Why can the arrow NOT point towards the quantifier? (Example 5)
Hi, In example/question 5, and as a general rule, we are told that the arrow (or conditional) cannot point towards the quantifier when we have Rule #1 and Rule #2 met to make a deduction. For example:
P: GP --> A
P: A - some - I
---------------------
C: GP - some - I
(Combined this would invalidly be: GP --> A - some - I /// GP - some - I)
Can someone please help me understand why this is wrong? I get the rule, I just want to understand "why". Maybe an explanation would help?
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Great Question! You are right that you need to have the arrow pointing away from the quantifier (that is, you need to have the sufficient condition of your conditional statement also in the quantifier). The reason being that there is not necessarily any overlap between the necessary statement (artists) and the artists that are also intellectuals. For example, let's say that we have 100 great photographers (all of which are artists). And we have 500 artists (some of which are intellectuals - let's say 50 of the 500 artists are intellectuals and 450 artists aren't intellectuals). It is possible that all 100 great photographers who are also artists are within the second category of artists (the 450 who are not intellectuals). Remember also, that "some" statements are reversible, so A - some - I is equivalent to I - some - A. So sometimes you can rewrite the some statement to make the conditional arrow point away from it (but not in this case.
