Theories of Definite Descriptions from a Proof-Theoretic Perspective.
A definite descriptions is an expression of the form ’the F’. In his celebrated analysis Russell proposed that these are incomplete symbols that have no meanings by themselves, but only in the context of sentences of the form ’The F is G’. It had significant impact on the development of Russell’s philosophy and, it is fair to say, of analytic philosophy as a whole. The theory played a major role in his work with Whitehead, Principia Mathematica, which contains its formal development. Despite being often cited as a paradigm of philosophy, it is not entirely satisfactory. In these talks we will look at recent work on the theory of definite descriptions from the perspective of another paradigm: Gentzen’s sequent calculi and natural deduction in proof theory. Three different cut-free sequent calculi will be presented which essentially realise the Russellian account of definite descriptions, but in significantly different ways: 1) A system with enriched set of identity rules 2) A system with lambda-abstracts 3) A system with binary quantifiers to formalise definite descriptions in the context of complete sentences.
Andrzej Indrzejczak and Nils Kürbis
Both Andrzej and Nils are part of an ERC Grant on “ExtenDD - Coming to Terms”, based at the University of Lodz, Poland
2:00-3:30pmAndrzej Indrzejczak: Definite descriptions via term forming operators.
3:30-4.00pm Coffee break
4.00-5.00pm Nils Kürbis: Definite descriptions via binary quantification.
The Centre for Logic and Language was inaugurated in Nov 2008 as part of the Institute of Philosophy. It was created to produce and support high quality research on logic and language in philosophy and neighbouring disciplines.