Bunuel wrote:
Franklin: The only clue I have as to the identity of the practical joker is the handwriting on the note. Ordinarily I would suspect Miller, who has always been jealous of me, but the handwriting is not hers. So the joker is apparently someone else.
Which one of the following provides the strongest grounds for criticizing Franklin’s reasoning?
(A) It fails to consider the possibility that there was more than one practical joker.
(B) It fails to indicate the degree to which handwriting samples should look alike in order to be considered of the same source.
(C) It provides no explanation for why Miller should be the prime suspect.
(D) It provides no explanation for why only one piece of evidence was obtained.
(E) It takes for granted that if the handwriting on the note had been Miller’s, then the identity of the joker would have been ascertained to be Miller.
(E) is a very tricky wrong answer. “Takes for granted” can be rephrased as “believe”.
Does the author BELIEVE that “if the handwriting on the note had been Miller’s, then the identity of the joker would have been ascertained to be Miller?” NOPE!
All we know about the authors belief in this situation is where the hand writing on the note had NOT been Miller’s.
How do we know this for sure? The answer involves a type of logic that according to those who study the history of logic, wasn’t understood until about 130 years ago.
A basic paraphrase of the original argument: IF the handwriting was not Miller’s THEN the joker must have been someone else.
This if/then structure can be called formal logic, with some interesting “rules”.
We know that IF it rains THEN the ground is wet. So which of the following is a logical deduction from this statement?
If the ground is wet then it rains. NOPE
If it does not rain then the ground is not wet. NOPE
If the ground is not wet, then it’s not raining. YUP
The last sentence above is known as the contrapositive, which is the only deduction that could be made from a conditional (if/then) statement. Anything else is NOT inferable from an if/then statement.
NOTE: some conditional statements, known as the biconditional, can go in the “opposite direction”. These are essentially definitions.
For example: IF I’m outside THEN I’m not inside (by definition). Thus all of the following are logical deductions from the statement/definition:
IF I’m not inside, THEN I’m outside.
IF I’m not outside, THEN I’m inside.
IF I’m inside THEN I’m not outside.
For those of you struggling with this concept, you’re in good company. Mathematicians like Euclid & Fermat and philosophers like Aristotle & Descartes were apparently clueless about this type of logic.
In the end, for E, best to ask: does the author believe this to be true? NOPE.
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