CRITICAL INQUIRY PART THREE CHAPTER 2 OBJECTIVES • Students will learn to: • Recognize complications regarding premises and conclusions • Distinguish between deductive and inductive arguments • Understand the standards for validity, soundness, strength, and weakness in arguments • Assess an argument with an unstated premise • Distinguish between ethos, pathos, and logos • Identify a balance-of-considerations argument • Identify an inference to the best explanation (IBE) • Use techniques for understanding arguments CHAPTER 2 • Arguments: General Features • • • • Introduction Examples of Arguments Conclusions Used as Premises (Extended Argument) Unstated Premises & Unstated Conclusions • Two Kinds of Arguments • Deductive Arguments • Good Deductive Argument • Valid Argument • Invalid Argument • Sound Argument • Unsound Argument CHAPTER 2 • Inductive Arguments • Inductive Arguments • Strong Argument • Weak Argument • Uses of Inductive Arguments • • • • Generalization Analogy Past to Future Causal Reasoning • Recap: The Basic Types of Arguments • Deductive: valid/invalid, sound/unsound • Inductive: strong/weak • Beyond a Reasonable Doubt • Deductive Proof CHAPTER 2 • Deduction, Induction & Unstated Premises • Introduction • Deductive or Inductive Reconstruction • Reconstruction CHAPTER 2 • Balance of Considerations and IBES • Balance of Considerations Reason • Inference to the Best Explanation • Deductive: Valid or invalid? • Inductive: Strong or weak? • What are Not Premises, Conclusions or Arguments • • • • • Introduction Pictures If…then…sentences Lists of Facts “A because B” CHAPTER 2 • Ethos, Pathos and Logos • • • • Aristotle’s Theory of Persuasion Ethos Pathos Logos • Techniques for Understanding Arguments • Introduction • Steps • Distinguishing arguments from window dressing • What is the author trying to prove? • What reasons are given? CHAPTER 2 • Evaluating Arguments • Introduction • Do the premises support the conclusion? • Deductive: Valid or invalid? • Inductive: Strong or weak? • Are the premises reasonable? • Guidelines • Credible source, observations, background information, credible claims. • Conflict • Vague, ambiguous, unclear. CHAPTER 2 RECAP • Arguments consist of a premise (or premises) and a conclusion. • The same claim can be a premise in one argument and a conclusion in a second argument. • The two fundamental types of reasoning are deductive demonstration and inductive support. • A deductive argument is used to demonstrate or prove a conclusion, which it does if it is sound. • An argument is sound if it is valid and its premise (or premises) is true. • An argument is valid if it is impossible for its premise (or premises) to be true and its conclusion to be false. • An inductive argument is used to support rather than to demonstrate a conclusion. • Support is a matter of degrees: An argument supports a conclusion to the extent its premise (or premises) makes the conclusion likely. • An argument that offers more support for a conclusion is said to be stronger than one that offers less support; the latter is said to be weaker than the former. • , compatibility with well-accepted explanations, and freedom from unnecessary assumptions. CHAPTER 2 RECAP • Some instructors use the word “strong” in an absolute sense to denote inductive arguments whose premise (or premises) makes the conclusion more likely than not. • Inductive arguments and deductive arguments can have unstated premises. • Whether an argument is deductive or inductive may depend on what the unstated premise is said to be. • If the argument you are contemplating is one someone has offered you, and you are having trouble tracking the part of an argument that appears in a written passage, try diagramming the passage. • Balance of considerations reasoning involves deductive and inductive elements. If considerations are compared quantitatively, weighing them involves deductive reasoning. Predictions as to outcomes involve inductive reasoning. • Inference to best explanation is a common type of inductive reasoning in which one tries to determine the best explanation for a phenomenon by comparing alternative hypotheses in terms of their explanatory adequacy, predictive accuracy CHAPTER 10 OBJECTIVES • Students will learn to: • Identify and differentiate statistical syllogisms, inductive generalizations from samples, and inductive arguments from analogy • Explain the Principle of Complete Evidence in inductive reasoning • Define and explain the key terms related to samples and sampling • Differentiate between scientific generalizing from samples and everyday generalizing from samples • Apply the two principles of evaluating everyday generalizations from samples • Analyze analogies and analogues • Identify informal indicators of confidence levels and error margins • Understand and identify various fallacies related to induction CHAPTER 10 • Introduction • Inductive Arguments • Defined • Strong/Weak • Relative Strength & Relative Probability • Relative strength of the argument/probability of the conclusion. • Principle of Total Evidence • Additional Information • Makes the conclusion more likely. • The original argument is neither stronger nor weaker. CHAPTER 10 • Arguing from the General to the Specific (Statistical