Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Essays in Philosophical Moral Psychology

The dissertation consists of four essays and a comprehensive introduction that discusses the topics, methods, and most prominent theories of philosophical moral psychology. I distinguish three main questions: What are the essential features of moral thinking? What are the psychological conditions of moral responsibility? And finally, what are the consequences of empirical facts about human nature to normative ethics? Each of the three last articles focuses on one of these issues. The first essay and part of the introduction are dedicated to methodological questions, in particular the relationship between empirical (social) psychology and philosophy. I reject recent attempts to understand the nature of morality on the basis of empirical research. One characteristic feature of moral thinking is its practical clout: if we regard an action as morally wrong, we either refrain from doing it even against our desires and interests, or else feel shame or guilt. Moral views seem to have a conceptual connection to motivation and emotions – roughly speaking, we can’t conceive of someone genuinely disapproving an action, but nonetheless doing it without any inner motivational conflict or regret. This conceptual thesis in moral psychology is called (judgment) internalism. It implies, among other things, that psychopaths cannot make moral judgments to the extent that they are incapable of corresponding motivation and emotion, even if they might say largely the words we would expect. Is internalism true? Recently, there has been an explosion of interest in so-called experimental philosophy, which is a methodological view according to which claims about conceptual truths that appeal to our intuitions should be tested by way of surveys presented to ordinary language users. One experimental result is that the majority of people are willing to grant that psychopaths make moral judgments, which challenges internalism. In the first article, ‘The Rise and Fall of Experimental Philosophy’, I argue that these results pose no real threat to internalism, since experimental philosophy is based on a too simple conception of the relationship between language use and concepts. Only the reactions of competent users in pragmatically neutral and otherwise conducive circumstances yield evidence about conceptual truths, and such robust intuitions remain inaccessible to surveys for reasons of principle. The epistemology of folk concepts must still be based on Socratic dialogue and critical reflection, whose character and authority I discuss at the end of the paper. The internal connection between moral judgment and motivation led many metaethicists in the past century to believe along Humean lines that judgment itself consists in a pro-attitude rather than a belief. This expressivist view, as it is called these days, has far-reaching consequences in metaethics. In the second essay I argue that perhaps the most sophisticated form of contemporary expressivism, Allan Gibbard’s norm-expressivism, according to which moral judgments are decisions or contingency plans, is implausible from the perspective of the theory of action. In certain circumstances it is possible to think that something is morally required of one without deciding to do so. Morality is not a matter of the will. Instead, I sketch on the basis of Robert Brandom’s inferentialist semantics a weak form of judgment internalism, according to which the content of moral judgment is determined by a commitment to a particular kind of practical reasoning. The last two essays in the dissertation emphasize the role of mutual recognition in the development and maintenance of responsible and autonomous moral agency. I defend a compatibilist view of autonomy, according to which agents who are unable to recognize right and wrong or act accordingly are not responsible for their actions – it is not fair to praise or blame them, since they lacked the relevant capacity to do otherwise. Conversely, autonomy demands an ability to recognize reasons and act on them. But as a long tradition in German moral philosophy whose best-known contemporary representative is Axel Honneth has it, both being aware of reasons and acting on them requires also the right sort of higher-order attitudes toward the self. Without self-respect and self-confidence we remain at the mercy of external pressures, even if we have the necessary normative competence. These attitudes toward the self, in turn, are formed through mutual recognition – we value ourselves when those who we value value us. Thus, standing in the right sort of relations of recognition is indirectly necessary for autonomy and moral responsibility. Recognition and valuing are concretely manifest in actions and institutions, whose practices make possible participation on an equal footing. Seeing this opens the way for a kind of normative social criticism that is grounded in the value of freedom and automomy, but is not limited to defending negative rights. It thus offers a new way to bridge the gap between liberalism and communitarianism.

