Philosophy Question (Semantics)
14 Nov '09 17:48Any philosophy pro's. I am trying to get my mind around these two questions...
1. If #= [Fx->[[upsidedownAxFx->Fx]->Fx]] and a='x' and b=y, then #[a/b] equals...
So what I think is being asked here is all free occurences of "a" need to be replaced by the variable "b."
So there are 5 "x's" and this problem will be solved by a recognition of that the scope of upsidedown Ax is...
I agree that the first "x" is clearly outside of its scope, and that the third "x" is clearly inside it's scope, but even though the 4th and 5th "x's" are not under its scope to the same degree, they still seem to be under it.
So where do I go from here... What's it going to look like?
5. Find a sentence ! of L such that ! contains each of the logical signs in L at least once....
As for this one, would it be correct, do you think, to assume that we are referring to the major logical signs (and, or, if/then, if and only if, not...). A sentence in this context would be a formula that contains no free occurence of a variable.
1. If #= [Fx->[[upsidedownAxFx->Fx]->Fx]] and a='x' and b=y, then #[a/b] equals...
So what I think is being asked here is all free occurences of "a" need to be replaced by the variable "b."
So there are 5 "x's" and this problem will be solved by a recognition of that the scope of upsidedown Ax is...
I agree that the first "x" is clearly outside of its scope, and that the third "x" is clearly inside it's scope, but even though the 4th and 5th "x's" are not under its scope to the same degree, they still seem to be under it.
So where do I go from here... What's it going to look like?
5. Find a sentence ! of L such that ! contains each of the logical signs in L at least once....
As for this one, would it be correct, do you think, to assume that we are referring to the major logical signs (and, or, if/then, if and only if, not...). A sentence in this context would be a formula that contains no free occurence of a variable.
