Foundations of Logical Reasoning

A comprehensive set of vocabulary flashcards covering key concepts in logical reasoning.

Logic

Studies the relationship between indicator facts and target facts.

Inference

Mental process which moves from premises to a conclusion.

Perception

Learning about a fact through direct experience.

Testimony

Learning about the world through the assertion of a reliable authority.

Argument

A set of two or more sentences, one designated as the conclusion.

Premise Indicators

Words like Since, Because, As, For, Given that, indicating premises.

Conclusion Indicators

Words like Therefore, Thus, So, indicating conclusions.

Conditional Proposition

A statement in the form "if p, then q".

Sufficient Condition (P)

A condition that guarantees something else is true.

Necessary Condition (Q)

A condition that must be the case if something else is true.

Deductive Argument

An argument intended to be valid, providing a guarantee of conclusion truth.

Deductively Valid (Validity)

An argument is valid if premises cannot be true and the conclusion false.

Deductively Invalid

An argument where premises can be true and conclusion false.

Deductive Soundness

An argument is sound if it is valid and has all true premises.

Deductively Unsound

An argument that is either invalid or has false premises.

Inductive Argument

An argument intended to establish the probability of its conclusion.

Inductive Strength

Extent to which the conclusion is probable based on premises.

Logical Consistency

A set of sentences is consistent if all can be true.

Logical Truth

A sentence is true if it cannot be false.

Logical Falsity

A sentence is false if it cannot be true.

Logical Indeterminacy

A sentence that is neither true nor false.

Logically Equivalent

Conditional statements with the same truth value.

Syllogism

A deductive argument with a major premise, minor premise, and conclusion.

Categorical Syllogism

A syllogism with a universal or particular relation between categories.

Universal Affirmative (A)

A claim expressing an inclusive relationship where all X are Y.

Universal Negative (E)

A claim negating inclusion where no X is Y.

Particular Affirmative (I)

A claim where some X are Y.

Particular Negative (O)

A claim where some X are not Y.

Disjunctive Syllogism

A syllogism asserting that at least one premise is correct.

Hypothetical Syllogism

An argument containing conditional premises.

Modus Ponens

A valid argument: If P, then Q; P; therefore, Q.

Modus Tollens

A valid argument: If P, then Q; not Q; therefore, not P.

Denying the Antecedent

An invalid form: If P then Q; not P; therefore, not Q.

Affirming the Consequent

A formal fallacy reasoning: If P then Q; Q; therefore, P.

Fallacies of Relevance

Arguments that use irrelevant considerations for support.

Ad Hominem

A fallacy attacking the person rather than the argument.

Appeal to False Authority

Citing an authority who is not relevant to the subject.

Appeal to Force

Attempting to persuade through threats.

Appeal to Consequence

Motivating beliefs based on potential consequences.

Appeal to Pity

Persuading using sympathy rather than reason.

Appeal to Tradition

Assuming something is correct simply because it is traditional.

Fallacies of Ambiguity

Fallacies that arise from imprecise language.

Equivocation

Using terms with different meanings in an argument.

Straw Man Fallacy

Misrepresenting someone's position to refute it easily.

Red Herring Fallacy

Introducing irrelevant topics to divert focus.

Fallacy of Composition

Drawing conclusions about wholes based on parts.

Fallacies of Presumption

Arguments based on false or unwarranted assumptions.

Begging the Question

Claiming the conclusion is true within the premises.

False Dilemma

Presenting only two options when more exist.

Hasty Generalization

Drawing a conclusion based on insufficient evidence.

Post Hoc Ergo Propter Hoc

Assuming causation based on sequential events.

Slippery Slope

Arguing that one event inevitably leads to another.

Common Connectives

Words and phrases used to connect logical statements.

Universal Quantifier

A quantifier asserting a proposition is true for all in a class.

Existential Quantifier

A quantifier asserting existence of at least one true instance.

Truth Table for Negation

Shows the truth values of ~P.

Truth Table for P & Q

Shows the truth values for the conjunction of P and Q.

Truth Table for P v Q

Shows the truth values for the disjunction of P and Q.

Truth Table for P > Q

Shows the truth values for the implication of P on Q.

Truth Table for P if and only if Q

Shows values for the biconditional between P and Q.

Truth Table for 3 Variables

Shows truth values for three variables.

Truth Table for Tautology

Shows truth values for a tautological statement.