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# EXAM1 study guide PHI210

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This 6 page Study Guide was uploaded by UkwithMax Notetaker on Friday February 20, 2015. The Study Guide belongs to PHI210 at University of Miami taught by Ted Locke in Spring2015. Since its upload, it has received 218 views. For similar materials see symbolic logic in PHIL-Philosophy at University of Miami.

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Date Created: 02/20/15

EXAMl Study Guide ililji E2 20152 20 El Unit 1 INDUCTIVE An inductive argument is an argument in which the premises are intended to provide some degree of support for the conclusion DEDUCTIVE A deductive argument is an argument in which the premises are intended to provide absolute support for the conclusion VALID DEDUCTIVE ARGUMENT The truth of the premises absolutely guarantees the truth of the conclusion and it is impossible for the premises to be true but conclusion to be false SOUND ARGUMENT A sound argument is a valid deductive argument in which all of the premises are true COUNTEREXAMPLE FOR AN ARGUMENT FORM A counterexample to an argument form is an instance of that form a particular example in which all of the premises are true and the conclusion is false Which means this argument form is not a valid one Unit 2 SIMPLE AND COMPOUND SENTENCES A sentence is simple if and only if it is not compound A sentence is compound if it logically contains another complete sentence as a component either literally contains the other as a component or can be paraphrased into an explicitly compound sentence that contains the other as a component If one sentence is a component of another sentence replace the component sentence by any other declarative sentence the result is still a grammatical sentence MAJOR OPERATOR OF THE FORMULA the one that determines the overall form of the sentence and is the operator introduced last in the process of constructing the formula from its more elementary components Unit 3 LI O39I LLI LL QI I LLLL bcd v aslezl esuvueqlo fem em luenbesuoo 4 fem aslezl luepeoelue l ueqH leuolllpuoO El lElVJ Hi tlJ J l d l J d GSJGAGJ mu uone eN EI IEIVJ Hint l J l 1 J b a d b 93e1ueJelufGnuewes ml MUG pue J 9U01PU00E EI IEIVJ Hi tlJ l J l J b eslezl Me n eslezl 10 uonounlsm EI IEIVJ Hint QI I LLLL lllLI QI I LLLL bd v I uuu l LLl LL l l LLLL b d d am Me n emi pun uonounluoo EI IEIVJ Hint A I IIA Computer Truth Value Unit 4 SYMBOLIZING ENGLISH SENTENCES step 1 Identify the simple components of the compound step 2 Use different capital letters to stand for each simple sentence use the same letter to stand for repeated simple sentences 0 Some times compound sentences need to be rewrite to pick out simple components eg rewrite negation as it is not the case 0 Sentences with nontruthfunctional operators such as believes that necessary that because etc will be simple sentences step 3 symbolizing truthfunctional English operators Conjunctions using dot p q 0 English and but however nonetheless nevertheless still though even though also while moreover despite the fact that in addition etc Disjunctions using wedge p V q 0 English or eitheror or else unless etc unless can be symbolized in other ways Negation using tilde NS 0 Negative prefixes such as a dis i im in ir non un do not negotiate a sentence 0 Not both p q is not equivalent to p q p q E p V q o Neithernornoteitheror p V q is not equivalent to p V q p V q E H q Conditional usingw 0 when p is the sufficient condition of q as consequent p 3 q o EngHsh If p then q if p q q if p q provided p provided p then q q whenever p q in the event that p given that p q supposing that p q n iQ a Cl Iffininnf nnndifinn fnr r1 I V IO U QUIIIUIUIIL UUI IUILIUII IUI 1 etc 0 when p is the necessary condition of q as consequent q 3 p o EngHsh p is a necessary condition for q qonly if p only if p will q p is required for q for q to occur p must be the case if p does not happen then q will not occur 1p is the sufficient condition for q p 3 q 2 p is the necessary condition for q q 3 p p unless q q 3 p or p 3 q or p V g Biconditional using triple bar p E q 0 When p and q are sufficient and necessary condition of each other p 3ClaCIDIC aIC EClaClECl o EngHsh if and only if just in case just in the event that is necessary and sufficient etc Step 4 identify the major operator and the components of components Unit 5 TRUTH TABLE total number rows in a truth table will always a power of 2 o 12 0 24 0 38 0 416 construct a truth table find counter example to determine if an argument is valid or invalid counterexample all the premises are true but the conclusion is false mechanical method full truth table method short method 0 try to construct a counterexample try to assign truth values to the variables that will yield a false conclusion and true premises svmbolize an argument and test it for validitv Unit45 J Uquotquotquotquot39 quotquotquotquot39J quotquotquot 39 Unit 6 TAUTOLOGY a single statement form that is true for every substitution instance true under the major operator for every row in the truth table CONTRADICTION a single statement form that is false for every substitution instance false under the major operator for every row in the truth table the negation of a contradiction is a tautology the negation of a tautology is a contradictiontruth value under major operator of the formula has been changed CONTINGENCY a single statement form that I can be false or trueboth T s and F s under the major operator in the truth table The negation of a contingency os a contingency LOGICAL EQUIVALENCE Two or more statement forms are logically equivalent if and only if their truth tables are identical under their major operators LOGICAL IMPLICATION One statement form logically implies another if and only if there is no row in their joint truth table in which the first comes out true and the second comes out false Two statement forms are logically equivalent just in case they logically imply each other INCONSISTENCY A set of formulas is inconsistent if and only if there is no row in their joint truth table in which they all come out true at once 0 When conjoin inconsistent formulas as a single formula the resulting formula will be a contradiction o a set of formulas is inconsistent if and only if the conjunction of all the formulas is a contradiction CONSISTENCY A set of statements forms is consistent if and only if there is a row in their joint truth table in which they all come out true at once Any disjunction with a tautology as one of its disjuncts will be a tautology Any conjunction with a contradiction as a conjunct will be a contradiction It is not all the case that conjoining two contingent statements will be con ngent A biconditional with components that are logically equivalent will be a tautology A biconditional of two contradictions will be a tautology A conjunction of an inconsistent set of statements will be a contradiction A biconditional of two inconsistent statements will be a contingency Every sentence logically implies itself because of the identical truth table A contradiction logically implies all the other statement because of there is no instance of the first statementcontradiction comes out true l i u Evernote Evernote f Iff E lili I li ltb

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