A perfectly valid argument can prove that no cats are frogs using false premises
Deduction cares about form, not truth. Say every frog is a mammal and no cat is a mammal, and it follows flawlessly that no cat is a frog. The reasoning is valid even though a premise is nonsense. Only when valid structure meets true premises do logicians call an argument sound.
An inference is deductively valid when its premises cannot all be true while its conclusion is false. The textbook case runs from all men being mortal and Socrates being a man to Socrates being mortal. Logicians approach validity two ways. The semantic view asks whether any interpretation makes the premises true and the conclusion false; the syntactic view asks whether the conclusion follows by a rule of inference such as modus ponens or modus tollens. Arguments that break such rules are formal fallacies.
Alfred Tarski described logical consequence as having three features: it is necessary, it is formal, and it can be known a priori. Swap the content of a valid argument for anything else with the same shape and it stays valid, and no survey of the world is needed to check it. That is why a rainy street and spoiling meat can share one skeleton: if A then B; A; therefore B.
Deduction buys certainty at a price. Inductive and abductive reasoning, called ampliative, only make conclusions likely, yet they can deliver information that was not already packed into the premises. Logic also tolerates pointless conclusions: from the claim that a printer has ink you may validly infer that it has ink, has ink and has ink, which no sensible person would bother to say.
Psychologists find that people handle modus ponens more reliably than modus tollens, judge arguments valid more readily when the conclusion sounds plausible, and do better with concrete cases than abstract ones. Rival theories explain this through mental rules resembling language, through mental models of possible situations, or through two distinct reasoning systems. Mark Vorobey proposed a speaker-based definition, where an argument is deductive if its author believes the premises guarantee the conclusion, though authors rarely state such intentions.
Source: Deductive reasoning
