What Is Logic? The Systematic Study of Valid Reasoning

Direct Answer

Logic is the systematic study of the principles of valid inference — the rules that determine when a conclusion genuinely follows from premises. The word comes from the Greek logos, meaning word, reason, or account, and the discipline has been understood since Aristotle as the organon, the instrument by which all the sciences reason. Logic is not psychology: it does not describe how people actually think, with all our shortcuts and errors, but prescribes how they ought to reason, identifying the patterns of inference that reliably preserve truth.

The central object of logic is the argument: a set of premises offered in support of a conclusion. Logic classifies arguments into two great kinds. In a deductive argument, the premises are meant to guarantee the conclusion — if the premises are true, the conclusion must be true. In an inductive argument, the premises are meant to make the conclusion probable without guaranteeing it. A deductive argument that in fact has the guaranteeing property is valid; a valid argument with true premises is sound. These distinctions — validity, soundness, deductive and inductive strength — are the basic vocabulary of logical evaluation.

Because validity depends on the form of an argument rather than its subject matter, logic is a formal science. The pattern "If p, then q; p; therefore q" is valid whether p stands for "it rains" or "the stock falls." By abstracting away content and exposing structure, logic reveals why some inferences are reliable and others are traps, and it provides the standards against which fallacies are recognized as failures.

Historical Context

Logic begins as a science with Aristotle in the fourth century BCE. In the Organon — the treatises later collected under that name — Aristotle identified the syllogism as the fundamental form of deductive argument: two premises sharing a middle term that force a conclusion, as in "All humans are mortal; Socrates is human; therefore Socrates is mortal." For over two thousand years, the study of logic was largely the study of the syllogism and its figures and moods. The Stoics added the propositional logic of conditionals and negation, and the medieval scholastics, including William of Ockham, refined the theory of terms and consequences.

The modern transformation came in 1879, when Gottlob Frege published the Begriffsschrift, the first system of quantified logic. Frege introduced variables, quantifiers, and functions, showing that the full range of mathematical and relational reasoning could be captured in a precise formal language. Bertrand Russell and Alfred North Whitehead extended the program in Principia Mathematica, attempting to show that mathematics is reducible to logic. Ludwig Wittgenstein, Willard Van Orman Quine, and Saul Kripke then explored the philosophical foundations of the new logic — its scope, its semantics, and its limits.

Philosophical Perspectives

The philosophy of logic asks what validity itself consists in. The semantic account, developed by Alfred Tarski, defines validity as truth-preservation: an argument is valid if its conclusion is true in every interpretation in which its premises are true. The proof-theoretic account defines validity in terms of derivation within a formal system. For classical logic, the two coincide — Kurt Gödel proved the completeness of first-order logic in 1930 — but the question of which conception is fundamental remains open.

Philosophers also disagree about the status of logical truths. The logical positivists, including A. J. Ayer, held that logical truths are analytic — true in virtue of meaning alone, and therefore certain but empty of factual content. Quine argued in "Two Dogmas of Empiricism" that the analytic-synthetic distinction cannot be sustained and that even the laws of logic are revisable in principle. Relatedly, the existence of alternative logics — intuitionistic, many-valued, modal — raises the question whether there is one correct logic or many. What is not in dispute is that logic provides the normative standard of inference: the measure by which reasoning is judged.

Modern Reflection

In the modern world, logic has escaped the philosophy seminar. It is the mathematical foundation of computer science: the circuits of processors implement Boolean algebra, and every programming language embodies a system of formal rules. It underpins the formal verification of software and hardware, the design of databases, and the logic programming of artificial intelligence. In law, medicine, and policy, the evaluation of arguments — of evidence, of inference, of probability — is logic in action.

Logic also matters more personally. The informal descendant of the discipline, critical thinking, applies logical standards to everyday discourse: recognizing when a conclusion follows, when a premise is assumed, and when rhetoric has replaced reasoning. In an age of misinformation and algorithmic persuasion, the ability to evaluate arguments — to distinguish valid inference from manipulative association — has become a civic skill of the first order. The formal science founded by Aristotle and transformed by Frege remains the deepest source of that skill.

Related Thinkers

• Aristotle — Founded logic as a science with the syllogism and the Organon
• William of Ockham — Advanced medieval logic of terms and consequences
• Gottlob Frege — Invented quantified logic and the modern formal language
• Bertrand Russell — Extended logic to the foundations of mathematics in Principia Mathematica
• Ludwig Wittgenstein — Explored the limits of logical language in the Tractatus
• Willard Van Orman Quine — Challenged the analytic-synthetic distinction
• Charles Sanders Peirce — Developed the logic of relations and abduction

Related Quotes

• Frege Quote on Sense and Reference — Meaning, reference, and the structure of language
• Ayer Quote on Verification — The analytic account of logical and mathematical truth
• Aristotle on the Desire to Know — The opening of the Metaphysics on the love of knowledge

Further Learning

• Explore the two branches of the discipline: formal logic and informal logic
• Read the philosophy of logic for the deep questions about validity and logical truth
• Compare deductive reasoning and inductive reasoning
• See how logic connects to knowledge in the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy
• Visit the Critical Thinking & Logic collection for the full learning path

Sources

• Stanford Encyclopedia of Philosophy, "Classical Logic" — https://plato.stanford.edu/entries/logic-classical/
• Stanford Encyclopedia of Philosophy, "Philosophy of Logic" — https://plato.stanford.edu/entries/logic-philosophy/
• Internet Encyclopedia of Philosophy, "Logic" — https://iep.utm.edu/logic/