Logic And Critical Thinking

Formal logic is the study of inference with purely formal content, where the validity of an argument depends solely on its logical form rather than the meaning of its terms.

An argument is a set of statements (premises) offered as reasons to support a conclusion.

A premise is a statement in an argument that provides evidence or reasons for the conclusion.

The conclusion is the statement that the premises of an argument are intended to support or prove.

A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth.

A sound argument is one that is both valid and has all true premises. Soundness guarantees a true conclusion.

Deductive reasoning moves from general premises to a specific, certain conclusion. Inductive reasoning moves from specific observations to a general, probable conclusion.

All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Every swan I have observed is white. Therefore, all swans are probably white. The conclusion is probable but not certain.

A syllogism is a form of deductive reasoning consisting of two premises and a conclusion, typically involving a major premise, a minor premise, and a conclusion.

The major term (predicate of conclusion), minor term (subject of conclusion), and middle term (appears in both premises but not the conclusion).

A truth table is a mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its components.