that I shall call Dialectical Bouts of Material Admissibility (BMA). The rationale behind such kind of argumentation-pattern is to examine the incorporation of new (epistemological, ontological or logical) principles against the background of the commitments undertaken by endorsing a specific set of assertions and meaning explanations. They display the kind of abductive procedure stressed by Crubellier’s (2014) study of syllogism. Under this perspective Ebbinghaus’s (1964) casting of the inferential moves that reduce imperfect syllogisms to perfect ones as implementing an admissibility procedure, represents a logical generalization of the material procedures at stake in the Dialectical Bouts of Material Admissibility. Furthermore if, as stressed by Duthil-Novaes (2005) Medieval Obligations represent a development of Aristotelian Bouts aimed at the ludic exercise of consistency maintenance, DMA should be rather linked to the Islamic tradition of dialectical theory [jadal, munāẓara, ādāb al-baḥth], aimed at the epistemological task of what Young (2017) calls the forging of principles, including legal and deontic ones. In a more contemporary setting, DMA can be related to Brandom’s (2000, pp. 66-77) considerations on Non-Conservative Extensions, where the point of dialectical procedures is put under public Socratic scrutiny the discovery and elucidation of concepts. This general point on Dialectical Bouts of Material Admissibility can be seen as underlying Vuillemin’s project of linking the study of the MA with the classification of philosophical systems.The present paper does not contain a fully developed study on such Dialectical Bouts, but it is rather is an invitation to pick up the gauntlet that Jules Vuillemin threw into the ring. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Avicenna's Theory of Science: Logic, Metaphysics, Epistemology by Riccardo StrobinoThérèse-Anne DruartRiccardo Strobino. Avicenna's Theory of Science: Logic, Metaphysics, Epistemology. Oakland: University of California Press, 2021. Pp. xvi + 428. Hardback, $95.00.Strobino's remarkable book does not simply present Avicenna's theory of science; it also highlights the importance of demonstration not only for logic but also for metaphysics and epistemology. Hence, Strobino's work is essential to appreciate and better understand (...) Avicenna's philosophy as a whole.Strobino grounds his research on Avicenna's theory of science in his Book of Demonstration in the Shifā', which focuses on Aristotle's Posterior Analytics. Taking into account the lack of any translation into English or any other main modern language as well as the lack of a full medieval Latin translation (only chapter 7 of book 3 exists in a medieval Latin version) of Avicenna's text, Strobino kindly provides in appendix C (357–71) a detailed "map" of this text, useful not only to readers who cannot handle Arabic but even to those who can, as the [End Page 326] text is so rich and complex. A simple but careful look at this map confirms what Strobino makes clear and insists upon: Avicenna greatly develops, enriches, completes, and even outgrows some of Aristotle's views. The Book of Demonstration is far more than a commentary on the Posterior Analytics; it is a complete reworking of it.Strobino shows that Avicenna grounds his theory of demonstration and science on two basic notions—conception (tasawwur) and assertion (tasdīq, which some other scholars translate as "assent")—and so gives a unified approach to his theory. Scientific conceptions require better understanding of definition and description. Avicenna builds definitions and descriptions on essentialism and, therefore, grounds them in metaphysics. As for scientific assertions, in contradistinction to nonscientific ones, they must be necessary and give the cause. Therefore, Avicenna places great importance on modality and develops modal syllogisms, whereas Aristotle focused on categorical syllogisms and neglected hypothetical and disjunctive syllogisms. Avicenna also elaborates a sophisticated account of modality and its metaphysical implications. Furthermore, he broadens and enriches the appreciation of causality and explanation. These developments, according to Strobino, lead Avicenna to set forth an intricate division and hierarchy of the sciences under metaphysics, which provides their ultimate principles and allows for a unified understanding of the sciences while respecting their particularities.According to Strobino, Avicenna is keen to develop a theory of science that gives a good account of science as it is practiced. Strobino carefully shows how Avicenna's theory better reflects this practice than does Aristotle's.Strobino does not simply highlight how much Avicenna distances himself from Aristotle and goes far beyond what the Posterior Analytics yields, but also shows how much Avicenna relies on points adumbrated by his predecessor al-Fārābī in his own Book of Demonstration.The way Strobino through his analysis of demonstration links Avicenna's understanding of logic, epistemology, and metaphysics underscores the coherence and unity of Avicenna's philosophy. Scholars were aware of the importance of demonstration for Avicenna in various philosophical fields, but until the release of this book, they seemed not to have fully grasped the centrality and essential role played by the Avicennian understanding and focus on demonstration.Of