Call for Papers for the 11th International Whitehead Conference 2017 http://whitehead2017.com/ You are invited to the 11th IWC under the topic "Nature in Process. Novel Approaches to Science and Metaphysics" 25th-28th July 2017 at the University of the Azores and to submit an abstract for presentation in any of its 16 sections by 31 JANUARY 2017 or as soon as possible. Reproduced below are the details for Section 8 on Whitehead, Mathematics and Logic where Category Theory can assist with his 'loose ends'. Current Category Theory is still founded on Whitehead's early Principia Mathematica (1912) that he soon repudiated in favour of the metaphysics of his Process & Reality (PR,1929). Today's real world problems of globalisation and higher order processes need an applicable Category Theory with a comparable shift from modelling 'up to the natural isomorphism' as in the Eilenberg-Mac Lane style of early Whitehead to the exactness of 'down from the natural isomorphism' in the metaphysics of the later Whitehead. Whitehead's search to represent our perceptions of nature as an extension of abstract space in logic was achieved only informally in his life time. Formally Alexandre Grothendieck picked up on Aristotle's metonym of the Topos for abstract space as a category but by satisfying Weil's conjectures (as appears from the Récoltes et Semailles) the Grothendieck topos was still confined to the limitations of Whitehead's early work. On the contrary the Topos in impredicative mathematics has neither the natural number object nor an initial object. For Whitehead rejects as beyond first order in abstract space the following constructs of the mind: . arithmetic (including zero and infinity) . Euclidean geometry . predication . ex absurdo reasoning . paradox (as error in antecedent reasoning) . 'vacuous actuality' (PR:xiii) Galileo's work took nearly a century to be integrated into mainstream science so we should perhaps not be too surprised with the same for Whitehead. This conference is an opportunity to contribute to these developments where they really matter -- in applicable Category Theory. ***************************************************************** 11th IWC 2017 section 8: Whitehead, Mathematics and Logic Head: Vesselin Petrov Abstract Until the end of his life Alfred North Whitehead maintained that symbolic logic was his first love. Logic dominated the mathematics of his early intellectual development at Cambridge. It was the driving force in his quest to understand process in nature and underpinned the novel approach to science and metaphysics in his subsequent influence on contemporary science and philosophy. Study of his logic and mathematics can therefore provide us with further understanding of his speculative metaphysics of nature. He would not as some sever logic from mathematics and much of his early work on mathematics was at its foundation level. Topics of interest include, but are not limited to: His initial work subsuming Grassmann's notion of logic and number into Universal Algebra and the study of axiomatics in projective and descriptive geometry with applications to the material world arising out of its own natural logic. The collaboration with Russell on the Principia Mathematica as the foundations of mainstream 20th Century mathematics, their influence on Kurt Gödel, the technical details behind why the fourth volume was abandoned and behind why they parted. Outstanding issues in Whitehead's writings particularly relating to the nature of space and time. Logical distinctions with the approaches of Kant, Poincaré, Bergson, Einstein, etc and comparison with alternative theories of extension and process. His identification of Desargues theorem as the logic behind three dimensional Euclidean space. Whitehead's theory of extension in Process and Reality as a transformation of mathematical ideas into metaphysical ones. The logic of parthood with part-whole and part-part relations as relevant today in mathematics applied to globalisation, theoretical computer science, artificial intelligence and studies in consciousness and evolutionary biology. Whitehead's informal descriptions in Process & Reality have helped spawn new subjects like mereology and contemporary mereotopology. The work of Whitehead's mature period has promoted advances on a wide front for postmodernism in the arts and humanities but these have yet to procreate postmodernism in mathematics or logic. Current topics in Whitehead's loose ends include a formal language for his cosmology of process and the clarification of his 'blind spot' for intuitionistic logic both of which are now possible to represent 'naturally' in the mathematics of Category Theory. Whitehead's last writings: Mathematics and the Good - a connection between modern mathematics and metaphysics is of importance in the philosophy of mathematics and is Whitehead's own 'footnote' on Plato's notion of Mathematics and the Good. . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]