Part 3: Arguments - The Power of Critical Thinking

Vocabulary and definitions from Part 3 (Arguments) of The Power of Critical Thinking (8th Edition).

Argument

A group of statements in which one or more statements (premises) are offered as reasons for another statement (the conclusion).

Premise

A statement that provides evidence or support for the conclusion.

Conclusion

The statement the argument is trying to prove.

Inference

The reasoning process of moving from premises to a conclusion.

Indicator Words

Words that help identify premises or conclusions.

Premise Indicators

Examples include because, since, for, given that, assuming that, and seeing that.

Conclusion Indicators

Examples include therefore, thus, hence, so, consequently, it follows that, and accordingly.

Deductive Argument

An argument in which the premises are intended to guarantee the truth of the conclusion.

Valid Argument

An argument where it is impossible for all the premises to be true and the conclusion false.

Invalid Argument

An argument where the premises could be true while the conclusion is false.

Sound Argument

A deductive argument that is both valid and has all true premises.

Unsound Argument

A deductive argument that is either invalid or contains at least one false premise.

Necessary Truth

A statement that cannot possibly be false.

Contingent Truth

A statement that could be true or false depending on reality.

Modus Ponens

A valid form expressed as: If $P$ then $Q$. $P$. Therefore, $Q$.

Modus Tollens

A valid form expressed as: If $P$ then $Q$. Not $Q$. Therefore, not $P$.

Hypothetical Syllogism

A valid form expressed as: If $P$ then $Q$. If $Q$ then $R$. Therefore, if $P$ then $R$.

Disjunctive Syllogism

A valid form expressed as: $P$ or $Q$. Not $P$. Therefore, $Q$.

Affirming the Consequent

An invalid form expressed as: If $P$ then $Q$. $Q$. Therefore, $P$.

Denying the Antecedent

An invalid form expressed as: If $P$ then $Q$. Not $P$. Therefore, not $Q$.

Statement (Proposition)

A sentence that is either true or false.

Simple Statement

Contains one idea and no logical connectives.

Compound Statement

Contains two or more simple statements joined by connectives.

Negation ($\sim$)

Means “not.”

Conjunction ($\bullet$)

Means “and.” True only if both statements are true.

Disjunction ($\lor$)

Means “or.” False only if both statements are false.

Conditional ($\supset$ or $\rightarrow$)

Means “if…then.” False only when the antecedent is true and the consequent is false.

Biconditional ($\equiv$ or $\leftrightarrow$)

Means “if and only if.” True when both statements have the same truth value.

Antecedent

The “if” part of a conditional.

Consequent

The “then” part of a conditional.

Truth Value

Whether a statement is true (T) or false (F).

Tautology

A statement that is always true.

Contradiction

A statement that is always false.

Contingency

A statement that is true in some situations and false in others.

Inductive Argument

An argument whose premises make the conclusion probably true instead of guaranteed.

Strong Argument

If the premises are true, the conclusion is highly likely.

Weak Argument

The premises provide little support for the conclusion.

Cogent Argument

A strong inductive argument with true premises.

Uncogent Argument

An inductive argument that is weak or has false premises.

Statistical Syllogism

Applies information about a group to an individual member.

Enumerative Induction

Draws a general conclusion from a sample.

Sample

The group actually observed.

Population

The entire group being studied.

Representative Sample

A sample that accurately reflects the whole population.

Biased Sample

A sample that unfairly favors one outcome.

Random Sample

A sample chosen so every member has an equal chance of selection.

Sample Size

The number of people or objects studied.

Argument by Analogy

Concludes that because two things are similar in important ways, they are probably similar in another way.

Relevant Similarity

A similarity that actually matters to the conclusion.

Relevant Difference

A difference that weakens the analogy.

Causal Argument

An argument claiming one event causes another.

Cause

Something that produces an effect.

Effect

The result produced by a cause.

Correlation

Two things occur together or change together.

Causation

One thing actually produces another.

Common Cause

A third factor causing both events.

Reverse Causation

The supposed effect actually causes the supposed cause.

Coincidence

Two events occur together by chance.

Inference to the Best Explanation

Choosing the explanation that best fits all the evidence.

Explanatory Power

How well an explanation accounts for the evidence.

Simplicity

A good explanation avoids unnecessary assumptions.

Consistency

An explanation should fit known facts.

Reliability

How dependable the evidence is.

Evidence

Information supporting a conclusion.

Probability

How likely something is to be true.

Counterexample

A case that contradicts a general claim.

Generalization

A conclusion about an entire group based on a sample.

Hasty Generalization

Drawing a broad conclusion from too little evidence.

Unrepresentative Sample

Using a sample that doesn’t reflect the population.

False Cause

Assuming one event caused another without enough evidence.

Correlation vs. Causation

Assuming that because two things happen together, one causes the other.

Weak Analogy

Comparing things that are not similar in relevant ways.

Alternative Explanation

Another possible cause or explanation that wasn’t considered.

Confirmation Bias

Looking only for evidence that supports your beliefs while ignoring evidence against them.

Loaded Language

Emotionally charged words used instead of good evidence.

Ambiguity

Language with more than one possible meaning.

Unsupported Assumption

An unstated premise that must be true for the argument to work.

False Dilemma

Presenting only two options when more exist.

Mean

The arithmetic average.

Median

The middle value when data are ordered.

Mode

The value that appears most often.

Outlier

A value much higher or lower than the rest.