2. © 2016 by Pearson Education, Inc.
Chapter 8
Valid Inferences
© 2016 by Pearson Education, Inc.

3. Learning Outcomes
Evaluate the logical strength of inferences presented to imply or entail that their conclusions must certainly be true if we take their premises to be true
Recognize reasoning fallacies masquerading as valid inferences
Learning Outcomes
The chapter first evaluates the logical strength of inferences presented to imply or entail that their conclusions must certainly be true if one takes their premises to be true.
It concludes by recognizing reasoning fallacies masquerading as valid inferences.

4. Chapter Opening Video Chapter Opening Video
The video explains the how valid inferences are drawn.
It shows how just a few valid inferences can be drawn given the limited constraints of the context.

5. Structure of the Reasoning
Inferences offered as certain
Reasoning with declarative statements
Reasoning about classes of objects
Reasoning about relationships
Structure of the Reasoning
Valid: Describes an argument or inference.
Truth of the premises implies that conclusion is true.
False conclusion implies that one or more of the premises is false.
Inferences offered as certain
People make arguments believing that truth of the premises guarantees the truth of the conclusion.
Reasoning with declarative statements
Include valid argument templates that derive their structures from the way simple statements interact grammatically when one uses logical prepositions or adverbs.
Reasoning about classes of objects
Words like some and all are used to express one’s ideas about how individual objects and groups of objects relate.
Reasoning about relationships
Terms that describe relationships help make valid inferences about the objects to which the terms apply.

6. Structure of the Organ Transplant Scenario
The organ transplant scenario is represented in the form of a map.

7. Inferences Offered as Certain
People make arguments believing that truth of the premises guarantees truth of the conclusion
Thoughtful and fair-minded interpretation is essential
Context and intention of the argument maker are to be considered
Inferences Offered as Certain
People make arguments believing that truth of the premises guarantees truth of the conclusion.
Aristarchus deduced that the Sun was much larger than the Earth.
Carl Sagan explains that there was no other inference Aristarchus could draw except that the Sun was large and far away.
Thoughtful and fair-minded interpretation is essential.
People do not always speak with logical precision.
Context and the intention of the argument maker should be considered.

8. Inferences Offered as Certain
Laws of nature or logic cannot be suspended
Logical strength of an inference can be evaluated by a counterexample
Inferences Offered as Certain
Laws of nature or logic cannot be suspended.
Strong critical thinking requires people not to attribute more than the argument maker intends.
Logical strength of an inference can be evaluated by a counterexample.
Argument is not valid if all the premises are true but the conclusion is false in a counterexample.

9. Reasoning with Declarative Statements
Denying the consequent
Premise #1 - If A, then B
Premise #2 - Not B
Conclusion - Therefore, not A
Affirming the antecedent
Premise #2 - A
Conclusion - Therefore, B
Reasoning with Declarative Statements
Denying the consequent
Premise #1 - If A, then B.
Premise #2 - Not B.
Conclusion - Therefore, not A.
Logical strength is not the only consideration when evaluating real life arguments.
Facts and logic are different things.
Affirming the antecedent - Argument template relies on the meaning and grammatical power of “if then” expressions and the second premise confirms that the “if” portion is true.
Premise #2 – A.
Conclusion - Therefore, B.

10. Reasoning with Declarative Statements
Disjunctive syllogism
Premise #1 - Either A or B
Premise #2 - Not A
Conclusion - Therefore, B
Reasoning with Declarative Statements
Disjunctive syllogism - People presented with various alternatives logically reduce options.
Premise #1 - Either A or B.
Premise #2 - Not A.
Conclusion - Therefore, B.

11. Grammatically Equivalent Structures
Certain grammatically equivalent structures provide multiple ways to express the same thing.

