Post
by timmydoeslsat » Wed May 16, 2012 11:52 pm
Yeah this is a lot going on here. I think this is one you would want to diagram out.
Terry:
AB some FC
AG ---> FC
__________
AB some AG
Pat:
AG some ~FC
AB ---> ~FC
___________
AB some AG
Both Terry and Pat are taking the necessary conditions of each respective conditional in their argument as a sufficient condition to reach their conclusions.
For instance, take Pat's argument:
AG some ~FC
AB ---> ~FC
___________
AB some AG
In this situation, our quantifying statement is going to be on the right hand side (necessary side) and we cannot conclude a some statement from this.
This is Pat's argument as one combined premise:
AB ---> ~FC some AG
To be able to conclude from this premise that AB some AG, Pat is mistakenly going from right to left with our arrow.
Notice the difference between what is an incorrect inference and a correct inference with some statements:
No inference can be derived: X ---> Y some Z
An inference can be derived: X some Y ---> Z
The quantifying statement is on our sufficient side of the arrow. We know that some X's are Y's. We know that every single Y is a Z. So we do know that some X's will be Z's.
The statement concerning the "no inference can be derived" is telling us that every single X is a Y. We know that some Y's are Z's. What if there is 1 X in the world, 5 Y's in the world, and 2 Z's in the world.
X
YYYYY
......ZZ
This shows that it does not have to be true that some X's are Z's. We can have that not be true. The Z's that are available can be with the Y's that do not have to be X's.
You will be able to motor through problems like this once you have a monster grasp on conditional logic.