The concept of proof can be studied from many different perspectives. Many types of proofs have been developed throughout history such as apodictic, dialectical, formal, constructive and non-constructive proofs, proofs by visualisation, assumption-based proofs, computer-generated proofs, etc. In this paper, we develop Goguen’s general concept of proof-events and the methodology of algebraic semiotics, in order to define the concept of mathematical style, which characterizes the proofs produced by different cultures, schools or scholars. In our view, style can be defined as (...) a semiotic meta-code that depends on the underlying mode of signification (semiosis), the selected code and the underlying semiotic space and determines the individual mode of integration (selection, combination, blending) into a narrative structure (proof). Finally, we examine certain historical types of styles of mathematical proofs, to elucidate our viewpoint. (shrink)

Science teaching always engages a philosophy of science. This article introduces a modern philosophy of science and indicates its implications for science education. The hermeneutic philosophy of science is the tradition of Kant, Heidegger, and Heelan. Essential to this tradition are two concepts of truth, truth as correspondence and truth as disclosure. It is these concepts that enable access to science in and of itself. Modern science forces aspects of reality to reveal themselves to human beings in events of disclosure. (...) The achievement of each event of disclosure requires the precise manipulation of equipment, which is an activity that depends on truth as correspondence. The implications of the hermeneutic philosophy of science for science education are profound. The article refers to Newton’s early work on optics to explore what the theory implies for teaching. Modern science—as the event of truth—is a relationship between an individual student, equipment, and reality. Science teachers provide for their students’ access to truth and they may show how their discipline holds a special relationship to reality. If the aim of science teaching is to enable students to disclose reality, the science curriculum will challenge some of the current practices of schooling. If teachers base science teaching upon the hermeneutic philosophy of science, science will assert itself as the intellectual discipline that derives from nature, and not from the inclinations of human beings. Science teachers teach nature’s own science. (shrink)

Meaning is a central concept of (bio)semiotics. At the same time, it is also a word of everyday language. Here, on the example of the world information, we discuss the “reduction-inflation model” of evolution of a common word into a scientific concept, to return subsequently into everyday circulation with new connotations. Such may be, in the near future, also the fate of the word meaning if, flexed through objectified semantics, will become considered an objective concept usable in semiotics. We argue (...) that reducing meaning to a technical term essentially synonymous to code and stripped of most of the original semantic field is not a necessary prerequisite for a meaningful application of the concept in semiotics and in biology. (shrink)

The point of this paper is to provide a principled framework for a naturalistic, interactivist-constructivist model of rational capacity and a sketch of the model itself, indicating its merits. Being naturalistic, it takes its orientation from scientific understanding. In particular, it adopts the developing interactivist-constructivist understanding of the functional capacities of biological organisms as a useful naturalistic platform for constructing such higher order capacities as reason and cognition. Further, both the framework and model are marked by the finitude and fallibility (...) that science attributes to organisms, with their radical consequences, and also by the individual and collective capacities to improve their performances that learning organisms display. Part A prepares the ground for the exposition through a critique of the dominant Western analytic tradition in rationalising science, followed by a brief exposition of the naturalist framework that will be employed to frame the construction. This results in two sets of guidelines for constructing an alternative. Part B provides the new conception of reason as a rich complex of processes of improvement against epistemic values, and argues its merits. It closes with an account of normativity and our similarly developing rational knowledge of it, including (reflexively) of reason itself. (shrink)

Two hundred years ago, Friedrich Schleiermacher took critical issue with Immanuel Kant's intellectual notion of intuition as applied to human nature (Wellmon 2006). He found it necessary to modify—"hermeneutically," as he said—Kant's notion of anthropology by enabling it to include as human the new and strange human tribes Captain Cook found in the Pacific South Seas. A similar hermeneutic move is necessary if physics is to include the local contextual empirical syntheses of relativity and quantum physics. In this hermeneutical revision (...) the synthesis is formed around the notion of a Hilbert Vector Space as the universal grammar of physics, adding to it the dynamic of the Schrödinger equation, and representing empirical "observables" by projection operators that map the subspaces of definite measurable values. Among the set of observable projection operators, some pairs share the same subspace, commute with one another, and share a common laboratory setting. Other pairs do not share this property and are described as being mutually complementary. Complementary symmetries introduce into the discursive language of physics the commonsense notion of contextuality. The new synthesis, proposed by Eugene Wigner, John von Neumann, and (in his own way) Paul Dirac, brought physics into the community of common language and established it as a work of general human achievement. 1. (shrink)

