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... 13 Following the same vein of organic and inorganic classifications of compound substances, the periodic system of elements shows the prevalence of the internal conception of relations among the entities that we propose as a characteristic of the chemical approach. Modern studies on the periodic system support this assertion by showing the dominant character of descriptors of reaction selectivity in reconstructing and transcending the periodic table through the use of cluster analysis and topology (Restrepo et al. 2004, Leal & Restrepo 2009 This dominant character of the ontological conception of the elements as internally related in the periodic system can also be seen in community reactions to the first reports on the noble gases. Upon their discovery, the existence of these substances was regarded a threat to the periodic system (Bensaude-Vincent 1986). ...
... Benkö et al. 2003 integrates some elements from quantum mechanics and structural formulas. Bernal 2008 andLeal 2009 use similar models for approaching the old problem of substance classification. ...
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Following several authors, we point out the importance of relations in the conceptual frame of chemistry. We propose that an important characteristic of chemistry is given by the epistemological challenge associated with selectively related entities. We also suggest that internal relation ontologies have been seen by chemists as better suited for assessing this challenge, and that this ontological perspective has played an important role in shaping chemical concepts.
... The set of chemical elements and compounds can be formally studied by defining a relational property and using network theory [44, 45]. In this sense, we know that in chemistry it is usual to classify substances according to their activity, i.e. how they interact with each other [46]. ...
... For instance, in organic chemistry we talk about typical reactions of alkanes, alcohols, carboxylic acids, esters, etc. [47]; i.e. we define families of compounds which are related via chemical reactions with compounds of the same given families, and are regarded as similar in that sense [23]. In the same way, here we consider a network whose vertices are chemical elements, related by their mutual presence in a compound [45]. For convenience, in this article we consider only the subset of binary compounds. ...
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It has been claimed that relational properties among chemical substances are at the core of chemistry. Here we show that chemical elements and a wealth of their trends can be found by the study of a relational property: the formation of binary compounds. We say that two chemical elements A and B are similar if they form binary compounds AC and BC, C being another chemical element. To allow the richness of chemical combinations, we also included the different stoichiomet-rical ratios for binary compounds. Hence, the more combinations with different chemical elements, and with similar stoichiometry, the more similar two chemical elements are. We studied 4,700 binary compounds by using network theory and point set topology, we obtained well-known chemical families of elements, such as: alkali metals, alkaline earth metals, halogens, lanthanides, actinides, some transi-tion metal groups and chemical patterns like: singularity principle, knight's move, and secondary periodicity. The methodology applied here can be extended to the study of ternary, quaternary and other compounds, as well as other chemical sets where a relational property can be defined.
... Then, Mendeleev's work can be regarded as a topological arrangement of the chemical elements. Recently, Leal and co-workers [39,40] In so doing, a network of binary compounds and elements was built up and the resemblances among elements were extracted as structural equivalences in such a network. The size of the equivalence classes was set up according to the procedure illustrated in references [10,12]. ...
... The most important conclusion of this work is that a wealth of chemical knowledge on chemical elements can be derived from "chemical" resemblances among elements. This [39,40] is the first chemotopological study of chemical elements exclusively based on chemical information i.e. the fact of knowing or not binary compounds for any pair of chemical elements. ...
We have shown in several papers the importance of using topology, particularly set-point topology, to deal with chemical questions related to the concept of similarity. The procedure developed has been called "chemotopology" and it has been applied to different chemical sets e.g. chemical elements, benzimidazoles, sterorids, amino acids and hydrides. The idea behind chemotopology is to run a hierarchical cluster analysis study on a set of objects characterised by different attributes. From this study a dendrogram is obtained, which gathers similarity neighbourhoods for the set of objects. By using a mathematical characterisation of a dendrogram it is possible to select a collection of objects' neighbourhoods which in turn become a basis for a topology. With this basis at hand different properties of subsets of objects can be calculated, all of them related to the concept of similarity e.g. closures, derived sets, boundaries, interiors and exteriors. We have also shown the chemical meaning of each one of these properties. In this manuscript, we review the foundations of the chemotopological method as well as its different applications to chemical sets. By means of examples we illustrate how the method can be used as a versatile tool for drug discovery. We also study the relationship between the topologies generated from dendrograms of a given set of objects and the dendrograms that can be obtained for particular topologies on the set of objects.
