Lecture Notes for Mar 3, 2010

3/3/10 6. the form of standard-form categorical propositions (a) quantifier [subject term] copula (not) [predicate term] (i) subject/predicate terms- nouns of noun-phrases (ii) copula can vary in number and tense (iii) quantifiers: All, some, no (iv) the word 'not' can only appear if 'some' is quantifier (b) translating into standard form (i) singular propositions (a) aristotle is(copula) a jerk (b) All S are P (c) All aristotles are jerks (ii) adjectives (a) all logicians are handsome (b) all logicians are handsome things (iii) no copula (a) all logicians drink beer (b) all logicians are beer-drinkers (iv) negated quantifiers (a) not all S are P (some S are not P)= O (b) its not the case that that some S are P (no S are P)= E (v) alternative quantifiers (a) any, each, every, etc = All (b) problem: a negated 'any' is not the same as a negated 'every' -not every logician is a jerk= not all logicians are jerks -not any logician is a jerk= no logicians are jerks (c) restricted to people (ex: everybody, someone, no one, etc) -everybody loves logic= all people are logic-lovers (d) 'only' (ex: only logicians love logic) (vi) missing quantifiers (a) Bears have fur= All bears are furry things (b) The bat is blind= All bats are blind things (c) A logician is a kind of philosopher (A) (d) A logician stole my wallet= Some logicians is a stealer of my wallet (e) If-sentences -If its a logician, its a jerk (A) = all logicians are jerks -If its a logician, its not a handsome thing (E) -If its not a chevy, i wont drive it= only chevys are things i will drive= i only drive chevys -if its not S, its not P= only S are P= All P are S III. the square of opposition ex: A(All S are P) E(no S are P) I(Some S are P) O(some S are not P) the contradictions are along the diagonal.. if one is true, the other is false A. contradictories 1. cant have same truth value 2. A, O 3. E, I B. Contraries 1. both cant be true, can both be false 2. A, E C. Sub contraries 1. cant both be false, can both be true 2. O, I D. Subalternatives 1. If A true, I must be true (but not other way around 2. E --> O