The Philosophical Age. Almanac. Issue 36. The Northern Lights

keywords: Enlightenment, Northern countries, Finland, Russia, Scotland In the 36 th edition of the almanac "Philosophical Age" published materials of international symposium «The Northern Lights - Facets of Enlightenment Culture», (held September 25-26, 2009) in The Aleksanteri Institute the University of Helsinki. Contents: Vesa Oittinen Between Radicalism and Utilitarianism — On the Profile of the Finnish Enlightenment Tatiana Artemyeva The Status of Intellectual Values in the Russian Enlightenment Oili Pulkkinen The Cosmopolitan Experience, Theoretical Histories and the Universal Science of the Scottish Enlightenment Аlla Zlatopolskaya L’autocritique des Lumières chez Rousseau et le rousseauisme russe Johannes Remy Alexander Radishchev, Ethical Consuming, and North American Quakers Kimmo Sarje Anders Chydenius and Radical Swedish Enlightenment Johan Sten Anders Johan Lexell: A Finnish Astronomer at St. Petersburg Academy of Sciences and His European Contacts Mikhail Mikeshin A Russian Adam Smith in French Style: An Example of the Transfer of Ideas Larisa Agamalian The Library of an Enlightened Russian Landowner

La relación entre imputación y responsabilidad

Resumen: El autor analiza los conceptos de imputación y responsabilidad penales, y las realidades jurídicas y antrópicas a las que dichas nociones se refieren desde dos perspectivas principales: una, teórica, y otra, la historia del pensamiento. La investigación está precedida por una breve introducción semántica. El marco teórico es una concepción realista del derecho, subalternada a la antropología (psicología) filosófica, y más específicamente, al concepto del hombre como persona.

La calidad de vida y salud desde una antropología cristiana

Resumen: Este trabajo examina con atento discernimiento los términos “calidad de vida” y “promoción de la salud” que identifican uno de los principales objetivos de las sociedades contemporáneas. En el mismo se cita la encíclica Evangelium vitae que dice “La llamada ‘calidad de vida’ se interpreta principal o exclusivamente como eficiencia económica, consumismo desordenado, belleza y goce de la vida física, olvidando las dimensiones más profundas -relacionales, espirituales y religiosas- de la existencia” (n. 23). Todas las dimensiones de la persona -la corpórea, la psicológica, la espiritual y la moral- han de promoverse en armonía. Esto supone la presencia de condiciones sociales y ambientales aptas para favorecer ese desarrollo armonioso. En la actualidad la expresión “calidad de vida” no está fundada en una antropología filosófica y teológica, favoreciendo una noción restrictiva y selectiva. En referencia al concepto de salud también ha sufrido una desviación análoga. Se debe proteger y cuidar la salud como equilibrio físico, psíquico y espiritual del ser humano. Se analiza, asimismo, el concepto de “bien común” en relación a la sociedad, la democracia y el trabajo de la política en la construcción del mismo. En el texto se discute sobre la priorización de intervenciones de salud y se presentan posibles respuestas. Se muestran criterios de decisión al momento de distribuir recursos entre las distintas necesidades de salud, buscando definir principios éticos relevantes para una priorización de intervenciones.

