ACB:<\/p>\n
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.)<\/p>\n
2. One of the statements in the textbook is that Quito is the capital of Ecuador.<\/p>\n
3. Therefore, S knows that Quito is the capital of Ecuador, even if he has never heard of Quito or Ecuador.<\/p>\n
This doesn’t seem right to me. What do you think?<\/p>\n
Emil:<\/p>\n
Hmm. Formalization may help.<\/p>\n
1. (\u2200P)(TP\u2192K(P))
\nFor all propositions, that a proposition is expressed in the textbook (TP) materially implies that S knows that P.
\n2. TA
\n(proposition) A is expressed in the textbook.
\n\u22a2, 3. K(A)
\nThus, S knows that A.<\/p>\n
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.<\/p>\n
My (1) above is not a correct formulation of what if meant by the premise phrase in the natural language. What about:<\/p>\n
1′. K((\u2200P)(TA\u2192A))<\/p>\n
\nS knows that for all propositions, that a proposition is expressed in the textbook (TP) materially implies that P.<\/p>\n
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.<\/p>\n