Papers by Amirouche Moktefi
Axiomathes
In this paper we argue that there were several currents, ideas and problems in 19th-century logic... more In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’.
Lecture Notes in Computer Science, 2022
Diagrammatic Representation and Inference, 2020
Academic writing courses tend to focus on rhetorical and linguistic components rather than on arg... more Academic writing courses tend to focus on rhetorical and linguistic components rather than on argument making. This is unfortunate since it is precisely the purpose of scientific writing to expose arguments. We present an attempt to overcome this divide. For the purpose, we introduce colourful argument trees that do not merely exhibit the structure of a complex argument but also the state of our confidence in its statements and its inferences. The visualisation of the argument and the integration of the sources into its structure provide students with a better understanding of scientific writing.
Le Centre pour la Communication Scientifique Directe - HAL - Inria, Apr 27, 2016
Cahiers 22 Cahiers « Soyons logiques » est une invitation à double sens. Bien que la logique dési... more Cahiers 22 Cahiers « Soyons logiques » est une invitation à double sens. Bien que la logique désigne couramment une disposition d'esprit partagée par tout un chacun, cette disposition prête à confusion dès lors que l'on s'interroge sur ses sources théoriques. Le présent volume propose treize articles de logique portant sur plusieurs aspects de la discipline logique et de ses méthodes, notamment le formalisme, la théorie des oppositions, la vérité mathématique et l'histoire de la logique. Ce volume a été préparé avec le souci pédagogique de parler au plus grand nombre des lecteurs de logique et de philosophie. " Let´s be Logical " is a double invitation. Although logic often refers to a disposition of mind that we all share, this disposition might be confused once its theoretical sources are questioned. The present volume offers thirteen articles that address various aspects of the discipline of logic and its methods, notably formalism, the theory of opposition, mathematical truth, and history of logic. This volume has been prepared with the pedagogical concern of making it accessible to a wide audience of logic and philosophy readers.
Revista Internacional de Pesquisa em Educação Matemática, 2020
There are many mathematical references in Lewis Carroll’s two tales for children: Alice’s Adventu... more There are many mathematical references in Lewis Carroll’s two tales for children: Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass (1872). Many critics suggested that Carroll inserted hidden meanings in those passages. We rather consider them as part of the story’s setting and narrative. Yet, those passages may be interpreted and used as convenient to illustrate mathematical ideas. In this paper, we consider two passages from the Alice tales that relate to arithmetic, and we discuss them in relation to issues of personal identity, mathematical certainty, the role of notations and the processes of composition and decomposition in mental calculation. Hence, we show how literary texts can be used to convey ideas related to mathematics, mathematical culture and mathematical education. We conclude on the importance of mathematical writings as literary texts.
Diagrammatic Representation and Inference, 2018
Extension and intension are two ways of indicating the fundamental meaning of a concept. The exte... more Extension and intension are two ways of indicating the fundamental meaning of a concept. The extent of a concept, C, is the set of objects which correspond to C whereas the intent of C is the collection of attributes that characterise it. Thus, intension defines the set of objects corresponding to C without naming them individually. Mathematicians switch comfortably between these perspectives but the majority of logical diagrams deal exclusively in extension. Euler diagram indicate sets using curves to depict their extent in a way that intuitively matches the relations between the sets. What happens when we use spatial diagrams to depict intension? What can we infer about the intension of a concept given its extension, and vice versa? We present the first steps towards addressing these questions by defining extensional and intensional Euler diagrams and translations between the two perspectives. We show that translation in either direction leads to a loss of information, yet preserves important semantic properties. To conclude, we explain how we expect further exploration of the relationship between the two perspectives could shed light on connections between diagrams, extension, intension, and well-matchedness.
