“Aristotle's successor as director of the Lyceum was Theophrastus, his friend and disciple; Eudemus, another of the Stagirite's important disciples should also be mentioned. Other philosophers belonging to the Peripatetic school were: Aristoxenus, Dikaiarchos, Phanias, Straton, Duris, Chamaeleon, Lycon, Hieronymus, Ariston, Critolaus, Phormio, Sotion, Hermippus, Satyrus and others. Straton even succeeded Theophrastus as director of the Lyceum but his name and those of the other Peripatetics of Aristotle's old school should not be considered in a history of logic (...) as they were mainly concerned with history and the natural sciences. Theophrastus rejoiced in an enormous prestige at this time and for long afterwards. Diogenes Laertius attributes a tremendous number of works to him. Of them a significant proportion are writings on logic: Analytica Priora (3 books); Analytica Posteriora (7 books); Analysis of Syllogisms (1 book); Summary of the Analytic s (1 book); Polemic on the Theory of Euristic Arguments. On Definition (1 book); The First Premises (18 books); The Sophisms (2 books); On the Solution of Syllogisms (1 book); Topics (2 books); On Artless Demonstrations (1 book); On Negation (1 book); On Intellect (1 book); Classifications (2 books); On Entymemes (1 book); On the Appreciation of Syllogism (1 book); On Lies and Truth (1 book); Argumentations (2 books); Theses (3 books); On Definition (2 books); On the Data of Problems (1 book); On the Liar (3 books); Preface to the Topics (1 book); On Arguments proper (1 book); Specifications on The Texts of Syllogisms (1 book). Eudemus also wrote some treatises on logic, concerning which some information has come down to us; Ammonius, in his Commentary On Aristotle's Categories attributes to him a writing on The Analytics -- 'Analitika', and another On Expressions -- Peri lexeos, in which he deals with the grammatical and logical functions of the sentence. The commentator David in Prolegomena to Isagoge by Porphiry also mentions these works.. (shrink)

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In (...) the 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

ABSTRACT: Galen’s Institutio Logica is the only introduction to logic in Greek that has survived from antiquity. In it we find a theory that bears some resemblance to propositional logic. The theory is commonly understood as being essentially Stoic. However, this understanding of the text leaves us with a large number of inconsistencies and oddities. In this paper I offer an comprehensive alternative interpretation of the theory. I suggest that it is Peripatetic at base, and has drawn (...) on Stoic elements, but adapted them to an overall decidedly non-Stoic conception of logic and language, a conception indebted to Aristotelian logic in many respects. This interpretation makes it possible to reduce the seeming inconsistencies dramatically. The Peripatetic theory on which Galen draws was possibly developed in the first century BCE. Importantly, it differs from Stoic logic in that it shuns the latter’s syntactic approach, and considers certain linguistic assumptions and language conventions as part of the logical theory itself. My reconstruction of the theory results in a logic of propositions which differs wildly both from Stoic logic and from the ‘classical’ propositional logic of the 20th century. Interestingly, though, the theory in Galen shows that the ancients grappled with a number of logico-linguistic problems that over the last two decades have again become a matter of debate among contemporary logicians and linguists. (shrink)

Name der Zeitschrift: Archiv für Geschichte der Philosophie Jahrgang: 99 Heft: 3 Seiten: 237-299.

