# Ad hominem Argument Affirmative claim Affirming the antecedent Affirming the consequent Argument by force Argument from analogy Ambiguity

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2 502 GLOSSARY Better-than-average illusion When a majority of a group estimates they are better at something than a majority of the group, the group is said to be subject to this illusion. When the majority of a group estimates they are worse at something than a majority of group, they are said to be subject to the worse than average illusion. Biased generalization, fallacy of Overestimating the strength of an argument based on a biased sample. Biased sample A sample is said to be biased with respect to a feature if a disproportionate number of things in the sample have or lack the variable. Burden of proof, misplaced A form of fallacious reasoning in which the burden of proving a point is placed on the wrong side. One version occurs when a lack of evidence on one side is taken as evidence for the other side, in cases where the burden of proving the point rests on the latter side. Categorical claim Any standard-form categorical claim or any claim that means the same as some standard-form categorical claim. See standard-form categorical claim. Categorical imperative Kant s term for an absolute moral rule that holds unconditionally or categorically. Categorical logic A system of logic based on the relations of inclusion and exclusion among classes ( categories ). This branch of logic specifies the logical relationships among claims that can be expressed in the forms All Xs are Ys, No Xs are Ys, Some Xs are Ys, and Some Xs are not Ys. Developed by Aristotle in the fourth century b.c.e., categorical logic is also known as Aristotelian or traditional logic. Categorical syllogism A two-premise deductive argument in which every claim is categorical and each of three terms appears in two of the claims for example, all soldiers are martinets and no martinets are diplomats, so no soldiers are diplomats. Causal claim A statement that says or implies that one thing caused or causes another. Causal factor A causal factor for an effect is a variable whose presence in a population raises the probability that the effect will be present as well. Causal hypothesis A provisional explanation of the cause or effect of something. Causal mechanism An interface between cause and effect that has the property of making the effect happen, given the cause. Cause-and-effect claim See causal claim. Chain argument An argument consisting of three Conditional claims, in which the antecedents of one premise and the conclusion are the same, the consequents of the other premise and the conclusion are the same, and the consequent of the first premise and the antecedent of the second premise are the same. Circularity The property of a causal claim where the cause merely restates the effect. Circumstantial ad hominem The illogical notion that an individual s personal circumstances somehow refute his or her views. Claim When a belief (judgment, opinion) is asserted in a declarative sentence, the result is a claim or statement. Claim variable A letter that stands for a claim. Cognitive bias A psychological factor that unconsciously affects belief formation. Common practice, argument from Attempts to justify or defend an action or a practice on the grounds that it is common that everybody, or at least lots of people, do the same thing. Common thread When an effect is present on multiple occasions, look for some other shared feature (common thread) as a possible cause. Complementary term A term is complementary to another term if and only if it refers to everything that the first term does not refer to. Composition, fallacy of To think that what holds true of a group of things taken individually necessarily holds true of the same things taken collectively. Conclusion In an argument, the claim for which a premise is supposed to give a reason. Conclusion indicator A word or phrase (e.g., therefore ) that ordinarily indicates the presence of the conclusion of an argument. Conditional claim A claim that state-of-affairs A cannot hold without state-of-affairs B holding as well e.g., If A, then B. The A-part of the claim is called the antecedent; the B-part is called the consequent. Conditional proof A deduction for a conditional claim If P, then Q that proceeds by assuming that P is true and then proving that, on that assumption, Q must also be true. conditio sine qua non A condition without which it could not be. Often referred to as a but for cause. Confidence level A quantitative expression of the probability that the random variation found from random sample to random sample will lie within the error margin. Conflicting claims Two claims that cannot both be correct. Confusing explanations and excuses, fallacy of Mistaking an explanation of something for an attempt to excuse it. Conjunction A compound claim made from two simpler claims. A conjunction is true if and only if both of the simpler claims that compose it are true. Consequent See conditional claim. Consequentialism In moral reasoning, the view that the consequences of a decision, deed, or policy determine its moral value. Consistency principle The first principle of moral reasoning, which states that, if separate cases aren t different in any relevant way, they should be treated the same way, and if separate cases are treated in the same way, they should not be different in any relevant way. Contradictory claims Two claims that are exact opposites that is, they could not both be true at the same time and could not both be false at the same time.

