In several accounts of what models are and how they function a specific view dominates. This view contains the following characteristics. First, there is a clear-cut distinction between theories, models and data and secondly, empirical assessment takes place after the model is built. This view in which discovery and justification are disconnected is not in accordance with several practices of mathematical business-cycle model building. What these practices show is that models have to meet implicit criteria of adequacy, such as satisfying (...) theoretical, mathematical and statistical requirements, and be useful for policy. In order to be adequate, models have to integrate enough items to satisfy such criteria. These items include besides theoretical notions, policy views, mathematisations of the cycle and metaphors also empirical data and facts. So, the main thesis of this chapter is that the context of discovery is the successful integration of those items that satisfy the criteria of adequacy. Because certain items are empirical data and facts, justification can be built-in. (shrink)

Since the February 2020 publication of the article ‘Flattening the curve’ in The Economist, political leaders worldwide have used this expression to legitimize the introduction of social distancing measures in fighting Covid-19. In fact, this expression represents a complex combination of three components: the shape of the epidemic curve, the social distancing measures and the reproduction number \. Each component has its own history, each with a different history of control. Presenting the control of the epidemic as flattening the curve (...) is in fact flattening the underlying natural-social complexity. The curve that needs to be flattened is presented as a bell-shaped curve, implicitly suggesting that the pathogen’s spread is subject only to natural laws. The \ value, however, is, fundamentally, a metric of how a pathogen behaves within a social context, namely its numerical value is affected by sociopolitical influences. The jagged and erratic empirical curve of Covid-19 illustrates this. Although the virus has most likely infected only a small portion of the total susceptible population, it is clear its shape has changed drastically. This changing shape is largely due to sociopolitical factors. These include shifting formal laws and policies, shifting individual behaviors as well as shifting various other social norms and practices. This makes the course of Covid-19 curve both erratic and unpredictable. (shrink)

In this chapter, we discuss a specific kind of progress in economics, namely, progress that is pushed by the repeated use of mathematical models in most sub-branches of economics today. We adopt a functional account of progress to argue that progress in economics occurs via the use of what we call ‘common recipes’ and the use of model templates to define and solve problems of relevance for economists. We support our argument by discussing the case of twentieth-century business cycle research. (...) By presenting this case study in detail, we show how model templates are not only re-applied to different phenomena. We also show how scientists come up with them in the first place and how – once they are considered less useful – they are replaced with new ones. Finally, our case also illustrates that it is not only the mathematical structure that is re-used but that such a re-use also requires a shared conceptual vision of core properties of the phenomenon. If that vision is not shared anymore among economists, a model template can become useless and has to be replaced – sometimes through overcoming resistance – with a different one. (shrink)

The theory of opposition has always been viewed as the founding principle of structuralism within contemporary linguistics and semiotics. As an analytical technique, it has remained a staple within these disciplines, where it continues to be used as a means for identifying meaningful cues in the physical form ofsigns. However, as a theory of conceptual structure it was largely abandoned under the weight of post-structuralism starting in the 1960s — the exception tothis counter trend being the work of the Tartu (...) School of semiotics. This essay revisits opposition theory not only as a viable theory for understanding conceptual structure, but also as a powerful technique for establishing the interconnectedness of language, culture, and cognition. (shrink)

In the social sciences we hardly can create laboratory conditions, we only can try to find out which kinds of experiments Nature has carried out. Knowledge about Nature's designs can be used to infer conditions for reliable predictions. This problem was explicitly dealt with in Haavelmo's (1944) discussion of autonomous relationships, Friedman's (1953) as-if methodology, and Simon's (1961) discussions of nearly-decomposable systems. All three accounts take Marshallian partitioning as starting point, however not with a sharp ceteris paribus razor but with (...) the blunt knife of negligibility assumptions. As will be shown, in each account reflection on which influences are negligible, for what phenomena and for how long, played a central role. (shrink)

Templates travel because they offer a tractable format that can be used for model-building in a variety of domains. It is often because of this quality that a particular template is chosen. But one cannot assume that there are always templates ready to model a new phenomenon, and moreover, templates have also been designed at some point. A critical aspect of this designing process is the choice of the mathematical objects with which one hopes to capture this phenomenon. This means (...) that one has to assess which of the properties of different kinds of mathematical objects and which combinations of them are most appropriate. The selection of these objects is based on whether their properties enable the model to perform its function. This selection of mathematical objects is similar to the selection of materials in mechanical design. (shrink)

Glenn Harrison [Journal of Economic Methodology, 2013, 20, 103–117] discusses four related forms of methodological intolerance with respect to field experiments: field experiments should rely on some form of randomization, should be disconnected from theory, the concept of causality should only be defined in terms of observables, and the role of laboratory experiments is dismissed. As is often the case, the cause of intolerance is ignorance, as it is here. To acquire knowledge about potential influences, which we need for both (...) the evaluation of internal and external validity of experimental results, we cannot do without theory. A purely empiricist methodology will be unable to give us sufficient understanding of the validity of these results. An account of causality only based on directly observed things, is an account based on factual influences only. This account will be too restricted, because it will not deal with the unobserved potential influences, which we need – again – for the evaluat... (shrink)

