Logic and Argumentation: Key Terms and Fallacies in Critical Thinking

Argument

A group of statements where premises support a conclusion.

Premise

A statement that gives support or evidence for the conclusion.

Conclusion

The claim an argument tries to prove.

Proposition/Statement

A declarative sentence that is either true or false.

Sentence

Any group of words with meaning — not all sentences are propositions (e.g., questions or commands).

Inference

The mental process of moving from premises to a conclusion.

Truth

A property of statements — a statement is true if it matches reality.

Validity

A property of arguments — valid if the conclusion logically follows from the premises.

Valid/Invalid

Valid: If premises are true, the conclusion must be true. Invalid: The conclusion doesn't necessarily follow.

Soundness

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

Sound/Unsound

Sound: Valid + true premises. Unsound: Invalid or has at least one false premise.

Deductive Argument

Claims the conclusion follows necessarily from the premises.

Weak Inductive Argument

The conclusion probably follows but evidence is weak.

Strong Inductive Argument

The premises make the conclusion very probable, though not certain.

Syllogism

An argument with two premises and one conclusion.

Hypothetical Syllogism

Uses 'if...then' statements.

Antecedent

The 'if' part of a conditional statement.

Consequent

The 'then' part of a conditional statement.

Modus Ponens (MP)

If P → Q and P is true, then Q must be true.

Modus Tollens (MT)

If P → Q and ¬Q, then ¬P.

Pure Hypothetical Syllogism

Two conditional statements linked together (If A → B, and B → C, then A → C).

Affirming the Consequent (AC)

If P → Q and Q, then P (Invalid).

Denying the Antecedent (DA)

If P → Q and ¬P, then ¬Q (Invalid).

Disjunctive Syllogism

Either A or B. Not A. Therefore B.

Categorical Syllogism

Based on categories (All, No, Some).

Barbara

A valid categorical syllogism form: All A are B. All B are C. Therefore, All A are C.

Barbara-Type

Any syllogism that follows Barbara's logical structure.

Middle Term

The term that appears in both premises but not in the conclusion.

Fallacies

Errors in reasoning that make an argument invalid or weak.

Formal Fallacies

Mistakes in the logical structure or form of an argument.

Informal Fallacies

Errors due to content, relevance, or language, not form.

Vagueness vs Ambiguity

Vagueness: Meaning is unclear or blurry. Ambiguity: Word/phrase has multiple meanings.

Fallacies of Ambiguity

Caused by unclear or double meanings of words.

Fallacies of Presumption

Assume something without proper evidence.

Fallacies of (Ir)Relevance

Premises don't relate to the conclusion.