Logic

Logical Consequence

What makes a conclusion follow logically from its premises?

Positions

  1. Model-Theoretic Consequence

    A conclusion is a logical consequence of premises when every admissible interpretation or model that makes the premises true also makes the conclusion true.

  2. Proof-Theoretic Consequence

    A conclusion is a logical consequence of premises when there is a valid proof that establishes it from those premises through meaning-governed rules of inference.

Discussion

Logical consequence is the relation that makes an argument deductively valid: if its premises hold, its conclusion cannot fail as a matter of logic. The central question is what explains that necessity and formality.

Model-theoretic accounts look for the absence of a countermodel. Proof-theoretic accounts look for a valid route from premises to conclusion. The two approaches often classify the same arguments as valid, but they explain validity in different terms.

References