Logic and good reasoning

Logic is the study of what makes reasoning good. It does not tell you which facts are true; it tells you when a conclusion really follows from the reasons given for it. That makes it useful in every subject, from mathematics to law to everyday disagreements.

Aristotle developed the first systematic logic in the fourth century BCE, and logicians in India, China and the medieval Islamic world made important contributions. In the nineteenth and twentieth centuries, thinkers such as George Boole and Gottlob Frege turned logic into a mathematical discipline that later became the foundation of computer science.

In a deductive argument, if the premises are true, the conclusion must be true. The classic example: all humans are mortal; Socrates is a human; therefore Socrates is mortal. An argument whose conclusion follows necessarily from its premises is called valid.

Validity concerns form, not truth. The argument all fish can fly; a salmon is a fish; therefore a salmon can fly is perfectly valid but has a false premise. An argument that is valid and has true premises is called sound, and only sound arguments guarantee true conclusions.

Inductive arguments move from observations to general conclusions that are probable rather than certain. Every swan I have seen is white, so all swans are white, was considered a strong inference in Europe until Europeans encountered black swans in Australia.

Most everyday and scientific reasoning is inductive. Its strength depends on the size and variety of the evidence and whether the sample is representative. The philosopher David Hume pointed out that induction cannot be proved by deduction, since the future need not resemble the past, a puzzle known as the problem of induction.

• Ad hominem: attacking the person making an argument instead of the argument itself.
• Straw man: misrepresenting someone's position to make it easier to attack.
• False dilemma: presenting only two options when others exist.
• Slippery slope: claiming a small step will inevitably lead to extreme outcomes without showing why.
• Appeal to popularity: assuming something is true because many people believe it.
• Circular reasoning: assuming the conclusion in the premises.
• Post hoc: assuming that because one event followed another, the first caused the second.

Some errors are mistakes of logical form. Affirming the consequent is a common one: if it rains, the ground is wet; the ground is wet; therefore it rained. The ground might be wet for other reasons, such as a sprinkler. The reverse pattern, if it rains the ground is wet, the ground is not wet, therefore it did not rain, is valid.

Most fallacies encountered in daily life are informal: their problem lies in content, context or relevance rather than structure. Recognising them does not automatically make a conclusion false, but it shows that the argument given does not support it.

Good reasoners separate the question of whether a claim is true from whether they want it to be true, a hard habit because people naturally favour evidence that supports what they already believe. It helps to state the strongest version of an opposing view before criticising it, sometimes called steelmanning.

Other useful questions include: what exactly is being claimed, what evidence supports it, what would change my mind, and are there other explanations? These questions apply equally to news stories, advertising, political speeches and our own convictions.