|Presuppositions and Active Logic.|
Presuppositions occur in natural language when something which is not asserted is assumed to be true based on some other assertion. If someone asserts:
"The king of France is hiding."
we presuppose that there is a king of France. The speaker did not assert that there exists a king of France but nonetheless commits himself to the existence of the king of France. So, that the king of France exists is a presupposition of the utterance. Presuppositions can arise in many other language constructions as well.
There are a number of features that distinguish presuppositions from assertions:
The T or F criterion.
The assertability criterion.
Four major approaches to presuppositions have been::
Logical Presuppositions. (Frege.)
Expressive presuppositions. (Strawson.)
Pragmatic Presuppositions. (Stalnaker.)
Pragmatic Presuppositions based on Discourse Semantics. (Heim.)
We think that active logics can contribute to understanding presuppositions. One of the aspects of presuppositions we are looking at is the problem of presupposition projection. Projection has not had a totally satisfactory account in any of the current theories of presuppositions.
Active Logics have some unique features which can help satisfactorily handle the problems of projection:
Reasoning about the history of the logic.
Robustness in the face of contradictions.