Mathematical chemistry is often thought to be a 20th-century subdiscipline of chemistry, but in this paper we discuss several early chemical ideas and some landmarks of chemistry as instances of the mathematical way of thinking; many of them before 1900. By the mathematical way of thinking, we follow Weyl's description of it in terms of functional thinking, i.e. setting up variables, symbolizing them, and seeking for functions relating them. The cases we discuss are Plato's triangles, Geoffroy's affinity (...) table, Lavoisier's classification of substances and their relationships, Mendeleev's periodic table, Cayley's enumeration of alkanes, Sylvester's association of algebra and chemistry, and Wiener's relationship between molecular structure and boiling points. These examples show that mathematical chemistry has much more than a century of history. (shrink)

The drastically increasing availability ofmodern computers coupled with the equally drasticallylower cost of a given amount of computer power inrecent years has resulted in the evolution of thetraditional experimental/theoretical dichotomy inchemistry into anexperimental/theoretical/computational trichotomy. This trichotomy can be schematically represented by atriangle with experimental,theoretical, and computational chemistry at the threevertices. The ET and EC edges of the ETC triangledepict the uses of theoretical and computationalchemistry, respectively, to predict and interpretexperimental results. The TC edge depicts therelationship between theoretical and computationalchemistry. (...) Mathematics plays an increasing role in allaspects of chemistry, particularly theoreticalchemistry, and has led to the evolution of thediscipline of mathematical chemistry. Research inmathematical chemistry can be considered to lie on achemistry-mathematics continuum depending on therelative depths of the underlying chemistry andmathematics. Examples of the author's own researchlying near each end of the chemistry-mathematicscontinuum include his work on applications of graphtheory and topology in inorganic coordination andcluster chemistry lying near the chemistry end and hiswork on chirality algebra lying near the mathematicsend. The general points in this essay are illustratedby an analysis of the roles of computational andtheoretical chemistry in developing an understandingof structure and bonding in deltahedral boranes andrelated carboranes. This work has allowed extensionof the concept of aromaticity from two dimensions asin benzene and other planar hydrocarbons to the thirddimension in deltahedral boranes. (shrink)

In his Metaphysische Anfangsgründe der Naturwissenschaft, Kant claims that chemistry is a science, but not a proper science (like physics), because it does not adequately allow for the application of mathematics to its objects. This paper argues that the application of mathematics to a proper science is best thought of as depending upon a coordination between mathematically constructible concepts and those of the science. In physics, the proper science that exhausts the a priori knowledge of objects of (...) the outer sense, only motions and concepts reducible to motions can be legitimately coordinated with mathematical constructions. Since chemistry can neither achieve its own a priori principles of coordination nor be reduced to the coordinated doctrine of motion, it is a merely improper science. (shrink)

Three-dimensional material models of molecules were used throughout the 19th century, either functioning as a mere representation or opening new epistemic horizons. In this paper, two case studies are examined: the 1875 models of van ‘t Hoff and the 1890 models of Sachse. What is unique in these two case studies is that both models were not only folded, but were also conceptualized mathematically. When viewed in light of the chemical research of that period not only were both of these (...) aspects, considered in their singularity, exceptional, but also taken together may be thought of as a subversion of the way molecules were chemically investigated in the 19th century. Concentrating on this unique shared characteristic in the models of van ‘t Hoff and the models of Sachse, this paper deals with the shifts and displacements between their operational methods and existence: between their technical and epistemological aspects and the fact that they were folded, which was forgotten or simply ignored in the subsequent development of chemistry. (shrink)