course, Strobino does not limit himself to an analysis of passages in the Book of Demonstration. He has an encompassing knowledge of Avicenna's texts and uses them well to flesh out and enrich what remains terse in the Book of Demonstration. He even takes into account the way one of his successors, al-Tūsī, reads him. He also shows an extensive and wide-ranging knowledge of Aristotle's texts and of Aristotelian scholarship, as well as an interest in the Greek commentators and Galen and their relevance for interpreting Avicenna.Avicenna's Theory of Science is not an easy book to read, as it is often very technical, particularly when dealing with purely logical points or issues, but reading it is rewarding if one does so slowly and meditatively. The author, in fact, illuminates difficult matters but does not waste words. From... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant’s Theory of ActionLara DenisRichard McCarty. Kant’s Theory of Action. Oxford-New York: Oxford University Press, 2009. Pp. xxiv + 250. Cloth, $74.00.This significant, stimulating contribution to Kantian practical philosophy strives to interpret Kant’s theory of action in ways that will increase readers’ understanding and appreciation of Kant’s moral theory. Its thesis is that Kant combines metaphysical freedom and psychological determinism: our actions within the phenomenal world are causally (...) determined by our prior psychological states in that world and are appearances of our free action in the noumenal world. McCarty argues for a metaphysical, “two-worlds” interpretation of Kant’s transcendental distinction between appearances and things in themselves over epistemological or methodological “two-standpoints” interpretations familiar from Christine Korsgaard [End Page 533] and Henry Allison (along the way, McCarty also challenges Allison’s “Incorporation Thesis”). Some of the book’s arguments are textual, displaying perceptive readings of Kant’s lecture notes, published works, and philosophical influences. Others primarily concern the philosophical plausibility or moral tenability of various positions one might attribute to Kant. The book’s greatest strength is McCarty’s positive account of Kant’s theory of action. He presents a coherent, even elegant, two-worlds model. His interpretations of maxims, incentives, empirical character, and Gesinnung are insightful.The book’s first two chapters introduce McCarty’s understanding of maxims and incentives and begin tackling what he calls “the problem of justification and explanation.” Chapter 3 defends the claim that Kant embraced psychological determinism. Chapters 4 and 5 present McCarty’s two-worlds interpretation of the transcendental distinction, defend it from objections, and argue for its superiority over two-standpoint interpretations. Chapter 6 focuses on moral motivation, presenting respect for the moral law as an incentive capable of explaining morally justified actions, and distinguishing between morally worthy and virtuous action so as to defend Kant’s ethics from common objections. Chapter 7 similarly disentangles notions of a good will and virtue, provocatively claiming that all human agents have both a good will and virtue. The main task of chapter 7, however, is analysis of the radical evil in human nature. Chapter 8 raises questions about Kant’s conception of the highest good—particularly, the afterlife in which we are to continue our moral progress—as an object of rational hope.I read the book’s main argument as follows:1. Kant’s theory of action must solve “the problem of justification and explanation”: it must show how the reasons that justify a judgment that one ought to do something can also explain one’s doing it. Kant’s theory of action must solve this problem because if what justifies an action cannot also explain it, such justification is “irrelevant.” Only if our actions are explicable in terms of practical reasoning is justification of action by practical reasoning (e.g. by reference to hypothetical or categorical imperatives) “relevant” to our conduct. The problem of justification and explanation arises as it does within Kant’s ethics because Kant holds that pure reason is capable of issuing in action; yet he also holds that human beings and other imperfectly rational agents do not invariably act as we recognize we ought. So we cannot explain our acting as we ought (when we do) simply by appeal to “ought implies can,” internalism, or “the causality of freedom.”2. Psychological determinism, combined with a metaphysical interpretation of Kant’s transcendental distinction, allows Kant to solve the problem of justification and explanation. Through a timeless, free act in the noumenal world, we each fix our empirical character, which serves as the “causal law” for our actions in the phenomenal world. Maxims, which function as both major premises in practical syllogisms and rules of our empirical characters, provide bases for both the imperatival justifications and motivational explanations of human actions. The “logical force” of a maxim justifies action on it; the “psychological force” of the maxim—specifically, of the incentive incorporated into the maxim—explains action on it.3. Psychological determinism is compatible with and beneficial for Kant’s moral theory. Most crucially, it is compatible with the freedom necessary for moral agency and responsibility.4. Two-standpoint... (shrink)