This paper describes Heidegger as a robust scientific realist, explains why his view has received such conflicting treatment, and concludes that the special significance of his position lies in his insistence upon linking the discussion of science to the question of its relation with technology. It shows that Heidegger, rather than accepting the usual forced option between realism and antirealism, advocates a realism in which he embeds the antirealist thesis that the idea of reality independent of human understanding is unintelligible. (...) This reading is defended against Rorty's antirealist interpretation, as well as Dreyfus' depiction of him as a deflationary realist, and his assessment of background realism is contrasted with Fine's. Further, the robustness of Heidegger's realism is laid out across several texts from 1912 to 1976, in order to show that he is neither an instrumental realist nor an internal realist. Finally, the point is made that the development of his view concerning realism gives rise to a critique of objectivity that is now being similarly advocated by numerous thinkers from a variety of disciplines, and that this critique is inevitably ethical and political. (shrink)

In this paper, I consider the relevance of the view of cognitive existentialism to a multi-gendered picture of science education. I am opposing both the search for a particular feminist standpoint epistemology and the reduction of philosophy of science to cultural studies of scientific practices as championed by supporters of postmodern political feminism. In drawing on the theory of gender plurality and the conception of dynamic objectivity, the paper suggests a way of treating the nexus between the construction of gender (...) within the interrelatedness of scientific practices and the constitution of particular objects of inquiry. At stake is the notion of characteristic hermeneutic situation which proves to be helpful in designing a multi-gendered pedagogy as well. (shrink)

This paper discusses a version of the hermeneutic philosophy of science. Special focus is placed on the ways of reading theoretical objects in scientific inquiry. In implementing readable technologies, this reading succeeds in contextually visualizing the theoretical objects by means of various sorts of signs. A configuration of readable technology accomplishes a further step. The configuration textualizes the contextually produced signs. Textualizing the reading of theoretical objects interlaces the meaningful articulation and objectification of scientific domains. The horizon of possibilities for (...) textualizing is constantly shifting in the process of normal-scientific inquiry, and the shifting horizon plays the role of a hermeneutic fore-structuring of the outcomes of textualizing. The paper explores the importance of “material hermeneutics” for the contextual reading of theoretical objects. The conclusion is drawn that the hermeneutic study of the entanglement of technological artifacts with the outcomes from reading-as-textualizing requires the introduction of ontic-ontological difference. (shrink)

Patrick Heelan, with background in quantum theory and in hermeneutic phenomenology, investigated not only the hermeneutical philosophy of science but also the parallels between quantum mechanics and human experience in general and the logic of changes of worldview. Heelan’s closeness to Aristotle and Lonergan, often neglected, is discussed, and issues concerning Heelan’s treatment of the social context of science are raised.

This essay raises the question of material hermeneutics in Heelan’s philosophy of techno-science. For Heelan, a continental philosophy of technoscience, referring to Husserl and Heidegger and especially to Merleau-Ponty, features hermeneutic contexts of mathematics and measurement as well as laboratory observation, including what the later Heelan spoke of as “portable laboratories,” for the sake of objectivity and “meaning making.” For Paul Feyerabend, this material practice corresponded to the use of both techniques of observation and instrumentation, and not less “propaganda” in (...) the case of Galileo which practice for Heelan included the ontological status of measures and numbers as well as apprenticeship in what Heelan called “contingent local practical cultural milieus.” The essay includes a discussion of Heidegger on mathematics and Bruno Latour on pasteurization. (shrink)

This essay raises the question of material hermeneutics in Heelan’s philosophy of techno-science. For Heelan, a continental philosophy of technoscience, referring to Husserl and Heidegger and especially to Merleau-Ponty, features hermeneutic contexts of mathematics and measurement as well as laboratory observation, including what the later Heelan spoke of as “portable laboratories,” for the sake of objectivity and “meaning making.” For Paul Feyerabend, this material practice corresponded to the use of both techniques of observation and instrumentation, and not less “propaganda” in (...) the case of Galileo which practice for Heelan included the ontological status of measures and numbers as well as apprenticeship in what Heelan called “contingent local practical cultural milieus.” The essay includes a discussion of Heidegger on mathematics and Bruno Latour on pasteurization. (shrink)