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 inconsistencies. (...) There are some philosophers of chemistry who attribute to chemists, collectively, a more tolerant attitude towards inconsistency, and so, mathematicians can learn from the chemists’ attitude to inform their choice of strategies. (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 work utilizes examples from chemical sciences to present fundamentals of dialectics and synergetics. The laws of dialectics remain appropriate at the level of atoms, at the level of molecules, at the level of the reactions, and at the level of ideas. The law of the unity and conflict of opposites is seen, for instance, in the relationships between the ionization energy and electron affinity of atoms, between the forward and back reactions, as well as in the differentiation and integration (...) between the various areas of chemistry. The law of the passage of quantitative changes into qualitative changes describes the transformation properties of the compounds when the number and arrangement of atoms in the molecule undergoes changes. According to this law, the development is accompanied by breaks and jumps. This paper suggests equations for the description of these relationships. The law of the negation of the negation is manifested in the Periodic Law, in the evolution of ideas about the mutual transformation of chemical elements, in the development the concept of triads of elements, etc. Small changes in the conventional Periodic Table on the basis of previously rejected versions allow reflecting secondary and additional periodicity. Synergetics, similarly to dialectics, is dedicated to the studies of general laws of evolution. Synergetics includes highly advanced and specified ideas of dialectics. The cornerstone of synergetics is the principles of self-organization and nonlinearity. Mathematical development of these concepts was substantially facilitated by considering oscillating chemical reactions as an example. These reactions are quite complex and therefore provide adequate models for self-organization. Oscillations may exist only upon execution of specific thermodynamic, mathematical, and chemical conditions. Mechanisms of several oscillatory reactions are briefly reviewed. The construction of novel biomimetic or smart materials based on oscillating reactions is described. (shrink)

The decades of the 1920s to the 1960s were a period of transformation in chemical science. The era was marked by erosion of boundaries that had often been drawn between chemistry and other scientific disciplines. In particular, theories, instruments, and mathematical approaches associated with the new physics of X-rays, the electron particle, and the electron wave enabled chemists and other physical scientists to address unsolved chemical problems of structure and mechanism and to ask new questions that further expanded and (...) transcended disciplinary borders. In turn, the historiography of these developments reflects the pluralism of chemistry in historical narratives written by scientists, historians, philosophers, and sociologists. (shrink)

The paper traces the entrance of German women into the chemistry profession from the 1890s to 1925, examining how they first overcame social and cultural conservatism to obtain access to opportunities for a chemical education during the later Kaiserreich, then began to seek academic and industrial careers and to establish a professional organization in the face of resistance from the established Verein Deutscher Chemiker. The paper examines the effect of World War I and the advent of the Weimar Republic (...) in completing the process whereby German women achieved a small but significant role in the profession of chemistry, in science as well as industry. Finally, it discusses the considerable limitations on women’s full and equal participation that still remained by 1925. (shrink)

By analysing a contemporary criticism to the so called “mathematical chemistry”, we discuss what we understand by mathematizing chemistry and its implications. We then pass to ponder on some positions on the subject by considering the cases of Laszlo, Venel and Diderot, opponents to the idea of mathematization of chemistry. In contrast, we analyse some scholars’ ideas on the fruitful relationship between mathematics and chemistry; here Dirac and Brown are considered. Finally, we mention that the (...) mathematical–chemistry relationship should be considered beyond the mere aspect of whether chemistry is or not able to be mathematized. This discussion is based upon opinions by Kant and Comte, the first one having two positions on chemistry based upon mathematics and the latter mooting the idea of doing chemistry with mathematical spirit. (shrink)

There is a particular irony that chemistry – the most visual, tactile, and pungent of sciences – is rarely associated with modern notions of aesthetics and science. Indeed, as any examination of aesthetics and modern science reveals, physics, rather than chemistry or biology, is considered the paradigm because of its extraordinary ability to comprehend and communicate through the symbolic language of mathematics. Echoing Heisenberg’s 1970 essay, "The Meaning of Beauty in the Exact Sciences", this perspective on physics (...) takes the inherent abstraction of quantum mechanics and relativity as the result of the physicists’ search for beauty in nature. (shrink)

Molecular models are typical topics of chemical research depending on the technical standards of observation, computation, and representation. Mathematically, molecular structures have been represented by means of graph theory, topology, differential equations, and numerical procedures. With the increasing capabilities of computer networks, computational models and computer-assisted visualization become an essential part of chemical research. Object-oriented programming languages create a virtual reality of chemical structures opening new avenues of exploration and collaboration in chemistry. From an epistemic point of view, virtual (...) reality is a new computer-assisted tool of human imagination and recognition. (shrink)

Molecules have more or less symmetric and complex structures which can be defined in the mathematical framework of topology, group theory, dynamical systems theory, and quantum mechanics. But symmetry and complexity are by no means only theoretical concepts of research. Modern computer aided visualizations show real forms of matter which nevertheless depend on the technical standards of observation, computation, and representation. Furthermore, symmetry and complexity are fundamental interdisciplinary concepts of research inspiring the natural sciences since the antiquity.

