Papers by Matías Osta-Vélez
Ratio, 2024
Generic statements play a crucial role in concept learning, communication and education. Despite ... more Generic statements play a crucial role in concept learning, communication and education. Despite many efforts, the semantics of generics remain a controversial issue, as they do not seem to fit our standard theories of meaning. In this article, we attempt to shed light on this problem by focusing on how these sentences function in reasoning. Drawing on a distinction between property and diagnostic generics, we defend three theses: First, property generics are not about facts but express relations between concepts. Second, generics play an important role in everyday reasoning by interacting with our expectations about the world. Third, diagnostic generics emphasise properties that separate the category in the generics from other categories in the same contrast class. We use the theory of conceptual spaces to advance measures of typicality and diagnosticity capable of modelling different
aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of gene
Studies in Philosophy and Education
Knowledge and ignorance have been treated asymmetrically throughout the history of epistemology. ... more Knowledge and ignorance have been treated asymmetrically throughout the history of epistemology. Not only knowledge has hogged the spotlight, but it has been widely understood as explanatory prior to ignorance. In recent years, however, scholars have started to counterbalance this tendency and the problem of ignorance has been gaining prominence in philosophy and related areas. Not surprisingly, and despite these recent efforts, finding a satisfactory philosophical definition of the notion has proven to be particularly difficult. Ignorant Cognition, Selene Arfini's first book, is a bold attempt to face the problem of ignorance with full awareness of the issues mentioned above. Instead of ruminating about the analytical definition of ignorance, Arfini's strategy consists of exploiting our basic intuitions about ignorance throughout an analysis of its role in various dimensions of individual and social cognition. With a strong influence from Peirce's epistemology, she develops a thorough examination of the place of ignorance in the dynamics of belief and doubt, its influence on reasoning, and its "diffusion" in large groups. The book is composed of twelve chapters (in an article-like format) grouped into three parts. Part I presents an epistemological analysis of the "fugitive" nature of ignorance, its role in belief fixation, doubt, and metacognition. Part II deals with reasoning under uncertainty and explores what the author calls the "tenacity" of ignorance. Finally, Part III puts the focus on social cognition, and in particular, on how ignorance spreads in online communities and how this affects individual reasoning in various ways. It is impossible to do justice to all the sophisticated arguments and the wide range of topics that compose the book. In this review, I will focus on what I considered the most important and thought-provoking points of it. Fugitive Ignorance As said above, the first part of the book is devoted to explaining why ignorance has a "fugitive nature", and to exploring some of the consequences of this fact. Arfini's analysis mirrors John Woods' theory of knowledge and belief. According to Woods, an epistemic property is fugitive when it cannot be fully grasped or confirmed by the agent from
Cette thèse porte sur le rôle du contenu conceptuel dans l'inférence et le raisonnement. Les ... more Cette thèse porte sur le rôle du contenu conceptuel dans l'inférence et le raisonnement. Les deux premiers chapitres offrent une analyse critique de la "thèse formaliste", i.e., l'idée selon laquelle l'inférence rationnelle est un mécanisme qui applique des règles syntaxiques à des pensées avec structure linguistique. Le Chapitre 3 porte sur la relation entre l'inférence et la représentation. Il est avancé que l'inférence doit être étudiée depuis une perspective pluraliste en raison de sa dépendance à l'égard de différents formats de représentation des informations qui caractérisent la cognition humaine. Les quatre chapitres suivants sont ceux de la mise en œuvre de la théorie des espaces conceptuels à trois types d'inférence basés sur des concepts. Tout d'abord, une explication formelle de la notion d'inférence matérielle chez Wilfrid Sellars est avancée. Ensuite, le modèle est étendu pour saisir l’inférence non monotone en étudiant le ...
