What is meant by projection problem in semantics?

Presupposition (Stanford Encyclopedia of Philosophy)

http://eecoppock.info/Presupposi…

Simple clauses have presuppositions. For example, The current king of France is bald presupposes that there is a current king of France.

If you do various things to a clause, like negate it, question it, or say it’s unlikely, the claim of the clause is no longer affirmed. But the presupposition still remains intact. So I can negate The current king of France is bald, and say that The current king of France is not bald at all.

But the presupposition that there is a current king of France still survives. That’s called projection of the presupposition. If X +> Y (X presupposes Y), then Not X +> Y. You need to say something different to the clause, to say “that doesn’t make sense, there is no current king of France”.

Some combinations of clauses do not project: not all the presuppositions survive. Working out how and why is the projection problem. For example:

If there is a knave, then the knave stole the tarts.

There is a knave +> … There is a knave.

If there is a knave, then the knave stole the tarts +> There is a knave? Obviously not: the presupposition of a hypothesis can’t be projected, precisely because it is a hypothesis.

The conditions under which projection happens are messy, and it’s 11:15 pm, so you can go to the links to work out what the debate is about.