[looked at several examples of Venn diagrams on the white board] * a few QUIRKS in categorical logic: * "All A are B" and "No A are B" do NOT actually require that A has any members...! (Group A may be empty) All unicorns are pink. ...you can say this without requiring that unicorns exist (!!!) <-- labeled as VACUOUSLY TRUE * "Some A are B" and "Some A are not B", however, DO require there be at LEAST one member in group A, because (in categorical logic) "some" means "AT LEAST ONE" * so, "Some unicorns are pink" requires that there must somewhere be a unicorn that is pink for this to be true; "Some unicorns are not purple" requires that there must somewhere be a unicorn that is NOT purple to be true; ******** * STANDARDIZING categorical statements ******** * basic structure: <QUANTIFIER> <SUBJECT> <VERB> <PREDICATE> QUANTIFIER -> All, Some, or None SUBJECT -> some SET of things VERB -> a LINKING verb (or copula) (are, are not) PREDICATE -> some SET of things * STEP 1 -> REPHRASE subjects and predicates so they refer to groups/classes/sets of things Before: All horses are brown. After: All horses are brown animals. Before: All spiders have 8 legs. After: All spiders are 8-"appendaged" creatures Before: Some ballgames are postponed. After: Some ballgames are postponed events. * STEP 2 -> REPHRASE all non-standard linking verbs into forms of the verb "to be" Before: Some students walk to school. After: Some students are people who walk to school. Before: All wet dogs smell musty. After: All wet dogs are animals that smell musty. Before: Some faculty just don't get it. After: Some faculty are people who just don't get it. * STEP 3 -> If a quantifier is NOT explicitly stated, STATE it (applying the Principle of Charity) Before: Koalas are marsupials. After: All koalas are marsupials. Before: Faculty are strange. After: Some faculty are strange. <-- princ of charity...! * STEP 4 - A statement about ONE thing can be translated (possibly awkwardly) into a category ...to be continued on Friday!