History and Philosophy of Logic, 2017
Studies in Universal Logic, 2020
Philosopher Arthur Schopenhauer included some logic diagrams in his major work: The World as Will... more Philosopher Arthur Schopenhauer included some logic diagrams in his major work: The World as Will and Representation, published in 1818. Few years later, he made a thorough use of diagrams in his Berlin Lectures that have not been published until 1913. These works are seldom mentioned in logic diagrams literature. This paper surveys and assesses Schopenhauer’s diagrams and the extent to which they conform to the scholarship of his time. It is shown that Schopenhauer adopted a scheme that is largely inspired from Leonhard Euler’s circles but includes some interesting innovations that were unknown to Euler. Two curiosities are particularly inspected: an inventory of logical relations and a diagram on the routes to good and evil.
Symbolic logic faced great difficulties in its ea rly stage of development in order to acquire re... more Symbolic logic faced great difficulties in its ea rly stage of development in order to acquire recognition of its utility for the n eds of science and society. The aim of this paper is to discuss an early attempt by the British logician Lewis Carroll (1832– 1898) to promote symbolic logic as a social good. T his examination is achieved in three phases: first, Carroll’s belief in the social utili ty of logic, broadly understood, is demonstrated by his numerous interventions to fight fall acious reasoning in public debates. Then, Carroll’s attempts to promote symbolic logic, specifically, are revealed through his work on a treatise that would make the subject ac essible to a wide and young audience. Finally, it is argued that Carroll’s ideal of ogic as a common good influenced the logical methods he invented and allowed him to tackle more efficiently some problems that resisted to early symbolic logicians.
L'oeuvre logique de lewis caroll a ete diversement appreciee. si ses travaux ont ete commente... more L'oeuvre logique de lewis caroll a ete diversement appreciee. si ses travaux ont ete commentes et cites par de grands philosophes et logiciens des dix-neuvieme et vingtieme siecles, ils sont cependant plus apprecies pour leur portee pedagogique et ludique que logique. il s'agit essentiellement de deux ouvrages populaires : the game of logic (1887) et symbolic logic. part 1 (1895). il faudra y ajouter deux articles : ''a logical paradox'' (1894) et ''what the tortoise said to achilles'' (1895), tous deux publies dans mind. en 1977, w.w. bartley iii publie de larges fragments inedits de la seconde partie de symbolic logic. cette publication permet une meilleure comprehension de l'oeuvre logique de lewis caroll. mon travail consiste a discuter cette oeuvre dans son cadre historique qu'est la logique anglaise de la fin du dix-neuvieme siecle.
There is growing interest in the logic of imagination. A widespread position holds that all that ... more There is growing interest in the logic of imagination. A widespread position holds that all that is imagined is conceived and all that is conceived is possible. Hence, (logical) impossibilities such as ‘round squares’ cannot be imagined. Yet, during a tutorial at the Diagrams 2018 conference, we asked participants to undertake this impossible task: to imagine a round square, and we collected their drawings. Should we then dismiss the collected round squares on the ground that they cannot be? We present the outcomes of this experiment and explore what it teaches us on imagination, impossible objects and diagrams. In particular, we argue that there is no need to draw an object that is actually round and square in order to visualise an object that is round and square. All that is needed is to visualise the possession of those properties of round-ness and square-ness. Diagrams help considerably.
Diagrammatic Representation and Inference, 2020
Diagrammatic Representation and Inference, 2018
The use of diagrams in logic is old. Euler and Venn schemes are among the most popular. Carroll d... more The use of diagrams in logic is old. Euler and Venn schemes are among the most popular. Carroll diagrams are less known but are occasionally mentioned in recent literature. The objective of this tutorial is to expose the working of Carroll’s diagrams and their significance from a triple perspective: historical, mathematical and philosophical. The diagrams are exposed, worked out and compared to Euler-Venn diagrams. These schemes are used to solve the problem of elimination which was widely addressed by early mathematical logicians: finding the conclusion that is to be drawn from any number of propositions given as premises containing any number of terms. For this purpose, they designed symbolic, visual and sometimes mechanical devices. The significance of Venn and Carroll diagrams is better understood within this historical context. The development of mathematical logic notably created the need for more complex diagrams to represent n terms, rather than merely 3 terms (the number demanded by syllogisms). Several methods to construct diagrams for n terms, with different strategies, are discussed. Finally, the philosophical significance of Carroll diagrams is discussed in relation to the use of rules to transfer information from a diagram to another. This practice is connected to recent philosophical debates on the role of diagrams in mathematical practices.
