Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Homology of Distributive Lattices

We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semi-lattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law.Comment: 30 pages, 3 tables, 3 figure

Come back Marshall, all is forgiven? : Complexity, evolution, mathematics and Marshallian exceptionalism

Marshall was the great synthesiser of neoclassical economics. Yet with his qualified assumption of self-interest, his emphasis on variation in economic evolution and his cautious attitude to the use of mathematics, Marshall differs fundamentally from other leading neoclassical contemporaries. Metaphors inspire more specific analogies and ontological assumptions, and Marshall used the guiding metaphor of Spencerian evolution. But unfortunately, the further development of a Marshallian evolutionary approach was undermined in part by theoretical problems within Spencer's theory. Yet some things can be salvaged from the Marshallian evolutionary vision. They may even be placed in a more viable Darwinian framework.Peer reviewedFinal Accepted Versio

An Evaluation Framework for Controlled Natural Languages

Abstract. This paper presents a general framework called ontographs that relies on a graphical notation and enables the tool-independent and reliable evaluation of human understandability of knowledge represen-tation languages. An experiment with 64 participants is presented that applies this framework and compares a controlled natural language to a common formal language. The results show that the controlled natural language is easier to understand, needs less learning time, and is more accepted by its users.

A dynamic and multifunctional account of middle‐range theories

This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.Peer reviewe

Questioning and organization studies

This essay identifies a cleavage in the organisation literature that separates ‘questions’ and ‘questioning’ at a very fundamental philosophical level. On the one hand, the objective notion of ‘questions’ has already been well addressed within organization studies, evident in how scholars have scrutinized questions as objects of analysis; for example, paying close attention to the forms and functions of questions as instruments of research. More recently, the linguistic turn within the social sciences has influenced how organization studies researchers have considered organizations as discursive entities, with debate extending to the discursive nature of ‘questions’. On the other hand, the process of ‘questioning’ remains under-researched. From one perspective, questioning the process of questioning is challenging, but, as we submit, this is precisely where American pragmatism can be helpful. As we explore in this essay, the forward-looking quality of pragmatist inquiry is what motors the process of questioning. Our pragmatist-inflected argument is that questioning does not have to always serve critique and position building in the organization studies field. Rather, questioning out of curiosity can build new dialogue and open up new methodological avenues. This may help change the habitual ways in which we explore ideas, problems and situations in organization studies as well as lead to more democratic forms of organizing. Crucially, in this essay we are not looking for ultimate ‘answers’; rather we hope to excite discussion about questioning by giving prominence to something that is so ubiquitous and taken-for-granted as to be invisible to many of us as an object of inquiry

What is information? Toward a theory of information as objective and veridical

Information systems are a strong and ever-growing discipline of enormous relevance to today’s informated world, and yet, as recent reviews have shown, there is still not an agreed and explicit conceptualization or definition of information. After an evaluative review of a range of theories of information, this paper develops and defends a particular theory, one that sees information as both objective and veridical. By objective, we mean that the information carried by signs and messages exists independently of its receivers or observers. The information carried by a sign exists even if the sign is not actually observed. By veridical, we mean that information must be true or correct in order to be information – information is truth-constituted. False information is not information, but misinformation or disinformation. The paper develops this theory and then discusses four contentious issues – information as objective rather than subjective; information as true or correct; information and knowledge; and information and the ambiguity of meaning. It concludes with a discussion of the practical implications of the theory