Syllogism) • Form of an Inductive/Statistical Syllogism • Premise 1: Such-and such Xs are Ys • Premise 2: This is an X • Conclusion: Therefore this is a Y. • Real World Syllogisms • Assessment • The higher the % of Xs that are Ys, the stronger the argument. • Other factors might affect the probability that a specific X is Y. CHAPTER 10 • Arguing from the Specific to the General (Inductive Generalization) • Determining What %of Xs are Ys • Samples • Form of an Inductive Generalization • Premise 1: P% of observed Xs are Ys • Conclusion: P% of all Xs are Ys. • Terms • • • • Sample N Target/Target Class/Target Population (all Xs) Feature/Property in Question (Y) • Sample Frame • How likely? • Target Population & Feature • Sampling Frames CHAPTER 10 • Bias & Representative • The strength depends on whether Y/X in the sample = Y/X in the population. • Representative sample. • • • • Random Sample Error Margin & Confidence Level Sample Size Confidence Level of 95 CHAPTER 10 Sample Size Error Margin (%) Corresponding Range (percentage points) 10 +/- 30 60 25 +/- 22 44 50 +/- 14 28 100 +/- 10 20 250 +/- 06 12 500 +/- 04 8 1,000 +/- 03 6 1,500 +/- 02 4 CHAPTER 10 • Everyday Generalizing from a Sample • Everyday generalizing differs from scientific generalization • Samples • Variable • Representative • Assessing Samples • • • • Size Diversity Bias Homogeneous • Two Basic Principles for Assessing samples • A difference that biases a sample weakens the argument. • Samples that are too small or undiversified weaken the argument. • Examples CHAPTER 10 • Reasoning from the Specific to the Specific: Inductive Arguments from Analogy • Introduction • The Way Inductive Arguments from Analogy Work • Form • Premise 1: X and Y both have properties P, Q, R • Premise 2: X has feature F. • Conclusion: Therefore Y has feature F. • Example • Concepts • Analogues • Probabilities • Not about gauging the probability of the conclusion. • Principle of Total Evidence CHAPTER 10 • Assessment • • • • • Relative strength Relevant similarities & differences The more diversified the similarities, the stronger the argument. The more diversified the differences, the weaker the argument. Contrary analogue • Attacking the Analogy • Guidelines for thinking critically about an argument from analogy • The more numerous and diversified the similarities, the stronger the argument. • The more numerous and diversified the differences, the weaker the argument. • Examples CHAPTER 10 • Other Uses of Analogies • Analogies • Moral & Legal Analogies • The principle of relevant difference • Explanations • Historical Analogies • Logical Analogies CHAPTER 10 • Reasoning from General to General • Summary • Reasoning from the general to the specific: statistical syllogism. • Reasoning from the specific to general: inductive generalizing from samples. • Reasoning from the specific to the specific: inductive arguments from analogy. • Reasoning from the General to the General • Drawing a conclusion about one population by considering the attributes of another. • An argument from analogy using populations. • Examples CHAPTER 10 3 KINDS OF INDUCTIVE ARGUMENTS • Illicit Inductive Conversions • Conversion • Deduction • The Form • Premise 1: __ Xs are Ys • Conclusion: Therefore __Ys are Xs • The blank is filled in with percentages or terms implying percentages. • Deductive categorical logic & conversion • Inductive logic & conversion • Examples • Examples • Example: medical tests CHAPTER 10 • Informal Error-Margin and Confidence Level Indicators • Introduction • Confidence level • • • • Informal confidence level indicator phrases Informal error margin indicator words. More on Confidence Levels Estimation of Probability • Estimation • Matching error margin and confidence level indicators to the size and representativeness of the sample. CHAPTER 10 • Fallacies in Inductive Reasoning • Fallacy of Hasty Generalization • A generalization based on a sample that is too small to be representative. • The fallacy arises from overestimating the strength of the argument based on a small sample. • Examples • Fallacy of Anecdotal Evidence • Drawing a conclusion from an anecdote about one or a very small number of cases. • Overestimating the strength of the argument based on overestimating • Ignoring data that supports a general claim in favor of an example or two that runs against the evidence. • Examples • Fallacy of Biased Generalization/Analogy • Basing a generalization/analogy on a biased sample. • Overestimating the strength of an argument based on a non-representative sample. • Examples CHAPTER 10 • The Self Selection Fallacy • Self-selected sample • Self-selection fallacy: estimating the probability of a conclusion derived from a relatively large but self-selected sample. • Examples • Person on the street interviews, telephone surveys, and questionnaires. • Slanted Questions • • • • • Ways of asking Sequence No opinion Loaded questions Push polling CHAPTER 10 • Weak Analogy • Overestimating the probability of a conclusion derived from an argument from analogy. • Weak/poor/false analogy: the analogues in an analogical argument are too dissimilar to justify the inference from one to another. • Vague Generalities • • • • • A general statement that is too vague to be meaningful. Examples