Philosophical Psychology, 2019
meaningful experience of one’s body is fundamental to a life lived well. Although Young explicitl... more meaningful experience of one’s body is fundamental to a life lived well. Although Young explicitly discusses motility, her work is fundamental to any attempt to understand the affective character of the oppression of women. Because affect is primarily about meaningful experience of the body, the oppression of bodies and bodily movements is affective in nature. The concluding part of the volume, Part 8, is about moods and concepts closely related to moods. It contains two of the most significant contributions to what is a very highstandard collection: Otto Friedrich Bollnow’s “The nature of stimmungen: The concept of stimmung” and Matthew Ratcliffe’s “The feeling of being.” Bollnow’s chapter is extracted from his 1956 work Das Wesen der Stimmungen and is translated for this edition into lucid English. It is a richly descriptive piece, detailing general affective states that color our experience of ourselves and the world. Bollnow also advances some very strong theses about Stimmung and its role in lived experience. Stimmung is not quite a mood, or, rather, what we ordinarily call moods are caricatures of the overall tonal nature of our experience. Stimmung is foundational: “The emotions thus develop – alongside the other faculties of mind – only on the basis of the foundation of Stimmung that precedes them, and they are determined in character by this foundation” (p. 245). Stimmung is not experienced as an object of consciousness but as a mode of consciousness, and it unifies the experience of self and world: “The great philosophical significance of Stimmung lies precisely in the fact that it goes beyond the separation of subject and object, which theoretical consciousness takes for granted, back into the level of an original unity between the two” (p. 247). Matthew Ratcliffe’s paper takes up a similar set of ideas and develops them with a more cautious, analytic approach, concentrating on what he calls “existential feelings.” The significance of moods, the tonal affective character of experience, and the embodied feeling of existence that underlies all lived experience and colors experience of ourselves and of the world (not necessarily separately) are of fundamental significance for the project of understanding the relationship between emotion, affectivity, and a life well lived. When psychologists investigate subjective well-being, they often search for short, summary descriptions of affect that can be rated on a ten-point scale. Bollnow and Ratcliffe’s papers are timely reminders of the folly – more politely, limitations – of this approach. As with every part of this book, the work represented in Part 8 offers both a challenge to and an invaluable resource for the task of understanding the relationship between emotion, affect, and the good life. I wholeheartedly recommend this volume to everybody interested in the task.
Minds and Machines
Over the past few decades, cognitive science has identified several forms of reasoning that make ... more Over the past few decades, cognitive science has identified several forms of reasoning that make essential use of conceptual knowledge. Despite significant theoretical and empirical progress, there is still no unified framework for understanding how concepts are used in reasoning. This paper argues that the theory of conceptual spaces is capable of filling this gap. Our strategy is to demonstrate how various inference mechanisms which clearly rely on conceptual information—including similarity, typicality, and diagnosticity-based reasoning—can be modeled using principles derived from conceptual spaces. Our first topic analyzes the role of expectations in inductive reasoning and their relation to the structure of our concepts. We examine the relationship between using generic expressions in natural language and common-sense reasoning as a second topic. We propose that the strength of a generic can be described by distances between properties and prototypes in conceptual spaces. Our t...
Journal of Mathematical Psychology, 2020
Category-based induction is an inferential mechanism that uses knowledge of conceptual relations ... more Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions.
Frontiers in Psychology
Whereas the validity of deductive inferences can be characterized in terms of their logical form,... more Whereas the validity of deductive inferences can be characterized in terms of their logical form, this is not true for all inferences that appear pre-theoretically valid. Nonetheless, philosophers have argued that at least some of those inferences—sometimes called “similarity-based inferences” —can be given a formal treatment with the help of similarity spaces, which are mathematical spaces purporting to represent human similarity judgments. In these inferences, we conclude that a given property pertains to a category of items on the grounds that the same property pertains to a similar category of items. We look at a specific proposal according to which the strength of such inferences is a function of the distance, as measured in the appropriate similarity space, between the category referenced in the premise and the category referenced in the conclusion. We report the outcomes of three studies that all support the said proposal.