Shén神: categoria estruturante da racionalidade médica chinesa

A Medicina chinesa divulgada no ocidente tem sido estudada de forma fragmentada entre as suas diferentes formas de expressão desenvolvidas ao longo da história do Pensamento Médico Chinês. Nesse sentido o texto destaca três possíveis vertentes desta expressão, que denomina: Medicina Clássica Chinesa (GÜ DÀI ZHÖNG YÏ), Medicina Tradicional Chinesa (ZHÖNG YÏ) e Medicina Chinesa Contemporânea (DÄNG DÀI ZHÖNG YÏ). A primeira expressa as formulações nas obras clássicas surgidas a partir do período formativo da Medicina Chinesa, na Dinastia HÀN (206 a.C. a 221 d.C.). A segunda como corpo teórico e prático de conhecimento que, se disseminou no Oriente em geral e, posteriormente, no Ocidente como uma continuidade da Medicina Clássica Chinesa (GÜ DÀI ZHÖNG YÏ). A terceira refere-se à corrente hegemônica, hoje, na República Popular da China e mais tarde nos meios ocidentais. O objetivo do trabalho é investigar como tem sido divulgada no Ocidente por diferentes autores representantes de cada uma dessas vertentes a categoria SHÉN , frequentemente traduzida no Ocidente como Mente ou Espírito. Para tal, leva-se em conta a notoriedade acadêmica, a familiaridade com o idioma chinês, os pressupostos adotados, a história pessoal de cada um desses autores, entendidas como determinantes para suas apreensões de sentidos e significados da categoria SHÉN e, consequentemente, para os sentidos que assumem sua divulgação no Ocidente. Entendendo a Medicina Chinesa como uma Racionalidade Médica, conforme definição de Madel Therezinha Luz composta de seis dimensões: cosmologia, doutrina médica, dinâmica vital, morfologia, diagnose e terapêutica, o trabalho investiga do ponto de vista teórico-conceitual, amparado na Filosofia e Antropologia Médicas como a categoria SHÉN relaciona-se a cada uma das dimensões da Racionalidade Médica Chinesa. SHÉN relaciona-se com diversas outras categorias do Pensamento Médico e Filosófico Chinês, não sendo possível conceituá-lo sem mencionar categorias, tais como DÀO, YÏN YÁNG , TIÄN (Céu), RÉN (Homem), DÌ (Terra), MING (Destino), WÜ XÍNG (Cinco Fases), SÄN BÄO (Três Tesouros), GUÏ e LING Manifesta-se de diferentes formas através de sua relação com os ZÁNG FÜ (Órgãos e Vísceras), interferindo no funcionamento orgânico-visceral, nos aspectos de personalidade, nas emoções, entendidas como uma totalidade corpo-mente-espírito no Pensamento Médico chinês. SHÉN está presente em todas as dimensões da Racionalidade Médica Chinesa, diferindo o grau de importância dado por autores representantes de cada uma das três vertentes da Medicina Chinesa. Autores representantes da Medicina Clássica Chinesa (GÜ DÀI ZHÖNG YÏ) E DA Medicina Tradicional Chinesa (ZHÖNG YÏ) tendem a valorizar sua presença em todas as dimensões. Autores representantes da Medicina Chinesa Contemporânea (DÄNG DÀI ZHÖNG YÏ) tendem a valorizar a participação de SHÉN na dimensão Diagnose. Percebe-se, portanto, que SHÉN ao participar de todas as dimensões ganha o importante papel de estruturante da Racionalidade Médica Chinesa, não podendo, portanto, ser negligenciado nos estudos da Medicina Chinesa, sob pena de comprometer a importância da Racionalidade Médica.

A philosophical stance on developing industrially relevant strategic technology management toolkits

When considering the potential uptake and utilization of technology management tools by industry, it must be recognized that companies face the difficult challenges of selecting, adopting and integrating individual tools into a toolkit that must be implemented within their current organizational processes and systems. This situation is compounded by the lack of sound advice on integrating well-founded individual tools into a robust toolkit that has the necessary degree of flexibility such that they can be tailored for application to specific problems faced by individual organizations. As an initial stepping stone to offering a toolkit with empirically proven utility, this paper provides a conceptual foundation to the development of toolkits by outlining an underlying philosophical position based on observations from multiple research and commercial collaborations with industry. This stance is underpinned by a set of operationalized principles that can offer guidance to organizations when deciding upon the appropriate form, functions and features that should be embodied by any potential tool/toolkit. For example, a key objective of any tool is to aid decision-making and a core set of powerful, flexible, scaleable and modular tools should be sufficient to allow users to generate, explore, shape and implement possible solutions across a wide array of strategic issues. From our philosophical stance, the preferred mode of engagement is facilitated workshops with a participatory process that enables multiple perspectives and structures the conversation through visual representations in order to manage the cognitive load in the collaborative environment. The generic form of the tools should be configurable for the given context and utilized in a lightweight manner based on the premise of start small and iterate fast. © 2011 IEEE.

The Implications of Philosophical Foundations for Knowledge Representation and Learning in Agents

N.J. Lacey and M.H. Lee, ?The Implications of Philosophical Foundations for Knowledge Representation and Learning in Agents?, Springer-Verlag Lecture Notes on Artificial Intelligence, Vol 2636 on Adaptive Agents and Multi-Agent Systems, 2002.

The Implications of Philosophical Foundations for Knowledge Representation and Learning in Agents

Lacey N and Lee M.H., The Implications of Philosophical Foundations for Knowledge Representation and Learning in Agents, in Proc. AISB?01 Symposium on Adaptive Agents and Multi-agent Systems, York, March 2001, pp13-24.