Grain of Salt

Logical reasoning

Struck diagram on assay stock: Logical reasoning

Logical reasoning is the practice of moving from stated premises to a conclusion by a rule that carries support, so that anyone who accepts the premises has a reason to accept the conclusion. It is not the same as being right, and it is not the same as sounding convincing. An argument can land on a true conclusion through a broken rule, and a perfect rule can carry you to a false conclusion when one premise is false. Logical reasoning is the discipline of separating those two questions, the form and the facts, and answering them one at a time.

That discipline is what a logical reasoning test measures, what an interview panel is probing when it asks you to justify a decision, and what you are doing whenever you decide that a claim someone handed you does not follow. The rest of this page sets out the 2 parts of an argument, the 2 great families of inference, the 3 conditions a working argument meets, and a repeatable method for answering reasoning questions under time pressure.

Premises and conclusion: the only two parts

Premises and a conclusion are the only two parts an argument has. A premise is a claim offered as support. The conclusion is the claim being supported. Everything else in a piece of writing, including the tone, the credentials of the speaker and the confidence of the delivery, is packaging.

Take a small one. The footbridge over the canal is closed every Monday for inspection. Today is Monday. So the footbridge is closed. Two premises, one conclusion, and the word so marking the join. English signposts these joins reliably: because, since, given that and for introduce premises, while therefore, so, hence, which means and it follows that introduce conclusions. Circling those words is the first move in any argument analysis.

Most real arguments also carry an unstated premise, the thing the speaker assumes rather than says. Add a third sentence to the footbridge case: So you will be late. That conclusion needs a premise nobody wrote down, namely that your route depends on the footbridge. Finding the missing premise is the single most productive habit in reasoning, because a hidden assumption is where a weak argument almost always hides. Taking an argument fully apart into a labeled premise set, an outline or a diagram, is a task in its own right, and Argument structure is the page that does it.

Deduction and induction: the two families of inference

Deduction and induction are the two families of inference that logical reasoning runs on, and they promise different things. A deductive step promises that the conclusion cannot be false if the premises are true: the footbridge case above is deductive. An inductive step promises only that the conclusion is probable given the evidence: the footbridge has been closed on each of the last nine Mondays, so it will be closed next Monday is inductive, and next Monday can still surprise you.

Neither family is the better one in the abstract. Deduction gives certainty but only about what was already contained in the premises, so it never tells you anything new about the world. Induction tells you new things about the world but never with certainty, so it can be overturned by the next observation. Which one a claim is using, and which one it ought to be using, is a diagnostic question worth asking early, and Deductive vs inductive reasoning is the page that lays the two side by side in full.

Three conditions a working argument meets

A working argument meets 3 conditions, and a reasoning question almost always attacks one of them:

Whether a deductive argument is correctly formed, and whether its premises are additionally true, are two separate verdicts with two separate names, validity and soundness. Valid vs sound arguments is the page that keeps them apart.

How to solve a logical reasoning question in five steps

To solve a logical reasoning question, work the argument before you look at the answers. Reading the options first invites you to pick the one that feels agreeable, which is the trap most items are built around. 5 steps, in order:

  1. Read the question stem first and name the task: find the assumption, draw an inference, identify the flaw, strengthen or weaken, or match the pattern of reasoning.
  2. Mark the conclusion in the passage, then mark every premise that feeds it, ignoring background sentences that support nothing.
  3. State the gap in your own words before reading any option, in one sentence: what would have to be true for these premises to reach that conclusion.
  4. Test each option against your sentence, not against your opinion of the topic, and eliminate anything that is merely true but does nothing to the gap.
  5. Check the survivor by negation on assumption items: deny the option, and if the argument collapses, that was the assumption.

The 5 recurring question types map onto the same anatomy, which is why one method covers all of them.

Question typeWhat it asksWhere to aim
AssumptionWhat unstated premise does this argument needThe gap between the last premise and the conclusion
InferenceWhat must be true if the passage is trueThe premises only, never the conclusion
FlawWhat is wrong with the reasoningRelevance or sufficiency, named as a pattern
Strengthen or weakenWhich new fact changes the supportThe same gap, pushed shut or pried open
Parallel reasoningWhich argument has the same shapeThe form, with the subject matter stripped out

Where logical reasoning tests appear

Logical reasoning tests appear in three places: graduate admissions, employer aptitude assessments, and structured interviews. The Law School Admission Council builds Logical Reasoning sections into the LSAT, where short passages are followed by a single question of the kinds listed above. The Common Admission Test used by Indian management programs sets logical reasoning alongside data interpretation. Employers buy off the shelf aptitude batteries that mix verbal reasoning, numerical reasoning and abstract sequence items, and an interview question that begins how did you decide is a reasoning item without a multiple choice list.

Question counts, section counts and time limits are set by each test administrator and are revised from time to time, so read the current specification published by the body that runs your test rather than a figure quoted in a study guide. The commercial guides sold as reasoning bibles are useful for one thing, exposure to many worked items, and misleading for another: memorizing answer patterns produces a reader who recognizes questions instead of a reader who can take an argument apart. To pass a logical reasoning test, practice the mapping step until it is automatic, then add timing.

How to practice without a test book

To practice logical reasoning without a test book, run arguments you meet anyway through the same three questions. Take a notice at a train station, a product claim on a box, a manager's rationale for changing a delivery route. Write the conclusion in one line. List the premises underneath it. Then ask the one question that does most of the work:

What would have to be true for these premises to be correct and this conclusion still be false?

If you can answer that in a sentence, you have found the assumption, and you now know exactly where the argument is load bearing. If you cannot, the argument is probably deductive and the fight is about the premises instead. Critical thinking exercises collects graded versions of this drill with the answers worked out, and Critical thinking skills names the six separate abilities the drill is training. Neither replaces the habit of doing it live, on the next claim someone hands you.

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