Minds and Machines , 2023
Over the past few decades, cognitive science has identified several forms of reasoning that make ... more Over the past few decades, cognitive science has identified several forms of reasoning that make essential use of conceptual knowledge. Despite significant theoretical and empirical progress, there is still no unified framework for understanding how concepts are used in reasoning. This paper argues that the theory of conceptual spaces is capable of filling this gap. Our strategy is to demonstrate how various inference mechanisms which clearly rely on conceptual information-including similarity, typicality, and diagnosticity-based reasoning-can be modeled using principles derived from conceptual spaces. Our first topic analyzes the role of expectations in inductive reasoning and their relation to the structure of our concepts. We examine the relationship between using generic expressions in natural language and common-sense reasoning as a second topic. We propose that the strength of a generic can be described by distances between properties and prototypes in conceptual spaces. Our third topic is category-based induction. We demonstrate that the theory of conceptual spaces can serve as a comprehensive model for this type of reasoning. The final topic is analogy. We review some proposals in this area, present a taxonomy of analogical relations, and show how to model them in terms of distances in conceptual spaces. We also briefly discuss the implications of the model for reasoning with concepts in artificial systems.
This thesis studies the role of conceptual content in inference and reasoning. The first two chap... more This thesis studies the role of conceptual content in inference and reasoning. The first two chapters offer a theoretical and historical overview of the relation between inference and meaning in philosophy and psychology. In particular, a critical analysis of the formality thesis, i.e., the idea that rational inference is a rule-based and topic-neutral mechanism, is advanced. The origins of this idea in logic and its influence in philosophy and cognitive psychology are discussed. Chapter 3 consists of an analysis of the relationship between inference and representation. It is argued that inference has to be studied from a pluralistic per- spective due to its dependence on different formats of representing information. The following four chapters apply conceptual spaces, a formal theory of concepts within cognitive semantics, to three concept-based inference-types. First, an explication of Sellars notion of material inference is advanced. Later, the model is extended to account for n...
Journal of Logic, Language and Information, 2021
In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge represent... more In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.
Journal of Experimental and Theoretical Artificial Intelligence , 2022
In this paper, we outline a comprehensive approach to composed analogies based on the theory of c... more In this paper, we outline a comprehensive approach to composed analogies based on the theory of conceptual spaces. Our algorithmic model understands analogy as a search procedure and builds upon the idea that analogical similarity depends on a conceptual phenomena called 'dimensional salience.' We distinguish between category-based, property-based, event-based, and part-whole analogies, and propose computationally-oriented methods for explicating them in terms of conceptual spaces.
El relato más difundido sobre la revolución cientí!ca en la modernidad muestra a Galileo como un ... more El relato más difundido sobre la revolución cientí!ca en la modernidad muestra a Galileo como un pionero del método experimental que pone a los hechos como fuente primera y último juez del conocimiento cientí!co. Esta visión suele opacar otro aporte revolucionario del físico italiano a la metodología cientí!ca que contrasta (aunque de!nitivamente no contradice) con su imagen experimantalista: el método idealizatorio conocido como la matematización de la física y de la naturaleza.
Journal of Logic, Language and Information, 2021
In Gärdenfors and Makinson (1994) and Gärdenfors (1992) it was shown that it is possible to model... more In Gärdenfors and Makinson (1994) and Gärdenfors (1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectationbased ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects.
Journal of Mathematical Psychology , 2020
Category-based induction is an inferential mechanism that uses knowledge of conceptual relations ... more Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions.
Journal for General Philosophy of Science , 2019
In this article I’m going to reconstruct Stephen Toulmin’s procedural theory of concepts and expl... more In this article I’m going to reconstruct Stephen Toulmin’s procedural theory of concepts and explanations in order to develop two overlooked ideas from his philosophy of science: methods of representations and inferential techniques. I argue that these notions, when properly articulated, could be useful for shedding some light on how scientific reasoning is related to representational structures, concepts, and explanation within scientific practices. I will explore and illustrate these ideas by studying the development of the notion of instantaneous speed during the passage from Galileo’s geometrical physics to analytical mechanics. At the end, I will argue that methods of representations could be considered as constitutive of scientific inference; and I will show how these notions could connect with other similar ideas from contemporary philosophy of science like those of models and model-based reasoning.