ResumoO texto aqui apresentado pretende dar uma pequena contribuição à discussão sobre a relação entre lógicae ontologia na filosofia kantiana. Seu objetivo é mostrar como Kant segue a lógica dos wolffianos, mantendosua abordagem geral, não sem introduzir algumas mudanças importantes. Ao contrário dos filósofosdogmáticos, Kant, como se sabe, enfatiza a neutralidade ontológica e epistemológica da lógica geral, diferenciando-a da lógica transcendental, que apresenta as condições universais necessárias apenas com basenas quais se pode falar de conhecimento objetivo. Leibniz, Wolff e seus (...) seguidores teriam negligenciadoessa distinção e dado à lógica geral um significado ontológico e heurístico, que absolutamente não lhepertence. Este artigo examina até que ponto essa versão da lógica dogmática, tão bem construída por Kante geralmente aceita pelos estudiosos, é confiável; tenta também mostrar que Kant flerta aqui e ali comasserções ontológicas e, ao fazê-lo, sua lógica também funciona como uma heurística. Os juízos categóricoe hipotético, bem como seus respectivos silogismos, serão aqui examinados em sua relação recíproca comocasos emblemáticos desse uso menos neutro da lógica formal por Kant. Além disso, espera-se que esteexame revele alguns dos procedimentos metódicos seguidos pelo filósofo em sua investigação conceitual,modo de proceder que, embora respeitando estritamente as regras lógicas estabelecidas, introduz modulaçõesdentro dessas mesmas regras, para enfrentar os desafios do pensamento crítico.Palavras-chave: Kant, lógica, ontologiaAbstractThe text presented here intends to make a small contribution to the discussion on the relationship betweenlogic and ontology in Kantian philosophy. Its purpose is to show how Kant follows the logic of theWolffians, maintaining their general approach, not without introducing some important changes. Unlikedogmatic philosophers, Kant, as is well known, lays stress on the ontological and epistemological neutralityof general logic, differentiating it from transcendental logic, which presents the necessary universal conditionsonly on the basis of which one can speak of objective knowledge. Leibniz, Wolff and his followerswould have neglected this distinction and given general logic an ontological and heuristic meaning, whichabsolutely does not belong to it. This article examines to what extent this version of dogmatic logic, so wellconstructed by Kant and generally accepted by the scholars, is reliable; it also tries to show that Kant flirtshere and there with ontological assertions and, in doing so, his logic also functions as a heuristic. The categoricaland the hypothetical judgments, as well as their respective syllogisms, will be examined here in theirreciprocal relationship as emblematic cases of this less neutral use of formal logic by Kant. Furthermore, thisexamination will hopefully reveal some of the methodical procedures followed by the philosopher in hisconceptual investigation, a way of proceeding that, although strictly respecting the established logical rules,introduces modulations within these same rules, to face the challenges of the critical thought. (shrink)

