What is logic?
5 min read
Core idea
Logic is the study of the methods and principles that distinguish good reasoning from bad reasoning. It is normative: it does not describe how people actually think (that is psychology), but prescribes how they should think when their goal is truth. Its basic unit of analysis is the argument — a structured pair of premises offered as support for a conclusion. Every chapter of formal logic that follows is built out of three primitive ideas introduced here: argument, validity, and the distinction between deduction and induction.
The crux is a single, easily-missed distinction: a statement is true or false, but an argument is valid or invalid. Validity is not a property of any single sentence — it is a relation between premises and a conclusion that says: "if the premises were true, the conclusion would have to be true." Mixing up these two evaluations is the most common error in everyday reasoning, and untangling them is what makes formal logic possible.
Why it matters
A normative discipline
Logic does not ask whether you reason well in fact. It asks what good reasoning would look like if you did. That is why the same rules apply across mathematics, law, science, and everyday argument: the discipline studies structure, not subject matter.
Why beginners get stuck
The first wall most learners hit is the truth-versus-validity distinction. A valid argument may have completely false premises. A sound-looking argument with all true sentences in it may still be invalid. Once that distinction lands, the rest of the formal apparatus — truth tables, syllogisms, quantifiers — is essentially bookkeeping over the same idea.
Mental model
The anatomy of an argument
Every argument decomposes into the same parts: one or more premises, exactly one conclusion, and an inferential relation that the premises are supposed to bear to the conclusion. Premise-indicator words (because, since, for, as) and conclusion-indicator words (therefore, so, hence, thus) are surface signals that point you at the parts in ordinary prose.
Deduction vs induction
Two families of inference. Deductive arguments claim that the conclusion must be true given true premises — the inference is necessary. Inductive arguments claim only that the conclusion is probably true given the premises — the inference is supportive but defeasible. New evidence can overturn the strongest induction, but never a sound deduction.
The three escalating standards
Validity is the floor: the inferential form is correct. Soundness adds true premises on top of validity. Cogency adds evident truth — premises the intended audience can recognize as true. Each level is strictly stronger than the previous one.
Practical application
When you encounter a piece of reasoning in the wild — an op-ed, a court ruling, a research paper, a friend's argument over dinner — run it through three quick passes:
- Locate the conclusion. Find the one sentence the author wants you to believe. Look for conclusion-indicators (
therefore,so,hence). If the conclusion is implicit, state it explicitly. - Locate the premises. What sentences are offered as reasons? Look for premise-indicators (
because,since,for). Fill in obvious missing premises — most real arguments are elliptical. - Evaluate at each level. Is the inference valid (would the conclusion follow if the premises were true)? Is it sound (are the premises actually true)? Is it cogent (would the intended audience recognize the premises as true)?
This three-pass discipline catches more bad arguments than memorizing fallacy names. Most rhetorical sleight-of-hand happens at the second step — premises that look plausible but smuggle in unstated assumptions that the audience would reject if surfaced.
Example
Suppose your colleague says: "We have to ship the feature this week. The board meeting is Friday and the CEO promised it. If she does not deliver, the funding round is at risk."
Rewriting in standard form:
- Premise 1: The CEO promised the feature would ship before the board meeting.
- Premise 2: The board meeting is on Friday.
- Premise 3 (implicit): Failing to deliver on a CEO promise to the board would put the funding round at risk.
- Premise 4 (implicit): The funding round must be protected.
- Conclusion: Therefore, we must ship the feature this week.
Now the three-pass evaluation:
- Valid? If all four premises are true, the conclusion follows. Yes.
- Sound? Premise 1 and 2 are checkable facts. Premise 3 is a debatable claim about how the board reacts — is missing one feature really fatal? Premise 4 is a value claim, defensible but not self-evident.
- Cogent? Depends on the audience. To an investor, premise 4 is obviously true. To an engineer who thinks a botched ship harms the round worse than a missed deadline, premise 3 is contested.
The argument is valid but its soundness and cogency turn on the unstated premises. That is where the real debate lives — and surfacing those premises is what gives you a foothold. The colleague was not lying; they were arguing from an unstated risk model. You can now ask "do we agree premise 3 is true?" instead of arguing in circles.