Reductionism remains the dominant philosophical framework of modern science. Within reductionism, the universe is conceived as a probabilistic and deterministic system guided solely by the laws of physics and mathematics. Under the guidance of reductionist thought, the development of the modern atomic theory and quantum mechanics has drastically changed science, medicine, and philosophy. In particular, the standard model of particle physics remains the crowning achievement of over three hundred years of reductionist thought in both physics and chemistry. Yet (...) developments within chemistry suggest a new paradigm is required to overcome the limitations of reductionism and provide chemists a more fruitful model. This article will argue that a version of relational ontology provides an avenue for elucidating and predicting chemical and atomic phenomena. In relational ontology, the ontological status of an enduring entity in any moment is viewed as a composite of its own inherited properties and the influences of other entities, especially those closely related to it within a system. This view encompasses the causal aspects of the world without denying its dynamic and creative nature while providing a richer understanding of chemistry and other scientific fields. (shrink)

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)

This book examines the interface between mathematics and applied sciences. The editor examines the present and future needs for the interaction between various science and engineering areas. This edited book brings together the cutting-edge research on mathematics, combining various fields of science and engineering. The book begins with an introduction to computing and modeling. Next, computation and modeling trends are covered, along with chapters on structural static and vibration problems, heat conduction and diffusion problems, and fluid dynamics problems. (...) Soft computing and machine intelligence based modeling are also discussed, along with bio medical problems. The book concludes with a chapter on modeling in mining, electrical, electronics, and chemical problems. This book is a reference for students and researchers in various fields of engineering such as computer, mechanical, civil, aerospace, electrical, and chemical, as well as and other sciences such as applied mathematics, physics, chemistry, and life sciences. (shrink)

In his Metaphysische Anfangsgründe der Naturwissenschaft (MAN), Kant claims that chemistry is an improper, though rational science. The chemistry to which Kant confers this status is the phlogistic chemistry of, for instance, Georg Stahl. In his Opus Postumum (OP), however, Kant espouses a broadly Lavoiserian conception of chemistry. In particular, Kant endorses Antoine Lavoisier's elements, oxygen theory of combustion, and role for the caloric. As Lavoisier's lasting contribution to chemistry, according to some histories of the (...) science, was his emphasis on quantitative methods, Kant's assimilation of the chemical revolution raises the question: did Kant continue to think of chemistry as an improper, though rational, science in OP? In this paper, I answer this question affirmatively. I explain that a proper science requires a priori laws for the mathematical construction of its objects: the mere use of quantitative measurements is insufficient for the satisfaction this requirement. Further, I argue, contra Burkhard Tuschling, that in OP Kant retains a central role for mathematical construction in the foundations of proper natural science. Finally, I contend that the prominent a priori components of chemistry discussed in OP—the aether and the enumeration of the elements—do not make chemistry into a proper science. (shrink)

Chemistry, especially its historical practice, has in the philosophy of science in recent decades attracted more and more attention, influencing the turn from the vision of science as a timeless logic-centred system of statements towards the history- and practice-centred approach. The problem of pluralism in science has become a popular topic in that context. Hasok Chang’s “active normative epistemic pluralism” manifested in his book Is water H2O? Evidence, realism and pluralism, pursuing an integrated study of history and philosophy of (...) science, has provoked quite a widespread debate. It provides a good opportunity to discuss the topical philosophical issue of the nature of disagreements. The differences among disagreements in different domains have been pointed out in the disagreement literature. It has been noticed that in mathematics and science consensus is established more clearly than in philosophy where it remains largely unachievable. However, this conclusion is derived in the context of traditional logic-centred view of science. The aim of this paper is to consider the different nature of disagreements in science and in philosophy in the context of the history- and practice-centred approach. The analysis is focused on the critique of the received view of the Chemical Revolution which played quite a central role in Chang’s becoming a pluralist about science. Unlike Chang, however, a modified Kuhnian paradigm-conception of science and scientific revolutions is defended. (shrink)

