2. Chapter 9
Warranted Inferences

3. Learning Outcomes
Evaluate the logical strength of inferences presented to justify or support the belief that their conclusions are very probably, but not necessarily, true if we take their premises to be true
Recognize reasoning fallacies masquerading as warranted inferences
Learning Outcomes
The chapter evaluates the logical strength of inferences presented to justify or support the belief that their conclusions are probably true.
It further helps to recognize reasoning fallacies masquerading as warranted inferences.

4. Chapter Opening Video Chapter Opening Video
The video explains the concept of warranted inferences.
It shows how the evaluation of logical strength of inferences can lead to believing that the conclusions are probabilistically true.

5. Evidence Currently at Hand
Weight of evidence
Evaluating generalizations
Coincidences, patterns, correlations, and causes
Evidence Currently at Hand
Warranted: Describes an inference or argument.
Truth of the premises justifies accepting the conclusion as very probably true, but not necessarily true.
New information allows to reconsider conclusions without abandoning original premises.
Weight of evidence
Leads people towards a single conclusion.
Evaluating generalizations
Involves examining whether the sampling of cases is adequate to support the probabilistic inferences.
Coincidences, patterns, correlations, and causes
Progression from coincidence to correlation to causal explanations enable us to explain and predict events.

6. Weight of Evidence Leads people towards a single conclusion
Logical strength of probabilistic arguments can be evaluated by systematic method for assigning levels of confidence
Weight of Evidence
Leads people towards a single conclusion.
Logical strength of probabilistic arguments can be evaluated by systematic method for assigning levels of confidence.
Example.
CSI murder story
ISU–Butler

7. Evaluating Generalizations
Generalization is based on data gathered systematically or unsystematically
People over the age of 60 tend to prefer to listen to oldies
73 percent of the hotel room beds in the city are infested with bedbugs
Evaluating Generalizations
Generalization is based on data gathered systematically or unsystematically.
People over the age of 60 tend to prefer to listen to oldies.
73 percent of the hotel room beds in the city are infested with bedbugs.
Greater confidence is placed on the claim supported by data gathered systematically.
Conclusions are supported by:
Premises that report personal experiences.
Conversations focused on topics.
Information derived from historical records or opinion surveys.

8. Evaluating Generalizations
Evaluation of logical strength of probabilistic generalizations
Requires asking questions and finding satisfactory answers
Was the correct group sampled?
Were the data obtained in an effective way?
Were enough cases considered?
Was the sample representatively structured?
Evaluating Generalizations
Evaluation of logical strength of probabilistic generalizations.
Requires asking questions and finding satisfactory answers.
Was the correct group sampled?
Were the data obtained in an effective way?
Were enough cases considered?
Was the sample representatively structured?
Requires more than two counter examples.
Involves examining whether the sampling of cases is adequate to support the probabilistic inferences.

9. Coincidences, Patterns, Correlations, and Causes
Events that occur together by chance
Patterns
Observed in events that initially appear to be random coincidences
Concentration of multi-million dollar luxury casinos in Las Vegas, Atlantic City
Coincidences, Patterns, Correlations, and Causes
Progression from coincidence to correlation to causal explanations enable us to explain and predict events.
Coincidences
Events that occur together by chance.
Probabilistic reasoning and statistical facts are used to calculate the probabilities of a coincidence.
Patterns
Observed in events that initially appear to be random coincidences.
Concentration of multi-million dollar luxury casinos in Las Vegas, Atlantic City.

10. Coincidences, Patterns, Correlations, and Causes
Describe the degree to which two different sets of events are aligned
Calculated using statistical analyses
Causes
Causal explanations are desirable as they enable us to explain, predict, and control parts of the natural world
Coincidences, Patterns, Correlations, and Causes
Correlations
Describe the degree to which two different sets of events are aligned.
Calculated using statistical analyses.
Certain manufacturers use statistical correlations as basis for confidence in their products.
Well-researched correlations are powerful tools.
Causes
Causal explanations are desirable as they enable us to explain, predict, and control parts of the natural world.
Moving from coincidence to correlation to causal explanation is not possible in every field of inquiry.

