Exam Two over chap4 and 7
Exam Two over chap4 and 7 Philos 1500
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Date Created: 03/09/15
Exam 2 Chapters 4 amp 7 1500 Intro to Logic Vocab Fallacy a psychologically persuasive error in reasoning Formal fallacy an error in reasoning that involves the explicit use of an invalid form Informal fallacy an error in reasoning that does not involve the explicit use of an invalid form Fallacies of irrelevance use of premises that are logically irrelevant to their conclusions But premises may seem relevant for psychological reasons Fallacies involving ambiguity contain ambiguous words phrases or statements or involve a subtle confusion between two closely related concepts Unwarranted assumption an assumption that in context is not supported Atomic statement statement that does not have any other statement as a component Compound Statement statement that has at least one atomic statement as a component Scheme of abbreviation assign each atomic statement a distinct capital letter Logical operators Main logical operators governs the largest component or components of a compound statement Only one per compound Minor logical operator governs smaller components of a compound statement Expression of statement logic any sequence of symbols Wellformed formula WFF grammatically correct symbolic expression Statement variables stand for any statement Atomic and compound Truthfunctional Truth value of compound statement is completely determined by truth value of the atomic statements Truth table Diagram showing truthfunctional compounds Tautology statement that is true on every assignment of truth values to its atomic components Contradiction statement that is false on every assignment of truth values to its atomic components Contingent statement that is true on some assignments of truth values to its atomic components and false on others Logically equivalent two statements that agree in truth value on every assignment of truth values to their atomic components Logically contradictory two statements that disagree in truth value on every assignment of truth values to their atomic components Logically consistent two or more statements that are all true on some assignment of truth values to their atomic components Logically inconsistent two or more statements that are never all true on any assignment of truth values to their atomic components Informal Fallacies Can be put into valid argument form mmary of Fallacies Involving Irrelevant Premises Argument Against the Person Ad Hominem Fallacy Premises Instead of providing a rational critique of a statement or argument attack the person who advances it Conclusion The Statement is false or dubious or the argument is unsound or uncogenU Abusive ad hominem involves direct personal attack Circumstantial ad hominem involves an attempt to discredit an argument or view by calling attention to the circumstances or situation of those who advance it Tu quoque charges opponent with hypocrisy or inconsistency The Straw Man Fallacy Premises A misrepresentation of the view is false Conclusion The view itself is false Appeal to Force ad baculum fallacy Premises You can avoid Harm by accepting this statement Conclusion This statement is true Appeal to the People ad populum fallacy Premises You will be accepted or valued if you believe this statement Conclusion This statement is true Appeal to Pity ad misericordiam fallacy Premises You have reason to pity this person or group Conclusion You should do X for the bene t of the person or group although doing it is not called for logically by the reason given Appeal to Ignorance ad ignorantiam fallacy Premises This statement has not been proven true Conclusion This statement is false or may be reasonably believed false Premises This statement has not been proven false Conclusion This statement is true or may be reasonably believed true Red Herring Fallacy ignorantia elenchi Premises Something relevant to the topic at hand is described Conclusion A distracting but often unnoticed change of subject occurs mmary of Fallacies Involving Ambiguity Equivocation Premises contain a key word or phrase that is ambiguous Conclusion is reached not by valid logical inference but by trading on the ambiguity of the key work or phrase Amphiboly Premises contain a sentence that is ambiguous due to faulty structure ex grammar punctuation Conclusion is reached not by valid logical inference but by trading on the structural ambiguity Composition Premises the parts or members have attribute X Conclusion the whole or group has attribute X Division Premises the whole or group has attribute X Conclusion the parts or members have attribute X ummary of Fallacies InvolvingUnwarranted Assumptions Begging the Question petitio principii Assuming the point to be proved The premises are similar in content to the conclusion but not better known than the conclusion False Dilemma Using a premise that unjustifiany reduces the number of alternatives to be considered Appeal to Unreliable Authority ad verecundiam fallacy Appealing to an authority when the reliability of the authority may reasonably be doubted False Cause Fallacy Illegitimater assuming that one possible cause of a phenomenon is a or the cause although reasons are lacking for excluding other possible causes Fallacy of Complex Question Asking a question that illegitimater presupposes some conclusion alluded to in the question Logical Qperators Operator Name Translates Type of Compound tilde not negation Q dot and conjunction v vee or disjunction gt arrow if then conditional a doublearrow if and only if biconditional Symbolic expression is a Wellformed formula if Capital letters which stand for atomic statements If p is a WFFlt then so is p If p and q are WFFs then so is p 0 q If p and q are WFFs then so is p v q If p and q are WFFs then so is p gt q If p and q are WFFs then so is p lt gt q P P PP N Summary of truth tables for the Five Compounds Negation Conjunction Disjunction Conditional Biconditional P 1 PQPCQPq PV Pq Pquot Pqpquot q q q F T T T T T T T T T T T T F T T F F T F T T F F T F F F T F F T T F T T F T F F F F F F F F F T F F T Other Notes Unless can be translated with gt or v 52 We will lose unless we do our best L We will lose B We will do our best L v B B gt L Double negatives are ok A p can be compound or atomic p can be A p is then A Example T Texas is a small state T Texas is not a small state T It is not true that Texas is not a small state Tripledot mark conclusion Conclusion is written on the last line to the far right Suf cient Condition Is a condition that guarantees that a statement is true Antecedent of a true condition statement provides a sufficient condition for truth of consequent Necessary condition Is a condition that if lacking guarantees that a statement is false Consequent of a true statement provides a necessary condition for truths of antecedent Use Truth Tables to Determine Validity of an Argument 1Generate all possible truthvalue assignments for atomic components list statement Iieters in the order in which they appear 0 Two truth values true false 2quotn where n is the number of atomic components 0 In column nearest to vertical line alternate T F T F ect 0 Next column alternate in twos T T F F TT F F ect 0 Third column from vertical line alternate in fours TTTT F F F F ect 2 Write steps of the argument on the line at the top 3 Fill in columns under each step of the argument using truth conditions 4 Circle columns under main operator of each premise and conclusion 5 Look for row where all premises are true with a false conclusion mark with star o If there is then the argument is invalid Lo icall Si ni cant Cate ories and Relamnships Tautology Contradiction and Contingency How appear on a truth table Tautology true on every row Contradiction false on every row Contingency true on some rows false on others Equivalence Contradictoriness Consistency and Inconsistency How appear on a truth table Equivalence two statements have the same truth value on each row Contradictoriness two statements have a different truth value on each row Consistency two or more statements have the same truth value on at least one FOW Inconsistency two or more statements where there is no row where they are bothall true Relationships Every argument whose conclusion is a tautology is valid Any argument that includes a contradiction among its premises is valid Any argument with logically inconsistent premises is valid and unsound Any argument that has a tautology as its premise and a contingent statement as its conclusion is invalid If premises of an argument when made into a conjunction form a contingent statement and the conclusion is a contradiction the argument is invalid If a biconditional statement is a tautology then its two constituent statements are logically equivalent
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