A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)

Abu Nasr Muhammad Al-Farabi (870–950 AD), the second outstanding representative of the Muslim peripatetic after al Kindi (801–873 AD), was born in Turkestan about 870 AD. Al-Farabi’s studies commenced in Farab, then he travelled to Baghdad, where he studied logic with a Christian scholar named Yuhanna b. Hailan. Al-Farabi wrote numerous works dealing with almost every branch of science in the medieval world. In addition to a large number of books on logic and other sciences, he came to be known (...) as the “Second Teacher” (al-Mou’allim al-Thani), Aristotle being the first. One of Al-Farabi’s most important contributions was clarifying the func- tions of logic as follows: 1. He defined logic and compared it with grammar, and discussed the clas- sification and fundamental principles of science in a unique and useful manner. 2. He made the study of logic easier by dividing it into two categories: Takhayyul (idea) and Thubut (proof). 3. He believed that the objective of logic is to correct faults we may find in ourselves and in others, and faults that others find in us. 4. He said that if we do not comprehend logic, we must either have faith in all people, or mistrust all people, or differentiate between them. Such actions would be undertaken without a basis of evidence or experimen- tation. In this paper, I will analyse the functions of logic in Al-Farabi’s works, Enumeration of the Sciences, Book on the Syllogism, Book on Dialectic, Book on Demonstration and Ring Stones of Wisdom, in order to present his contributions in the field of logic. (shrink)

This paper analyzes a classification of different types of demonstration introduced by Alfarabi in his Kitāb al-Burhān. Alfarabi identifies eight combinations of demonstrative syllogisms, grouped in function of the different types of per se relations expressed by their premises and conclusions, where terms are definitionally connected with one another. The list contains a total of thirty-nine moods illustrated by a rich array of examples drawn from various scientific disciplines, including arithmetic, geometry, and natural philosophy. The combinations and moods are discussed (...) extensively by Averroes in the section of his Epitome of the Organon devoted to the Posterior Analytics and in his Quaesita on logic. Alfarabi’s classification also possibly inspired a simplified taxonomical effort in Avicenna’s Kitāb al-Burhān. (shrink)

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books, from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. (...) He ascribes a special status to the categories Quantity and Quality, whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. (shrink)

"The world is a finite body, and therefore has finite power." John Philoponus is remembered for using this Aristotelian premise to break ranks with Aristotle and argue that the world is not everlasting. This investigation reconsiders Philoponus’s arguments from finite power, and then explores the aftermath of this line of thinking in the works of three lesser-known Arabic intellectuals active in the generation before Avicenna (d. 1037): Abū l-Ḫayr Ibn Suwār (d. after 1017), Abū al-Ḥasan al-ʿĀmirī (d. 992), and Abū (...) Sahl al-Masīḥī (d. after 1025). Each engaged with this dictum in unique and novel ways, and in so doing anticipated a number of central features of Avicenna’s writings. The history of this argument is of crucial importance for understanding the evolution of natural philosophy and metaphysics in this formative period, away from tedious and simplistic arguments about creation and towards a more robust modal ontology based on intrinsic and extrinsic necessity. (shrink)

Ibn Sīnā proposed an analysis of arguments by reductio ad absurdum. His analysis contains, perhaps for the first time, a workable method for handling the making and discharging of assumptions in a formal proof. We translate the relevant text of Ibn Sīnā and put his analysis into the context of his general approach to logic.

RésuméLe présent article propose la liste des œuvres médicales composées par Ibn Bājja, donne une présentation synthétique de celles qui nous ont été transmises et étudie le métacommentaire au commentaire de Galien sur lesAphorismesd'Hippocrate (Sharḥ fī al-Fuṣūl). Ce texte montre une influence profonde d'al- Fārābī, en particulier dans sa conception de l'expérience médicale, qui remonte à la façon dont ce dernier construit l'expérience (tajriba) comme le procédé inductif, décrit par Aristote dans lesSeconds Analytiques, produisant les prémisses de la démonstration. Sur (...) cette base, Ibn Bājja défend la pertinence d'une médecine moins scolastique et plus empirique, une position dont Ibn Rushd se fera l'écho. Des similitudes entre le texte d'Ibn Bājja et leK. al-Kulliyyāt fī al-ṭibbd'Ibn Rushd suggèrent que celui-ci avait lu leSharḥ fī al-Fuṣūl. Cette œuvre, en outre, pourrait bien attester que la dissection humaine était pratiquée à l'époque d'Ibn Bājja. (shrink)

Avicenna (d. 1037) and Tūsī (d. 1274) have different doctrines on the contradiction and conversion of the absolute proposition. Following Avicenna's presentation of the doctrine in Pointers and reminders, and comparing it with what is given in Tūsī's commentary, allow us to pinpoint a major reason why Avicenna and Tūsī have different treatments of the modal syllogistic. Further comparison shows that the syllogistic system Rescher described in his research on Arabic logic more nearly fits Tūsī than Avicenna. This in turn (...) has consequences for analysing Avicenna's logic, and for writing the history of a fascinating period of change and diversity in the discipline in the medieval Islamic world. (shrink)

Ancient commentators like Ammonius and Boethius tried to solve Aristotle's “sea battle argument” in On Interpretation 9 by saying that statements about future contingents are “indefinitely” true or false. They were followed by al-Fārābī in his commentary on On Interpretation. The article sets out two possible interpretations of what “indefinitely” means here, and shows that al-Fārābī actually has both conceptions: one applied in his interpretation of Aristotle, and another that he is forced into by the problem of divine foreknowledge. It (...) also explains the relevance of al-Fārābī's remarks as a link between the non-statistical modal theories of Philo and Avicenna. (shrink)

In his Kitab al-ḥuruf, al-Fârâbî exposed a problem: Arabic language doesn’t have a word corresponding to the Greek verb einai. This paper examines the way Arabic philosophers managed to practice me...