11. Fallacies Masquerading as Warranted Arguments
Erroneous generalization
Playing with numbers
False dilemma
Gambler’s fallacy
False cause
Slippery slope
Fallacies Masquerading as Warranted Arguments
Fallacies closely resemble genuine article and possess the power to deceive and persuade people.
Erroneous generalization
Generalizations can be deceptively fallacious.
Playing with numbers
Arguments that cite statistics or numbers but do not provide sufficient information to make a good judgment about the significance of numerical data.
False dilemma
Frequently appear to be limited to one option or another.
Gambler’s fallacy
Random events that are not patterned, correlated, or causally connected.
False cause
Assumption that two events are causally related as one happens after the other.
Slippery slope
False assumption that events are linked together.

12. Erroneous Generalization
People make hasty and erroneous generalizations by:
Relying on little information
Exaggerating the importance of one or two particular experiences
Generalizations can be deceptively fallacious
Erroneous Generalization
People make hasty and erroneous generalizations by:
Relying on little information.
Exaggerating the importance of one or two particular experiences.
Generalizations can be deceptively fallacious.
Can result in a claim going beyond what it can support.
Tend to spring from and to reinforce preconceptions.

13. Playing with Numbers Arguments that use:
Raw numbers when percentages would present a fair-minded description
Percentages when raw numbers would present a fair-minded description
Playing with Numbers
Arguments that use:
Raw numbers when percentages would present a fair-minded description.
Percentages when raw numbers would present a fair-minded description.
Arguments that cite statistics or numbers but do not provide sufficient information to make a good judgment about the significance of numerical data.

14. False Dilemma
Real dilemma - Situation in which all our choices are bad
At times, turns out to be a false dilemma on closer analysis
Referred to as the either/or fallacy
False Dilemma
Real dilemma - Situation in which all our choices are bad.
At times, turns out to be a false dilemma on closer analysis.
Frequently appear to be limited to one option or another.
Additional options emerge on further examination.
Referred to as the either/or fallacy.
Creativity offers a way out of a false dilemma.

15. Gambler’s Fallacy
Random events that are not patterned, correlated, or causally connected
People make arguments with wrong assumption that what happens by chance is somehow connected with things we can control
Gambler’s Fallacy
Random events that are not patterned, correlated, or causally connected.
People make arguments with wrong assumption that what happens by chance is somehow connected with things we can control.
Umbrella term to remind ourselves that random events are actually random.
Drawing inferences based on the assumption that they are patterned, correlated, or causally connected is a mistake.

16. False Cause
Assumption that two events are causally related as one happens after the other
Referred as post hoc, propter hoc
False Cause
Assumption that two events are causally related as one happens after the other.
Jumping to a conclusion that the first event caused the second event is a mistake.
Referred as post hoc, propter hoc.
Examples
Confusing temporal proximity with causality.
Confusing a correlation with a cause.

17. Discussion Questions
Give an example of when you connected some action you took with a positive result and then found yourself repeating it in the hope of producing a similar outcome
How did that associational inference work out for you?
Give reasons to support your conclusion
Discussion Questions
Give an example of when you connected some action you took with a positive result and then found yourself repeating it in the hope of producing a similar outcome.
How did that associational inference work out for you?
Was it a warranted inference or was it the result of one of the fallacies described in the chapter?
Give reasons to support your conclusion.

18. Slippery Slope False assumption that events are linked together
First step in the process necessarily results in problems
Slippery Slope
False assumption that events are linked together.
First step in the process necessarily results in problems.
Fallacy fails to remember that people have the power to avoid situations that lead to major issues.

19. Fallacies
Fallacies
Common misleading errors of reasoning in valid and warranted arguments are listed in the above table.

20. Sketchnote Video Sketchnote Video
The video summarizes the process of evaluation of the logical strength of a probabilistic argument.