3 GLOSSARY 503 Contrapositive The claim that results from switching the places of the subject and predicate terms in a categorical claim and replacing both terms with complementary terms. Contrary analogue In an argument from analogy, an analogue which does not have the attribute of interest. Contrary claims Two claims that could not both be true at the same time but could both be false at the same time. Control group See controlled cause-to-effect experiment. Controlled cause-to-effect experiment An experiment designed to test whether something is a causal factor for a given effect. Basically, in such an experiment two groups are essentially alike, except that the members of one group, the experimental group, are exposed to the suspected causal factor, and the members of the other group, the control group, are not. The effect must be found to occur with significantly more frequency in the experimental group for the suspected causal agent to be considered a causal factor for the effect. Converse The converse of a categorical claim is the claim that results from switching the places of the subject and predicate terms. Covariation The accompaniment of variations in one phenomenon by variations in another phenomenon. Critical thinking We think critically when we rationally evaluate our own or others thinking. cum hoc, ergo propter hoc The fallacy of thinking that correlation or covariation between two variables proves that one causes the other. Deduction (proof) A numbered sequence of truthfunctional symbolizations, each member of which validly follows from earlier members by one of the truth-functional rules. Deductive argument An argument intended to prove or demonstrate, rather than merely support, a conclusion. Definition by example Pointing to, naming, or otherwise identifying one or more examples of the term being defined; also called ostensive definition. Definition by synonym Giving another word or phrase that means the same thing as the term being defined. Denying the antecedent An argument consisting of a conditional claim as one premise, a claim that denies the antecedent of the conditional as a second premise, and a claim that denies the consequent of the conditional as the conclusion. Denying the consequent See modus tollens. Deontologism See duty theory. Dependent premises Premises that depend on one another as support for their conclusion. If the assumption that a premise is false cancels the support another provides for a conclusion, the premises are dependent. Disinterested party A person who has no stake in our belief or disbelief in a claim. See interested party. Disjunction A compound claim made up of two simpler claims. A disjunction is false only if both of the simpler claims that make it up are false. Divine command theory The view that our moral duty (what s right and wrong) is dictated by God. Division, fallacy of To think that what holds true of a group of things taken collectively necessarily holds true of the same things taken individually. Downplayer An expression used to play down or diminish the importance of something. Duty theory The view that a person should perform an action because it is his or her moral duty to perform it, not because of any consequences that might follow from it. Also called deontologism. Dysphemism A word or phrase used to produce a negative effect on a reader s or listener s attitude about something or to minimize the positive associations the thing may have. Emotive meaning The positive or negative associations of a word; a word s rhetorical force. Envy, argument from Trying to induce acceptance of a claim by arousing feelings of envy. Equivalent claims Two claims are equivalent if and only if they would be true in all and exactly the same circumstances. Error margin Expression of the limit of random variation among random samples of a population. Ethical altruism The moral doctrine that discounts one s own happiness as being of lesser value than the happiness of others. Ethical egoism The idea that, if an act produces more happiness for oneself than will the alternatives, then it is the right thing to do. Euphemism An agreeable or inoffensive expression that is substituted for an expression that may offend the hearer or suggest something unpleasant. Experimental group See controlled cause-to-effect experiment. Expert A person who, through training, education, or experience, has special knowledge or ability in a subject. Expertise An unusual knowledge or ability in a given subject, most often due to specialized experience or education. Explanation A claim or set of claims intended to make another claim, object, event, or state of affairs intelligible. Explanatory analogy An analogy that is used to explain. Explanatory definition A definition used to explain, illustrate, or disclose important aspects of a difficult concept. Extension The set of things to which a term applies. Fact vs. opinion Sometimes people refer to true objective claims as facts, and use the word opinion to designate any claim that is subjective. Fallacy An argument in which the reasons advanced for a claim fail to warrant acceptance of that claim.