Templates travel because they offer a tractable format that can be used for model-building in a variety of domains. It is often because of this quality that a particular template is chosen. But one cannot assume that there are always templates ready to model a new phenomenon, and moreover, templates have also been designed at some point. A critical aspect of this designing process is the choice of the mathematical objects with which one hopes to capture this phenomenon. This means (...) that one has to assess which of the properties of different kinds of mathematical objects and which combinations of them are most appropriate. The selection of these objects is based on whether their properties enable the model to perform its function. This selection of mathematical objects is similar to the selection of materials in mechanical design. (shrink)

The Representational Theory of Measurement conceives measurement as establishing homomorphisms from empirical relational structures into numerical relation structures, called models. There are two different approaches to deal with the justification of a model: an axiomatic and an empirical approach. The axiomatic approach verifies whether a given relational structure satisfies certain axioms to secure homomorphic mapping. The empirical approach conceives models to function as measuring instruments by transferring observations of a phenomenon under investigation into quantitative facts about that phenomenon. These facts (...) are evaluated by their accuracy and precision. Precision is generally achieved by least squares methods and accuracy by calibration. For calibration standards are needed. Then two polar strategies can be distinguished: white-box modeling and black-box modeling. The first strategy of modeling aims at estimating the invariant equations of the phenomenon, thereby fulfilling Hertz’s correctness requirement. The latter strategy of modeling is to use known stable facts about the phenomenon to adjust the model parameters, thereby fulfilling Hertz’s appropriateness requirement. For this latter strategy, the requirement of models as homomorphic mappings has been dropped. Where one will find the axiomatic approach more often used for measurement in the laboratory, the empirical approach is more appropriate for measurement outside the laboratory. The reason for this is that for measurement of phenomena outside the laboratory, one also needs to take account of the environment to achieve accurate results. Environments are generally too relation-rich for an axiomatic approach, which are only applicable for relation-poor systems. The white-box modeling strategy, reflecting the complexity of the environment due to its correctness requirement, will, however, lead to immensely large models. To avoid this problem, modular design is an appropriate strategy to reduce this complexity. Modular design is a grey-box modeling strategy. Grey-box models are assemblies of modules; these are black boxes with standard interface. It should be noted that the structure of the assemblage need not be homomorphic to the relations describing the interaction between phenomenon and environment. These three modeling strategies map out the possible designs for computer simulations as measuring instruments. Whether a simulation is based on a white-box, grey-box or black-box model is only determined by the relationship between the phenomenon and its environment and not by e.g. its materiality or physicality. (shrink)

Generally, rational decision-making is conceived as arriving at a decision by a correct application of the rules of logic and statistics. If not, the conclusions are called biased. After an impressive series of experiments and tests carried out in the last few decades, the view arose that rationality is tough for all, skilled field experts not excluded. A new type of planner's counsellor is called for: the normative statistician, the expert in reasoning with uncertainty par excellence. To unravel this view, (...) the paper explores a specific practice of clinical decision-making, namely Evidence-Based Medicine. This practice is chosen, because it is very explicit about how to rationalize practice. The paper shows that whether a decision-making process is rational cannot be assessed without taking into account the environment in which the decisions have to be taken. To be more specific, the decision to call for new evidence should be rational too. This decision and the way in which this evidence is obtained are crucial to validate the base rates. Rationality should be model-based, which means that not only the isolated decision-making process should take a Bayesian updating process as its norm, but should also model the acquisition of evidence (priors and tests results) as a rational process. (shrink)

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality.

This paper presents the notion that verbal discourse is structured, in form and contents, by metaphorical reasoning. It discusses the concept of “metaphorical network” as a framework for relating the parts of a speech act to each other, since such an act seems to cohere into a meaningful text on the basis of “domains” that deliver common concepts. The basic finding of several research projects on this concept suggest that source domains allow speakers to derive sense from a verbal interaction (...) because they interconnect the topic of discussion to culturally-meaningful images and ideas. This suggests, in turn, that language is intertwined with nonverbal systems of meaning, reflecting them in the contents of verbal messages. Overall, the concept of metaphorical networks implies that human cognition is highly associative in structure. (shrink)