It has recently been reported that forward inferences from if p then q sentences (i.e., from antecedent to consequent) were faster than backward inferences from consequent to antecedent (Barrouillet, Grosset, & Lecas, 2000). The standard mental model theory assumes that this directionality effect is a figural effect due to the order the information enters working memory, whereas we claim that it results from the nature of the mental models that represent oriented relations from hypothetical values introduced by the word (...) If . We tested these hypotheses in an experiment in which adult participants evaluated conditional syllogisms from either if p then q , p only if q , or p if q statements. Contrary to the predictions resulting from the standard theory, the three forms of the conditional provoked a reversed directionality effect and denial inferences took longer to endorse than affirmative inferences for all the forms of conditionals. We argue from these results that mental models of the conditional represent oriented relations instead of mere co-occurrences between events. (shrink)

This work is an introductory textbook for deductive logic being primarily concerned with truth-functional logic, but also containing an introduction to syllogisms with the application of Venn diagrams, an introduction to quantification theory, and a brief discussion of axiom systems. Harrison employs six logical operators in his truth-functional calculus, including both inclusive and exclusive disjunction. The six operators are initially defined by truth tables, but in the natural deduction presentation negation and conjunction are taken as primitive and the other (...) connectives are defined in terms of these two. The conditional and indirect methods of proof are included with the approach being essentially the same as that given in Copi’s Symbolic Logic. Categorical statements and syllogisms are analyzed from both hypothetical and existential viewpoints. The treatment of quantification theory includes two-place predicates and employs the four standard rules for generalization and instantiation. The book contains an abundance of explanations, examples, and exercises. Selected answers, usually for the odd numbered problems, are given in an appendix.—T. G. N. (shrink)

This paperback is a programed text designed for teaching introductory logic, either in conjunction with a standard text based upon traditional logic or as a do-it-yourself supplement for students taking courses stressing symbolic logic. The student learns logical theory by answering a variety of short answer, objective type exercises. The correct answer is given directly below each question or exercise, and the student is required to cover the answer while working the exercise; the purpose of this immediate access to the (...) answer is to enable the student to determine quickly whether or not he comprehends the material. The content of the book concentrates primarily upon categorical statements, presenting both the existential and hypothetical interpretations of the square of opposition, but unfortunately continues to promulgate the historically inaccurate terminology of "Aristotelian" and "Boolean." [Categorical statements were first expressed as existential statements by Franz Brentano in 1874.] Categorical statements not in standard form are standardized, e.g., "No roaches feel despair" is standardized by being rewritten as "No roaches are entities who feel despair." In addition to considering the logical relations of opposition with respect to A, E, I, O statements, these same relations are extended to non-categorical statements, e.g., "George Washington did not die in Europe" and "George Washington did not die in Asia" are subcontraries, while "There is philosophical activity on Venus" and "There is philosophical activity in the universe" are alterns. Determining validity of syllogisms is based upon the distribution of terms, and also by the use of Venn diagrams. The traditional figures and moods of the syllogism are ignored, as is the distinction between major and minor terms, with these latter two being lumped together as end terms. Immediate inferences and non-syllogistic arguments are treated by Venn diagrams. One-, two-, three- and four-term Venn diagrams are utilized throughout a substantial part of the book.--T. G. N. (shrink)

Mediaeval logicians inherited from Boethius an account of conditional propositions and the syllogisms which may be constructed using them. In the following paper it is shown that there are considerable difficulties with Boethius' account which arise from his failure to understand the nature of compound propositions and in particular to provide for their negation. Boethius suggests that there are two different conditions which may be imposed for the truth of a conditional proposition but he really gives no adequate account (...) of how such propositions may be obtained. The true greatness of Peter Abaelard as a philosophical logician is revealed in what he is able to do with the material which he found in Boethius. It is shown that he developed a precise theory of conditionals giving an account of how true conditionals may be obtained and principles which may be used to reject others as false. Unlike Boethius Abaelard properly appreciates that conjunctions must be treated as logical units. Even he, however, falls victim to difficulties which arise when this connective is brought into contact with negation and the conditions which he lays down for the truth of a conditional. (shrink)

Since Aristotle it is recognised that a valid syllogism cannot have two particular premises. However, that is not how a lay person sees it; at least as long as the premises read many, most etc, instead of a plain some. The lay people are right if one considers that these syllogisms do not have strict but approximate (Zadeh) validity. Typically there are only particular premises available in everyday life and one is dependent on such syllogisms. – Some rules (...) on the usage of particular premises are given below. (shrink)