4 504 GLOSSARY Fallacy of anecdotal evidence A version of hasty generalization in which the sample is a story. Often used in an attempt to rebut a general claim. See also appeal to anecdote. Fallacy of composition Concluding that, because each member of a group has a certain property, therefore the group as a whole must have that property. Fallacy of division Concluding that, because a claim about a group taken collectively is true, therefore the same claim is true about members of the group taken individually. False consensus effect Assuming that the views held by members of our group are held by society at large. False dilemma This pattern of fallacious reasoning: X is true because either X is true or Y is true, and Y isn t, said when X and Y could both be false. Force, argument by Using a threat rather than legitimate argument to support a conclusion. Fundamental attribution error The tendency to not appreciate that others behavior is as much constrained by events and circumstances as our own would be if we were in their position. Gambler s fallacy Believing that recent past events in a series can influence the outcome of the next event in the series is fallacious when the events have a predictable ratio of results, as flipping a coin. Generality Lack of detail and/or specificity. The less detail a claim provides, the more general it is. General causal claim A statement to the effect that occurrences of one type cause occurrences of another type. General claim A statement that refers to multiple members of a population nonspecifically. Generalization This term is used to refer to a general claim or to an inductive generalization from a sample. Genetic fallacy Rejecting a claim on the basis of its origin or history. Glowing generality A vague generality couched in language with strongly positive associations. Good deductive argument An argument whose premises being true would mean the conclusion absolutely must be true. Good inductive argument An argument whose premises being true would mean the conclusion probably is true. Grouping ambiguity A kind of semantic ambiguity in which it is unclear whether a claim refers to a group of things taken individually or collectively. Groupthink fallacy Fallacy that occurs when someone lets identification with a group cloud reason and deliberation when arriving at a position on an issue. Guilt trip Trying to get someone to accept a claim by making him or her feel guilty for not accepting it. Harm principle The claim that the only way to justify a restriction on a person s freedom is to show that the restriction prevents harm to other people. Hasty generalization, fallacy of Overestimating the strength of an argument based on a small sample. Heuristic A rule of thumb employed unconsciously by people when they estimate probabilities. In psychology, the field known as heuristics and biases was originated by Daniel Kahneman and Amos Tversky. Horse laugh A pattern of fallacious reasoning in which ridicule is disguised as a reason for rejecting a claim. Hyperbole Extravagant overstatement. Hypothesis A causal explanation offered for further investigation or testing. Hypothetical imperative Kant s term for a command that is binding only if one is interested in a certain result. Illicit inductive conversion An argument of the form Most Xs are Ys; therefore, most Ys are Xs. Inconsistency ad hominem The illogical idea that you rebut an opponent s position by showing that he or she didn t always subscribe to it. Indirect proof Proof of a claim by demonstrating that its negation is false, absurd, or self-contradictory. Inductive analogical argument See analogical argument. Inductive argument from analogy See argument from analogy. Inductive generalization from a Deriving a conclusion about a population from a consideration of a sample. Inductive syllogism See statistical syllogism. Inference to the Best Explanation (IBE) A form of inductive reasoning in which the best explanation for a phenomenon is concluded to be the proper explanation of the phenomenon. In-group bias A predisposition to find fault with outsiders. Initial plausibility One s rough assessment of how credible a claim seems. Innuendo An insinuation of something deprecatory. Intension The set of characteristics a thing must have for a term correctly to apply to it. Interested party A person who stands to gain from one s belief in a claim. See disinterested party. Invalid argument An argument that isn t valid. Issue A point that is or might be disputed, debated, or wondered about. Essentially, a question. Knowledge If you believe a claim, have an argument for it that is beyond reasonable doubt, and have no reason to think you are mistaken, you may be said to have knowledge that the claim is true. Law of large numbers A rule stating that the larger the number of chance-determined, repetitious events considered, the closer the alternatives will approach predictable ratios. Example: The more times you flip a coin, the closer the results will approach 50 percent heads and 50 percent tails.

7 GLOSSARY 507 Rhetorical explanation An explanation intended to influence attitudes or affect behavior; such explanations often make use of images with positive or negative emotional associations. Rhetorical force See emotive meaning. Sample A subset of a population. Sample size Sample size can affect the size of the error margin or the confidence level of inductive generalizations from a sample. Sampling frame A precise definition of a sample or attribute, that makes it unambiguous whether any given thing is a member of the sample and has the attribute. Scapegoating Placing the blame for some bad effect on a person or group of people who are not really responsible for it but who provide an easy target for animosity. Scare tactics Trying to scare someone into accepting or rejecting a claim. A common form includes merely describing a frightening scenario rather than offering evidence that some activity will cause it. Self-contradictory claim A claim that is analytically false. Self-selection A situation where the members of a sample are there because they themselves chose to be there. Self-selection fallacy Overestimating the probability of a conclusion derived from a self-selected sample Semantically ambiguous claim An ambiguous claim whose ambiguity is due to the ambiguity of a word or phrase in the claim. Semantic ambiguity Ambiguity produced by the inclusion of an ambiguous word or phrase. Significant mention See paralipsis. Slanter A linguistic device used to affect opinions, attitudes, or behavior