[Alta-Logic] Talk On Wednesday

[ggpayett at ucalgary.ca]

Speaker: David Boutillier

Room: ICT 616

Time: 13:00

Frege’s logicist programme is celebrated as the first account of
arithmetical knowledge that is based on a formulation and defence of the
thesis that fundamental arithmetical laws can be obtained on the basis of
definitions and logic alone. It is well-known that Frege’s attempt to
carry out this programme, by deriving the principles of (second-order)
Peano arithmetic from the basic laws of a system of second-order logic,
runs aground due to its reliance on what is known as Basic Law V, which
Russell showed to entail a contradiction. Various attempts, both
historical and contemporary, have been made to show that Russell’s paradox
can be avoided. But even if one of these attempts succeeds, a number of
questions remain concerning the underlying logic on which the logicist
thesis depends. One of these questions concerns the assumption that logic
is somehow epistemologically privileged. The question is whether the
philosophy of logic can provide a clear and satisfactory explanation of
the fundamentality of logic.

My paper describes a strategy for providing such an explanation, and
offers a sketch of one way in which the strategy might be carried out. The
strategy rests on two claims: that logical laws are “analytic of”
primitive logical concepts, and that primitive logical concepts are given
to us as the invariants of the transformations of a given domain of
individuals, which respects the structure of the properties of the
individuals in that domain. The sketch of how the strategy might be
carried out involves a discussion of Tarski’s extension of Klein’s
“Erlanger Programm,” which yields an explication of the general concept of
logical notion, and a modification of Tarski’s explication, which places
it within a functional type framework fashioned after the simple theory of
types.



-- 
Gillman Payette
Department of Philosophy
University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4, Canada
Ph 403.220.7518
Fax 403.289.5698