Chemistry is a highly technical field that relies heavily on a range of symbolic and imagic formalisms. These formalisms conceptualize specific chemical knowledge into semiotic resources that are rarely used elsewhere in most other academic fields or contexts. To develop an understanding of semiosis in highly technical fields such as chemistry, key questions include what this range of formalisms do and why they occur. These are key questions not only for our understanding of semiosis, but also if we wish (...) to develop integrated literacy programs that can support students to marshal the multimodal discourse of chemistry. This paper explores these questions by examining how three key chemical formalisms organize their meaning: symbolic formalisms known as chemical formulas and chemical equations, and an imagic formalism known as structural formulas. Drawing on Systemic Functional Linguistics and using a corpus of formalisms from secondary school chemistry, these formalisms are explored in terms of their overarching grammatical organization and the content meanings they realize through the concept of “field.” This is used to compare and contrast each formalism in terms of a semiotic typology so as to understand how they work and what meanings they realize. By exploring chemical formalisms in this way, this paper establishes a means of seeing the similarities and differences in meaning-making across formalisms and explaining why different formalisms occur. This then begins to provide a base upon which applied programs can interpret the literacy needs of chemistry. (shrink)

Given the rich diversity of research fields usually ascribed to chemistry in a broad sense, the present paper tries to dig our characteristic parts of chemistry that can be conceptually distinguished from interdisciplinary, applied, and specialized subfields of chemistry, and that may be called chemistry in a very narrow sense, or 'the chemical core of chemistry'. Unlike historical, ontological, and 'anti-reductive' approaches, I use a conceptual approach together with some methodological implications that allow to develop step by step a (...) kind of cognitive architecture for chemistry, which basically contains: (1) systematic chemical knowledge on the experimental level; (2) clarification of chemical species; (3) chemical classification systems; (4) theoretical foundation through the chemical theory of structural formulas. In a succeeding paper the results will be checked for resisting physicalistic reduction. (shrink)

Late nineteenth‐century opponents of atomism questioned whether the evidence required any notion of an atom. In this spirit, Duhem developed an account of the import of chemical formulas that is clearly neutral on the atomic question rather than antiatomistic. The argument is supplemented with specific inadequacies of atomic theories of chemical combination and considerably strengthened by the theory of chemical combination provided by thermodynamics. Despite possible counterevidence available at the time, which should have tempered some of (...) Duhem's concluding remarks, there was no atomic theory of chemical combination, which is wholly a product of the twentieth century. †To contact the author, please write to: Department of Philosophy, University of Stockholm, SE‐106 91 Stockholm, Sweden; e‐mail: [email protected]. (shrink)

Similarities in properties among pairs of metallic elements and their compounds in the lower-right quadrant of the Periodic Table have been named the ‘Knight’s Move’ relationship. Here, we have undertaken a systematic study of the only two ‘double-pairs’ of ‘Knight’s Move’ elements within this region: copper-indium/indium-bismuth and zinc-tin/tin-polonium, focussing on: metal melting points; formulas and properties of compounds; and melting points of halides and chalcogenides. On the basis of these comparisons, we conclude that the systematic evidence for ‘Knight’s Move’ (...) relationships derives from similarities in formulas and properties of matching pairs of compounds in the same oxidation state. Physical properties, such as melting points, do not provide consistent patterns and trends and hence should not be considered as a common characteristic of this relationship. (shrink)

I argue and demonstrate in this essay that interconnected systems of science and technology, or technoscience, existed long before the late nineteenth century, and that eighteenth-century chemistry was such an early form of technoscience. Based on recent historical research on the early development of carbon chemistry from the late 1820s until the 1840s—which revealed that early carbon chemistry was an experimental expert culture that was largely detached from the mundane industrial world—I further examine the question of the internal preconditions within (...) the expert culture of carbon chemistry that contributed to its convergence with the synthetic-dye industry in the late 1850s. I argue that the introduction of new types and techniques of organic-chemical reactions and organic substances in this experimental expert culture, along with the application of chemical formulae as paper tools for modeling reactions as well as the chemical constitution and structure of substances, enabled academic chemists to make specific, novel contributions to chemical technology and industry in the second half of the nineteenth century. (shrink)

