TY - Generic T1 - 'Argumentandi modus huius scientiae maximè proprius: ' Guidobaldo's mechanics and the question of mathematical principles Y1 - 2013 A1 - Van Dyck, Maarten ED - Becchi, Antonio ED - Bertoloni Meli, Domenico ED - Gamba, Enrico JA - Guidobaldo del Monte (1545-1607) : theory and practice of the mathematical disciplines from Urbino to Europe PB - Edition Open Access SP - 9–34 SN - 9783844242836 UR - http://www.edition-open-access.de/media/proceedings/4/Proceedings4.pdf ER - TY - JOUR T1 - Rationally evaluating inconsistent theories JF - PHILOSOPHICA Y1 - 2012 A1 - Weber, Erik A1 - Van Dyck, Maarten AB -

What happens if one applies the "evaluation methodology" of The Kuipers to inconsistent theories? What happens if one applies the "problem solving methodology" of Larry Laudan to inconsistent theories? We argue that in both cases something unacceptable happens. We show that application of Kuipers' methodology to inconsistent theories leads to a methodological stalemate: inconsistent theories are incomparable to consistent ones. Then we show that according to Laudan's methodology inconsistent theories are always better than consistent ones. Finally, we offer partial solutins to these problems.

VL - 86 SP - 83–99 ER - TY - Generic T1 - From the second unknown to the symbolic equation Y1 - 2010 A1 - Heeffer, Albrecht ED - Heeffer, Albrecht ED - Van Dyck, Maarten AB -

The symbolic equation slowly emerged during the course of the sixteenth century as a new mathematical concept as well as a mathematical object on which new operations were made possible. Where historians have of- ten pointed at Francois Viète as the father of symbolic algebra, we would like to emphasize the foundations on which Viète could base his logistica speciosa. The period between Cardano’s Practica Arithmeticae of 1539 and Gosselin’s De arte magna of 1577 has been crucial in providing the necessary build- ing blocks for the transformation of algebra from rules for problem solving to the study of equations. In this paper we argue that the so-called “second unknown” or the Regula quantitates steered the development of an adequate symbolism to deal with multiple unknowns and aggregates of equations. Dur- ing this process the very concept of a symbolic equation emerged separate from previous notions of what we call “co-equal polynomials”.

JA - Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics PB - College Publications VL - 26 SP - 57–102 SN - 978-1-84890-017-2 ER - TY - BOOK T1 - Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics T2 - Studies in Logic Y1 - 2010 ED - Heeffer, Albrecht ED - Van Dyck, Maarten AB -

This book presents a selection of peer-reviewed papers which were presented on a conference organized in Ghent, Belgium, from 27 till 29 August, 2009. The conference was given the title Philosophical Aspects of Symbolic Reasoning in Early modern Science and Mathematics (PASR). For this book we selected papers which deal with the consequences for mathematics in particular, hence the omission of ‘science’ in the title of this book. Another selection, dealing with the understanding of nature and a broader range of topics, will appear in the journal Foundations of Science. The conference was sponsored by the Research Foundation Flanders (FWO) and Ghent University, which indirectly made this book possible. We also have to thank the other members of the programme committee Marco Panza, Chikara Sasaki, and Erik Weber and our keynote speakers Jens Høyrup, Doug Jesseph, Eberhard Knobloch, Marco Panza, Mathias Schemmel and Michel Serfati. Five of their papers are included in this volume. Most of the papers benefited from valuable and sometimes substantive comments by our referees which must remain anonymous. Special thanks to Michael Barany who assisted in the editorial process.

JA - Studies in Logic PB - College Publications VL - 26 SP - 302 SN - 978-1-84890-017-2 ER - TY - JOUR T1 - Dynamics of Reason and the Kantian Project JF - Philosophy of Science Y1 - 2009 A1 - Van Dyck, Maarten AB -

I show why Michael Friedman’s idea that we should view new constitutive frameworks introduced in paradigm-change as members of a convergent series, introduces an uncomfortable tension in his views. It cannot be justified on realist grounds, as this would compromise his Kantian perspective, but his own appeal to a Kantian regulative ideal of reason cannot do the job either. I then explain a way to make better sense of the rationality of paradigm-change on what I take to Friedman’s own terms.

VL - 76 SP - 389–400 ER - TY - JOUR T1 - On the epistemological foundations of the law of the lever JF - Studies in History and Philosophy of Science Y1 - 2009 A1 - Van Dyck, Maarten AB -

In this paper I challenge Paolo Palmieri’s reading of the Mach-Vailati debate on Archimedes’s proof of the law of the lever. I argue that the actual import of the debate concerns the possible epistemic (as opposed to merely pragmatic) role of mathematical arguments in empirical physics, and that construed in this light Vailati carries the upper hand. This claim is defended by showing that Archimedes’s proof of the law of the lever is not a way of appealing to a non-empirical source of information, but a way of explicating the mathematical structure that can represent the empirical information at our disposal in the most general way.

