The work done so far on the understanding of mathematical (proof) texts focuses mostly on logical and heuristical aspects; a proof text is considered to be understood when the reader is able to justify inferential steps occurring in it, to defend it against objections, to give an account of the “main ideas”, to transfer the proof idea to other contexts etc. (see, e.g., Avigad in The philosophy of mathematical practice, Oxford University Press, Oxford, 2008). In contrast, there is a rich (...) philosophical tradition dealing with the concept of understanding and interpreting texts, namely philosophical hermeneutics, represented, e.g., by Schleiermacher, Dilthey, Heidegger or Gadamer. In this tradition, “understanding” generally refers to the integration in a comprehensive (historical, existential, life-worldly,...) context. In this article, we take some first steps towards exploring the question how the ideas from philosophical hermeneutics presented in Gadamer’s “Truth and Method” apply to mathematical texts and what (if anything) can be learned from these for the didactics and presentation of mathematics. (shrink)

Dreyfus's model of expert skill acquisition is philosophically important because it shifts the focus on expertise away from its social and technical externalization in STS, and its relegation to the historical and psychological context of discovery in the classical philosophy of science, to universal structures of embodied cognition and affect. In doing so he explains why experts are not best described as ideologues and why their authority is not exclusively based on social networking. Moreover, by phenomenologically analyzing expertise from a (...) first person perspective, he reveals the limitations of, and sometimes superficial treatment that comes from, investigating expertise from a third person perspective. Thus, he shows that expertise is a prime example of a subject that is essential to science but can only be fully elaborated with the aid of phenomenological tools. However, both Dreyfus's descriptive model and his normative claims are flawed due to the lack of hermeneutical sensitivity. He assumes an expert's knowledge has crystallized out of contextual sensitivity plus experience, and that an expert has shed, during the training process, whatever prejudices, ideologies, hidden agendas, or other forms of cultural embeddedness, that person might have begun with. One would never imagine, from Dreyfus's account, that society could possibly be endangered by experts, only how society's expectations and actions could endanger experts. The stories of actual controversies not only shows things do not work the way Dreyfus claims, but also that it would be less salutary if they did. Such stories amount to counterexamples to Dreyfus's normative claims, and point to serious shortcomings in his arguments. (shrink)

Philosophical hermeneutics claims that human understanding, while being contingent and historical, is likewise universal and bears within itself some pervasive features detectable via hermeneutical analyses of historically imparted tradition and language. Similarly, hermeneutical philosophy of science is confident that hermeneutical methods are the only proper tool to adequately assess, reconstruct, explain or give a meaning to historical but universal scientific knowledge and its various forms. I point out two versions of hermeneutical philosophy of science and argue that whenever philosophical hermeneutics (...) pursues rescuing "scientificity", human rationality, human rights, common values, and so forth under the pretence of its universality and competence, it necessarily transcends and violates the tenets of its own. I conclude in the favour of moderate interpretation of practical hermeneutics, perhaps in the very essence of it rest postmodern concepts of historicality, transparency and tolerance, without which there is no possibility of extricating oneself from hermeneuticism. (shrink)