Testable by specifying a sample frame Glowing generality Opposite of a glowing generality CHAPTER 10 RECAP • • • • • • • • • • Inductive reasoning is used to support a conclusion rather than to demonstrate or prove it. Inductive arguments can be depicted as relatively strong or relatively weak, depending on how much their premises increase the probability of the conclusion. The strength of an argument is distinct from the overall probability of the conclusion. You can have a relatively strong argument for a conclusion whose overall probability is very low, and a relatively weak argument for a conclusion whose overall probability is quite high. Statistical syllogisms have the form: Most Xs are Ys; this is an X; therefore this is a Y. The strength of a statistical syllogism is distinct from the probability of its conclusion everything considered. The latter depends on The Principle of Total Evidence. The former depends on the proportion of Xs that are Ys. Everyday inductive generalizations from samples differ from scientific inductive generalizations from samples in that everyday samples are not scientifically selected to eliminate bias, and probabilities in everyday generalizing cannot be calculated precisely. Thinking critically about everyday generalizations from samples involves the two principles stated on page 355. Inductive reasoning from analogy is based on the idea that things alike in some respects will be alike in further respects. Thinking critically about inductive arguments from analogy involves the principles stated on page 365. The time-honored strategy for rebutting an argument from analogy is to “attack the analogy” by calling attention to important dissimilarities between the analogues. CHAPTER 10 RECAP • Arguments from analogy are especially important in ethics, history, and law, and to refute other arguments. • We can support a conclusion about one population by reasoning analogically from a second population that has similar attributes. • Page 383 • An overestimation of the strength of an argument based on a small sample is “hasty generalization.” • An overestimation of the strength of an argument based on a biased but not-so-small sample is “biased generalization.” • The fallacy of “anecdotal evidence” is a version of hasty generalization in which the sample is presented as a narrative. • Generalizations based on anecdotes are often persuasive psychologically, even though they are based on a sample of one. • The self-selection fallacy is a version of biased generalization in which the sample is self-selected. • When we overestimate the probability of a conclusion derived from an argument from analogy, we commit the fallacy called weak analogy. • Vague generalizations suffer not so much from lack of support as from lack of substantive meaning. CHAPTER 11 OBJECTIVES • Students will learn to: • • • • • • • Differentiate between arguments and explanations Recognize two important types of explanations Apply standards for evaluating explanations Apply methods for forming causal hypotheses Learn methods for confirming causal hypotheses Recognize mistakes in causal reasoning Distinguish the concept of cause as it applies to law CHAPTER 11 CAUSAL ARGUMENTS • Introduction • Explanations & Arguments • Arguments • Explanations • Arguments & Explanations • Two Kinds of Explanations • Physical causal explanations • • • • Examples Physical background Complication Adequate • • • • • Examples Behavioral Not fully predictable Future Mistake: reason for vs. a person’s reason for • Behavioral causal explanations CHAPTER 11 CAUSAL ARGUMENTS • Explanatory Adequacy: A Relative Concept • Introduction • Adequate explanations cannot be: • • • • • Self contradictory Vague Ambiguous Incompatible with established facts/theories Lead to false predictions • The Importance of Testability • Predictions • Nontestable Explanations • Circular Explanations CHAPTER 11 CAUSAL ARGUMENTS • Unnecessary Complexity • Adequate explanations should: • • • • • Be consistent Not conflict with established fact/theory Be testable Not be circular Avoid unnecessary assumptions/complexities. • Forming Hypotheses • Introduction • Hypothesis • Forming a hypothesis and testing an hypothesis • Inference to the best explanation CHAPTER 11 CAUSAL ARGUMENTS • The Method of Difference • The method • Examples • Hypothesis confirmation • The Method of Agreement • • • • • • • • Correlation Associated events Cause Covariation The Method Correlation Cum hoc, ergo propter hoc (with that, therefor because of that) Post hoc, ergo propter hoc (after this, therefore because of this) CHAPTER 11 CAUSAL ARGUMENTS • Causal Mechanism s & background Knowledge • The method • Examples • Hypothesis confirmation • The Best Diagnosis Method • Finding a causal hypothesis • Best Diagnosis Method • General Causal Claims • Introduction • Specific & General Causal Claims • Specific casual claim • General causal claim • X causes Y in population P: there would be more cases of Y in P if every member of P were exposed to Y than if no member of P were exposed to X. CHAPTER 11 CAUSAL ARGUMENTS • Confirming Causal Hypotheses • Introduction • Controlled Cause-to-Effect Experiments • Process • Concepts • Frequency & Statistical Significance CHAPTER 11 CAUSAL