Areas of Expertise
Philosophy of mathematics, philosophy of logic, logic, philosophy of science, metaphysics, epistemology, philosophy of language, philosophy of ecological economics, philosophy of computer science
Teaching: University of Reading, London School of Economics, and University of Manchester.
Work in artificial intelligence as ontological engineer for Cycorp.
By December 2019 I hope to have finished writing three papers. One is on the notion of a scientific theory being true. I make six arguments to be skeptical about the claim that a scientific theory, as such, could be true. This is not an anti-science move. Rather it is a call to be more precise in our use of language, and more aware of the metaphysical choices, subjective elements and boundaries to objectivity in science.
The other two papers extend the work that has just been published dev eloping a formal language for the conceptual analysis of processes in macro-chemistry. One extension is to add thermodynamic theory. The formal representation takes on a “systems approach”. The other extension is towards biology, to include concepts such as life and death, growth, evolution, mutation, health, nutrition and so on.
In late January 2020 I shall be joining a pilot project at the University of Lille, in France. The pilot project is on re-conceiving science in the light of the changes in the planet. My research will begin with writing a book giving the method for constructing what I call an “institutional compass”. This consists in an original method of data analysis and an original method of representing the data. In particular, one of the permutations of the compass takes into account the principles of ecological economics. The plan after is to write another book, this time on the formal languages and formal representations I have been developing for conceptual analysis in chemistry.
Ph.D. 1997 University of St. Andrews
(2014) Pluralism in Mathematics; a New Position in Philosophy of Mathematics. Logic, Epistemology and the Unity of Science, Springer.
Introducing Philosophy of Mathematics. Published by Acumen publishers in the U.K. (March 2007), by McGill - Queens in Canada and by Cornell University Press in the U.S.A.
Induction, Algorithmic Learning Theory and Philosophy. A collection of papers jointly edited by Valentina Harizanov, Norma Goethe and Michele Friend, in the series: Logic, Epistemology and the Unity of Science, edited by Shahid Rahman and John Symons. (Springer, Aug. 2007). To order a book, go to the Springer website. In this book I co-authored the Introduction chapter wrote the chapter "Some Philosophical Issues Concerning the Confidence in Confident Learning Theory".
Co-Edited Special Issue of a Journal:
2017 Co-Edited with Mihir Chakraborty. Mathematical Pluralism, Special Issue of the Journal of the Indian Council of Philosophical Research, Springer. JICPR Vol. 34.2
(Submitted Dec. 2018) “In the Footsteps of Hilbert, The Andréka-Németi Group’s Logical Foundations of Theories in Physics”. Co-written with Giambattista Formica. Submitted to Hajnal Andéka and István Németi on the Unity of Science: From Computing to Relativity Theory Through Algebraic Logic. Judit Madarász and Gergely Székely (Eds.) Series: Outstanding Contributions to Logic, Springer.
(Submitted, 2018, proof corrections submitted March 2019) “Varieties of Pluralism and Objectivity in Mathematics” To be re-printed in: Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Editors: Dr. Stefania Centrone, Dr. Deborah Kant, and Dr. Deniz Sarikaya. Synthese Library, Springer.
(2018) “Keeping Globally Inconsistent Scientific Theories Locally Consistent”. Co-written with María del Rosario Martínez-Ordaz. Contradictions, From Consistency to Inconsistency. Trends in Logic 47. Walter Carnielli and Jacek Malinowski (eds.) Springer Nature Switzerland. pp. 53 – 89.
(2018) Remarks of a Philosopher of Mathematics and Science; Commentary on Louis Kauffman’s “Cybernetics, Reflexivity and Second-Order Science”, in (Alexander Riegler, ed.) New Horizons for Second-Order Cybernetics. Series on Knots and Everything, Vol. 60. Alexander Reigler, Karl H. Müller & Stuart A. Umpleby (Eds.) World Scientific, pp. 327 – 333.
(Submitted) “Environmentally Sound Practice in Chemistry” for a conference proceedings edited by Jean-Pierre Llored, following the International Society for the Philosophy of Chemistry meeting held in Paris 2017.
(2017) Mathematical Theories as Models. Humanizing Mathematics and its Philosophy; Essays Celebrating the 90th Birthday of Reuben Hersh. Bharath Sriraman (Ed.) Birkhäuser. DOI 10.1007/978-3-319-61231-7_21
(2015) A Eulogy to Classical Dressage Riding. The Palace. Salla Tykkä. Gallery Anhava, Helsinki.