VL - 40 SP - 315–318 UR - http://dx.doi.org/10.1016/j.shpsa.2009.06.001 ER - TY - JOUR T1 - The practical value of spurious correlations: selective versus manipulative policy JF - Analysis Y1 - 2008 A1 - Leuridan, Bert A1 - Weber, Erik A1 - Van Dyck, Maarten VL - 68 SP - 298–303 ER - TY - RPRT T1 - Causality and conservation. Elements of the new metaphysics behind the mathematization of nature in the seventeenth century Y1 - 2007 A1 - Van Dyck, Maarten PB - VUB ER - TY - Generic T1 - Constructive Empiricism and the Argument from Underdetermination. Y1 - 2007 A1 - Van Dyck, Maarten ED - Monton, Bradley AB -

It is argued that, contrary to prevailing opinion, Bas van Fraassen nowhere uses the argument from underdetermination in his argument for constructive empiricism. It is explained that van Fraassen’s use of the notion of empirical equivalence in The Scientific Image has been widely misunderstood. A reconstruction of the main arguments for constructive empiricism is offered, showing how the passages that have been taken to be part of an appeal to the argument from underdetermination should actually be interpreted.

JA - Images of empiricism: Essays on science and stances, with a reply from Bas van Fraassen PB - Oxford University Press SP - 11–31 ER - TY - Generic T1 - An Archaeology of Galileo's Science Y1 - 2006 A1 - Van Dyck, Maarten PB - Ghent University U1 -

Erik Weber

ER - TY - JOUR T1 - Gravitating towards stability: Guidobaldo's Aristotelian-Archimedean synthesis JF - History of science Y1 - 2006 A1 - Van Dyck, Maarten VL - 44 SP - 373–407 UR - http://dx.doi.org/1854/10929 ER - TY - JOUR T1 - The paradox of conceptual novelty and Galileo's use of experiments JF - Philosophy of Science Y1 - 2005 A1 - Van Dyck, Maarten AB -

Starting with a discussion of what I call ‘Koyré’s paradox of conceptual novelty’, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo’s work. I then argue that although their view on the nature of Galileo’s conceptual innovation is convincing, it misses an essential element: Galileo’s use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to my analysis is the idea that Galileo’s pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way, Galileo’s experiments constitute an essential part of the meaning of the new concepts of classical mechanics.

VL - 72 SP - 864–875 UR - http://dx.doi.org/1854/10928 ER - TY - RPRT T1 - Weighing Falling Bodies. Galileo's Thought Experiment in the Development of his Dynamical Thinking. Y1 - 2005 A1 - Van Dyck, Maarten JA - Unpublished ER - TY - Generic T1 - Cassirer's critical idealism: a comment on Thomas Mormann. Y1 - 2004 A1 - Van Dyck, Maarten A1 - Weber, Erik ED - Gillies, D. JA - Laws and Models in Science PB - King's College Publications CY - London SP - 161–171 SN - 0954300661 ER - TY - JOUR T1 - The roles of one thought experiment in interpreting quantum mechanics: Werner Heisenberg meets Thomas Kuhn JF - Philosophica Y1 - 2003 A1 - Van Dyck, Maarten VL - 72 SP - 79–103 ER - TY - Generic T1 - Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction Y1 - 2002 A1 - Meheus, Joke A1 - Verhoeven, Liza A1 - Van Dyck, Maarten A1 - Provijn, Dagmar AB -

In this paper, we propose a reconstruction of logic-based approaches to abductive reasoning in terms of ampliative adaptive logics. The advantages of this reconstruction are important: the resulting logics have a proper theory (that leads to justified conclusions even for undecidable fragments), they nicely integrate deductive and abductive steps, and they are much closer to natural reasoning than the existing systems.
We present two new adaptive logics for abduction, CP1 and CP2. CP1 enables one to generate explanations for novel facts from a consistent theory. CP2 moreover enables one to abduce explanatory hypotheses for novel facts and for anomalous facts from a possibly inconsistent theory. We illustrate both logics with some examples from the history of the sciences (the discovery of Uranus and of Neptune), and present some alternatives to CP1 and CP2 that are better suited for non-creative forms of abductive reasoning and for practical reasoning.

JA - Logical and Computational Aspects of Model-Based Reasoning PB - Kluwer Academic CY - Dordrecht SP - 39–71 ER - TY - JOUR T1 - Unification and explanation - A comment on Halonen and Hintikka, and Schurz. JF - Synthese Y1 - 2002 A1 - Weber, Erik A1 - Van Dyck, Maarten AB -

In this article we criticize two recent articles that examine the relation between explanation and unification. Halonen and Hintikka (1999), on the one hand, claim that no unification is explanation. Schurz (1999), on the other hand, claims that all explanation is unification. We give counterexamples to both claims. We propose a pluralistic approach to the problem: explanation sometimes consists in unification, but in other cases different kinds of explanation (e.g., causal explanation) are required; and none of these kinds is more fundamental.

VL - 131 SP - 145–154 ER - TY - JOUR T1 - Adaptive Logic and Covering Law Explanations JF - Logique et Analyse Y1 - 2001 A1 - Weber, Erik A1 - Van Dyck, Maarten AB -

In his theory of explanation Hempel introduced two basic types of covering law explanations for particular events: deductive-nomological and inductive-statistical. In this article we argue that there is more than one reason why adaptive logics provide the right tools for analyzing the argument patterns involved in these covering law explanations. To this end we claim that in the case of inconsistent knowledge systems, neither classical logic, nor a paraconsistent logic suffice to capture the right class of permissible arguments that can make up a deductive-nomological explanation, whereas an adaptive logic gives just the right results. The arguments behind inductive-statistical explanations face the well-known problem of inductive ambiguities, which Hempel tried to solve by his requirement of maximal specifity. We show how this requirement can be nicely incorporated in a logic for these arguments, again using an adaptive logic (which we describe in some detail).

VL - 44 SP - 237–254 ER -