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8Measuring ecologically sound practice in the chemical industryFoundations of Chemistry 1-11. forthcoming.I present a comparative and holistic method for qualitatively measuring sound ecological practice in chemistry. I consider chemicals developed and used by man from cradle to grave, that is, from the moment they are extracted from the earth, biomass, water or air, to their transportation, purification, mixing and elaboration in a factory, to their distribution by means of the market, to waste products both from the factory, packaging, transportations and by the consumer. I divide the locations of…Read more
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10In the Footsteps of Hilbert: The Andréka-Németi Group’s Logical Foundations of Theories in PhysicsIn Judit Madarász & Gergely Székely (eds.), Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic, Springer. pp. 383-408. 2021.Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andréka-Németi group use several formal axiomatic theories together to re-capture, predict, recove…Read more
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7Varieties of Pluralism and Objectivity in MathematicsIn Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts, Springer Verlag. pp. 345-362. 2019.The phrase ‘mathematical foundation’ has shifted in meaning since the end of the nineteenth century. It used to mean a consistent general theory in mathematics, based on basic principles and ideas to which the rest of mathematics could be reduced. There was supposed to be only one foundational theory and it was to carry the philosophical weight of giving the ultimate ontology and truth of mathematics. Under this conception of ‘foundation’ pluralism in foundations of mathematics is a contradictio…Read more
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10The beginnings of a formal language for conceptual analysis of processes in macro-chemistryFoundations of Chemistry 22 (1): 31-42. 2019.I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.
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10The beginnings of a formal language for conceptual analysis of processes in macro-chemistryFoundations of Chemistry 22 (1): 31-42. 2019.I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.
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Varieties of Pluralism and Objectivity in MathematicsIn Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics, Springer Verlag. 2019.
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12The beginnings of a formal language for conceptual analysis of processes in macro-chemistryFoundations of Chemistry 22 (1): 31-42. 2019.I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.
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37Keeping Globally Inconsistent Scientific Theories Locally ConsistentIn Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency, Springer. pp. 53-88. 2018.Most scientific theories are globally inconsistent. Chunk and Permeate is a method of rational reconstruction that can be used to separate, and identify, locally consistent chunks of reasoning or explanation. This then allows us to justify reasoning in a globally inconsistent theory. We extend chunk and permeate by adding a visually transparent way of guiding the individuation of chunks and deciding on what information permeates from one chunk to the next. The visual representation is in the for…Read more
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77Distances between formal theoriesReview of Symbolic Logic 13 (3): 633-654In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” or not. In this article, we do something subtler. We provide a means to measure distances between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number …Read more
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13Second-order logic is logicDissertation, St. Andrews. 1997."Second-order logic" is the name given to a formal system. Some claim that the formal system is a logical system. Others claim that it is a mathematical system. In the thesis, I examine these claims in the light of some philosophical criteria which first motivated Frege in his logicist project. The criteria are that a logic should be universal, it should reflect our intuitive notion of logical validity, and it should be analytic. The analysis is interesting in two respects. One is conceptual: it…Read more
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3Varieties of Pluralism and Objectivity in MathematicsJournal of the Indian Council of Philosophical Research 34 (2): 425-442. 2017.Realist philosophers of mathematics have accounted for the objectivity and robustness of mathematics by recourse to a foundational theory of mathematics that ultimately determines the ontology and truth of mathematics. The methodology for establishing these truths and discovering the ontology was set by the foundational theory. Other traditional philosophers of mathematics, but this time those who are not realists, account for the objectivity of mathematics by fastening on to: an objective accou…Read more
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30Inconsistency in Mathematics and Inconsistency in ChemistryHumana Mente 10 (32): 31-51. 2017.In this paper, I compare how it is that inconsistencies are handled in mathematics to how they are handled in chemistry. In mathematics, they are very precisely formulated and identified, unlike in chemistry. So the chemists can learn from the precision and the very well-worked out strategies developed by logicians and deployed by mathematicians to cope with inconsistency. Some lessons can also be learned by the mathematicians from the chemists. Mathematicians tend to be intolerant towards incon…Read more
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103Book Review: Extensionalism: The Revolution in LogicBar-AmNimrodExtensionalism: The Revolution in LogicNew York: Springer, 2008. xxii + 172 pp. $129.00 . ISBN 978-1-4020-8167-5 (review)Philosophy of the Social Sciences 43 (1): 116-120. 2013.
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56The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart from conside…Read more
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3Leigh S. Cauman, First-order Logic, an Introduction Reviewed byPhilosophy in Review 20 (4): 240-244. 2000.
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68Confronting Ideals of Proof with the Ways of Proving of the Research MathematicianStudia Logica 96 (2): 273-288. 2010.In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic text boo…Read more
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51On the epistemological significance of the hungarian projectSynthese 192 (7): 2035-2051. 2015.There are three elements in this paper. One is what we shall call ‘the Hungarian project’. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini’s philosophical work on the nature of mathematical explanations in science. The third is my pluralist approach to mathematics. The theses of this paper are that the Hungarian project gives genuine mathematical explanations for physical phenomena. A pluralist account of mathematical explanation can help us wi…Read more
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Areas of Specialization
Science, Logic, and Mathematics |
Metaphysics and Epistemology |
Philosophy, Misc |