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)

Organic chemists have been able to develop a robust, theoretical understanding of the phenomena they study; however, the primary theoretical devices employed in this field are not mathematical equations or laws, as is the case in most other physical sciences. Instead it is diagrams, and in particular structural formulas and potential energy diagrams, that carry the explanatory weight in the discipline. To understand how this is so, it is necessary to investigate both the nature of the diagrams employed in organic (...) chemistry and how these diagrams are used in the explanations of the discipline. I will begin this paper by characterizing some of the major ways that structural formulas used in organic chemistry. Next I will present a model of the explanations in organic chemistry and describe how both structural formulas and potential energy diagrams contribute to these explanations. This will be followed by several examples that support my abstract account of the role of diagrams in the explanations of organic chemistry. In particular, I will consider both the appeal to ‘hyperconjugation’ in the explanation of alkene stability and how the idea of ‘ring strain’ was developed to explain the relative stability of cyclic compounds. (shrink)

The Timaeus is the dialogue that was for many centuries the most influential of Plato’s works. Among its readers we find Descartes, Boyle, Kepler and Heisenberg. In the first division of Timaeus Plato deals with the theory of celestial motion, in the second he presents us with the first mathematical theory of the structure of matter. Here, in a gigantic step forward with respect to the preceding Democritean atomistic theory with its unalterable micro-entities, he introduces the intertransformability of elementary corpuscles (...) and with that the first “chemical” reactions in history. Plato’s geometrical interpretation of Empedocles’ elements and his geometrical atomism is described at the molecular, atomic and sub-atomic level. The “chemical” reactions reported in Timaeus are written in the enlightening chemical symbolism, analogies with modern chemistry are noticed throughout. (shrink)

This book explains how limitations in the movement and perception of information constrain human behavior, cognition, interaction, and perspective. How fast can we learn? How much? Why are habits and biases unavoidable? Aspects considered include: how much information can one human absorb in a lifetime? How far does a process of perturbation propagate? How do specialization or generalization, critical thinking or belief, influence what people accomplish? It is aimed at general readers and scientists with an interest in how limitations of (...) the physical sciences affect society and human behavior. (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.

The way of thinking of mathematicians and chemists in their respective disciplines seems to have very different levels of abstractions. While the firsts are involved in the most abstract of all sciences, the seconds are engaged in a practical, mainly experimental discipline. Therefore, it is surprising that many luminaries of the mathematics universe have studied chemistry as their main subject. Others have started studying chemistry before swapping to mathematics or have declared some admiration and even love (...) for this discipline. Here I reveal some of these mathematicians who were involved in chemistry from a biographical perspective. Then, I analyze what these remarkable mathematicians and statisticians could have learned while studying chemical subjects. I found analogies between code-breaking and molecular structure elucidation, inspiration for statistics in quantitative analytical chemistry, and on the role of topology in the study of some organic molecules. I also analyze some parallelisms between the way of thinking of organic chemists and mathematicians in terms of the use of backward analysis, search for patterns, and use of pictures in their respective researches. (shrink)

Organic chemists have been able to develop a robust, theoretical understanding of the phenomena they study; however, the primary theoretical devices employed in this field are not mathematical equations or laws, as is the case in most other physical sciences. Instead it is the diagram, and in particular the structural formula, that carries the explanatory weight in the discipline. To understand how this is so, it is necessary to investigate both the nature of the diagrams employed in organic chemistry (...) and how these diagrams are used in the explanations of the discipline. I will begin this paper by describing and characterizing the roles of the most important sort of diagram used in organic chemistry. Next I will present a model of explanations in organic chemistry and describe how diagrams contribute to these explanations. This will be followed by two examples that will support my abstract account of the role of diagrams in the explanations of organic chemistry. (shrink)