: I argue and demonstrate in this essay that interconnected systems of science and technology, or technoscience, existed long before the late nineteenth century, and that eighteenth-century chemistry was such an early form of technoscience. Based on recent historical research on the early development of carbon chemistry from the late 1820s until the 1840s—which revealed that early carbon chemistry was an experimental expert culture that was largely detached from the mundane industrial world—I further examine the question of the internal preconditions (...) within the expert culture of carbon chemistry that contributed to its convergence with the synthetic-dye industry in the late 1850s. I argue that the introduction of new types and techniques of organic-chemical reactions and organic substances in this experimental expert culture, along with the application of chemical formulae as paper tools for modeling reactions as well as the chemical constitution and structure of substances, enabled academic chemists to make specific, novel contributions to chemical technology and industry in the second half of the nineteenth century. (shrink)

An exposition of Pierre Duhem’s formulation of the structure of chemical substances as expressed by their formulas is given, presenting it as a development of his essentially Aristotelian view of mixtures. Duhem’s masterly development of the subject displays an eye for logical clarity familiar from his work in thermodynamics but applied here to the extraction of what he regarded as true from the history of chemistry. Though no longer defensible, the account has a conceptual interest in its own (...) right and illuminates a less frequently discussed side of Duhem’s views. (shrink)

This paper suggests that the cases made for atoms and the aether in nineteenth-century physical science were analogous, with the implication that the case for the atom was less than compelling, since there is no aether. It is argued that atoms did not play a productive role in nineteenth-century chemistry any more than the aether did in physics. Atoms and molecules did eventually find an indispensable home in chemistry but by the time that they did so they were different kinds (...) of entities to those figuring in the speculations of those natural philosophers who were atomists. Advances in nineteenth-century chemistry were a precondition for rather than the result of the productive introduction of atoms into chemistry. (shrink)

This article was first published as “Notation atomique et hypothèses atomistiques”, Revue des questions scientifiques, 31 (1892), 391– 457. It is the second of a series of articles Duhem was to publish in the Catholic journal Revue des questions scientifiques, in which he presents his understanding of what can justifiably be said about the structure of chemical substances as captured by chemical formulas. The argument unfolds following a broadly historical development of events throughout the course of the (...) century which was coming to a close as he wrote. He later reflected in his classic The Aim and Structure of Physical Theories – based in large part on articles which had appeared in the Revue – that “To give the history of a physical principle is at the same time to make a logical analysis of it” (p. 269). Logical analysis clearly dominates in the present article. The historical context was elaborated considerably in a later work, Le mixte et la combinaison chimique: Essai sur l’évolution d’une idée, which did not lead him to retract any aspect of his earlier position but provided a broader setting in which it could be elaborated. In particular, the Aristotelian influence, which is only hinted at here in some of the formulations (see especially the beginning of section VII) without mentioning Aristotle by name, is explicit in the later work, making Duhem’s own ontological conception a little clearer. A discussion of stereoisomerism, conspicuously absent in the present article, is also integrated into the later book. The same holds for Avogadro’s hypothesis. (shrink)

The ArgumentIn Germany during the 1870s and 1880s a number of important scientific innovations in chemistry and biology emerged that were linked to advances in the new technology of synthetic dyestuffs. In particular, the rapid development of classical organic chemistry was a consequence of programs in which chemists devised new theories and experimental strategies that were applicable to the processes and products of the burgeoning dye factories. Thereafter, the novel products became the means to examine and measure biological systems. This (...) took place as a result of two trends. The first was a move toward diversification in the dye industry – made possible by the extensive range of products – which in turn was stimulated by economic and political conditions. The second was the increasing availability of techniques, substances, and processes used in industry. This made possible a concrete program of introducing the qualitative and quantitative methods of chemistry into the domain of laboratory experimentation on biological materials, thereby realizing the abstract desire to transform cell biology into an exact science.Moreover, the conceptualization of biological systems that emerged from this endeavor leaned heavily on a theory of dye chemistry that indicated which particular arrangements of atoms performed specific functions. This biological modeling used the imagery of chemical structural formulae to transform chemical nuclei and their side chains into adequate representations of protoplasmic structure. (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)

The ArgumentThe status of the person is analyzed as represented by the life sciences under the influence of modern physico–chemical and molecular biology.At the same time the linguistic structure of reality as seen through formalized scientific discourse is not that of a language, but rather that of operational symbolisms, so that the judeo–Greek tradition of Verb as creating and Logos as procreating — which is probably at the origin of the surprising confidence in the possibility of dominating nature through (...) words and formulae — could be suc–cessful only through the depersonalization of language.Notwithstanding appearances, the phenomena of structural and functional self–organization do not really change this situation.In this context the question of the status of the person and of the intentional subject has to be dealt with pragmatically, giving up the notion of a unified scientific theory that would take into consideration at the same time the experi–mental sciences and the human sciences as linking subjectivity and intentionality. (shrink)