El modelo viquiano propuesto en este trabajo tiene hoy día implicaciones concretas para la lingüística y las ciencias cognitivas. A nuestro parecer, hoy las investigaciones en estos campos no hacen otra cosa que verificar la existencia de un vínculo gnoseológico entre sentido, concepto y metáfora que Vico exponía en la Scienza nuova. Vico demostró, ante todo, que la lógica poética constituye la facultad preliminar que permite el comportamiento simbólico humano. Dicha noción falta del todo en las actuales investigaciones sobre la (...) metáfora; y falta claramente la noción de Homo Poeticus en todas las visiones hasta ahora expuestas en lingüística. La concepción viquiana de la lógica poética permitirá a estas ciencias trazar el recorrido científico que deberán seguir en el futuro.Recent researches in linguistics and cognitive sciences may be brought as to show that there exist a empistemological bound between sense, concept and metaphor which Vico already acknowledged in his Scienza nuova. While Vico clearly showed that poetical logic helps to developing the human symbolic behavior; the concept of Homo poeticus is lacking in recent scholar contributions on issues related with metaphors and linguistics. It is assumed that the Vichian conception on poetical logic may improve a better understanding of the problems with which those sciences have hitherto been concerned. (shrink)

Listening -- Discourse -- Interaction -- Affect -- Voice -- Engagement.

" Si, après Auschwitz, croire en un Dieu-raison n'est plus possible, reste, d'un côté, la foi simple - la foi qui n'est qu'un cri -, de l'autre la raison, pure de religion. Philosopher comme avant, on ne le peut, mais seulement mieux qu'avant - ou pas du tout. Refermée, pour la philosophie, la parenthèse judéo-chrétienne ; fini le temps des castors - des Descartes, Kant, Hegel, des bâtisseurs de digues pour dompter le flot de la Libre Pensée issu de la (...) source grecque. L'heure est aux philosophies du refus. Refus de toute logicisation philosophico-théologique du monde, où le mal absolu n'est plus qu'un détail. De là une vision a-théiste et a-cosmique du monde, une vision déréalisante du " réel ", mais aussi, devant la vie, l'appel à un nouveau courage. Car, dans la défaite des absolus sécurisants, reste, comme corrélat du mal absolu, l'absolu de la mort et du Temps. " M. C. (shrink)

We characterize the notion of validity relatively to models, for comprehension axioms, containing gluts.

Word problems in mathematics seem to constantly pose learning difficulties for all kinds of students. Recent work in math education (for example, [Lakoff, G. & Nuñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books]) suggests that the difficulties stem from an inability on the part of students to decipher the metaphorical properties of the language in which such problems are cast. A 2003 pilot study [Danesi, M. (2003a). Semiotica, 145, (...) 71–83] confirmed this hypothesis in an anecdotal way. This paper reviews the implications of that study and of a follow-up one that is described here as well, in the light of how the metaphorical analysis of word problems allows learners to overcome typical difficulties in word problem-solving by teaching them how to flesh out the underlying concepts and convert them into appropriate representations. (shrink)

Enigmatología es el término que ha sido usado para designar el estudio de los puzzles en la cultura humana. La estructura poética de los puzzles implica que quien intenta resolverlos debe literalmente imaginar escenarios que trasciendan un razonamiento lineal. En tiempo de Vico, el cartesianismo dominaba la escena académica de la época, haciendo que la vieja tradición, centrada en el estudio de la lengua y la literatura perdiera terreno frente a un énfasis puesto en la matemática, la filosofía crítica y (...) las ciencias. Los puzzles eran considerados como productos de un pensamiento lógico-racional. Pocos los consideraron como productos de una fuerza creativa más fundamental. El concepto de fantasia de Vico vino a proporcionar una poderosa estructura explicativa para comprender cualquier ingenio enigmatológico.Enigmatology is the term that has been used to designate the study of puzzles in human cultures. The poetic structure of puzzles implies that they require the solver to literally imagine scenarios in ways that transcend linear reasoning. In Vico's times, Cartesianism dominated the academic scene of the day, causing the older tradition, centered on the study of language and literature, to lose ground to an emphasis on mathematics, critical philosophy, and the sciences. Puzzles were viewed as products of rational-logical thinking. Few saw them as products of a more fundamental creative force. Vico's concept of fantasia came forward to provide a powerful explanatory framework for understanding enigmatological artifacts. (shrink)

This study looks at the relation between mathematical discovery and semiosis, focusing on the famous Fibonacci sequence. The serendipitous discovery of this sequence as the answer to a puzzle designed by Italian mathematician Leonardo Fibonacci to illustrate the efficiency of the decimal number system is one of those episodes in human history which show how serendipity, semiosis, and discovery are intertwined. As such, the sequence has significant implications for the study of creative semiosis, since it suggests that symbols are hardly (...) arbitrary products of human reason, but rather unconscious probes of reality. (shrink)

This study looks at the relation between mathematical discovery and semiosis, focusing on the famous Fibonacci sequence. The serendipitous discovery of this sequence as the answer to a puzzle designed by Italian mathematician Leonardo Fibonacci to illustrate the efficiency of the decimal number system is one of those episodes in human history which show how serendipity, semiosis, and discovery are intertwined. As such, the sequence has significant implications for the study of creative semiosis, since it suggests that symbols are hardly (...) arbitrary products of human reason, but rather unconscious probes of reality. (shrink)