This chapter shows that the combination of mathematical and chemical thinking in particular, as evidenced by Charles Sanders Peirce’s chemical training at Harvard, formed a solid conceptual basis for his account of diagrams. The connection between the Lawrence school and the chemical tradition established by Justus von Liebig in Giessen is of crucial importance to understand the context of Peirce’s own chemistry training. A completely different picture emerges if one pays greater attention to the nature of the chemistry (...) curriculum in Harvard at the time, and in particular to the pedagogical innovations introduced by Peirce’s chemistry teacher, Josiah Parsons Cooke. Historians of science have investigated the rise of institutional scientific laboratories from a range of perspectives. The chapter concludes with some suggestions for further investigation into the role of chemistry in Peirce’s philosophical system more broadly and the potential this new avenue of inquiry might have for the direction of Peirce scholarship. (shrink)

In modern German ‘Anschauung’ is translated as intuition. But in Kant’s technical philosophical context, it means an intuition derived from previous visualizations of physical processes in the world of perceptions. The nineteenth century chemists’ predilection for Kantian Anschauung led them to develop an intuitive representation of what exists beyond the bounds of the senses. Molecular structure is one of the illuminating outcomes. (Ochiai 2021, pp. 1–51) This mental habit seems to be dominant among chemists even in the twentieth century, as (...) is illustrated by the electronic theory of organic chemistry and the frontier orbital theory as well. The former assumes that (1) bonds are paired electrons shared by bonded atoms—in fact, electrons in molecules are not localized in bonds; (2) the difference of electronegativities between bonded atoms causes electron drifts—expressed by the curly arrow—that result in bond formation or bond cleavage. The latter focuses on the orbitals that make the greatest contribution to the energy of a system undergoing electron delocalization, while the LCAO method says, as is suggested by the word Linear Combination of Atomic Orbitals, molecular orbitals should be constructed from all of the atomic orbitals that have the appropriate symmetry. In other words, every molecular orbital contributes to some extent to the electronic state of a molecule. The curly arrow in the electronic theory and the orbital lobe in the frontier orbital theory illustrate an intuitive character of these theories. Although both theories rely on such simple and qualitative models rather than mathematically rigid quantum mechanical calculations, they are successful in explaining, predicting, and designing chemical reactions. What makes these prima facie intuitive theories so successful? In this study we address this problem from a historical and philosophical as well as scientific point of view. The key to solve this problem is that they are concerned with only bond formation or bond cleavage, in which the localized-bond principle holds. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem (...) using an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

We analyze the connections of Lavoisier system of nomenclature with Leibniz’s philosophy, pointing out to the resemblance between what we call Leibnizian and Lavoisian programs. We argue that Lavoisier’s contribution to chemistry is something more subtle, in so doing we show that the system of nomenclature leads to an algebraic system of chemical sets. We show how Döbereiner and Mendeleev were able to develop this algebraic system and to find new interesting properties for it. We pointed out the resemblances (...) between Leibniz program and Lavoisier legacy, particularly regarding the lingua philosophica for understanding and thinking Nature, in this particular case, chemistry. In the second part we discuss, from the linguistic viewpoint, how Lavoisian algebraic system may be taken further to build a language. We study the constituents of such a chemical language. Finally, we formalize some of the ideas here presented by using elements of network theory and discrete mathematics. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

