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.