La Filosofía y su Enseñanza , 2016
El relato más difundido sobre la revolución científica en la modernidad muestra a Galileo como un... more El relato más difundido sobre la revolución científica en la modernidad muestra a Galileo como un pionero del método experimental que pone a los hechos como fuente primera y último juez del conocimiento científico. Esta visión suele opacar otro aporte revolucionario del físico italiano a la metodología científica que contrasta (aunque definitivamente no contradice) con su imagen experimantalista: el método idealizatorio conocido como la matematización de la física y de la naturaleza.
Thesis Chapters by Matías Osta-Vélez
dumas-01101587 - Université Paris 1 Panthéon-Sorbonne
La motivation centrale de ce travail est d’essayer de comprendre l’énoncé suivant : "La logique ... more La motivation centrale de ce travail est d’essayer de comprendre l’énoncé suivant : "La logique est la science du raisonnement correcte". Cette affirmation, d’apparence simple, a traversé l’histoire de la philosophie et continue encore aujourd’hui. L’idée exprimée par cet énoncé a eu un rôle central dans le développement de la philosophie occidentale, et particulièrement, aux origines de la philosophie analytique, avec Frege, et encore avant, avec Kant. Son contenu, dépend d’au moins trois variables : le contexte philosophique, l’état de développement théorique de la théorie logique et le contenu du concept raisonnement. C’est-à-dire que, pour comprendre, d’un point de vue philosophique, l’affirmation considérée, il faut prendre en compte, au moins, ces trois aspects. Nous nous réfèrerons à la discussion sur l’idée selon laquelle la logique est la science du raisonnement comme la problématique sur la normativité logique. Dans ce travail, nous analyserons cette problématique à la lumière des considérations précédentes, tout en nous focalisant sur le problème à travers trois contextes philosophiques différents : la philosophie de Kant, la philosophie de Frege et la philosophie analytique contemporaine.
Talks by Matías Osta-Vélez
Grounding mathematical concepts in practices, 2019
During the last few decades, philosophy of mathematics has turned to the notion of practice for d... more During the last few decades, philosophy of mathematics has turned to the notion of practice for developing an analysis of mathematics as a social and historically situated activity. Despite the progress made in this direction, philosophers have not yet agreed on how to relate mathematical concepts to actual practices.
Building on Wittgenstein’s use theory of meaning and Toulmin’s theory of concepts; we propose a semantic framework that could solve this problem. The “later” Wittgenstein famously argued that concepts gain their meaning embedded in (rule-governed) language games which are “grounded” in different behavioral and practical contexts (forms of life). Following these ideas, Toulmin claimed that scientific concepts cannot be analyzed in abstracto, because they have a stratified nature. That is, their contents are the products of the evolution of sequences of language games, which are, at the same time, associated with different culturally situated collective practices. In this sense, analyzing the content of a scientific concept imply to look into its developmental history and, more specifically, to look into the collective practices that constitute the language games in which it was involved.
We will apply these ideas to a case where we found a mathematization of a non-mathematical (technical) practice: the mathematization of perspective painting in the work of Guidobaldo del Monte (1600). In this case, we have for the one hand, a perspective painting practice characterized by the effort of imitate visual impression, inspired a rule for drawing all orthogonals with one common point of intersection -i.e. the principal vanishing point, the so-called convergence rule; for the other hand, we have the so-called by Taylor (1719), main theorem in Guidobaldo’s work (Andersen, 2007). This result say that the image of a line l non-parallel to the horizontal plane, is determined by the vanishing point, and the point resulting of the intersection between l and the horizontal plane. So, this theorem guarantee the unique existence of the vanishing point. Our suggestion, is that reincorporation of the convergence rule in a mathematical setting by the main theorem involve, as a result of an interplay of pre-existing languages games (perspective painting and euclidean geometry and optic), a conceptual innovation consisting in the introduction of the concept of vanishing point.