In his classic work The Mind and its Place in Nature published in 1925 at the height of the development of quantum mechanics but several years after the chemists Lewis and Langmuir had already laid the foundations of the modern theory of valence with the introduction of the covalent bond, the analytic philosopher C. D. Broad argued for the emancipation of chemistry from the crass physicalism that led physicists then and later—with support from a rabblement of philosophers who knew (...) as much about chemistry as etymologists—to believe that chemistry reduced to physics. Here Broad’s thesis is recast in terms more familiar to chemists. In the hard sell of particle physics, several prominent figures in chemistry—Hoffmann, Primas, and Pauling—have had their views interpreted to imply that they were sympathetic to greedy reductionism when in fact they were not. Indeed, being chemists without physicists as alter egos, they could not but side with Broad’s contention that chemistry, as a science that deals primarily in emergent phenomena which are beyond the purview of physicalism, owes no acquiescence to particle physics and its ethereal wares. Historically, among the most widely used expediencies in chemistry and materials science are additivity or mixture rules and their cohort transferability, all of which are devised and used under the mantle of naive reductionism. Here it is argued that while the transfer of functional groups between molecules works empirically to an extent, it is strictly outlawed by the no-cloning theorem of quantum mechanics. Several illustrative examples related to chemistry’s irreducibility to physics are presented and discussed. The failure of naive reductionism exhibited by the deep-inelastic scattering of leptons by A > 2 nuclei is traced to the same flawed reasoning that was the original basis of Moffitt’s ‘atoms in molecules’ hypothesis, the neglect of context, nuclei in the case of high-energy physics and molecules in the case of chemistry. A non-exhaustive list of other contexts from physics, chemistry, and molecular biology evidencing similar departures from the ideal of additivity or reductionism is provided for the perusal of philosophers. Had the call by the mathematician J. T. Schwartz for developments in mathematical linguistics possessed of a less single, less literal, and less simple-minded nature been met, perhaps it might have persuaded scientists to abandon their regressive fixation with unphysical reductionism and to adapt to new methodologies that engender a more nuanced handling of ubiquitous emergent phenomena as they arise in Nature than is the case today. (shrink)

The quality of doctoral-level chemistry (N=145), computer science (N=58), geoscience (N=91), mathematics (N=115), physics (N=123), and statistics/biostatistics (N=64) programs at United States universities was assessed, using 16 measures. These measures focused on variables related to: program size; characteristics of graduates; reputational factors (scholarly quality of faculty, effectiveness of programs in educating research scholars/scientists, improvement in program quality during the last 5 years); university library size; research support; and publication records. Chapter I discusses prior attempts to assess quality in (...) graduate education, development of the study plans, and the selection of disciplines and programs to be evaluated. Chapter II discusses the methodology used, focusing on each of the assessment measures. Chapters III to VIII present, respectively, findings from the analyses of the chemistry, computer science, geoscience, mathematics, physics, and statistics/biostatistics programs. Chapter IX includes a summary of results, correlations among measures, several additional analyses, and suggestions for future studies. Among the findings reported are those indicating that mathematics programs had, on the average, the largest number of faculty (N=33) in December 1980 followed closely by physics (N=28) and chemistry (N=23), and that 80 percent of computer science students had job commitments by graduation. (Survey instruments and supporting documentation are included in appendices.) (JN). (shrink)

What was the impact of Lavoisier's new elementary chemical analysis on the conception and practice of chemistry in the vegetable kingdom at the end of the eighteenth century? I examine how this elementary analysis relates both to more traditional plant analysis and to philosophical and mathematical concepts of analysis current in the Enlightenment. Thus I explore the relationship between algebra, Condillac's philosophy and Lavoisier's chemical system, as well as comparing Lavoisier's analytical approach to those of his predecessors, such as (...) Baumé and Bucquet. With reference to the aims of vegetable analysis, I show how the dominance of elementary analysis devalued a tradition that sought to isolate immediate principles , marginalizing the chemical practices of many doctors and pharmacists in the context of the new chemistry in France. (shrink)

Summary Linus Pauling played a key role in creating valence-bond theory, one of two competing theories of the chemical bond that appeared in the first half of the 20th century. While the chemical community preferred his theory over molecular-orbital theory for a number of years, valence-bond theory began to fall into disuse during the 1950s. This shift in the chemical community's perception of Pauling's theory motivated Pauling to defend the theory, and he did so in a peculiar way. Rather than (...) publishing a defence of the full theory in leading journals of the day, Pauling published a defence of a particular model of the double bond predicted by the theory in a revised edition of his famous textbook, The Nature of the Chemical Bond. This paper explores that peculiar choice by considering both the circumstances that brought about the defence and the mathematical apparatus Pauling employed, using new discoveries from the Ava Helen and Linus Pauling Papers archive. (shrink)