Chemical structures are among the trademarks of our profession, as surely chemical as flasks, beakers and distillation columns. When someone sees one of us busily scribbling formulas or structures, he or she has no trouble identifying a chemist. Yet these familiar objects, which accompany our work from start to end, from the initial doodlings (Fig. I) to the final polished artwork in a publication (Fig. II), are deceptively simple. They raise interesting and difficult questions about representation. It (...) is the intent of this article to reflect upon molecular graphics. (shrink)

In the last twenty years or so there has been a renewed interest in Pliny the Elder, once an immensely popular author whose reputation began to suffer after Renaissance scholars challenged the accuracy of his work. The recent interest has been interdisciplinary, producing contributions from classical scholars, historians, scientists, and technologists, sometimes working as a team. What “interdisciplinary” has meant in practice is a collaboration rather than a blend of disciplines. What you see in Pliny is what your training makes (...) obvious.John Healy's book is a robust defense, indeed promulgation, of the thesis that Pliny practiced “science.” This thesis implies not only that science was a recognizable, and recognized, activity in antiquity but that “science” can tell us more clearly than any other rubric what Pliny was up to. Science can certainly tell us about Pliny's natural world, because it was very much like our own, but it does not tell us anything about Pliny's enterprise. We may feel a sense of intellectual satisfaction in knowing the formula for the acetic acid in vinegar and the chemical equation that represents its attack on calcareous rocks, but Pliny's story is about something else.In this study Healy, a distinguished classical scholar, has taken aboard a lot of science. He provides us with valuable information about the suitability of the Latin language for the development of technical terms and about its borrowings from Greek and other languages. After Healy the classicist considers Pliny as a writer and describes his life, sources, mode of work, language, and style, Healy the scientist addresses the topic of ancient science. Chapter 10 lays down the program, taken from a modern classification of fields of research. Healy takes the ten subdivisions of the “natural sciences, technologies and engineering” as a structure for his investigation into Pliny and for the format of the book. He thus looks at Pliny's thought in relation to chemistry, physics, earth sciences, engineering , applied sciences, biology, and agriculture. A footnote tells us that he has omitted any reference to medicine, pharmacology, and astronomy—a pity, as these subjects, with their own identities and practitioners, come closer to science than most of what either Pliny or Healy discusses. In the style of a modern scientific textbook, Healy's text is broken down into numerous subsections to accommodate modern categories. The chapters on minerals and gems are alphabetical lists.The combination of classical learning and scientific knowledge looks formidable and is certainly unusual. But the book is more an exercise in applying science to classical studies than an example of science illuminating history. The confidence his scientific material gives Healy leads to a certain historical insensitivity. I declare an interest here, for he badly misreads what I have argued about “science” in antiquity. His rigid use of modern—our—categories inevitably leads to instances in which he finds Pliny confusing them or failing to separate them. Our categories take on a life of their own in this exposition: the section on “electricity,” for example, is largely independent of Pliny. Its subsection 12.2.1c is on piezoelectricity, of which “neither Pliny, nor other ancient authorities, appear to have been aware.” Gravity has to be there, because it is part of modern physics, but Pliny does not mention it.There is no reason why classical scholars and scientists should not be interested in Pliny and find each other's disciplines enlightening. But the claim that Pliny was, as Healy says, making “contributions” to our science is a historical one and relates to Pliny's purposes. No amount of modern mathematical or chemical formulas will tell us what was in Pliny's mind, and he was fairly clear, after all, on his purposes in writing the Natural History. It's back to “Science in Antiquity?” again. (shrink)

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

Ritualistic formulae and acts pervade the political, legal, societal and religious life of the ancient world. In many instances there are striking similarities between the formulae of the Greco-Roman world and those of the Near East. Often illumination exists from one to the other. Here I wish to notice a few passages in Greek drama where I think such illumination is possible.

