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Introduction to Logic Exam One

by: Hannah B.

Introduction to Logic Exam One PHIL 1017

Marketplace > Auburn University > PHIL-Philosophy > PHIL 1017 > Introduction to Logic Exam One
Hannah B.
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Honors Intro to Logic PHIL 1017, Dr. Jolley Study Guide for exam one
Honors Intro to Logic
Study Guide
Auburn University, au, auburn, philosophy, phil, phil 1017, phil 1010, logic, intro to logic, introduction to logic, honors, jolley
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This 3 page Study Guide was uploaded by Hannah B. on Thursday March 10, 2016. The Study Guide belongs to PHIL 1017 at Auburn University taught by Jolley in Winter 2016. Since its upload, it has received 121 views. For similar materials see Honors Intro to Logic in PHIL-Philosophy at Auburn University.


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Date Created: 03/10/16
PHIL 1017 Exam 1 Section 2: Conjunction the conjunction is only true if both conjuncts are true p q (dot means “and”) associative: internal grouping doesn't matter (p.q).r = p.(q.r) commutive: p.q = q.p not a conjunction if it conveys a succession in time. Section 3: Negation the negation is true is the negated statement is false “it is not the case that” is the symbol ‘—‘ negation of p is —p Section 4: Disjunction “or” means at least one statement is true —> inclusive sense inclusive —> p v q —> “p or q or both” exclusive sense: p or q is true if only one is true exclusive —> (p v q) . — (p . q) —> “p or q but not both” commutive: pvq = qvp Section 5: Grouping we group things to avoid confusion de Morgan’s Law —(p.q) is the same as —p v —q —(pvq) is the same as —p . —q Section 6: Truth-Functions truth-values: whether the statement is true or false truth-functions: negation, conjunction, and disjunction truth-tables: T=true, F=false p q p.q pvq —(p.q) T T T T F T F F T T F T F T T F F F F T Section 6: Conditionals p>q means “if p then q” a conditional is true if either its consequent is true or its antecedent is false, & is false otherwise material conditional: truth-functional analysis of conditional (basics) generalized conditional: allows you to analyze the conditionals counterfaced conditionals: antecedent is already assumed false contrapositive: the same converse: not the same inverse: contrapositive of converse biconditionals: statements of the form p=-q (three lines horizontally) the biconditional of two statements is true if both the statements are true or if both are false p=-q is the same as (p.q)v(—p.—q) p q p>q p=-q T T T T T F F F F T T F F F T T Section 8: Logical Paraphrase logical paraphrase requires three tasks: 1) the locutions that serve as connectives have to be identified and suitably translated into symbols; conjunctions can also be expressed by “but” and “although” “the senator will not testify unless he is granted immunity” is the same as “the senator will testify>the senator is granted immunity” 2) the constituents of the statement have to be demarcated, and possibly rephrased to make their content explicit; fallacy of equivocation: not always interpreting the same expression in the same manner apparently this is bad 3) the organization of the constituents, that is, the grouping, has to be determined. look for the outermost structure first then paraphrase inward step by step “If Figaro does not expose the court and force him to reform, then the Countess will discharge Susanna” —(p.q)>(r.s) **look at the example on page 33-35 of Goldfarb’s Deductive Logic Section 9: Schemata and Interpretation truth-functional schemata: the compounds constructed from sentence letters (p,q,r) and the truth-functional connectives stand-in for statements interpretation of sentence letters is a correlation of a statement with each of the sentence letters truth-assignments: interpretations of truth-value behavior if compounds p q r pvq (pvq)>r T T T T T T T F T F T F T T T T F F T F F T T T T F T F T F F F T F T F F F F T Truth-functional Connective Rules 1) a negation is true if what is negated is false, and is false otherwise; 2) a conjunction is true if it’s conjuncts are all true, and is false otherwise; 3) a disjunction is true if at least one of it’s disjuncts is true, and is false otherwise; 4) a conditional is true except is its consequent is false and its antecedent is true, in that case it is false; 5) a biconditional is true if its two constituents have the same truth-value, and it false otherwise. p q r p.q —(p.q) q.r p=-(q.r) —(p.q)v(p=-(q.r)) T T T T F T T T T T F T F F F F T F T F T F F T T F F F T F F T F T T F T T F T F T F F T F T T F F T F T F T T F F F F T F T T the final column: the column that actually gives us what we are looking for v marks a greater break than . > and =- mark greater breaks than v and . p . q v r = (p . q) v r p . q v (r > s) . —(q . r) = (p . q) v ((r > s) . —(q . r)) p . q v r > s . (p v r) = ((p . q) v r) > ((s . p) v r) p . q v r =- s . p v r = ((p . q) v r) =- ((s . p) v r) Section 10: Validity and Satisfiability valid: a truth-functional schema that comes out true under all interpretations of it’s sentence letters (example is p > p) satisfiable: a truth-functional schema that comes out true under at least one interpretation (example is p . —q) unsatisfiable: one that comes out true under no interpretation (example is p . —p) truth-functionally valid statement: logical truth Section 11: Implication one truth-functional schema implies another if and only if there is no interpretation of the sentence letters under which the first schema is true and the second is false schema implies another if the other is true when the first is true one statement truth-functionally implies the other implication is the validity of the conditional Section 12: Use and Mention implication holds when and only when the relevant conditional is valid we use words to talk about things “Frege devised modern logic” mentions the logician by using his name “The author of Thoughts used truth tables” mentions the logician a name for an expression is formed by surrounding the expression with quotation marks “Frege” is a name of a German logician “Frege” refers to Frege syntactic variables: variables that range over schemata


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