Logic
deductive reasoning
The study of valid inference — the rules by which conclusions follow from premises.
In practice
A plan concludes that revenue will grow because the market is growing. The inference is inductive, and its strength depends on a premise nobody stated: that this company will hold its share.
The common mistake
Calling an argument illogical when you reject its premises. If the form is valid, the disagreement is about the inputs, and saying so makes the real dispute visible.
Logic is the study of what follows from what. It sets out the forms of argument that preserve truth, independently of the subject being argued about.
Validity and soundness
An argument is valid when the conclusion cannot be false while the premises are true. Validity concerns structure alone. "All fish are mammals; all mammals breathe air; so all fish breathe air" is valid and has a false premise. An argument is sound when it is valid and its premises are true, which is what gives you a reason to accept the conclusion.
Keeping the two apart is the first discipline the subject teaches. Most disagreements that appear to be about logic are disagreements about premises.
From Aristotle to formal systems
Aristotle built the first system in the Organon, centered on the syllogism — two premises and a conclusion, in patterns he catalogued exhaustively. His logic dominated for two thousand years and cannot represent relations or multiple quantifiers, so "every student read some book" is beyond it.
Gottlob Frege rebuilt the subject in 1879 with quantifiers and variables, producing modern predicate logic and with it the tools for the foundations of mathematics. Bertrand Russell and Whitehead pursued that program, and Kurt Gödel closed it in 1931 by showing that any consistent system strong enough for arithmetic contains truths it cannot prove.
Deduction and induction
Deductive arguments aim at validity: the conclusion is already contained in the premises. Inductive arguments aim at strength: the premises make the conclusion likely without guaranteeing it. Science depends on the second, which is why Hume's problem of induction is a problem about evidence rather than about logic in the narrow sense.
Concept web
Open the full webQuestions
What is logic?
Logic is the study of correct inference — which conclusions follow from which premises. It examines the forms of argument that preserve truth regardless of subject matter.
What is the difference between valid and sound?
A valid argument has a form where true premises guarantee a true conclusion. A sound argument is valid and has true premises. A valid argument can have false premises and a false conclusion.
What is the difference between deductive and inductive reasoning?
Deductive reasoning aims at conclusions guaranteed by the premises. Inductive reasoning aims at conclusions made probable by the premises, as when past observations support a general claim.