Why is algebra not the heart of analysis or critical, English

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Why is algebra not the heart of analysis or critical

(1) Why is algebra not the heart of analysis or critical thinking, according to Dupin? The lesson?

(2) Why are the Police methods a "Procrustean bed," acc. to Dupin? The lesson?

(3) How does Dupin use deductive thinking to conclude the location of the purloined letter, before he uses observation? The lesson?

(4) How does Dupin's methods in this letter case validate the case for intellect over intelligence, using Hofstader's terminology?

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