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that such (...) operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...) are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called \emph{elementary}. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called \emph{canonical}. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

The paper is intended to provide a full-scale defence of the infamous Barcan Formulae. Not only do I put forth some arguments, both semantic and metaphysical, against recent criticism; I also take pains at supplying some rationale in favour of the formal semantics underlying the Formulae, namely Possibilist quantification. Such a task is carried out through an argument for Compositional Nihilism, according to which nothing but mereological simples ever exists, and consequently through an informal sketch of the metaphysics of possible (...) worlds grounded upon Compositional Nihilism. The paper closes by surveying the main reasons why the account championed here isn’t defective with respect to other possibilist accounts of existence and modality presently on stage. (shrink)

This article is a study of formulaic passages in the Sanskrit Avadanasataka. Alongside a preliminary discussion of work on oral studies within Buddhism, and some recourse to wider oral studies on Indian texts, the focus of this article is a two-part study of formulae and constituents of formulae. The first part of the article details formulaic sections from the Avadanasataka, from short formulae about wealthy merchants to lengthy counterparts that detail the consequences of a Buddha's smile. The second part looks (...) in detail at constituents of the formulaic passages. The passages are constructed around semantic lists, which either constitute the whole formulaic phrase or passages, or can be identified as the building blocks for the passages. To my knowledge this is the first study of semantic list-based formulae in a Sanskrit text. (shrink)

The most recent work dealing expressly with adoption in Greece is Wentzel's article in Hermes lxv , 167–76, ‘Studien über die Adoption in Griechen-land’. Her article ranges widely over the whole subject and includes a list of all the inscriptions known to her which refer to adoptions, as well as a list of the adoptive formulae found in these inscriptions. In the present article I shall deal more fully with these formulae.

Another sort of thing resembles works of art in combining existence, message and a kind of presentation, namely, symbols. Hence it seems reasonable to take works of art as symbols. And yet works of art are a special kind of symbol, because in them presentation has a double function. All symbols directly present their meaning; indeed the essential function of symbols is to serve as vehicles for conveying us into the immediate presence of what they mean. But works of art (...) have a second presentational mode of functioning. They also present themselves; and this is true both for abstract and for representational art. (shrink)

Let R be a real closed field, and X⊆Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq R^m}$$\end{document} semi-algebraic and 1-dimensional. We consider complete first-order theories of modules over the ring of continuous semi-algebraic functions X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\to R}$$\end{document} definable with parameters in R. As a tool we introduce -piecewise vector bundles on X and show that the category of piecewise vector bundles on X is equivalent to the category of syzygies of (...) finitely generated submodules of free modules. We give an explicit method to determine the Baur–Monk invariants of free modules in terms of pre-piecewise vector bundles. When R is a recursive real closed field this yields the decidability of the theory of free modules. Where it makes sense, we address the same questions for continuous definable functions in o-minimal expansions of a real closed field. From the free module case we are able to deduce generalisations of some results to arbitrary modules over the ring. We present a geometrically motivated quantifier elimination result down to the level of positive primitive formulae with a certain block decomposition of the matrix of coefficients. (shrink)

— via appropriate substitutions — syntactically identical. The method can be applied directly to quantifierfree formulae and, in this paper, will b e extended in a natural and strai ghlforward way to quantified formulae.

In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its (...) translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential contexts. (shrink)

This article suggests a novel way to advance a current debate in the philosophy of mathematics. The debate concerns the role of diagrams and visual reasoning in proofs—which I take to concern the criteria of legitimate representation of mathematical thought. Drawing on the so-called ‘maverick’ approach to philosophy of mathematics, I turn to mathematical practice itself to adjudicate in this debate, and in particular to category theory, because there (a) diagrams obviously play a major role, and (b) category theory itself (...) addresses questions of representation and information preservation over mappings. We obtain a mathematical answer to a philosophical question: a good mathematical representation can be characterized as a category theoretic natural transformation. (shrink)

The Lorentz-formulae are deduced from three factual statements the physical meaning of which is explained in terms of operations with clocks, light-signals and measuring rods. These statements are: (1) The time-length of a process is invariant. (2) The velocity of light is the same in all inertial systems. (3) The velocity of light is independent of the source. It is also shown that these statements can be deduced from the Lorentz-formulae. They are the physical content of the latter. The principle (...) of relativity and the light-principle together, however, contain more physical meaning than the Lorentz-formulae. Operational definitions are given for all relevant concepts. (shrink)

Shows that a certain temporal logic has infinitely many non-equivalent formulae in a single variable.

It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can be (...) also treated as results about the expressive power of certain languages in fi nite models. (shrink)

We present a sound and complete tableau calculus for the class of regular grammar logics. Our tableau rules use a special feature called automaton-labelled formulae, which are similar to formulae of automaton propositional dynamic logic. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. We show that the known EXPTIME upper bound for regular grammar logics can be obtained using our tableau calculus. We also give an effective Craig interpolation lemma for regular grammar (...) logics using our calculus. (shrink)

It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.