Amirouche Moktefi | Tallinn University of Technology (original) (raw)
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.
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.
Amirouche Moktefi & Stephen Read Preface, 1-5 Michael Astroh, Ivor Grattan-Guinness & Stephen Rea... more Amirouche Moktefi & Stephen Read
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
“What the Tortoise said to Achilles” (WTSA), sometimes known as Carroll’s paradox of inference, a... more “What the Tortoise said to Achilles” (WTSA), sometimes known as Carroll’s paradox of inference, appeared in the leading British journal "Mind" in 1895. Unlike Carroll’s earlier publication, “A logical paradox” (1894), commonly known as the barbershop paradox, which immediately attracted responses from serious logicians, none for WTSA was received in Carroll’s lifetime. However, WTSA has since been widely discussed among philosophers and is currently considered as a classic text in the philosophy of logic. What is more remarkable is that in the articles that have appeared in journals and books for over 120 years, there has been no accepted resolution to the problem Carroll posed in WTSA. Many scholars even believe that Carroll did not write his paper with a specific purpose in mind. It is true that little is known on the genesis and the writing of this fascinating article. Hence, confusion and mystery have long surrounded the reception of Carroll’s WTSA. Mystery might never vanish, but it is the aim of this volume to lessen confusion. Here we offer a set of papers providing key elements to the history and purpose of this enigmatic piece that will contribute to Carrollian studies and more generally, to philosophy.
"Amirouche Moktefi & Stephen Read Preface, 1-5 Michael Astroh, Ivor Grattan-Guinness &am... more "Amirouche Moktefi & Stephen Read 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"
Direction d'un numéro de revue (Communication & Langages)
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.
Logic, the discipline that explores valid reasoning, does not need to be limited to a specific fo... more Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning.
Contours of the Future: Technology and Innovation in Cultural Context, 2017
Works of fiction greatly contribute to the public (misunderstanding g of technology. As fictions,... more Works of fiction greatly contribute to the public (misunderstanding g of technology. As fictions, they create a universe where the statements they enunciate hold. Hence, they need not be subject to scepticism. It might thus be said that there is no true technological knowledge in fiction. Still, one cannot but observe that works of fiction often demonstrate a true technological creativity. This dilemma invites to a careful examination of how technology is depicted in fiction and what they do for each other. It will be argued that each produces possibilities that facilitate the acceptance of the other in a manner similar to jam facilitating the consumption of medicine. In particular, fictions instil the plausibility, but not necessarily the intelligibility, of technological possibilities into the public.
in Laurent Angard (ed.), Le Temps (In) Saisissable ?, pp. 114-117, 2006
Lewis Carroll, le mathématicien anglais plus connu pour ses contes pour enfants, publia en 1895 u... more Lewis Carroll, le mathématicien anglais plus connu pour ses contes pour enfants, publia en 1895 un dialogue intitulé « Ce que se dirent Achille et la Tortue » dans lequel il reprend les personnages de Zénon. Le texte ne discute cependant pas le problème original de Zénon sur l’indivisibilité du temps et de l’espace, mais plutôt la question des hypothétiques en logique. Par contre, d’autres écrits de Lewis Carroll, manuscrits ou publiés, abordent le problème de Zénon, et permettent d’en reconstituer une lecture Carrollienne. En effet, celui-ci réfute la vision indivisibiliste du temps dans un manuscrit datant de 1874. Dans des textes ultérieurs, notamment une lettre à un des ses amis et dans la seconde partie de sa logique symbolique, il s’efforce d’établir le paradoxe comme un simple sophisme mathématique, basé sur la fausse présomption qu’une infinité de sommes a l’infini pour somme.