This article aims to present a summary account of the role of Syriac in the transmission of Aristotle's Organon from Greek to Arabic. The main sources for that purpose lie in the Syriac and Arabic translations of Aristotle's works, that were achieved during the period from the 7th to the 9th centuries. Some problems related to these translations are discussed, with more attention paid to the emergence of a technical language of logic. Dans cet article on se propose de présenter (...) un bref état de la question touchant le rôle de l'intermediaire syriaque dans la transmission de l' Organon d'Aristote du grec à l'arabe. Les principales sources utilisées sont les traductions syriaques et arabes des traités d'Aristote, qui furent exécutées dans la période allant du VII e au IX e siècle. On examine diverses questions relatives à ces traductions, en s'attachant particulièrement à la formation d'un langage technique de la logique. (shrink)

The “lost” Yaḥyā ibn ʿAdī treatises recently discovered in the Tehran codex Marwī 19 include a record of a philosophical debate instigated by the Ḥamdānid prince Sayf-al-Dawla. More precisely, Marwī 19 contains Yaḥyā’s adjudication of a dispute between an unnamed Opponent and Yaḥyā’s younger relative Ibrāhīm ibn ʿAdī (who also served as al-Fārābī’s assistant), along with Ibrāhīm's response to Yaḥyā’s adjudication, and Yaḥyā’s final word. At issue was a problem of Aristotelian exegesis: should “body” be understood as falling under the (...) category of substance or under the category of quantity? The unnamed Opponent argues that body is a species of substance; Ibrāhīm argues that technically speaking, body is a species of quantity, and hence an accident; and Yaḥyā judges that body is a species of substance, though for very different reasons than the Opponent gives. For the first time, the Arabic text of this exchange is edited and translated into English. Also provided is an Introduction that sets the debate in historical context, and discusses in particular the possible influence of John Philoponus. The debate is interesting and important not only because of the philosophical ramifications of the issues under discussion, but because it constitutes evidence of dialectical practice among Arabic-speaking philosophers from the middle of the 10th century. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

Aristotle says at the start of the De interpretatione that words symbolise thoughts, which are in turn likenesses of things. The present paper argues that he is speaking here primarily of the signification of whole sentences, and at most secondarily of the semantics of individual words. This proposal is defended by drawing attention to a shift in the meaning of ‘sign’ and cognate terms that occurs in the course of the first chapter, one which enables us to separate the way (...) in which words ‘signify’ thoughts (declarative, interrogative, etc.), by expres­sing them, from the more narrowly semantic way in which, subsequently, they are said to signify things. Aristotle’s famous opening state­ment finds its main application, not in the rudimentary grammar of nouns and verbs that follows in chapters 2-3, but later in the treatise, and above all in chapter 14, where it is invoked to establish for dialectical purposes that the relation between a sentence and its negation is the strongest of all contrarieties. Aristotle’s insis­tence, in this same treatise, on the conventional character of language is also explained: for in chapters 8 and 11 it is because of the conventionality of language, and its consequent failure to map systemati­cally onto the divisions between things, that what is in surface grammar a single sentence may turn out to be in reality two or more sentences, in other words, to signify (i.e. express) two or more different thoughts. Aristotle’s primary focus on the meanings of entire sentences is thus explained by the role of the De interpretatione as a work ancillary to dia­lectic, a discipline for which the relation between contradictory pairs of assertions is fundamen­tal. In addition, such a focus is argued (with a comparison to the Stoic lekton) to reflect Aris­totle’s teleological frame of thought. (shrink)

El _De Institutione Musica_, uno de los primeros tratados científicos de Boecio, expone la relación entre el hombre y la música basada en la armonía musical del cuerpo y el alma, donde Platón y Aristóteles aparecen confirmando a Pitágoras, quien sería el creador de esta antropología. En nuestro análisis, la enseñanza de Boecio proviene del neo-pitagorismo de Nicómaco de Gerasa y es incompatible no sólo con las doctrinas correspondientes de Platón y Aristóteles, a quien Boecio dice honrar con la traducción (...) de sus obras, sino con otros tratados, especialmente el _Contra Eutychen_ que se analiza aquí, por tener un fuerte componente antropológico. La pregunta que nos hacemos es si Boecio era consciente de la incoherencia doctrinal de sus fuentes. Nuestra respuesta es que él no fue inconsciente ni un traductor servil de sus fuentes, sino que él se identifica con las enseñanzas de Nicómaco sólo en la etapa inicial de su desarrollo, y esta doctrina no está integrada con el resto de sus trabajos científicos y teológicos. (shrink)

Un certain nombre de sources arabes font état d'une polémique entre Alexandre et Galien. Une tendance marquée de la recherche a été de lire nos sources grecques, relativement peu nombreuses, à la lumière de cette tradition. L'objectif de cet article est de contester le bien-fondé d'une telle orientation, et de dégager en même temps le statut spécifique de ce genre de récit biographique.