Basic Logical Concepts

Fundamental logic vocabulary covering definitions of logic, propositions, arguments, types of reasoning (deduction and induction), and the relationship between truth and validity.

Logic

The study of the methods and principles used to distinguish correct reasoning from incorrect reasoning.

Proposition

The building blocks of every argument; something that may be asserted or denied, and is either true or false.

Sentence

The linguistic vehicle by which a proposition is asserted, which is always in a particular language.

Simple Proposition

A proposition that asserts one statement, such as "$Leslie \text{ won the election}$."

Compound Proposition

A proposition containing other propositions within itself.

Conjunctive Proposition

A compound proposition in which the assertion of the whole is equivalent to asserting each component proposition individually.

Alternative (Disjunctive) Proposition

A compound "either-or" proposition in which neither of its components is asserted individually.

Hypothetical (Conditional) Proposition

A compound "if-then" proposition in which neither the antecedent nor the consequent is asserted individually.

Inference

The process by which one proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point.

Argument

Any group of propositions of which one is claimed to follow from the others, which are regarded as providing support or grounds for the truth of that one.

Conclusion

In an argument, the proposition that is affirmed on the basis of the other propositions.

Premiss

In an argument, the propositions affirmed or assumed as providing support or reasons for accepting the conclusion.

Conclusion-indicator

Words or phrases typically serving to introduce the conclusion of an argument, such as "therefore," "hence," or "thus."

Premiss-indicator

Words or phrases typically serving to mark the premisses of an argument, such as "since," "because," or "for."

Rhetorical Question

A question that suggests or assumes a premiss when the author believes the answer is obvious or inescapable.

Enthymeme

An argument in which one or more of the constituent propositions is not stated explicitly but is assumed to be understood.

Deductive Argument

An argument that involves the claim that its premisses provide conclusive grounds for its conclusion.

Valid

A property of a deductive argument when its premisses, if true, provide conclusive grounds for the truth of its conclusion; it is impossible for the premisses to be true unless the conclusion is true.

Invalid

A property of a deductive argument when the claim that its premisses provide conclusive grounds for its conclusion cannot be sustained.

Inductive Argument

An argument in which the premisses provide some support for the conclusion, evaluated as better or worse, stronger or weaker, based on the degree of probability.

Truth and Falsity

Attributes of individual propositions (statements about the world) but not of arguments.

Validity and Invalidity

Attributes of arguments (the logical relations between propositions) but not of individual propositions.

Sound

A deductive argument that is valid and all of its premisses are true.

Explanation

A passage used to account for why a proposition (known to be true) is true, rather than seeking to establish its truth.