Question About Chapter 8 of Traditional Logic II

[Amazing Grace]

In talking about disjunctive moods, the author states that Ponendo Tollens (Either P or Q: Q/P: Therefore, not P) is invalid, the reason why being that just because Q is true doesn't mean that P is not true. The example given is:
Either Socrates is a farmer or Socrates is a philosopher
Socrates is a farmer
Therefore, Socrates is not a philosopher

What I don't understand is that if the first premise is either/or (meaning only one or the other can be correct), how that doesn't negate one alternant. If we know that one is correct or incorrect, that must mean that the other is the opposite.

So I don't understand how affirming the first/second alternant is a fallacy. Any help would be much appreciated.

[Amazing Grace]

Can someone please reply quickly, I really need to know soon, because it's hindering my work in logic. Thanks.

[martin]

If only one or the other can be true (that is called an exclusive disjunction), then affirming one alternant will necessitate the negation of the other. But in a normal disjunction (an inclusive disjunction), both alternants can be true, in which case Ponendo Tollens is invalid.

This is discussed on the third page of the chapter.

I hope this helps.

[Amazing Grace]

If only one or the other can be true (that is called an exclusive disjunction), then affirming one alternant will necessitate the negation of the other. But in a normal disjunction (an inclusive disjunction), both alternants can be true, in which case Ponendo Tollens is invalid.

This is discussed on the third page of the chapter.

I hope this helps.

But I thought that either/or is exclusive, that by using those words, you're automatically saying that either one is true or the other one is, but both can't be. That's what I was having trouble with. Thank you very much.

[weatherhogge]

I hear what you're struggling with. We often use "either/or" language to mean that only one or the other disjunct can be true. However, in logic "either/or" means one or the other may be true or they may be true at the same time. This is what is called, as Mr. Cothran mentioned, a "normal" or an "inclusive" disjunctive statement.