Diagrammatic Representation and Inference, 2021
Diagrammatic Representation and Inference, 2021
Diagrammatic Representation and Inference, 2020
While developing his system of Existential graphs which he viewed as the logic of the future, Cha... more While developing his system of Existential graphs which he viewed as the logic of the future, Charles S. Peirce continued working on variations of past diagrams. In particular, he introduced in the period 1896–1901 an original variation of Eulerian diagrams where the shape of the curves indicated the sign of the classes that were contained in them. These diagrams recently attracted attention for their ability to represent negative terms more directly than earlier schemes. Yet, we offer here a more general rationale: we argue that Peirce conceived these diagrams by making inclusion the main operator, a practice that is found in his other logical systems, both algebraic and diagrammatic. This is achieved by expressing universal propositions in an inclusional form. This shift allows him to classify syllogisms under just three diagrammatic forms in a style that is found in some of his contemporaries.
The Mathematical World of Charles L. Dodgson (Lewis Carroll), 2019
This chapter discusses Dodgson’s work on syllogisms (a topic that can be traced back to Aristotle... more This chapter discusses Dodgson’s work on syllogisms (a topic that can be traced back to Aristotle and Ancient Greece) and how to solve them systematically using a marked board and some counters. His method is explained in detail in this chapter. Dodgson introduced it in his Game of Logic, which he used to teach syllogisms to children, and which he then developed in his Symbolic Logic, Part I. The rest of the chapter is concerned with further work that Dodgson carried out, but which was not published at the time because of his premature death at the age of 65.
BSHM Bulletin: Journal of the British Society for the History of Mathematics, 2017
Private libraries of scientists offer valuable information on their character, work, and acquaint... more Private libraries of scientists offer valuable information on their character, work, and acquaintances. Charles L Dodgson (alias Lewis Carroll) constructed an impressive library of several thousand volumes. The sale catalogue of Carroll's library reveals that it contained at his death most of the major logic works that would be expected for a British mathematical logician of the time. However, there is dispute as to the presence of the most important logic book of all: George Boole's Laws of thought (1854). The absence of this work would make both an unfortunate and an intriguing gap. This paper explains the source of this dispute and introduces a new argument from the sale catalogues centred on the dissemination of the books after the sale of the library.
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Papers by Amirouche Moktefi
Preface, 1-5
Michael Astroh, Ivor Grattan-Guinness & Stephen Read
A survey of the life of Hugh MacColl (1837-1909), 7-30
Stein Haugom Olsen
Outside the intellectual mainstream? The successes and failures of Hugh MacColl, 31-54
Francine F. Abeles & Amirouche Moktefi
Hugh MacColl and Lewis Carroll: Crosscurrents in geometry and logic, 55-76
James J. Tattersall
Hugh MacColl’s contributions to The Educational Times, 77-96
Irving H. Anellis
MacColl’s influences on Peirce and Schröder, 97-128
Jean-Marie C.Chevalier
Some arguments for propositional logic: MacColl as a philosopher, 129-148
Shahid Rahman
Some remarks on Hugh MacColl’s notion of symbolic existence, 149-162
Fabien Schang
MacColl’s modes of modalities, 163-188
Ivor Grattan-Guinness
Was Hugh MacColl a logical pluralist or a logical monist? A case study in the slow emergence of metatheorising, 189-204
John Woods
MacColl’s elusive pluralism, 205-234
Hugh MacColl
On the growth and use of a symbolical language, 235-249