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  1. added 2014-12-10
    Judith V. Grabiner (2014). The Role of Mathematics in Liberal Arts Education. In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. 793-836.
    The history of the continuous inclusion of mathematics in liberal education in the West, from ancient times through the modern period, is sketched in the first two sections of this chapter. Next, the heart of this essay (Sects. 3, 4, 5, 6, and 7) delineates the central role mathematics has played throughout the history of Western civilization: not just a tool for science and technology, mathematics continually illuminates, interacts with, and sometimes challenges fields like art, music, literature, and philosophy – (...)
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  2. added 2014-12-08
    Eva-Maria Engelen, Christian Fleischhack, C. Giovanni Galizia & Katharina Landfester (eds.) (2010). Heureka: Evidenzkriterien in den Wissenschaften. Ein Kompendium für den interdisziplinären Gerauch. Spektrum Springer.
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  3. added 2014-10-16
    David Ellerman, Four Ways From Universal to Particular: How Chomsky's Language-Acquisition Faculty is Not Selectionist.
    Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...)
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  4. added 2014-10-16
    David Ellerman, Partitions and Objective Indefiniteness.
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
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  5. added 2014-10-16
    David Ellerman (2014). An Introduction to Partition Logic. Logic Journal of the Igpl 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...)
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