Logic and Epistemology: Proposition, Argument, Truth and Validity
Propositions and arguments
A proposition is what a declarative sentence asserts; it is truth-bearing. An argument is a set of premises offered as support for a conclusion. Deductive arguments aim at conclusions that follow necessarily; inductive arguments make probable conclusions. Truth belongs to propositions; validity belongs to argument form.
Validity and soundness
An argument is valid if it is impossible for all premises to be true and the conclusion false. Soundness requires validity plus true premises. Common forms: modus ponens (if P then Q; P; therefore Q), modus tollens (if P then Q; not Q; therefore not P), and disjunctive syllogism. Fallacies include affirming the consequent and denying the antecedent.
Worked example
'If it rains, the ground is wet. It rained. Therefore, the ground is wet' is modus ponens and valid. 'If it rains, the ground is wet. The ground is wet. Therefore, it rained' affirms the consequent and is invalid: a sprinkler could wet the ground. The conclusion may be true, but the form does not guarantee it. Validity is about the link, not the actual truth of premises.
Traps
Do not call an argument valid because its conclusion is true. Do not call it sound merely because it is valid. 'Proposition' is not the same as sentence or belief. In inference, distinguish validity from truth and from persuasive rhetoric. Do not treat inductive strength as deductive certainty.