In ancient philosophy, Logic was seen as the instrument and method of philosophy. However, sometimes detailed and profound discussions have been made about the demonstrativeness of philosophical sciences. Most philosophers have accepted that the mathematical sciences were especially demonstrative and likewise, most of the natural sciences are demonstrative for them. But can metaphysics be demonstrative or not? This is one of the fundamental issues around which the great debates were made in Islamic philosophy. While these issues are known to (...) specialists in this field, we can hardly find studies and research that deal with this issue to a sufficient degree and precise discussions in our day, I mean the issue of demonstrativeness of art of demonstration, art of dialectic, art of sophistry, art of rhetoric and art of poetry. It is clear that the peripatetic philosophers did not write a separate book or treatise on the issue of the demonstrativeness of the logical arts, but we can claim that they believed that all these arts were demonstrative and that they were extracted/abstracted using the art of demonstration. We can come across important phrases and statements that prove this claim between the lines of the books that these philosophers wrote in the science of logic. And while Aristotle is the founder of the science of logic, then how is it to be understood that there are practical particular examples and some easy rules of these arts? According to their texts, we can say that they believed that the actual performance of these arts by their actors in materials by particular and practical actions differs from extracting their universal rules by abstracting them from their materials through theoretical and analytical research. For example, the poems of the great poets; Homer and al-Mutanabbi, are particular works in the matter of the art of poetry performed by poets. The books written by Aristotle and Ibn Rushd in the art of poetry contain universal rules extracted abstractly from the materials of their particular poems. As for understanding the demonstrativeness of the remaining four arts, it is easier, but how should we understand the demonstrativeness of the art of demonstration itself? It seems that the peripatetic logicians also distinguished between applying demonstrative inferences to significant materials and extracting the universal rules of the art of demonstration from these materials. These five logical arts are not particular and practical things, but they are philosophical, demonstrative, and analytical studies for the peripatetic logicians in Islam. In this paper, we will try to draw attention to the issue of the demonstrativeness of the five arts and to open a new discussion about it based on some important sentences and phrases expressed by al-Fārābī, Ibn Zur‘a, Ibn Sīnā, Ibn Bājja and Ibn Rushd between the lines in their books, which they wrote in the field of logic and within different and multiple contexts. (shrink)

ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).

To meet a dilemma between the axiomatic theory of demonstrative science in Posterior analytics and the non-axiomatic practice of demonstrative science in the physical treatises, Jonathan Barnes has proposed that the theory of demonstration was not meant to guide scientific research but rather scientific pedagogy. The present paper argues that far from contributing directly to oral instruction, the axiomatic account of demonstrative science is a model for the written expression of science. The paper shows how this interpretation accords with related (...) theories in the Organon, including the theories of dialectic in Topics and of deduction in Prior analytics. (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)

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)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).

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.

The problem of Galileo's logical methodology has long interested scholars. In this volume William A. Wallace offers a solution that is completely unexpected, yet backed by convincing documentary evidence. His analysis starts with an early notebook Galileo wrote at Pisa, appropriating a Jesuit professor's exposition of the Posterior Analystics of Aristotle, and ends with one of the last letters Galileo wrote, stating that in logic he has been a Peripatetic all his life. Wallace's detective work unearths the complete (...) logic course from which the notebook was excerpted, then proceeds to show how its terminology and methodology continue to surface in Galileo's later writings in which he founds his new sciences of the heavens and of local motion. The result is a tour de force that commends itself not only to Galileo's scholars and to logicians, philosophers, and historians, but to anyone interested in the epistemic roots of modern science. (shrink)

The genesis of classical science was accompanied by a transition from logical to mathematical analysis. This change did not mean a rejection of Aristotle's canons of logic; it was simply that these canons became inadequate. They underwent a certain generalization and, in the course of this, came closely to approximate mathematical analysis, the foundations of the calculus of the infinitesimal. Classical science no longer took as its point of departure the notion of motion from "something" into "something," as did (...) Peripatetic physics and cosmology . The initial concept is motion, considered from point to point and instant to instant. This kind of differential notion of motion was clearly expressed by Kepler when he wrote: "Where Aristotle sees direct oppositeness between two things, with no mediating links, there I, looking at geometry philosophically, find a mediated opposition; so that where Aristotle employs a single term, ‘other,’ I use two: ‘larger’ and ‘smaller.’". (shrink)

The scientific status of logic is ambiguous within a broadly Aristotelian framework. As is well known, the Stoic position is frequently contrasted with that of the the classic Peripatetic outlook on these matters. For the former, logic is a unique division of philosophy, whereas for the latter, logic plays a merely instrumental role. This article explores how several Dominican thinkers articulated an outlook concerning logic that granted it a robust scientific status while maintatining a generally (...) Peripatietic philosophical outlook. Clarity in these matters required the passing of several centuries. This article presents a set of historical vignettes showing the development of an increasingly clearer definition of the nature of the subject of logic, tracing the topic in Aristotle, Avicenna, Aquinas, Hervaeus Natalis, and Antoine Goudin. (shrink)