... To take into account the stoichiometry of each combination, each chemical element of the mentioned list is weighted by the ratio of the stochiometric factors of the two elements in the binary compound. For further information the reader is referred to references (Leal and Restrepo 2009;Leal et al., under review). 33 Condillac criticized Newton for the use of the synthetic method in his research. ...
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.
Starting from the observation that substances and reactions are the central entities of chemistry, I have structured chemical knowledge into a formal space called a directed hypergraph, which arises when substances are connected by their reactions. I call this hypernet chemical space. In this thesis, I explore different levels of description of this space: its evolution over time, its curvature, and categorical models of its compositionality. The vast majority of the chemical literature focuses on investigations of particular aspects of some substances or reactions, which have been systematically recorded in comprehensive databases such as Reaxys for the last 200 years. While complexity science has made important advances in physics, biology, economics, and many other fields, it has somewhat neglected chemistry. In this work, I propose to take a global view of chemistry and to combine complexity science tools, modern data analysis techniques, and geometric and compositional theories to explore chemical space. This provides a novel view of chemistry, its history, and its current status. We argue that a large directed hypergraph, that is, a model of directed relations between sets, underlies chemical space and that a systematic study of this structure is a major challenge for chemistry. Using the Reaxys database as a proxy for chemical space, we search for large-scale changes in a directed hypergraph model of chemical knowledge and present a data-driven approach to navigate through its history and evolution. These investigations focus on the mechanistic features by which this space has been expanding: the role of synthesis and extraction in the production of new substances, patterns in the selection of starting materials, and the frequency with which reactions reach new regions of chemical space. Large-scale patterns that emerged in the last two centuries of chemical history are detected, in particular, in the growth of chemical knowledge, the use of reagents, and the synthesis of products, which reveal both conservatism and sharp transitions in the exploration of the space. Furthermore, since chemical similarity of substances arises from affinity patterns in chemical reactions, we quantify the impact of changes in the diversity of the space on the formulation of the system of chemical elements. In addition, we develop formal tools to probe the local geometry of the resulting directed hypergraph and introduce the Forman-Ricci curvature for directed and undirected hypergraphs. This notion of curvature is characterized by applying it to social and chemical networks with higher order interactions, and then used for the investigation of the structure and dynamics of chemical space. The network model of chemistry is strongly motivated by the observation that the compositional nature of chemical reactions must be captured in order to build a model of chemical reasoning. A step forward towards categorical chemistry, that is, a formalization of all the flavors of compositionality in chemistry, is taken by the construction of a categorical model of directed hypergraphs. We lifted the structure from a lineale (a poset version of a symmetric monoidal closed category) to a category of Petri nets, whose wiring is a bipartite directed graph equivalent to a directed hypergraph. The resulting construction, based on the Dialectica categories introduced by Valeria De Paiva, is a symmetric monoidal closed category with finite products and coproducts, which provides a formal way of composing smaller networks into larger in such a way that the algebraic properties of the components are preserved in the resulting network. Several sets of labels, often used in empirical data modeling, can be given the structure of a lineale, including: stoichiometric coefficients in chemical reaction networks, reaction rates, inhibitor arcs, Boolean interactions, unknown or incomplete data, and probabilities. Therefore, a wide range of empirical data types for chemical substances and reactions can be included in our model.
Through a parallel historical-conceptual reading of The Rules of Sociological Method and of The Division of Social Labor, the article shows that Durkheim’s central epistemological tool, “constraint”, besides having a descriptive function, also aimed to endow sociology with an explanatory and critical power. In addition to opening up the field of investigations, “constraint” had to guide the historical and political exploration of the modern division of labor, marked by an absence of justice that made solidarity weak and troubled, as revealed by the rise of social antagonism. The article highlights the extent to which, behind the opposition between the normal and the pathological, lied a quest for justice, expressed by workers’ aspirations, in which the idea of freedom was itself at stake. Far from having inaugurated sociology to curb socialism, Durkheim conceived it rather as its reflexive theoretical correlate, charged with the conceptual and empirical means to realize its political ambition: to transform modern society as a whole, thanks to those institutions that had to achieve modern solidarity by overthrowing capitalist exploitation through democratic participation.
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