Computation & The Real

Instructor: Anil Bawa-Cavia Date & Time: Saturdays, October 5, 12, 19, 26 11 AM - 1:30 PM ET

DESCRIPTION What is Computation? This naive question appears – eighty years on from the pioneering work of Alonzo Church – as an insistence that the computable domain lacks theoretical closure. A figure which presents itself as mere procedure, simply a recursive mode of calculation, has cast its shadow over a fundamental rift in modern mathematics. Its advances call for a reappraisal of Turing orthodoxy – the image of a Universal Machine endowed with Boolean logic – as no more than an ossified icon limiting the conceptual scope of what it means to compute.

The seminar will examine an alternative model of computation, proceeding from developments in three corresponding areas of 20th Century thought – constructive mathematics, intuitionistic logic, and type theory. We will explore the relation between propositions and types, proofs and programs, realizability and truth – discussing the work of LEJ Brouwer, Per Martin-Löf, Steve Awodey, Jean-Yves Girard and others. We develop a unified perspective on computation, logic and mathematics based on univalent foundations, exploring its ramifications in interactivist paradigms, sketching out a notion of computation as a ‘dialogics’ of reason.

Image: Brenna Murphy, GranularFlowIndex, 2016

To see The New Centre Refund Policy CLICK HERE.