Mathematics is so common-place in modern physics and chemistry that one may not realise how controversial its admittance was to these fields in the eightieth and ninetieth centuries respectively. This paper deals with the controversy during the formation of physical chemistry as a discipline in the late ninetieth and early twentieth centuries and sketches more recent criticisms of the way mathematics has been used in solution chemistry. The controversy initially related particularly to electrolyte chemistry (...) and its emerging use of mathematics to support Arrhenius’ theory of ionic dissociation. The impact of mathematics on the field is divided into three phases: that from 1880 to 1920 which was a period of heightened controversy; that from 1920 to 1990 which was a period of relative calm and mathematical development; and finally, that from 1990 to the present which has been a time of reflective criticism of the extensive use of empirical parameters in the emergent mathematics of the twentieth century. It is argued that the current solution to the criticism, as proposed by Heyrovska, is best viewed in the light of the historical development of the controversy. (shrink)

Algorithmic chemistries are often based on a fixed formalism which limits the fragment of chemistry expressible in the domain of the models. This results in limited applicability of the models in contemporary mathematical chemistry and is due to the poor fit between the logic used for model construction and the system being modeled. In this paper, I propose a system-oriented methodology which selects a formalism through a mapping of chemical transformation rules to proof-theoretic structural rules. Using a formal (...) specification framework from the field of artificial chemistry, expressive adequacy is ensured by the choice of logic being based on the system properties to be modeled. To illustrate the methodology, a case study is provided that shows how the proposed approach selects linear logic for modeling resource sensitivity and the proof-theoretic interpretation facilitates translation to a programming language. Since the method results in a plurality of models, I conclude with a discussion on how the proposal contributes to multi-model paradigms in computational pharmacology. (shrink)

In this paper we will discuss some of the issues related to the attempts of Ralph Howard Fowler and Nevil Vincent Sidgwick to create a legitimizing space for quantum and theoretical chemistry in Britain. Although neither Fowler nor Sidgwick made original contributions to quantum chemistry, they followed closely the developments in the discipline, participated in meetings and discussions and delivered lectures, talks and addresses, where methodological topics, ontological questions and implicitly the problem of autonomy of the new discipline (...) vis-à-vis both physics and chemistry were taken to be pressing issues. In particular, they encouraged young people to work within the nascent discipline. Viewing quantum chemistry as a branch of applied mathematics became an emblematic characteristic of the practice of the new discipline in Great Britain. (shrink)

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (_c_. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In (...) the present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations. (shrink)

Albert Lewis's article analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:i. Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical (...) education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.ii. Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.iii. Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann. (shrink)

Ostwald (born September 2, 1853, Riga, Latvia, Russia; died April 4, 1932, at his private estate near Leipzig, Germany) almost single-handedly established physical chemistry as an acknowledged academic discipline. In 1909, he was awarded the Nobel Prize in chemistry for his work on catalysis, chemical equilibria, and reaction velocities. Ostwald was graduated in chemistry at the University of Dorpat (now Tartu, Estonia) and appointed professor of chemistry in Riga in 1881, before he moved from Russia to (...) Germany on the chair in physical chemistry at the University of Leipzig in 1887. For about twenty years he made Leipzig an international center of physical chemistry: by establishing an instruction and research laboratory that attracted virtually the whole next generation of physical chemists; by editing the first journal of the field (Zeitschrift für physikalische Chemie); and by writing numerous textbooks. In 1906, he retired from university and devoted the rest of his life to various topics, including the history and philosophy of science, color theory, painting, the writing of textbooks and popular books about science, the international organization of science, and the formation of an artificial language for the international exchange of ideas. Since his master degree thesis in 1876, Ostwald followed the general approach of applying physical measurement and mathematical reasoning to chemical issues. One of his major research topics was the chemical affinity of acids and bases. To that end, he studied the point of equilibrium in reactions systems where two acids in aqueous solution compete with each other for reaction with one base and vice versa. Because chemical analysis would have changed the equilibria, he skillfully adapted the measurement of physical properties to that problem, such as volume, refractive index, and electrical conductivity. From his extensive data he derived for each acid and base a characteristic affinity coefficient independent of the particular acid-base reactions. To understand the different chemical affinities, Ostwald drew on a new, but then hardly accepted and not yet fully developed, theory advanced by Svante Arrhenius. According to this theory of electrolytic dissociation, electrolytes like acids, bases, and salts dissociate in solution into oppositely charged ions to a certain degree, such that at infinite solution dissociation is complete.. (shrink)

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study (...) the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine. (shrink)