The scientific status of logic is ambiguous within a broadly Aristotelian framework. As is well known, the Stoic position is frequently contrasted with that of the the classic Peripatetic outlook on these matters. For the former, logic is a unique division of philosophy (i.e., rational philosophy), whereas for the latter, logic plays a merely instrumental role. This article explores how several Dominican thinkers articulated an outlook concerning logic that granted it a robust scientific status while (...) maintatining a generally Peripatietic philosophical outlook. Clarity in these matters required the passing of several centuries. This article presents a set of historical vignettes showing the development of an increasingly clearer definition of the nature of the subject of logic, tracing the topic in Aristotle, Avicenna, Aquinas, Hervaeus Natalis, and Antoine Goudin. (shrink)

In Plato’s Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato’s theory of Forms. Some philosophers have even viewed Aristotle’s theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of self-reference that involves. Bocheński denies (...) any possibility of correct logical reasoning before Aristotle. In particular, he flatly declares of Plato that “correct logic we find none in his work” [1951, 15]. In this line, many papers have been written that call attention to the violation of a metalogical principle – the type rules – because of the Third Man Paradox. The problem of interpretation of the paradox raised many discussions, since the 50’s, and the literature devoted to this topic is today enormous. Nevertheless, many points in Plato’s reasoning remain obscure. Hitherto, it is commonly believed that the paradox was simply stated by Plato in his "Parmenides", but not actually solved. Even more, it is believed that it is hardly possible for Plato to have suggested a solution, because he confused the categories of substance and attribute. B. Russell has also argued that Plato violates in his arguments the restrictions imposed on language by the theory of logical types. This view is encouraged by the linguistic difficulties, which Plato has faced in his attempt to formulate an ontology of abstract entities, i.e. that in Greek language abstract and concrete terms are formally indistinguishable [Kneales 1984]. In this paper, we analyse the logical structure of the argument in an attempt to give a systematic consistent reconstruction of the text appealing to methods and concepts of modern logic and semantics. Already in 1954 G. Vlastos had noted in his seminal paper “The ‘Third Man’ Argument in the Parmenides” that “if any progress … is to be made at this juncture it must come from some advance in understanding the logical structure of the Argument”. Accordingly, our analysis is primarily focused on the line of logical reasoning, rather than the metaphysical underpinnings and philosophical implications of the paradox for Plato’s theory of Forms. We divide the Platonic text into three parts, presenting apparent thematic coherence: a) Formulation of the Third Man Paradox (132a-132b). The central issue of this part is a step-like generation of Forms that can continue ad infinitum. b) Discussion of the paradoxical situation (132b-c), by passing to the use of terminology echoing Eleatic philosophy. The concept of “thought” and the underlying semantics of Eleatic origin are central in this passage. c) Solution of the paradox (132d-133a). In our view, this part contains not only a resemblance regress, as most interpretators con-sider, but also the solution of the paradox by the introduction of a sound definition of the concept of “similarity”. We should note that the name ‘Third Man Paradox’ never occurs in Plato, who, strictly speaking, formulates a ‘Third Large Paradox’. The name ‘Third Man Paradox’ appears in the works of Aristotle and the commentators of the Peripatetic tradition. Later commentators have identified Aristotle’s Third Man with Plato’s Third Large Argument. In our paper, we also examine other testimonies about the Third Man Paradox found in the works of commentators in order to illuminate the logical structure of the argument. Although the vocabulary used in these versions is different, they do not affect its logical structure, but rather reveal different understandings by the ancient authors. These testimonies are divided into two main categories: those met in Neo-Platonic authors, notably in Proclus’ "Commentary on Plato’s Parmenides", and the versions of the Third Man Paradox found in texts of the Peripatetic tradition (Eudemus, Aristotle, Alexander). From our discussion, it becomes clear that the approaches to the paradox by the various scholars of antiquity are different, depending also on their participation in the one or the other campus of philosophical thought. We show that the Peripatetic authors are aware of the source of the paradox. However, the first scholar of antiquity who explicitly ascribes a solution to Plato seems to be Proclus. (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)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages (...) from Aristotle’s Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)