Some viewpoints on the foundations of mathematics and its philosophy are more connected to scientific practice and its heuristics, mainly with the construction of physical theories and the search for the best explanations of physical phenomena by means of abduction or the solution of problems by the analytical method. Some researchers have introduced the importance of human cultural activities into the cognitive aspects of the mental processes of scientists, proposing an embodied approach in the bridge between mathematics and reality. Fluid (...) mechanics is an interesting area in this sense due to its position if the network of mathematics. By means of an historical example on vortex motion by Helmholtz, we show that the intuitive idea of eddy contains cognitive properties of a mental schema and that it gives many heuristic options for an embodied mathematical explanation about vortex dynamics. (shrink)

Detectives and scientists are in the business of reasoning from observations to explanations. This they often do by raising cunning questionsduring their inquiries. But to substantiate this claim we need to know how questions arise and how they are nurtured into more specific hypotheses. I shall discuss what the problem is, and then introduce the so-called interrogative model of inquiry which makes use of an explicit logic of questions. On this view, a discovery processes can be represented as a model-based (...) game in which an inquirer subjects a source of information to a series of strategically organized questions. Strategic principles and why-questions are especially important in heuristical reasoning. Why-questions have their own peculiar nature among questions. They indicate that the inquirer's expectations are somehow disappointed, and that is cognitively challenging. In a finished argument why-questions can be omitted, but in the search for more specific questions they are highly important. As a detetective example I shall analyze Sherlock Holmes reasoning in Silver Blace, the scientific one is A.R. Wallace's discovery of the principle of natural selection. In both of these examples the meaning of questions, especially of well-chosen why-questions, of strategic principles, and of highly structured background knowledge come to the fore. Good questions frequent those who have orderly expectations, based on experience and expertise (detectives!) or highly structured background theories (scientists!). (shrink)

There are various ``classical'' arguments against abduction as a logic of discovery,especially that (1) abduction is too weak a mode of inference to be of any use, and (2) in basic formulation of abduction the hypothesisis already presupposed to be known, so it is not the way hypotheses are discovered in the first place. In this paper I argue, by bringing forth the idea of strategies,that these counter-arguments are weaker than may appear. The concept of strategies suggests, inter alia, that (...) many inferential moves are taken into account at the same time. This is especially important in abductive reasoning, which is basically a very weak mode of inference. The importance of strategic thinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abduction although they did not use the concept of``strategies.'' On the whole, I am arguing that the focus should be more on methodological processes, and not only on validity considerations, which have dominated the discussion about abduction. (shrink)

We begin by highlighting some points related to Kuhn’s later thoughts on the incommensurability thesis and then show to what extent the standard version of the thesis given by the structuralist metatheory allows us to capture Kuhn’s ideas. Our main aim is to establish what constitutes the basis of comparability between incommensurable theories, even in cases of incommensurability with respect to theoretical and non-theoretical terms. We propose that comparability between incommensurable theories requires some connection between their respective ontologies that can (...) be captured by means of an ontological non-reductive relation. At this point, the structuralist notion of “echeloned partial substructure” may be of help. When the incommensurability is very drastic, the existence of ontological connections between the theories involved may only be evident by common terms of their non-characteristic vocabularies. So, this notion of non-characteristic vocabulary becomes relevant in our proposal. (shrink)

This paper is about structuralism as a form of reconstructing theories, associated with the work Sneed, Balzar and Moulines among others, and not about "structuralism" is any of its other manifold senses. The paper is a reflection in that it looks back on some earlier work of my own on the subject of structuralism and explanation, in which I argued that structuralism and my 'instance view' of explanation go well together, with structuralism providing the means to develop the idea of (...) a theoretical instance. Bartelborth has suggested a view that has some similarity with my early ideas, so I reflect on those as well. I suggest, in opposition to both positions, that a causal account of explanation might also sit well with structuralism. This paper will appear in a special edition of Synthese edited by Moulines and devoted to structuralism themes. (shrink)