(2012) Pluralism and “Bad” Mathematical Theories: Challenging our Prejudices. Paraconsistency: Logic and Applications. Koji Tanaka, Franz Berto, Edwin Mares and Paoli Francesco (eds.). Berlin: Springer. 277 – 309.
(2012) God ‘Promptly Vanished in a Puff of Logic’. Philosophy and The Hitchhiker’s Guide to the Galaxy. Nicholas Joll (ed.). London: Palgrave. 185 – 212.
(submitted March 2019) “A Policy Compass for Ecological Economics”. DOI: 10.13140/RG.2.2.30052.01924.
(submitted Dec. 2018, re-submitted April 2019) “A Formal Representation for Conceptual Analysis in Macro-Chemistry” For a special issue of Foundations of Chemistry edited by Geoffrey Blumenthal, published with Springer.
(first submitted Oct. 2018, reviews came in Jan. We were asked to revise and re-submit, re-submitted in March 2019). “Distances between formal theories”. Co-written with Mohamed Khaled, Koen Lefever and Gergely Székely. A draft is available on the website: http://philsci-archive.pitt.edu/id/eprint/14849.
(Submitted April 2017, reviewed October, re-submitted January 2018) “Keeping Globally Inconsistent Theories Locally Consistent”. Co-written with María del Rosario Martínez-Ordaz. Submitted to Between Consistency and Inconsistency. Walter Carnielli and Jacek Malinowski (eds.) Trends in Logic XVI: Consistency, Contradiction, Paraconsistency and Reasoning – 40 Years of CLE.
(2017) “Inconsistency in Mathematics and Chemistry”, invited submission to a special issue of Humana Mente Vol. 32 The Special Issue is: Beyond toleration? Inconsistency and pluralism in the empirical sciences. (Luis Estrada-González and María del Rosario Martínez-Ordaz eds.) ISSN: 1972 – 1293. pp. 31 – 51.
(2017) Varieties of Pluralism and Objectivity in Mathematics, in Mathematical Pluralism, Special Issue of the Journal of the Indian Council of Philosophical Research, Mihir Chakraborty and Michèle Friend (Guest Editors) Springer. JICPR Vol. 34.2 pp. 425 – 442. DOI 10.1007/s40961-061-0085-3. ISSN: 0970-7794. pp. 425 – 442.
(2017) Co-written with Mihir Chakraborty. Preface. Mathematical Pluralism, Special Issue of the Journal of the Indian Council of Philosophical Research, Mihir Chakraborty and Michèle Friend (Guest Editors) Springer. JICPR Vol. 34.2 pp. 205-7. DOI 10.1007/s40961-017-0106-x. ISSN: 0970-7794. pp. 205 – 207.
(2016) Co-written with Daniele Molinini. ‘Using Mathematics to Explain a Scientific Theory’ Philosophia Mathematica. Vol. 24, issue 2, June 2016. DOI: 10.1093/philmat/nkv022 pp. 185 – 213.
(2015) Using Mathematics to Explain a Scientific Theory Co-written with Daniele Molinini. Philosophia Mathematica.
(2015) On the Epistemological Significance of the Hungarian Project. Synthese, special edition: Logic and Relativity Theory. Vol. 192, Issue 7 (2015), pp. 2035-2051.
(2013) Embracing the Crisis in the Foundations of Mathematics. La crise des fondements : quelle crise?, François Lepage et Karine Fradet. Les Cahiers d'Ithaque
(2011) Are Mathematicians Better Described as Formalists or Pluralists? Co-written with Andrea Pedeferri. L&PS – Logic and Philosophy of Science; selected proceedings of the SILFS 2010 International Congress. Vol.IX, No.1. Section 2.
(2011) An Analysis of the Notion of Rigour in Mathematical Proof. Co-written with Andrea Pedeferri. L&PS – Logic and Philosophy of Science; selected proceedings of the SILFS 2010 International Congress. Vol.IX, No.1. Section 2.
(2010) Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician. Co-written with Norma B. Goethe. Studia Logica Volume 96, Number 2. 273-288.