This article examines two syllogistic arguments contrasted in an ancient Chinese book, theMozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them (theone-horse argument) is valid but the other (thetwo-horse argument) is not. To explain this difference, the article uses English plural constructions to formulate the arguments. Then it shows that the one-horse argument is valid because it has a valid argument form, the plural cousin of a standard (...) form of valid categorical syllogisms (Plural Barbara), and argues that the two-horse argument involves equivocal uses of a key predicate (the Chinese counterpart of ‘have four feet’) that has the distributive/nondistributive ambiguity. In doing so, the article discusses linguistic differences between Chinese and English and explains why the logic of plural constructions is applicable to Chinese arguments that involve no plural constructions. (shrink)

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

We often assume that hypothetical approval – either in the form of preferences or consent – under ideal conditions adds to the legitimacy of an arrangement or act. I want to show that this assumption, reasonable as it may seem, will also give rise to ethical problems. I focus on three problem areas: prudence, euthanasia and coercive psychiatric treatment. If we are to count as prudentially or morally␣relevant those preferences you would have if you were informed and rational, we (...) will run into difficulties in all these areas if your actual and rational preferences are at variance with each other. In the prudential sphere we may question the personal value of satisfying preferences that a person does not actually have. In this case our problem concerns the point of satisfying a rational preference in conflict with an actual one. In the cases of euthanasia and coercive care it concerns instead whether it would be morally right to do such a thing. I doubt there is a simple solution to our problem. In this paper at most I prepare the way for a solution or for wiser decisions in the hard cases, by pointing out what they will have to deal with. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. (...) Lukasiewicz evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules (...) of argument forms of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers. (shrink)

Relational Syllogisms and the History of Arabic Logic, 900–1900. By Khaled El-Rouayheb. Islamic Philosophy, Theology and Science, vol. 80. Leiden: Brill, 2010. Pp. viii + 295. $168.

In this paper I examine how Aristotle thinks syllogisms establish existence. I argue against the traditional "Instantiation" reading and in favor of an alternative "causal" or "structural" account of existential syllogisms. On my interpretation, syllogisms establish the existence of kinds by revealing that they are per se unities whose features are causally underwritten by a single cause/essence. They do so by tracing correlations between propria--peculiar, coextensive features--of the kind in question.

In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections, including indirect reduction, quantifier transformations and equivalence of syllogisms. After determining the valid and invalid syllogisms in RELSYLL, we then introduce two Derivation Methods which can be used to derive valid relational syllogisms based on known valid (...) simple syllogisms. We also show that the two Methods are sound and complete for RELSYLL. In the second half of this paper, we discuss ways to extend the Derivation Methods, including the use of more valid syllogisms and the use of existential assumptions. In this way, we are able to derive more relational syllogisms that contain other types of non-classical quantifiers, including “only” and proportional quantifiers. Finally, we state and prove a proposition concerning the relationship between the two Methods. (shrink)

This book uncovers and examines the confusion in antiquity between Aristotle's hypothetical syllogistic and Stoic logic, and offers a fresh perspective on the ...

This volume explores the conceptual terrain defined by the Greek word eikos: the probable, likely, or reasonable. A term of art in Greek rhetoric, a defining feature of literary fiction, a seminal mode of historical, scientific, and philosophical inquiry, eikos was a way of thinking about the probable and improbable, the factual and counterfactual, the hypothetical and the real. These thirteen original and provocative essays examine the plausible arguments of courtroom speakers and the 'likely stories' of philosophers, verisimilitude in (...) art and literature, the likelihood of resemblance in human reproduction, the limits of human knowledge and the possibilities of ethical and political agency. The first synthetic study of probabilistic thinking in ancient Greece, the volume illuminates a fascinating chapter in the history of Western thought. (shrink)

This article starts by examining the appeal to hypothetical consent as used by law and economics writers. I argue that their use of this kind of argument has no moral force whatever. I then briefly examine, through some remarks on Rawls and Scanlon, the conditions under which such an argument would have moral force. Finally, I bring these considerations to bear to criticize the argument of judge Frank Easterbrook's majority opinion in Flamm v. Eberstadt.