There is a common idea that mathematical structures are formal languages, and as such, they are s... more There is a common idea that mathematical structures are formal languages, and as such, they are supposed to have some kind of representational flexibility and conceptual neutrality, this is, they can be applied to different domains of phenomena and they can express pre-established content without affecting it. In a similar vein, it is widely accepted that mathematics played a central role in the conceptual development of empirical sciences. But this role is far from being fully understood, and it is not clear how it could be explained if we accept the thesis of the conceptual neutrality of mathematical language.
I will argue that there is plenty historical evidence against this last thesis, notably, coming from mathematical physics. As various philosophers and historians of science have shown, there are cases in which the very content of ‘empirical concepts’ of scientific theories is deeply affected by the mathematical structure involved in the theory (see Toulmin 1953, Guisti 1994, Panza 2002, Blay 1992 or Roux 2010). I will analyse of one of these cases in order to argue against the conceptual neutrality of mathematical languages. I will explain the passage from the geometrisation to the mathematisation of motion from Galileo to Varignon, trying to show how the mathematisation of the notion of continuity made it possible to develop some central (empirical) concepts from the physics of motion, notably that of instantaneous velocity.
The main point of this analysis is to show how the use of geometrical methods of representation in physics posited serious constraints to conceptual development and conceptual use to physicists, and how some of these problems were solved when geometry was partially substituted by analytical methods of representation thanks to the development of infinitesimal calculus.
References:
M. Blay, La Naissance de la mécanique analytique. Presses Universitaires de France, 1992.
E. Giusti, “Il Filosofo Geometra. Matematica e Filosofia Naturale in Galileo”. Nuncius, 9 ( 2 ) ,
485–498, 1994.
M. Panza, “Mathematisation of the Science of Motion and the Birth of Analytical M e c h a n i c s : A Historiographical Note”. In P. Cerrai, P. Freguglia & C. Pellegrini (eds.), The Application of Mathematics to the Sciences of Nature (pp. 253–271). Springer US, 2002.
Palmerino, “The Geometrization of Motion: Galileo’s Triangle of Speed and its Various Transformations”. Early Science and Medicine, 15(4-5), 410–447, 2010.
S. Roux, “Forms of Mathematization (14th-17th Centuries)”. Early Science and Medicine, 15(4-5), 319–337, 2010.
S. Toulmi, An Introduction to Philosophy of Science. Hutchinson University Press, 1953.
Uploads
Papers by Matías Osta-Vélez
aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of gene
Thesis Chapters by Matías Osta-Vélez
Talks by Matías Osta-Vélez
Building on Wittgenstein’s use theory of meaning and Toulmin’s theory of concepts; we propose a semantic framework that could solve this problem. The “later” Wittgenstein famously argued that concepts gain their meaning embedded in (rule-governed) language games which are “grounded” in different behavioral and practical contexts (forms of life). Following these ideas, Toulmin claimed that scientific concepts cannot be analyzed in abstracto, because they have a stratified nature. That is, their contents are the products of the evolution of sequences of language games, which are, at the same time, associated with different culturally situated collective practices. In this sense, analyzing the content of a scientific concept imply to look into its developmental history and, more specifically, to look into the collective practices that constitute the language games in which it was involved.
We will apply these ideas to a case where we found a mathematization of a non-mathematical (technical) practice: the mathematization of perspective painting in the work of Guidobaldo del Monte (1600). In this case, we have for the one hand, a perspective painting practice characterized by the effort of imitate visual impression, inspired a rule for drawing all orthogonals with one common point of intersection -i.e. the principal vanishing point, the so-called convergence rule; for the other hand, we have the so-called by Taylor (1719), main theorem in Guidobaldo’s work (Andersen, 2007). This result say that the image of a line l non-parallel to the horizontal plane, is determined by the vanishing point, and the point resulting of the intersection between l and the horizontal plane. So, this theorem guarantee the unique existence of the vanishing point. Our suggestion, is that reincorporation of the convergence rule in a mathematical setting by the main theorem involve, as a result of an interplay of pre-existing languages games (perspective painting and euclidean geometry and optic), a conceptual innovation consisting in the introduction of the concept of vanishing point.
