12 January 2001, DIP Colloquium

12 January 2001, DIP Colloquium
Speaker: Paul Dekker (University of Amsterdam)
Title: Peirce puzzle
Place: Euclides Building, P3.27
Date: Friday January 12th, 2001
Time: 15.00-16.30

ABSTRACT:
A puzzle due to (and solved by) Charles Sanders Peirce has recently regained the interest of semanticists. The puzzle has been reformulated by Stephen Read and Brendan Gillon against the background of the following situation.

One-thousand people can participate in a sweep-stakes, and each participant is required to bring in one dollar. It seems the following two sentences can be asserted truthfully in this situation:
  (1) Someone wins $1.000 if everyone takes part.
  (2) Someone wins $1.000 or someone will not take part.
However, it seems the following two sentences are difficult to accept in the very same situation:
  (3) Someone wins $1.000 if he takes part.
  (4) Someone wins $1.000 or he will not take part.
Surprisingly, the natural translations of the four sentences in first order logic are fully equivalent. Apparently, something must be dubious somewhere. Are our intuitions about (1)-(4) dubious? Is the natural translation of (1)-(4) into first order logic dubious? Or is first order logic dubious itself?

In my talk I will answer both of the three questions. I will argue that Peirce's own, intuitively correct, observations about the puzzle can be seen to follow from independently motivated principles governing the use of conditional sentences and that of indefinite noun phrases.