12. Simulation Simulation
This simulation helps practice with “neither, unless and only” arguments.

13. Reasoning About Classes of Objects
Applying a generalization
Premise #1 - Every member of group F is a member of group G
Premise #2 - Individual object X is a member of F
Conclusion - Object X is a member of G
Reasoning About Classes of Objects
Applying a generalization - When a generalization asserts that a given characteristic to each of the members of a class of objects, it is logical to conclude that a given individual or subgroup of individuals that are members of the class possess that characteristic.
Premise #1 - Every member of group F is a member of group G.
Premise #2 - Individual object X is a member of F.
Conclusion - Object X is a member of G.

14. Reasoning About Classes of Objects
Applying an exception
Premise #1 - Every member of group F is a member of group G
Premise #2 - Object X is not a member of G
Conclusion - Object X is not a member of F
Power of only
Only has the ability to change the meaning of a sentence depending on where it is placed
Reasoning About Classes of Objects
Applying an exception - If every member of a given class of objects has a certain characteristic, and one or more specific objects do not have that characteristic, it is logical to infer that specific objects are not members of the class.
Premise #1 - Every member of group F is a member of group G.
Premise #2 - Object X is not a member of G.
Conclusion - Object X is not a member of F.
Power of only
Only has the ability to change the meaning of a sentence depending on where it is placed.

15. Simulation Simulation
This simulation helps practice with arguments pertaining to classes and objects.

16. Power of Only Power of Only
Meanings change depending on where only is positioned in the example.

17. Power of Only Power of Only
Meanings change depending on where only is positioned in the example.

18. Reasoning About Relationships
Terms that describe relationships help make valid inferences about the objects to which the terms apply
Transitivity relationship
If x has a transitive relationship to y, and y has the same transitive relationship to z
x has the same transitive relationship to z
Reasoning About Relationships
Terms that describe relationships help make valid inferences about the objects to which the terms apply.
Example - John is Susan’s younger brother. So, they must have the same mother or the same father.
Understanding of the logical implications of relational terms is part of one’s comprehension of language.
Transitivity relationship
If x has a transitive relationship to y, and y has the same transitive relationship to z.
x has the same transitive relationship to z.
Example - David is Stanley’s neighbor. So, Stanley is David’s neighbor.

19. Reasoning About Relationships
Reflexivity relationship
If x has a reflexive relationship to y, then y has the same reflexive relationship to x
Identity relationship
If x is y, then y is x
Reasoning About Relationships
Reflexivity relationship
If x has a reflexive relationship to y, then y has the same reflexive relationship to x.
Example - Leonardo DiCaprio played Jordan Belfort in the 2013 film The Wolf of Wall Street.
Actor who played Jordan Belfort in that film was nominated for an Oscar.
So, Leonardo DiCaprio received an Oscar nomination for his performance in that film.
Identity relationship
If x is y, then y is x.

20. Discussion Question
“Eliminate all other factors, and the one which remains must be the truth” - Sherlock Holmes
Is it possible to follow Sherlock Holmes’ advice on how to figure out the one right answer to a problem?
Discussion Question
Sir Arthur Conan Doyle’s character calls the arguments he put forth with certainty deductions.
"Eliminate all other factors, and the one which remains must be the truth“ - Sherlock Holmes
Is it possible to follow Sherlock Holmes’ advice on how to figure out the one right answer to a problem?

21. Fallacies Masquerading as Valid Arguments
Fallacies when reasoning with declarative statements
Fallacies when reasoning about classes of objects
Fallacies of false reference
Personal infallibility?—We don't think so
Fallacies Masquerading as Valid Arguments - Precision of thought and expression helps avoid mistakes when making or evaluating arguments offered as valid inferences.
A counterexample has the ability to:
Reveal the illogical structure.
Expose the fallacy.
Suppress the argument’s apparent persuasiveness.
Fallacies when reasoning with declarative statements
Familiar fallacies can mimic logically correct declarative statements.
Fallacies when reasoning about classes of objects
False classification, and fallacies of composition and division are errors committed while reasoning about classes of objects.
Fallacies of false reference
Occur when reasoning about relationships like identity, reflexivity, or transitivity.
Personal infallibility? —We don't think so
A healthy sense of skepticism, the study of human history, and life experience suggests that the probability of personal infallibility approximates zero.

