Reasoning and critical thinking test 1

Claim or proposition

A statement capable of being true or false.

Argument

A set of premises, a conclusion, and an inference connecting the premises to the conclusion.

Premise

A claim presented as a reason or as evidence supporting a conclusion.

Conclusion

The claim that an argument is intended to establish.

Inference

The reasoning step connecting premises to a conclusion.

Premise indicator

A word or expression that often introduces a premise, such as because, since, given that, or considering that.

Conclusion indicator

A word or expression that often introduces a conclusion, such as therefore, thus, hence, so, or it follows that.

Explanation

A passage that assumes something is true and gives reasons why it is true.

Argument versus explanation

An argument tries to establish that something is true; an explanation assumes it is true and explains why.

Simple argument

An argument containing one inference and one conclusion.

Complex argument

An argument containing multiple connected inferences.

Subargument

A smaller argument contained within a complex argument.

Intermediate conclusion

A conclusion supported by earlier premises that is subsequently used as a premise.

Final conclusion

The ultimate conclusion that the complete argument is intended to establish.

Standard form

A numbered presentation that separates premises and conclusions and states which premises support each conclusion.

Principle of charity

The practice of selecting the strongest reasonable interpretation compatible with what an arguer said.

Inference form or pattern

The general reasoning structure shared by different arguments.

Unstated premise

A premise required by an argument but left implicit by the arguer.

Unstated conclusion

A conclusion intended by an argument but not explicitly stated.

Argument diagram

A visual representation showing which premises support which conclusions.

Independent premises

Premises that each provide support for a conclusion separately.

Linked premises

Premises that provide support only when considered together.

Rational acceptability

The degree to which it is reasonable to accept a claim, even when it is not absolutely certain.

Entertaining a premise for the sake of argument

Temporarily assuming a claim in order to determine what would follow if it were true.

Scope

The number or range of objects covered by a claim.

Particular claim

A claim stating that at least one object of a certain kind has or lacks a property.

General claim

A claim concerning a substantial number of objects of a certain kind.

Statistical claim

A general claim that specifies a numerical proportion or percentage.

Universal generalization

A claim concerning every member of a group, such as “All A are B.”

Negative universal generalization

A claim that no member of a group has a property, such as “No A are B.”

Counterexample

A single case that disproves a universal claim or shows that an argument form is invalid.

Reliable source

A source with a good record of accuracy that is competent, informed, and appropriately positioned to know the facts.

Expert or authority

A person with relevant specialized knowledge in a genuine field of expertise.

Bias

A tendency or interest that may distort someone’s judgment or presentation of information.

Conflict of interest

A personal or professional interest that may interfere with impartial judgment.

Independent sources

Sources that reached their conclusions separately rather than merely repeating one original source.

Common knowledge

Information that members of the relevant audience can reasonably be expected to know.

Commonly held belief

A belief accepted by many people that may nevertheless be false.

Consistency

A set of claims is consistent when it is possible for all of them to be true together.

Inconsistency

A set of claims is inconsistent when there is no possible situation in which all of them are true together.

Contradiction

In the strict sense, a claim that directly denies another claim.

Deductive reasoning

Reasoning intended to guarantee the conclusion if the premises are true.

Non-deductive reasoning

Reasoning intended to make the conclusion probable or reasonable without guaranteeing it.

Valid argument

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

Invalid argument

An argument for which at least one possible situation has all true premises and a false conclusion.

Counterexample to validity

A possible situation or parallel argument with true premises and a false conclusion.

Argument form

A general pattern created by replacing parts of an argument with variables.

Instance of an argument form

A particular argument produced by replacing the variables in an argument form with specific content.

Truth-preserving form

An argument form with no instance containing true premises and a false conclusion.

Formally valid argument

An argument whose form is valid.

Logically valid form

A form that is valid solely because of its logical structure.

Sound argument

A valid argument with all true premises.

Valid but unsound argument

An argument with valid reasoning but at least one false premise.

Truth versus validity

Truth applies to individual claims; validity applies to the relationship between an argument’s premises and conclusion.

Implication or entailment

A set of premises implies or entails a conclusion when the corresponding argument is valid.

Equivalent claims

Claims that imply each other and therefore have the same truth value in every possible situation.

Logical meaning of “some”

“Some A are B” means that at least one A is B; it does not imply that some A are not B.

Propositional logic

The study of argument forms whose variable components are complete propositions.

Logical operator or connective

An expression that joins or modifies propositions, such as not, and, or, or if-then.

Negation

The denial of a proposition; symbolized as ¬A and read “not A.”

Double negation

Two consecutive negations; A and ¬¬A are equivalent.

Conjunction

A proposition of the form A & B, meaning “A and B.”

Conjunct

Either component of a conjunction.

Disjunction

A proposition of the form A ∨ B, meaning “A or B.”

Disjunct

Either component of a disjunction.

Inclusive disjunction

“A or B” meaning that at least one is true and possibly both are true.

Exclusive disjunction

“Either A or B but not both,” symbolized as (A ∨ B) & ¬(A & B).

Conditional

A proposition of the form A → B, meaning “If A, then B.”

Antecedent

The first component, A, in a conditional A → B.

Consequent

The second component, B, in a conditional A → B.

Converse

The converse of A → B is B → A; it is not generally equivalent to the original conditional.

Contrapositive

The contrapositive of A → B is ¬B → ¬A; it is equivalent to the original conditional.

Biconditional

A proposition of the form A ↔ B, meaning “A if and only if B.”

Iff

An abbreviation for “if and only if.”

Sufficient condition

A is sufficient for B when A guarantees B; symbolized as A → B.

Necessary condition

B is necessary for A when A cannot occur without B; symbolized as A → B.

Necessary and sufficient condition

Each condition guarantees the other; symbolized with a biconditional A ↔ B.

Not both A and B

Symbolized as ¬(A & B).

Neither A nor B

Symbolized as ¬(A ∨ B), equivalent to ¬A & ¬B.

A if B

Symbolized as B → A.

A only if B

Symbolized as A → B.

A unless B

Symbolized as ¬B → A.

A provided that B

Symbolized as B → A.

Double negation rule

From A infer ¬¬A, or from ¬¬A infer A; valid.

Conjunction rule

From A and B infer A & B; valid.

Simplification rule

From A & B infer A, or infer B; valid.

Weakening rule

From A infer A ∨ B; valid.

Disjunctive syllogism

A ∨ B, ¬A, therefore B; valid. It also works by eliminating B to conclude A.

Modus ponens

A → B, A, therefore B; valid.

Modus tollens

A → B, ¬B, therefore ¬A; valid.

Hypothetical syllogism

A → B, B → C, therefore A → C; valid.

Formal fallacy

An error in reasoning caused by using an invalid argument form.

Affirming the consequent

A → B, B, therefore A; invalid because B could occur for another reason.

Denying the antecedent

A → B, ¬A, therefore ¬B; invalid because B could still occur for another reason.

Formal proof

A chain of valid inferences deriving a conclusion from stated premises.

Proof justification

The inference rule and earlier line numbers that justify a line in a formal proof.

Reduction to absurdity

A proof method that assumes the opposite of the desired conclusion, derives a contradiction, and rejects the assumption.

Indirect proof

Another name for a proof by reduction to absurdity.