Evelyne Barbin & Marc Moyon (eds.), Les Ouvrages de Mathématiques dans l’Histoire : Entre Recherche, Enseignement et Culture, pp. 57-70, 2013
Catherine Allamel-Raffin, Elsa Poupardin & Françoise Willmann (eds.), Informaticiens et Médecins dans la Fiction Contemporaine : Exploration 2, pp. 15-32, 2016
Dans L’ordinatueur (1997), Christian Grenier plonge le lecteur dans l’univers informatique. Une i... more Dans L’ordinatueur (1997), Christian Grenier plonge le lecteur dans l’univers informatique. Une informaticienne, Logicielle, y enquête sur une série de meurtres dont l’arme serait un ordinateur, l’OMNIA3. Ce roman donne à voir différentes facettes de l’informatique selon les compétences des protagonistes et les usages qu’ils en font. L’informatique est à la fois décor de l’histoire, arme du crime, moteur de l’enquête et surtout objet de fascination et d’adoration. L’analyse du roman permet de mettre en évidence quelques-unes des représentations de l’informatique et des informaticiens dans la littérature contemporaine, notamment le profil des informaticiens, les rapports entre experts et profanes, la place de l’informatique dans la société et enfin la contribution de l’informatique au travail narratif de l’auteur même.
Proceedings of The Canadian Society for the History and Philosophy of Mathematics, vol. 20, pp. 189-199, 2007
Lewis Carroll’s fame today as a logician is partly due to his “Achilles and the Tortoise” dialogu... more Lewis Carroll’s fame today as a logician is partly due to his “Achilles and the Tortoise” dialogue, published in the journal of philosophy Mind (April 1895). This text has been widely reprinted, cited and discussed by the twentieth century’s leading logicians and philosophers. However, it is another much less well-known Mind paper which made Carroll known among his contemporary logicians. When the Barbershop problem appeared in July 1894, it was already the subject of dispute among British logicians. In effect Lewis Carroll wrote numerous versions of the problem, sent copies of them to the main logicians of the time and compared their solutions. The debate that was aroused knew the involvement of Britain’s main logicians, such as J. Venn, J. C. Wilson, H. McColl, J. N. Keynes, W. E. Johnson, F. H. Bradley, B. Russell, and many others.
Here are considered the conditions under which the method of diagrams is liable to include non-cl... more Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: a review of the main concepts involved in the definition of logical negation; an explanation of the epistemological obstacles against the introduction of non-classical negations within diagrammatic logic.
Proceedings of the International Workshop on Diagram Logic and Cognition , Calcutta, 28-29 ottobre 2013, a cura di J. Burton & L. Choudhury, CEUR Workshop Proceedings 1132, pp. 23-30 . ISSN: 1613-0073
This paper explores the notion of autarchy of diagrammatic notations for logic debated in the Ger... more This paper explores the notion of autarchy of diagrammatic notations for logic debated in the German- speaking world of the 18th-century, especially as applied to linear diagrams invented by G. W. Leibniz and J. H. Lambert.
Jim Burton & Lopamudra Choudhury (eds.), DLAC 2013: Diagrams, Logic and Cognition. Proceedings of the First International Workshop on Diagrams, Logic and Cognition (Kolkata, India, October 28-19, 2013), series CEUR Workshop Proceedings, vol. 1132, 2014, pp. 31-35. http://ceur-ws.org/Vol-1132/, 2014
This paper discusses the role of continuity, connectivity and regularity in the design of spatial... more This paper discusses the role of continuity, connectivity and regularity in the design of spatial logic diagrams for N terms. Three specific diagrammatic schemes are discussed: Venn diagrams, Marquand tables and Karnaugh maps.
Proceedings of The Canadian Society for the History and Philosophy of Mathematics, vol. 18, pp. 136-144, 2005
Many generally accepted ideas harm an objective appreciation of Carroll’s contributions in logic.... more Many generally accepted ideas harm an objective appreciation of Carroll’s contributions in logic. To correct these prejudices and misunderstandings, we will essentially discuss the genesis and the reception of Lewis Carroll’s logical work. By focusing on the connections between logic and Carroll’s other literary and mathematical works, we will answer some questions related to the use which Carroll made of his pseudonym, the growing interest which he had in logic, and the status he gave it.
We commonly represent a class with a curve enclosing individuals that share an attribute. Individ... more We commonly represent a class with a curve enclosing individuals that share an attribute. Individuals that are not predicated with that attribute are left outside. The status of this outer class has long been a matter of dispute in logic. In modern notations, negative terms are simply expressed by labeling the spaces that they cover. In this note, we discuss an unusual (and previously unpublished) method designed by Peirce in 1896 to handle negative terms: to indicate the position of the terms by the shape of the curve rather than by labeling the spaces.
BSHM Bulletin Journal of the British Society for the History of Mathematics