---
bibtex: @InCollection{sep-logical-consequence,
author = {Beall, Jc, Restall, Greg and Sagi, Gil},
title = {Logical Consequence},
booktitle = {The Stanford Encyclopedia of Philosophy},
editor = {Edward N. Zalta},
howpublished = {\url{https://plato.stanford.edu/archives/spr2019/entries/logical-consequence/}},
year = {2019},
edition = {Spring 2019},
publisher = {Metaphysics Research Lab, Stanford University}
}
---
A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline).
Contemporary analyses of the concept of consequence—of the follows from relation—take it to be both necessary and formal, with such answers often being explicated via proofs or models
Deductive validity
Some arguments are such that the (joint) truth of the premises is necessarily sufficient for the truth of the conclusions.
Inductive validity
In inductively valid arguments, the (joint) truth of the premises is very likely (but not necessarily) sufficient for the truth of the conclusion.
Deductive consequence can be thought of as metaphysical or conceptual neccessity. It must also be knowable a priori
Twentieth Century technical work on the notion of logical consequence has centered on two different mathematical tools, proof theory and model theory. Each of these can be seen as explicating different aspects of the concept of logical consequence, backed by different philosophical perspectives.
The model-centered approach to logical consequence takes the validity of an argument to be absence of counterexample.
On the proof-centered approach to logical consequence, the validity of an argument amounts to there being a proof of the conclusions from the premises.
in a valid argument, the truth of the conclusion follows from the truth of the premises by necessity of thought (Prawitz 2005).