ARGUMENTS Number in Experimental Group (with similarly sized control group) Approximate Figure That d Must Exceed To Be Statistically Significant (in percentage points) 10 40 25 27 50 19 100 13 250 8 500 6 1,000 4 1,500 3 CHAPTER 11 CAUSAL ARGUMENTS • Alternative Methods of Testing Causal Hypotheses in Human Populations • Nonexperimental Cause-To-Effect Studies • Definition • Difference from a controlled cause-to-effect experiment • Experimental group is not exposed to the suspected causal agent, C. • Are exposed to C by their own actions or circumstances. • Causal agent • Difference • The experimental group is randomly selected from individuals who • Have already been exposed to C. • Self-selection & Bias • Inherently weaker than controlled experiments. CHAPTER 11 CAUSAL ARGUMENTS • Nonexperimental Effect-To-CauseStudies • Definition: to test whether something is a causal factor for an effect. • Difference from a controlled cause-to-effect experiment • The experimental group displays effect E. • The control group does not display the effect. • Causal agent • The experimental group might differ in important ways . • Probably frequency of the cause, not the effect. • Animal Testing • Mistakes in Causal Reasoning • Reasons to Reject Causal Explanations • • • • Unduly complicated Incompatible with known facts and theories Vague, ambiguous, or circular Inherently untestable. CHAPTER 11 CAUSAL ARGUMENTS • Post Hoc, Ergo Propter Hoc • Defined • Form • P1: As immediately precede Bs (or this A precedes this B). • C: Therefore, As cause Bs (or this A causes this B). • Cum Hoc Ergo Propter Hoc • Defined • Form • P1: As are correlated with Bs. • C: As cause Bs. • Why These are Fallacies • They do not establish the improbability of three possibilities • Possibility 1: The connection between A and B is coincidental • Possibility 2: Both A and B result from a third thing (an underlying cause) • Possibility 3: B caused A, rather than A causing B (reversing cause and effect) CHAPTER 11 CAUSAL ARGUMENTS • Confusing Conditional Probability in Medical Tests • The probability that X given Y is distinct from the probability of Y given X. • Testing positive for a condition is the effect of that condition, not the cause. • Knowing the actual chance of having the condition • Example • Known symptoms of a condition • Overlooking Statistical Regression • Statistical regression/regression to the mean • Examples • More examples • Proof by Absence of Disproof • Absence of disproof • Disprove • Absence of disproof is not proof. CHAPTER 11 CAUSAL ARGUMENTS • Appeal to Anecdote • Defined • Examples • Establishing a Causal Factor • Confusing Explanations with Excuses • • • • Not all explanations are intended to be excuses Fallacy of Confusing Explanations & Excuses. Justification Explanation vs. Justification • Causation in the Law • Harm • Conditio sine qua non (“a condition without which nothing) • “But for”: Y would not have happened but for Xs having happened. • Punish • Indefinitely CHAPTER 11 CAUSAL ARGUMENTS • Legal/Proximate Cause • • • • • • Severe Restrictions on Sine Qua Non Sine qua non cause vs. legal proximate cause H.L.A. Hart and A.M. Honore Legal responsibility Intervening forces Coincidence CHAPTER 11 RECAP • 1. Explanations are different from arguments. They are used to elucidate a phenomenon; arguments are used to support or prove a claim. • 2. Sentence that can be used as explanations can also be used to state the conclusion of a premise of an argument. • 3. Explanations serve a variety of purposes. Two important purposes are (1) to provide physical causal explanations of something and (2) to provide behavioral causal explanations of something. • 4. What counts as an adequate explanation is relative to one’s purposes and needs. • 5. An adequate explanation shouldn’t be unnecessarily complicated, inconsistent, incompatible with known fact or theory, or untestable due to vagueness, circularity or other reasons. • 6. Arriving at a causal hypothesis involves an inference to the best explanation. • 7. Methods of arriving at causal hypotheses are the Method of Difference, the Method of Agreement and the Best Diagnosis Method. CHAPTER 11 RECAP • 8. These methods are guided by one’s background knowledge of causal mechanisms, what causes what and how things work. • 9. Confirming a causal hypothesis consists primarily in rigorously applying a combination of the Methods of Difference and Agreement. • 10. Two important mistakes in causal reasoning are post hoc, ergo propter hoc, and cum hoc, ergo propter hoc. • 11. These are mistakes because they do not eliminate the possibility of coincidence, an underlying cause, or confusion between cause and effect. • 12. An important case of confusing effect and cause is forgetting that symptoms are effects. • 13. Changes due to statistical regression are sometimes mistakenly assumed to be due to causation. • 14. Absence of disproof of causation is not equivalent to proof of causation. • 15. Using an anecdote to establish causation or to refute a general causal claim involves hasty generalizing. • 16. Explanations of bad behavior are not always intended to excuse bad behavior. • 17. In the law, in its broadest sense, a “cause” is that “but for” which an effect would not have happened.