Validity: What Follows from What?

Core idea

Logic is the study of reasoning — specifically, of what counts as a good reason for what, and why. When we argue, we offer premises (the claims before a "so" or "therefore") as support for a conclusion (the claim after it). Logic asks one narrow but fundamental question about that move: does the conclusion really follow from the premises?

An inference where the conclusion genuinely follows is called valid. Crucially, validity has nothing to do with whether the premises are actually true. "Moscow is the capital of the USA; so you cannot go to Moscow without going to the USA" has a false premise, yet if that premise were true, the conclusion would follow. Whether premises are true is the geographer's business. Whether the conclusion follows is the logician's.

Why it matters

Deductive versus inductive validity

Not all good reasoning is equally airtight. Priest distinguishes two kinds of validity. A deductively valid inference is one where the premises cannot be true without the conclusion also being true — the support is absolutely watertight. An inductively valid inference offers strong but not conclusive support: "storm clouds are gathering, so there will be rain" is a good bet, but a shift in the wind could spoil it.

We reason inductively constantly — diagnosing a fault, solving a crime, explaining an illness. Yet logicians have historically poured far more effort into the deductive case, perhaps because logicians tend to be mathematicians and philosophers rather than detectives. This book follows suit: until further notice, "valid" means deductively valid.

The puzzle of "can't"

The standard account says a deductively valid inference is one where, in every situation in which all the premises are true, the conclusion is true too. That looks tidy — but it hides a problem. There appear to be infinitely many situations: situations on distant planets, situations before life existed, situations a year hence, two years hence, and so on without end. We cannot possibly survey them all.

Priest's argument: If validity is defined over all situations, and we can nonetheless recognise inferences as valid, then we must have some special insight into something we can never finish inspecting.

Key takeaways

Mental model

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Practical application

Whenever someone tries to persuade you, separate two questions. First: are the premises true? Second: even if they were, would the conclusion follow? Most everyday disputes blur these together. A conclusion can be false because a premise is false, or because the reasoning is invalid, or both — and the remedy is different in each case.

Example

Consider: "Every employee who filed by Friday gets the bonus. Dana filed by Friday. So Dana gets the bonus." This is deductively valid — there is no situation where the premises hold and the conclusion fails. If Dana actually filed on time and the policy is real, it is also sound.

Now compare an inductive case: "The last five updates from this vendor broke nothing, so the sixth will be safe." The reasoning is reasonable — it is inductively strong — but no situation-by-situation guarantee backs it. A single counter-example does not make it fallacious; it simply confirms that induction trades certainty for usefulness.

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