I will argue that there is plenty historical evidence against this last thesis, notably, coming from mathematical physics. As various philosophers and historians of science have shown, there are cases in which the very content of ‘empirical concepts’ of scientific theories is deeply affected by the mathematical structure involved in the theory (see Toulmin 1953, Guisti 1994, Panza 2002, Blay 1992 or Roux 2010). I will analyse of one of these cases in order to argue against the conceptual neutrality of mathematical languages. I will explain the passage from the geometrisation to the mathematisation of motion from Galileo to Varignon, trying to show how the mathematisation of the notion of continuity made it possible to develop some central (empirical) concepts from the physics of motion, notably that of instantaneous velocity.
The main point of this analysis is to show how the use of geometrical methods of representation in physics posited serious constraints to conceptual development and conceptual use to physicists, and how some of these problems were solved when geometry was partially substituted by analytical methods of representation thanks to the development of infinitesimal calculus.
References:
M. Blay, La Naissance de la mécanique analytique. Presses Universitaires de France, 1992.
E. Giusti, “Il Filosofo Geometra. Matematica e Filosofia Naturale in Galileo”. Nuncius, 9 ( 2 ) ,
485–498, 1994.
M. Panza, “Mathematisation of the Science of Motion and the Birth of Analytical M e c h a n i c s : A Historiographical Note”. In P. Cerrai, P. Freguglia & C. Pellegrini (eds.), The Application of Mathematics to the Sciences of Nature (pp. 253–271). Springer US, 2002.
Palmerino, “The Geometrization of Motion: Galileo’s Triangle of Speed and its Various Transformations”. Early Science and Medicine, 15(4-5), 410–447, 2010.
S. Roux, “Forms of Mathematization (14th-17th Centuries)”. Early Science and Medicine, 15(4-5), 319–337, 2010.
S. Toulmi, An Introduction to Philosophy of Science. Hutchinson University Press, 1953.
aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of gene
Building on Wittgenstein’s use theory of meaning and Toulmin’s theory of concepts; we propose a semantic framework that could solve this problem. The “later” Wittgenstein famously argued that concepts gain their meaning embedded in (rule-governed) language games which are “grounded” in different behavioral and practical contexts (forms of life). Following these ideas, Toulmin claimed that scientific concepts cannot be analyzed in abstracto, because they have a stratified nature. That is, their contents are the products of the evolution of sequences of language games, which are, at the same time, associated with different culturally situated collective practices. In this sense, analyzing the content of a scientific concept imply to look into its developmental history and, more specifically, to look into the collective practices that constitute the language games in which it was involved.
We will apply these ideas to a case where we found a mathematization of a non-mathematical (technical) practice: the mathematization of perspective painting in the work of Guidobaldo del Monte (1600). In this case, we have for the one hand, a perspective painting practice characterized by the effort of imitate visual impression, inspired a rule for drawing all orthogonals with one common point of intersection -i.e. the principal vanishing point, the so-called convergence rule; for the other hand, we have the so-called by Taylor (1719), main theorem in Guidobaldo’s work (Andersen, 2007). This result say that the image of a line l non-parallel to the horizontal plane, is determined by the vanishing point, and the point resulting of the intersection between l and the horizontal plane. So, this theorem guarantee the unique existence of the vanishing point. Our suggestion, is that reincorporation of the convergence rule in a mathematical setting by the main theorem involve, as a result of an interplay of pre-existing languages games (perspective painting and euclidean geometry and optic), a conceptual innovation consisting in the introduction of the concept of vanishing point.
I will argue that there is plenty historical evidence against this last thesis, notably, coming from mathematical physics. As various philosophers and historians of science have shown, there are cases in which the very content of ‘empirical concepts’ of scientific theories is deeply affected by the mathematical structure involved in the theory (see Toulmin 1953, Guisti 1994, Panza 2002, Blay 1992 or Roux 2010). I will analyse of one of these cases in order to argue against the conceptual neutrality of mathematical languages. I will explain the passage from the geometrisation to the mathematisation of motion from Galileo to Varignon, trying to show how the mathematisation of the notion of continuity made it possible to develop some central (empirical) concepts from the physics of motion, notably that of instantaneous velocity.
