CfP for 11th IWC 2017

CfP for 11th IWC 2017

[michael.heather]

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.


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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.
.




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