Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...) by confronting these logical and philosophical analyses with the field of cognitive science. Surprisingly, central aspects of the philosophical and logical analyses resonate in very natural ways with research topics in mathematical cognition, spatial cognition and the psychology of reasoning. The paper develops these connections, concentrating on four issues: (1) the cognitive origins of Euclidean diagrammatic reasoning, (2) the cognitive representations of spatial relations in Euclidean diagrams, (3) the nature of the cognitive processes and cognitive representations involved in Euclidean diagrammatic reasoning seen as a form of visuospatial relational reasoning and (4) the complexity of Euclidean diagrammatic reasoning for the human cognitive system. For each of these issues, our analysis generates concrete experiment proposals, opening thereby the way for further empirical investigations. The paper is thus a prolegomenon to a research program on Euclidean diagrammatic reasoning at the crossroads of logic, philosophy and cognitive science. (shrink)

Three studies examined the effect of primed psychological distance on level of perceptual construal, using Navon’s paradigm of composite letters (global letters that are made of local letters). Relative to a control group, thinking of the more distant future (Study 1), about more distant spatial locations (Study 2), and about more distant social relations (Study 3) facilitated perception of global letters relative to local letters. Proximal times, spatial locations, and social relations had the opposite effect. The results are discussed within (...) the framework of Construal Level Theory of psychological distance (Liberman & Trope, 2008; Trope & Liberman, 2003). (shrink)

Philosophers of information, according to Luciano Floridi (The philosophy of information. Oxford University Press, Oxford, 2010, p 32), study how information should be “adequately created, processed, managed, and used.” A small number of epistemologists have employed the concept of information as a cornerstone of their theoretical framework. How this concept can be used to make sense of seemingly intractable epistemological problems, however, has not been widely explored. This paper examines Fred Dretske’s information-based epistemology, in particular his response to radical epistemological (...) skepticism. We discuss the relationship between information, evidence and knowledge in relation to the problem of skepticism and the options available to an information-based epistemology for dealing with it. (shrink)

We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an (...) inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object‐wise, could underlie diagram‐based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions. (shrink)

La discusión sobre el psicologismo lógico, que parecía ya superada desde Frege-Husserl, ha vuelto a posicionarse hoy en la filosofía de la lógica. Se examina, en primer lugar, la idea según la cual lo que hoy se entiende por lógica respondería en lo esencial a las tesis defendidas por el anti-psicologismo. En segundo término, se plantea que algunos enfoques actuales en ciencia cognitiva, como el de la facultad cognitiva proto-lógica de R.Hanna, y el de los dominios cognitivos, de Stennings y (...) van Lambalgen, permiten apoyar la idea de que la naturaleza de la lógica va más allá de los atributos antipsicologistas. (shrink)

This article discusses the epistemology of design as a process, arguing specifically that sketching and drawing are essential modes of thinking and reasoning. It demonstrates that the commonly accepted notion of a spontaneous and intuitive vision in the mind’s eye—encapsulated in the cliché of the napkin sketch—obscures the exploratory inferences that are made while scribbling with a pencil on a sheet of paper. The draughtsperson, along with their work tools, modes of notation, specific techniques, and epistemic strategies as well as (...) the resulting design artefacts form milieus of reflection that facilitate complex processes of exploration. Case studies, including the genesis of the Mini by Alec Issigonis, samples of work by Alvar Aalto, and a reinterpretation of student sketches from a classical design study by Gabriela Goldschmidt, serve to illustrate how drawing inferences with pencil and paper occurs. (shrink)

Philosophers have recently paid more attention to the physical aspects of scientific models. The attention is motivated by the prospect that a model’s physical features strongly affect its use and that this suggests re-thinking modelling in terms of extended or distributed cognition. This paper investigates two ways in which physical features of scientific models affect their use and it asks whether modelling is an instance of extended cognition. I approach these topics with a historical case study, in which scientists kept (...) records not only of their findings, but also of some the mental operations that generated the findings. The case study shows how scientists can employ a physical model as an external information store, which allows alternating between mental manipulations, recording the outcome externally, and then feeding the outcome back into subsequent mental manipulations. The case study also demonstrates that a models’ physical nature allows replacing explicit reasoning with visuospatial manipulations. I argue, furthermore, that physical modelling does not need to exemplify a strong kind of extended cognition, the sort for which external features are mereological parts of cognition. It can exemplify a weaker kind, instead. (shrink)