Discussing the relationship of mathematics to chemistry is closely related to the emergence of physical chemistry and of quantum chemistry. We argue that, perhaps, the most significant issue that the 'mathematization of chemistry' has historically raised is not so much methodological, as it is philosophical: the discussion over the ontological status of theoretical entities which were introduced in the process. A systematic study of such an approach to the mathematization of chemistry may, perhaps, contribute (...) to the realist/antirealist debate. To this end, in this paper we briefly discuss Lewis' introduction of fugacity and activity to his chemical thermodynamics and more fully analyze the issues surrounding the appropriation of resonance by Linus Pauling into quantum chemistry, particularly as these issues arose in organic chemistry as discussed by George W. Wheland. (shrink)

The birth of a new discipline, called 'physical chemistry', is sometimes related to the names OSTWALD, ARRHENIUS and VAN'T HOFF and dated back to the year 1887, when OSTWALD founded the Zeitschrift für physikalische Chemie.[1] But as many historians have pointed out, the phrase 'physical chemistry' was widely used before that and the topics under investigation partially go back to Robert BOYLE's attempts to connect chemistry with concepts of mechanical philosophy.[2] The idea of a sudden (...) birth of physical chemistry in 1887 seems to be a founder myth.[3] But there is no doubt that in the late nineteenth-century there was a rapid growth of research in fields now understood as physical chemistry: chemical thermodynamics, electrochemistry, photochemistry, spectroscopy, chemical kinetics etc. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable intellectual (...) wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable intellectual (...) wealth—are conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

The book starts with the assumption that vagueness is a fundamental property of this world. From a philosophical account of vagueness via the presentation of alternative mathematics of vagueness, the subsequent chapters explore how vagueness manifests itself in the various exact sciences: physics, chemistry, biology, medicine, computer science, and engineering.

This essay explores the gendered lifestyle of early twentieth-century physics and chemistry and shows how that way of life was produced through linking science and home. In 1905, the Swedish physical chemist Svante Arrhenius married Maja Johansson and established a scientific household at the Nobel Institute for Physical Chemistry in Stockholm. He created a productive context for research in which ideas about marriage and family were pivotal. He also socialized in similar scientific sites abroad. This essay (...) displays how scholars in the international community circulated the gendered lifestyle through frequent travel and by reproducing gendered behavior. Everywhere, husbands and wives were expected to perform distinct duties. Shared performances created loyalties across national divides. The essay thus situates the physical sciences at the turn of the twentieth century in a bourgeois gender ideology. Moreover, it argues that the gendered lifestyle was not external to knowledge making but, rather, foundational to laboratory life. A legitimate and culturally intelligible lifestyle produced the trust and support needed for collaboration. In addition, it enabled access to prestigious facilities for Svante Arrhenius, ultimately securing his position in international physical chemistry. (shrink)

This essay focuses on the place of the second law of thermodynamics in Wilhelm Ostwald's physical chemistry. After a brief introduction to his energetic theory, which was supposed to be a generalization of thermodynamics, I contrast Ostwald's understanding of the second law, which ignored entropy and irreversibility, with Max Planck's, which emphasized both. I then consider how Ostwald sought to develop physical chemistry without any concern for irreversibility and little concern for entropy, and I argue that (...) he was mistaken. (shrink)

In the paper it is demonstrated that Bell’s theorem is an unprovable theorem. The unprovable characteristic has, on the chemical side, repercussions for e.g. spin chemistry and the related magneto-reception studies. We claim that the unprovability of this basic mathematics cannot be ignored by the physics and chemical research community. The demonstrated mathematical multivaluedness could be an overlooked aspect of nature.

Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of (...) ordinary fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications. (shrink)

Chemistry and physics are two sciences that are hard to connect. Yet there is significant overlap in their aims, methods, and theoretical approaches. In this book, the reduction of chemistry to physics is defended from the viewpoint of a naturalised Nagelian reduction, which is based on a close reading of Nagel's original text. This naturalised notion of reduction is capable of characterising the inter-theory relationships between theories of chemistry and theories of physics. The reconsideration of reduction also (...) leads to a new characterisation of chemical theories. This book is primarily aimed at philosophers of chemistry and chemists with an interest in philosophy, but is also of interest to the general philosopher of science. (shrink)

In Neither Physics Nor Chemistry, Kostas Gavroglu and Ana Simoes examine the evolution of quantum chemistry into an autonomous discipline, tracing its development from the publication of early papers in the 1920s to the dramatic changes ...

Summary Opinion is divided as to whether chemistry is reducible to physics. The problem can be given a satisfactory solution provided three conditions are met: that a science not be identified with its theories; that several notions of theory dependence be distinguished; and that quantum chemistry, rather than classical chemistry, be compared with physics. This paper proposes to perform all three tasks. It does so by analyzing the methodological concepts concerned as well as by examining the way (...) a chemical rate constant is derivable with the help of the quantum atomic theory. The conclusion is that chemistry, and in particular quantum chemistry, is not a part of physics although it is certainly based on the latter. (shrink)

The "usual story" regarding molecular chemistry is that it is roughly an application of quantum mechanics. That is to say, quantum mechanics supplies everything necessary and sufficient, both ontologically and epistemologically, to reduce molecular chemistry to quantum mechanics. This is a reductive story, to be sure, but a key explanatory element of molecular chemistry, namely molecular structure, is absent from the quantum realm. On the other hand, typical characterizations of emergence, such as the unpredictability or inexplicability of (...) molecular structure based on quantum mechanics, do not characterize the relationship between molecular chemistry and quantum mechanics well either. A different scheme for characterizing reduction and emergence is proposed that accommodates the relationship between quantum mechanics and molecular chemistry and some initial objections to the scheme are considered. (shrink)

In the 1940s and 1950s, nuclear magnetic resonance , one of the most important analytical techniques in chemistry, grew to maturity in the intermediate research field of chemical physics. Chemists and physicists adapted the new technology to the experimental culture of molecular spectroscopy which was based on a pragmatic experimental style. In molecular spectroscopy, the purpose of experiments was the establishment of methods that suited both the physicists' quest for precision and theoretical model building and the chemists' longing for (...) empirical data and understanding of structural formulae and reaction courses. In this process, an experimental style emerged that can be characterized as reliance on self‐built instrumentation, theoretical foundation in quantum mechanics, and proof of utility in the solution of structural and dynamical questions. This article focuses on the early development of NMR at Harvard University, with particular emphasis on the contributions of the first chemist working in the field of NMR, Herbert S. Gutowsky. (shrink)

In this paper I reply to Olimpia Lombardi’s comment on my recent book Reducing Chemistry to Physics: Limits, Models, Consequences.