Weber and Coyote : polytheism as a practical attitude

This document is the Accepted Manuscript of an article accepted for publication in Sophia: International Journal of Philosophy and Traditions. Under embargo until 9 September 2018. The final, definitive version is available online at: https://link.springer.com/article/10.1007%2Fs11841-018-0641-1Hyde claims that the trickster spirit is necessary for the renewal of culture, and that he only lives in the ‘complex terrain of polytheism’. Fortunately for those of us in monotheistic cultures, Weber gives reasons for thinking that polytheism is making a return, albeit in a new, disenchanted form. The plan of this paper is to elaborate some basic notions from Weber (rationalisation, disenchantment, bureaucracy), to explore Hyde’s thesis in more detail and then to take up the question of the plurality of spirits both around and within us and whether the trickster is one of them. Weber has three roles in this argument. First, he theorises rationalisation, disenchantment and bureaucracy; second, he offers an argument that in a certain sense polytheism is returning (if it ever went away); and third, he presents a way to translate the mytho-poetic register in which Hyde works into terms acceptable to social science of a more materialist bent. The claim of the paper is that polytheism as a practical attitude means recognising that there are diverse and contradictory ethical orders built into the world around us and active with our psyches. Weber explains why this is especially difficult for us (because our lives are so thoroughly rationalised), and Hyde offers us the hope that we may be tricky enough to cope.Peer reviewe

Frankfurt counter-example defused

"This is a pre-copy-editing, author produced PDF of an article accepted for publication in Analysis following peer review. The definitive publisher-authenticated version Larvor, B. (2010) 'Frankfurt counter-example defused.' Analysis 70 (3) pp.506-508 is available online at: http://analysis.oxfordjournals.org/" Copyright the authorFrankfurt’s 1969 paper ‘Alternate possibilities and moral responsibility’ purports to refute the principle that a person is morally responsible for what he has done only if he could have done otherwise. It offers a case in which, Frankfurt claims, the agent is morally responsible even though he could not have done otherwise.Peer reviewedFinal Accepted Versio

Why the naïve Derivation Recipe model cannot explain how mathematicians’ proofs secure mathematical knowledge

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Philosophia Mathematica following peer review. Under embargo. Embargo end date: 7 July 2018 The version of record [Lavor, B., 'Why the Naive Derivation Recipe Model Cannot Explain How Mathematician's Proofs Secure Mathematical Knowledge', Philosophia Mathematica (2016) 24(3): 401-404, is available online at: https://doi.org/10.1093/philmat/nkw012. © The Author [2016]. Published by Oxford University Press. All rights reserved.The view that a mathematical proof is a sketch of or recipe for a formal derivation requires the proof to function as an argument that there is a suitable derivation. This is a mathematical conclusion, and to avoid a regress we require some other account of how the proof can establish it.Peer reviewedFinal Accepted Versio

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

The Concept of Culture in Critical Mathematics Education

© Springer International Publishing AG, part of Springer Nature 2018. This is a post-peer-review, pre-copyedit version of a chapter published in The Philosophy of Mathematics Education Today. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-77760-3A well-known critique in the research literature of critical mathematics education suggests that framing educational questions in cultural terms can encourage ethnic-cultural essentialism, obscure conflicts within cultures and promote an ethnographic or anthropological stance towards learners. Nevertheless, we believe that some of the obstacles to learning mathematics are cultural. ‘Stereotype threat’, for example, has a basis in culture. Consequently, the aims of critical mathematics education cannot be seriously pursued without including a cultural approach in educational research. We argue that an adequate conception of culture is available and should include normative/descriptive and material/ideal dyads as dialectical moments