without argumentation. Slanters rely heavily on the suggestive power of words and phrases to convey and evoke favorable and unfavorable images. Slippery slope A form of fallacious reasoning in which it is assumed that some event must inevitably follow from some other but in which no argument is made for the inevitability. Smoke screen An irrelevant topic or consideration introduced into a discussion to divert attention from the original issue. Social utility A focus on what is good for society (usually in terms of overall happiness) when deciding on a course of action. See also principle of utility. Sound argument A valid argument whose premises are true. Spin A type of rhetorical device, often in the form of a red herring or complicated euphemism, to disguise a politician s statement or action that might otherwise be perceived in an unfavorable light. Square of opposition A table of the logical relationships between two categorical claims that have the same subject and predicate terms. Standard-form categorical claim Any claim that results from putting words or phrases that name classes in the blanks of one of the following structures: All are ; No are ; Some are ; and Some are not. Stare decisis Letting the decision stand. Going by precedent. Statistically significant From a statistical point of view, probably not due to chance. Statistical regression In layman s terms statistical regression is the fact that if on one measurement the values of a variable are on average exceptionally high or low, then on a subsequent measurement the average will be closer to the norm. In other words, the exceptional average will regress toward the normal average on the subsequent measurement. Statistical syllogism A syllogism having this form: Such-and-such proportion of Xs are Ys. This is an X. Therefore this is a Y. Stereotype An oversimplified generalization about the members of a class. Stipulative definition A definition (of a word) that is specific to a particular context. Straw man A type of fallacious reasoning in which someone ignores an opponent s actual position and presents in its place a distorted, exaggerated, or misrepresented version of that position. Stronger/weaker arguments The more likely the premise of an inductive argument makes the conclusion, the stronger the argument, and the less likely it makes the conclusion, the weaker the argument. Subcontrary claims Two claims that can both be true at the same time but cannot both be false at the same time. Subject term The noun or noun phrase that refers to the first class mentioned in a standard-form categorical claim. Subjective claim A claim not subject to meaningful dispute if the speaker thinks it is true. See Subjective statement. Subjective expression An expression you can use pretty much as you please and still be using it correctly. Subjective issue See Subjective question. Subjective question A question that calls for a subjective opinion for an answer. Subjective statement A statement which is made true by the speaker s thinking it is true. Subjectivist fallacy This pattern of fallacious reasoning: Well, X may be true for you, but it isn t true for me, said with the intent of dismissing or rejecting X. Syllogism A deductive argument with two premises. Syntactically ambiguous claim An ambiguous claim whose ambiguity is due to the structure of the claim.

8 508 GLOSSARY Synthetic claim A claim whose truth value is not known by simply understanding the claim an observation of some sort is also required. Contrast with analytic claim. Term A noun or noun phrase. Tradition, argument from Arguing that a claim is true on the grounds that it is traditional to believe it is true. Truth In this book we use the concept in a commonsense way: A claim is true if it is free from error. Truth-functional equivalence Two claims are truth-functionally equivalent if and only if they have exactly the same truth table. Truth-functional logic A system of logic that specifies the logical relationships among truthfunctional claims claims whose truth values depend solely upon the truth values of their simplest component parts. In particular, truthfunctional logic deals with the logical functions of the terms not, and, or, if... then, and so on. Truth table A table that lists all possible combinations of truth values for the claim variables in a symbolized claim or argument and then specifies the truth value of the claim or claims for each of those possible combinations. Two wrongs make a right This pattern of fallacious reasoning: It s acceptable for A to do X to B because B would do X to A, said where A s doing X to B is not necessary to prevent B s doing X to A. Utilitarianism The moral position that, if an act will produce more happiness than its alternatives, that act is the right thing to do, and if the act will produce less happiness than its alternatives, it would be wrong to do it in place of an alternative that would produce more happiness. Vague claim A claim that lacks sufficient precision to convey the information appropriate to its use. Vague generality A general statement too vague to be meaningful for practical purposes. Vagueness A word or phrase is vague if the group of things to which it applies has borderline cases. Valid argument An argument for which it is not possible for the premise to be true and the conclusion false. See also good deductive argument. Value judgment A claim that assesses the merit, desirability, or praiseworthiness of someone or something. Also called a normative or a prescriptive statement. Variable Something that varies. In deductive reasoning, the most important variables are terms, claims, and arguments. In inductive generalizing from samples, inductive arguments from analogy, and arguments for causal claims, the most important variables are attributes. Venn diagram A graphic means of representing a categorical claim or categorical syllogism by assigning classes to overlapping circles. Invented by English mathematician John Venn ( ). Virtue ethics The moral position unified around the basic idea that each of us should try to perfect a virtuous character that we exhibit in all actions. Weak analogy Overestimating the probability of a conclusion derived from an argument from analogy, a fallacy. Weak argument See stronger/weaker arguments. Weaseler An expression used to protect a claim from criticism by weakening it. Wishful thinking Accepting a claim because you want it to be true, or rejecting it because you don t want it to be true. Worse than average illusion See better than average illusion.