(2010) Boole: From Calculating Numbers to Calculating Thoughts. Ferreira, F., Löwe, B., Mayordomo, E., Gomes, L.M. (eds.) Programs, Proofs and Processes; 6th Annual Conference on Computability in Europe; 6th Conference on Computability in Europe, Ponta Delgada, Azores Portugal, June/July 2010, Proceedings. Springer: Berlin 2010. 172-179.
(2018, May) “Present-Day Hilbertian Science” CNRS, Institut d'Histoire et de Philosophie des Sciences et des Techniques, Paris.
(2018, January) “Mathematical Explanations in Science” Workshop on Mathematics and Culture II. Institute for Studies in Science, Technology and Culture (ISSTaC) in association with the Department of Humanities and Social Science IIEST (Indian Institute of Engineering, Science and Technology) Shibpur. Kolkata.
(2018, January) “Environmental Economics and Ecological Economics” Faculty, Department of Humanities and Social Science IIEST Shibpur. Kolkata.
(2018, January) “A Next Step: Marrying Quality and Quantity for Policy Decisions” Plenary Lecture. Fifth International Conference on Emerging Applications of Information Technology (EAIT 2018). IIEST, Sibpur, Kolkata.
(2017) “Reasoning Abhorrently” Logic Colloquium 2017, Stockholm. Special Session on Philosophical Logic.
(2017) “Philosophy, Science Education and Tolerance”, Panel Discussion, International Society for Systems Science 2017, Vienna.
(2017) “Physical Observations as Eigenforms”, From Foundations to Applications; Workshop in the Philosophy of Mathematics, Milano.
(2017) A Policy Compass for Ecological Economics, Workshop on The System of Accounts for Global Entropy Production. International Society for Systems Science 2017, Vienna.
(2017) “Ecologically Sound Practice in Chemistry”. International Society for Philosophy of Chemistry.
(2017) “Mathematical Pluralism: What is it?” Reasoning Seminar, Faculdade de Ciéncias da Universidade de Lisboa.
(2017) “A Pluralist Mathematical Practice” Lecture at the VUB (Vrej Universitat Brussels) as part of the strategic research project on Logic and Philosophy of Mathematical Practices of the Centre for Logic and Philosophy of Science, organized by the Ghent-Brussels Alliance.
(2017) “Rational Reconstructions: Making sense of Proofs with Inconsistent Premises”. Workshop organized by the Centrum voor Logica en Watenschapsfilosofie, VUB (Vreij Universitat Brussels. Logic and Philosophy of Mathematical Practices Also presented Seminário de Lógica Matemática, Grupo de Lógica Matemática at the Faculdade de Ciéncias da Universidade de Lisboa.
(2016) “Inconsistent Proofs”. Mexican Philosophy Congress. San Cristobal de las Casas, Chiapas, Mexico.
(2016) “Inconsistency in Mathematics and Chemistry” Workshop: The Place of Inconsistent Science in Scientific Pluralism, UNAM (Autonomous National University of Mexico).
(2016) “A Tool for Policy Analysis: Aggregating Qualitative Indicators to Develop Robust, Defensible and Adaptive Policies” University Seminar on Reflexive Systems, George Washington University, Washington D.C.
(2016) “Is the Pluralist Reconciliation between Nominalism and Platonism too Easy?” Conference on: Reconciling Nominalism and Platonism, Columbia University, New York.
(2016) “Pluralism Versus Monism in Science” Workshop on Reflexive Systems in Science, George Washington University.
(2015) Set theory and pluralism. Talk given to the Calcutta Logic Circle. Jadavpur University, Kolkata.
(2015) Varieties of Pluralism. Two workshops on Pluralism in Mathematics, one at the Universidad Nacional Autónoma de México, El Instituto de Investigaciones Filosóficas (September). The other at the Asutosh Mookherjee Science Centre in Kolkata, India (December).
(2015) Paradoxes of Pluralism. Two workshops on Pluralism in Mathematics, one at the Universidad Nacional Autónoma de México, El Instituto de Investigaciones Filosóficas (September). The other at the Asutosh Mookherjee Science Centre in Kolkata, India (December).
Continuing with pluralism in mathematics, a book project on meta-philosophy, developing some aspects of a pluralist accounting system for the environment.
PHIL 3121, Symbolic Logic
PHIL 6281, Environmental Philosophy and Policy
GTCH 3201, Perspectives on Mathematics and Science for the GW Teach Program