Saturday, October 2, 2010

Busting a myth about Lesniewski and definitions

Some time ago I run into a few logicians chatting at a conference about how Lesniewski formulated the standard theory of definitions. For some reason I felt obliged to say a few words about this. One thing let to another, and this ended up in a footnote to Gupta's entry on definitions at the Stanford Encyclopedia (see footnote three). A few more coincidences and I started writing a paper about this with Severi Hamari. After a freakish number of revisions (around 20) we finally agreed on a version, and I posted it on academia.

Many thanks for their comments to John MacFarlane, Nuel Belnap, Wilfrid Hodges, Paolo Mancosu, Oystein Linnebo and Jan von Plato (I hope I didn't forget anyone).


A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to S. Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski’s published orunpublished work is known where the standard conditions are discussed. Second, Lesniewski’s own logical theories allow for creative definitions. Third, Lesniewski’s celebrated ‘rules of definition’ lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 30s, a study of these meta-theoretical conditions is more readily found in the works of J. Lukasiewicz and K. Ajdukiewicz.


Anonymous said...

There's a typo on p. 3. ' layers' ' should be ' lawyers' ' or ' layman's '.

Rafal Urbaniak said...

Our bad, thanks!