9 Answers, Suggestions, and Tips for Triangle Exercises Chapter 1: Critical Thinking Basics Exercise An argument consists of two parts, one of which is intended to provide a reason for accepting the other part. 4. F 7. T 10. F. As an example of an opinion that isn t subjective, we (the authors) are of the opinion there is life somewhere else in the universe. If there is life, our opinion is true. If there isn t, then it is false. We don t know whether our opinion is true or false, but we do know that it is one or the other, and we know that whether it is true or false is independent of what we think. 13. c. The first order of business is to determine what the issue is. 16. F. The only foolproof way we know of avoiding errors in thinking is to not think at all. 19. d Exercise This item belongs in one group. 4. This item belongs in the same group as item This belongs in a different group from 1 and This belongs in the same group as 1 and 4. Exercise Not objective 4. Not objective 7. Not objective 10. Objective Exercise Subjective 4. Subjective 7. Not subjective 10. Not subjective, unless the speaker intends to imply that Kerry s chin is unattractive, in which case the assertion would be subjective. Exercise Argument 4. Not an argument 7. No arguments here 10. Our conclusion is that this is an argument. Exercise Does not contain an argument. 4. Argument, whose conclusion is that computers will never be able to converse intelligently through speech. 7. Argument, whose conclusion is that chemicals in teething rings and soft plastic toys may cause cancer. 10. Does not contain an argument. Exercise a 4. c 7. b 10. b Exercise We (the authors) think we probably tend to overestimate the probability of types of events that are fresh in our minds (availability heuristic). 4. If we were in Jamela s position, we would want to get little Priglet. As a result, we would have a tendency to think that arguments in favor of our getting Priglet outweighed arguments against doing so. This is belief bias. Exercise Contains an argument whose conclusion is the stock market probably will go down. 4. Contains an argument whose conclusion is that probably more women than men are upset by pornography. 7. Does not contain an argument. 10. Subtle, but the speaker is giving a reason for thinking AI is the best talent show on TV. So the passage contains an argument whose conclusion is that contention. Exercise a 4. e. The issue is whether the United States should realize that reliance on imprisonment is not an effective method of reducing crime. 7. e. The issue is whether it is surprising that the winner of this year s spelling bee is a straight A student whose favorite subject is science.

11 ANSWERS, SUGGESTIONS, AND TIPS FOR TRIANGLE EXERCISES Premise: Presbyterians are not fundamentalists. Premise: All born-again Christians are fundamentalists. Conclusion: No born-again Christians are Presbyterians. 10. Premise: The clunk comes only when I pedal. Conclusion: The problem is in the chain, the crank, or the pedals. Exercise Conclusion: There is a difference in the octane ratings between the two grades of gasoline. 4. Conclusion: Scrub jays can be expected to be aggressive when they re breeding. 7. Conclusion: Dogs are smarter than cats. 10. Unstated conclusion: She is not still interested in me. Exercise Deductive demonstration 4. Inductive support 7. Inductive support 10. Deductive demonstration Exercise b 4. b 7. b 10. b Exercise Inductive 4. True 7. Deductive 10. Inductive 13. T 17. F Exercise Deductive demonstration 2. Inductive support 4. Inductive support 7. Two arguments here. In the first argument, if the speaker is assuming that the universe s not having arisen by chance increases the probability that God exists, then his or her argument is inductive. Likewise, in the second argument, if the speaker is assuming that an increase in the number of believing physicists increases the probability that God exists, then his or her argument is inductive. 8. Inductive support Exercise Separate arguments 6. Separate arguments 9. Separate arguments 10. Separate arguments 13. Does not contain separate arguments Exercise To explain 4. To explain 7. To explain 9. To argue Exercise a 4. a 7. a 10. a Exercise Anyone who keeps his or her word is a person of good character. 4. One cannot murder someone without being in the same room. 7. Anyone who commits murder should be executed. 10. All squeaking fans need oil. Exercises Puddles everywhere usually indicate a recent rain. 4. The next day after a week of cold weather usually is cold. 7. Having leftovers is an indication that a party wasn t successful. 10. My cold probably would not have disappeared like magic if I had not taken Zicam. Exercise Exercise Your distributor is the problem. 2 There s no current at the spark plugs. 3 If there s no current at the plugs, then either your alternator is shot or your distributor is defective.

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