Tilted Forum Project Discussion Community - View Single Post

cliche · 08-01-2003, 01:07 AM

CSFlim - the point about step 7 is that if (and I appreciate this is a big if, and a load of rubbish etc) you accept all the way to step 6 - which has been generated a priori, then you have to accept step 7; that it's true in all possible worlds. I am completely in agreement with you that the earlier steps are a a load of rubbish, but the step from 6 to 7 isn't. If you can prove something a priori then it holds in all possible worlds, as the proof does not depend on the world - only the axioms of the logical system you're using. Hence 'necessary'. We haven't redefined the word during the course of the argument; it has exactly the same meaning throughout - and a very specific one which it takes on when being used in modal logic.

ie, the fact that steps 1 to 6 are a load of arse doesn't affect step 7. If the earlier ones are true, it must be. If you still don't understand, try googling "Kripke" "modal logic" or "S5 semantics". S5 is one of the stronger modal systems (greatest number of equivalence relations between possible worlds) - if I have time I may copy out part of one of my essays. Does anyone know how to get the symbols for possibly (diamond) and necessarily (square) in TFP?

08-01-2003, 01:07 AM	#51 (permalink)
cliche Rookie Location: Oxford, UK	CSFlim - the point about step 7 is that if (and I appreciate this is a big if, and a load of rubbish etc) you accept all the way to step 6 - which has been generated a priori, then you have to accept step 7; that it's true in all possible worlds. I am completely in agreement with you that the earlier steps are a a load of rubbish, but the step from 6 to 7 isn't. If you can prove something a priori then it holds in all possible worlds, as the proof does not depend on the world - only the axioms of the logical system you're using. Hence 'necessary'. We haven't redefined the word during the course of the argument; it has exactly the same meaning throughout - and a very specific one which it takes on when being used in modal logic. ie, the fact that steps 1 to 6 are a load of arse doesn't affect step 7. If the earlier ones are true, it must be. If you still don't understand, try googling "Kripke" "modal logic" or "S5 semantics". S5 is one of the stronger modal systems (greatest number of equivalence relations between possible worlds) - if I have time I may copy out part of one of my essays. Does anyone know how to get the symbols for possibly (diamond) and necessarily (square) in TFP? __________________ I can't understand why people are frightened of new ideas. I'm frightened of the old ones. -- John Cage (1912 - 1992)