The main point of this analysis is to show how the use of geometrical methods of representation in physics posited serious constraints to conceptual development and conceptual use to physicists, and how some of these problems were solved when geometry was partially substituted by analytical methods of representation thanks to the development of infinitesimal calculus.
References:
M. Blay, La Naissance de la mécanique analytique. Presses Universitaires de France, 1992.
E. Giusti, “Il Filosofo Geometra. Matematica e Filosofia Naturale in Galileo”. Nuncius, 9 ( 2 ) ,
485–498, 1994.
M. Panza, “Mathematisation of the Science of Motion and the Birth of Analytical M e c h a n i c s : A Historiographical Note”. In P. Cerrai, P. Freguglia & C. Pellegrini (eds.), The Application of Mathematics to the Sciences of Nature (pp. 253–271). Springer US, 2002.
Palmerino, “The Geometrization of Motion: Galileo’s Triangle of Speed and its Various Transformations”. Early Science and Medicine, 15(4-5), 410–447, 2010.
S. Roux, “Forms of Mathematization (14th-17th Centuries)”. Early Science and Medicine, 15(4-5), 319–337, 2010.
S. Toulmi, An Introduction to Philosophy of Science. Hutchinson University Press, 1953.
One of the most interesting features of the notion of style is its potential to explain the complex relationship between individual and social dimensions of scientific cognition. Hacking believes that this interaction gives shape to scientific thinking and methodology in every particular science, and that it 'provides the space in which to understand scientific reason' (Hacking, 2009: 18).
Throughout his work, Hacking has highlighted the historical and social dimensions of styles of reasoning. However, in his most recent work, he claims that even if styles are culturally shaped, they are also rooted in some innate cognitive capacities which are part of our cognitive architecture. Hacking does not offer any argument to back up this idea, but he suggests that modularity is the key concept to understand the relation between styles and cognition. (ibid: 38)
I intend to follow Hacking's suggestion by exploring in what sense(s) styles of reasoning could be related to the idea that the mind/brain is modular. In particular, I will analyse three different versions of the latter concept: Fodor's classical notion (1983, 2001), Sperber's reformulation (1996, 2002), and Carey's version (1995).
I will favor Carey's account of mental modules as domain-specific cognitive abilities which can be seen as naive theories with a central explanatory role in our cognitive life. Then, I will try to argue that Carey's ideas about the modularity of mental capacities could play an important role in trying to give a coherent and systematic explanation of the elusive notion of style of reasoning.
The main goal of this symposium is to discuss different conceptions of continuity, from Aristotle to the first set-theoretical developments of the notion, both in physics and mathematics. The discussion aims to highlight some aspects of what we take to be the philosophical and scientific depth of the notion of continuity. In particular, the reflexion on continuity will give us the occasion to make two main philosophical points: on the one hand, the mathematisation of the notion of continuity, which made it possible to develop some central empirical concepts in the physics of motion, allows us to argue for the thesis that mathematical language can play a central role in the conceptual elaboration of empirical sciences. On the other hand, the existence of different mathematical notions of continuity offers us direct evidence of cases of incommensurability in mathematics. In this connection, we will discuss the possibility of taking into account the change of meaning of a given term (e.g. 'continuum') in the semantic interpretation of our mathematical statements. The whole discussion will also point out two different lines on which the notion of continuity develops through the history of science: namely, a spatial model and a temporal one. The symposium's discussion will be conducted as follows: the first talk analyses Aristotle's notion of continuity as a property of both physical and geometrical objects that cannot be understood in set-theoretical terms. The second presentation takes into account the passage from the geometrisation to the mathematisation of motion, from Galileo to Varignon: in this connection, we will discuss how the mathematisation of the notion of continuity made it possible to develop some central empirical concepts in physics, by focusing on the role of mathematical language within a process of scientific change. Our third talk will analyse Descartes' notion of continuity, highlighting how the theoretical force of the concept of continuity is determinant for the development of the Cartesian philosophical and geometric conception of space. The following presentation will deal with the development of a set-theoretical version of the notion of continuity, showing how Dedekind's and Cantor's constructions of the continuum in arithmetical terms can be seen as directly opposed to an Aristotelian, physical understanding of continuity: here the question will be how the change in the extension of of a given mathematical concept may be accepted, and which semantic account for mathematical terms-if any-may allow for that change to be taken into account.
