ACB:
1. S knows that every statement in his geography textbook is correct. (His well-qualified geography teacher has told him: “I have checked this book carefully, and everything in it is correct”. The teacher is right, and S believes him.)
2. One of the statements in the textbook is that Quito is the capital of Ecuador.
3. Therefore, S knows that Quito is the capital of Ecuador, even if he has never heard of Quito or Ecuador.
This doesn’t seem right to me. What do you think?
Emil:
Hmm. Formalization may help.
1. (∀P)(TP→K(P))
For all propositions, that a proposition is expressed in the textbook (TP) materially implies that S knows that P.
2. TA
(proposition) A is expressed in the textbook.
⊢, 3. K(A)
Thus, S knows that A.
This is valid. But I don’t think that is the argument expressed above. The argument expressed above relies on confusion/equivocation on premise 1. The difficulty is formalizing what the other thing that is meant by that phrase is. Hmm.
My (1) above is not a correct formulation of what if meant by the premise phrase in the natural language. What about:
1′. K((∀P)(TA→A))
S knows that for all propositions, that a proposition is expressed in the textbook (TP) materially implies that P.
That seems to capture what is meant. The equivocation has been explained to my satisfaction. (1′) and (2) does not logically imply the conclusion, so that argument is invalid.