Logic Seminar

[Karin Lustre]

>
>
>   UNIVERSITY OF CHICAGO LOGIC SEMINAR
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>DATE: Thursday, February 1, 2001.                        
>TIME:  3:30-5:00                                         
>PLACE: Ryerson  251.                              
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>TITLE: Conceptual Analysis
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>SPEAKER: Wilfried Sieg                                   
>           School of Computer Science                     
>           Carnegie Mellon University                     
>           Pittsburgh, PA                                 
>
>ABSTRACT:
>
>To investigate computations is to analyze symbolic processes that can,
>in principle, be carried out by calculators.  That is a philosophical
>lesson we owe to Turing and should be taken seriously.  Drawing on, and
>recasting, work of [1] and [2], I formulate finiteness and locality
>conditions for two types of calculators, human computing agents and
>mechanical computing devices; the distinctive feature of the latter is
>that they operate in parallel.
>
>Church's Thesis asserts, dogmatically, that an informal notion of
>effective calculability is captured by a particular precise
>mathematical concept.  The conceptual analysis of computations I will
>present dispenses with theses. Instead, it leads to axioms for
>discrete dynamical systems (that represent human and machine
>computations abstractly) and allows the reduction of models of these
>axioms to Turing machine computations.
>
>[1]	A. Turing,  On computable numbers with an application to the
>Entscheidungsproblem; Proceedings of the London Mathematical Society,
>vol. 42, 1936, 230-265.
>
>[2]	R. Gandy, Church's Thesis and principles for mechanisms; The Kleene
>Symposium (J. Barwise, H.J Keisler, and K. Kunen, editors), North
>Holland, 1980, 123-148.
>
>[3] W. Sieg, Calculations by man and machine: conceptual analysis; to
>appear.