There is an alternative way of thinking about inference that challenges the formalist thesis and propose to understand it as semantically-driven. This view emerged during the last decades, both in philosophy and in cognitive science following ideas of Sellars (1953), Piaget (Byrnes, 1992) and Sperber and Wilson (1995). According to it, rules of inference are mainly conceptual (or “material”), i.e. they are based on the content of the concepts involved in predicates and not only on the meaning of the logical constants. In this talk I will argue against the syntactic approach and in favor of the “conceptual” view, and I will propose an interpretation of the notion of “conceptual inference” based on recent developments in cognitive science and cognitive semantics. I will follow Gärdenfors’ (1997) triple distinction of explanatory levels to understand cognitive phenomena, for claiming that inferential production is largely dependent on the conceptual structure cognitive agents. In this sense, inference should be seen as a process that goes from the conceptual level to the symbolic (propositional) level, and which depends more on the “conceptual” abilities than on the “formal” abilities of agents. Finally, I will discuss different ways in which these conceptual structures may influence propositional-based inference and how this can relate to some recent ideas in cognitive semantics.
The attention of the philosophical community has been repeatedly drawn on the existence of phenomena of conceptual change in mathematics (Lakatos 1976, Gillies 1992, Tanswell 2017). However, the dominant view of definitions of mathematical concepts and theories (Russell, Whitehead 1910) tends to make it difficult to deal with cases in which a given mathematical term, which is taken to refer to a given object, is found to have different meanings in different contexts of use. Moreover, most theories of conceptual change in science are not suitable for mathematics: this is mostly because they are motivated by some philosophical concerns that do not arise in this discipline (e.g. the commitment to scientific realism, or the intention to preserve the stability of the reference for natural kinds terms). The present work aims at clarifying a suitable semantic framework to understand conceptual change within mathematics. In particular, we are going to investigate which are the conditions that a theory of meaning (and reference) has to meet in order to account for cases in which a mathematical term seems to change meaning through the historical development of the discipline. Our cases studies will be drawn from the history infinitesimal calculus (Boyer 1949, Salanskis 1999). We thus argue that reference should not be considered as a central semantic feature for mathematical terms. Instead, we suggest to understand the meaning of those terms as emerging from the collective cognitive practice of the mathematicians' community through times, their central semantic properties being inferential and operational.
References
Boyer 1949, The History of the Calculus and its Conceptual Development, Dover.
Gillies 1992, Revolutions in Mathematics, Clarendon Press.
Lakatos 1976, Proofs and Refutations, Cambridge University Press.
Russell, Whitehead 1910, Principia Mathematica, Vol. 1, Cambridge University Press.
Salanskis 1999, Le constructivisme non-standard, Presses Universitaires du
Septentrion.
Tanswell 2017, “Conceptual Engineering for Mathematical Concepts”, Inquiry.
I will explain Toulmin’s notion of model-based reasoning and how it relates with other central notions like explanation, conceptual use, and conceptual change. I will argue that, even if Toulmin’s approach overlaps in various ways with the contemporary notion of model-based reasoning (and in particular with the notion of manipulative abduction) it also offers some original and interesting theoretical tools to expand it.
Young minds need to be stimulated also during the winter break, when few conferences are on offer. The It.Si.Cat:2020 (Italy>Sicily>Catania) offered to young scholars and researchers across Europe the possibility to present and to discuss their recent work and to meet their colleagues at the University of Catania.