I'd like to start off by saying that I have read the other posts in the Math StackExchange and here about this paper, but I think my question is a bit different from those although it does stem from my being unable to understand the argument.
In Van McGee's paper, Counterexample to Modus Ponens (1985), he starts off by giving an inference which he says is not a valid belief. The inference is in the context of the 1980 presidential election in which the polls showed Reagan (Rep.) leading, then Carter (Dem.), and in third, Anderson (Rep.).
The deduction goes as follows,
- (Premise) If a Republican wins, then if it's not Reagan, then it will be Anderson. (Rep-->(notReg-->And)
- (Premise) A Republican will win.
- (Inference via 2,1 Modus Ponens) If it's not Reagan, then it will be Anderson.
Now here McGee says one does not have reason to believe the conclusion. Now I agree that taking the conclusion on it's own, I would not be right to believe the conclusion because Carter is more likely to win than Anderson, BUT in the light of the premises I do hold it to be true. Since a Republican won, it cannot be the case that Carter won.
Now I have attempted to resolve my confusion by speaking with two professors of mine. What I believe (emphasis on believe) they were trying to tell me is that I somehow do not know the premises or something akin to that, and that I had a misunderstanding of the way classical logic is done (which I am completely open to).
The way I thought classical logic was done is that in making my inferences, I hold the premises to be true. That, along with my rules of inference, is what allows my to make conclusions. It seems like the explanations are is that I am supposed to take the conclusion stand-alone which makes absolutely no sense to me because I thought that was the point of the premises. I know them to be true, and believe them to be true throughout my inferences, that knowledge is always there.
I am arguing that it is intuitively valid because there is no case where the premises are true, and the conclusion is false.
I would very very very much appreciate if anyone can try and explain why it's an invalid inference (intuitively) to me. I know it's a valid inference in classical logic via the deduction above. I believe my confusion is in this idea that I always have knowledge of my premises which is not how classical logic is done, maybe a difference in truth and belief? In classical logic, we take the premises to be absolute truths, not probabilistic.
To reiterate, the main question is, why is this an intuitively invalid inference? In what case is it possible for the premises to be true, and the conclusion to be false?