Logic · All lessons
Logic is the study of good reasoning — of what follows from what. It gives us tools to tell arguments that genuinely support their conclusions from ones that only seem to, and it underlies mathematics, science, computing, and clear thinking itself.
In logic, an argument is not a quarrel but a structure: one or more statements (the premises) offered in support of another (the conclusion). Logic sets aside whether the statements are rhetorically persuasive and asks a sharper question: does the conclusion really follow from the premises?
The key idea is validity. An argument is valid when, if its premises are true, its conclusion must be true — there's no way for the premises to hold and the conclusion to fail. Crucially, validity is about the form, not the facts: an argument can be valid even with false premises.
A sound argument is a valid argument whose premises are also actually true — and only sound arguments establish their conclusions. So there are two questions to ask of any argument: is it valid (does it hold together?), and are its premises true?
The arguments above are deductive: they aim to guarantee their conclusions. Aristotle was the first to study their forms systematically, above all the syllogism. The classic example:
All humans are mortal.
Socrates is human.
Therefore, Socrates is mortal.
If the two premises are true, the conclusion cannot be false. Modern logic has gone far beyond Aristotle — the twentieth century, with figures like Wittgenstein, transformed the study of logic and language — but the syllogism remains the gateway to the subject.
Not all good reasoning is deductive. In inductive reasoning we move from particular observations to a general conclusion — the sun has risen every day so far, so it will rise tomorrow. Induction can be strong or weak, but even the best induction only makes its conclusion likely, never certain. (That gap is the famous 'problem of induction' raised by Hume.)
A fallacy is a common mistake in reasoning that can make a bad argument look convincing — attacking the person instead of their argument (ad hominem), assuming what you set out to prove (begging the question), or treating correlation as causation. Learning to spot fallacies is one of logic's most practical gifts.