22. Fallacies When Reasoning with Declarative Statements
Affirming the consequent
Premise #1 - If A, then B
Premise #2 - B
Conclusion - Therefore, A
Not logical to believe that A must be true because B is true
Fallacies When Reasoning with Declarative Statements
Affirming the consequent
Premise #1 - If A, then B
Premise #2 - B
Conclusion - Therefore, A
A may not be the only condition that brings about B.
Not logical to believe that A must be true because B is true.

23. Fallacies When Reasoning with Declarative Statements
Denying the antecedent
Premise #1 - If A, then B
Premise #2 - Not A
Conclusion - Therefore not B
Not logical to think that B cannot happen because A does not happen
Fallacies When Reasoning with Declarative Statements
Denying the antecedent
Premise #1 - If A, then B
Premise #2 - Not A
Conclusion - Therefore not B
A may not be the only condition that brings about B.
Not logical to think that B cannot happen because A does not happen.

24. Fallacies When Reasoning About Classes of Objects
False classification
Example - Criminals enjoy mafia movies and Cassandra enjoys mafia movies
Does not apply that Cassandra is a criminal
Fallacies When Reasoning About Classes of Objects
False classification
Example - Criminals enjoy mafia movies and Cassandra enjoys mafia movies.
Does not apply that Cassandra is a criminal.
A feature or attribute can be true of two groups without requiring that one group must be classified as part of the other group.

25. Fallacies When Reasoning About Classes of Objects
Fallacies of composition
A group and each of its members may not have the same attributes
Fallacies of division
Attribute to each individual member of a group a characteristic that is true of the group as a whole
Fallacies When Reasoning About Classes of Objects
Attribute that applies to the parts may not apply to the whole, or vice versa.
Fallacies of composition
A group and each of its members may not have the same attributes.
Example - It is in each person’s financial interest to cheat a little on his or her income tax return.
So, it is financially good for the nation if people cheat on their taxes.
Fallacies of division
Attribute to each individual member of a group a characteristic that is true of the group as a whole.
Example - The United States of America has the right to enter into treaties and to declare war.
Therefore each of the 50 states has the right individually to declare war or to enter into treaties.

26. Fallacies of False Reference
Occur when reasoning about relationships
Identity, reflexivity, or transitivity
Comparable reasoning mistake
Occurs when people are not aware that same object, person, or event can be identified using multiple descriptions
Fallacies of False Reference
Occur when reasoning about relationships.
Identity, reflexivity, or transitivity.
The ambiguity of certain expressions can be the source of a mistaken inference.
Comparable reasoning mistake
Occurs when people are not aware that same object, person, or event can be identified using multiple descriptions.
Knowing, believing, wanting, or intending something when it is described or named in one way does not imply that the person knows, believes, wants, or intends that same thing as described or named in another way.
Example - Tyler at age 10 has often told his Mom that in college he wants to learn how big buildings and bridges are built. These are subjects addressed in civil engineering. Therefore, Tyler has announced that he plans to major in civil engineering in college.
Tyler is 10 years old. He has no idea what civil engineering is.

27. Personal Infallibility?
The human species is capable of inferring with certainty the implications of rules, laws, principles, and regulations
Capacity for certainty drives people toward wrongheaded conclusions
Probability of personal infallibility approximates to zero
Personal Infallibility?
The human species is capable of inferring with certainty the implications of rules, laws, principles, and regulations.
Power to reason with certainty can lead to ominous results.
Capacity for certainty drives people toward wrongheaded conclusions.
Probability of personal infallibility approximates to zero.
Not all beliefs, values, assumptions, and interpretations are true.

28. Sketchnote Video Sketchnote Video
The video summarizes how valid inferences can be made using the limited number of constraints and rules of the context.