Logic and arguments

You look at the reasons themselves, not at the people. Logic is the part of philosophy that studies when reasons actually support a conclusion. Lesson 1 showed Socrates testing beliefs by asking questions. Logic gives that testing a set of tools: a way to lay an argument out, a test for whether its conclusion follows, and a list of the most common ways reasoning goes wrong (Hurley & Watson, 2018).

The first person to write those tools down as a system was Aristotle, Plato's student, in the 300s BC. He is the figure on the right at the center of the painting at the top of this page, standing beside Plato.

In logic, an argument is a set of statements in which some statements, the premises, are offered as reasons to accept another statement, the conclusion. A quarrel can happen without any argument at all, and a calm conversation can contain several.

Arguments in real life rarely arrive labeled. Indicator words help. Words such as since, because, and given that usually introduce a premise. Words such as therefore, so, and it follows that usually introduce the conclusion. Writing the premises on separate numbered lines, with the conclusion last, is called putting the argument in standard form. Figure 2.1 does that with the most famous example in the history of logic.

That whether an argument works depends on its shape, not on its subject. In the Prior Analytics, Aristotle studied the syllogism: an argument with two premises and a conclusion, each relating two groups of things with all, no, or some (Smith, 2022). Replace the words in Figure 2.1 with letters and the pattern appears:

• All B are A. (All humans are mortal.)
• C is a B. (Socrates is a human.)
• So C is A. (Socrates is mortal.)

Any words at all can go in for the letters, and if the premises are true, the conclusion has to be true. Aristotle had found the idea of logical form: the skeleton of an argument, which can be checked without knowing anything about humans, Socrates, or death. His system was the standard logic of the Western world for more than two thousand years, until modern symbolic logic expanded it in the late 1800s.

In one important sense, yes. A deductive argument is valid when it is impossible for all its premises to be true and its conclusion false. Validity asks a conditional question: if the premises were true, would the conclusion have to be true? Validity does not ask whether the premises are in fact true.

So this argument is valid: all fish can fly; a shark is a fish; so a shark can fly. The first premise is false and so is the conclusion, but the form is the same as in Figure 2.1, and the form never lets true premises lead to a false conclusion. The reverse also happens. All dogs are mammals; all cats are mammals; so all cats are dogs. Both premises are true and the argument is invalid, because sharing one group does not make two groups the same.

Validity plus true premises. An argument is sound when it is valid and all of its premises are actually true. A sound argument cannot have a false conclusion. That gives you exactly two ways to challenge any deductive argument, and Figure 2.2 lays them out: attack the form (show the argument is invalid), or attack a premise (show at least one premise is false).

Yes, and the difference is easy to miss in conversation. Many everyday arguments use an if-then premise, called a conditional. Two forms built on a conditional are always valid. Modus ponens ("the way of affirming") confirms the if part and concludes the then part. Modus tollens ("the way of denying") denies the then part and concludes that the if part is false. Each has a counterfeit that looks almost the same and is invalid. Figure 2.3 sets all four side by side using one conditional: if it rained, then the street is wet.

Affirming the consequent is everywhere. "If he were guilty, he would look nervous; he looks nervous; so he is guilty." Nervousness has many causes. Spotting the shape lets you ask the right question: what else could explain this?

It is reasoning, but of a different kind. A deductive argument aims to guarantee its conclusion. An inductive argument aims only to make its conclusion probable, usually by reasoning from observed cases to cases not yet observed. Medicine, science, and daily life depend on induction: the drug worked in large trials, so it will probably work for you.

Inductive arguments are not valid or invalid. They are stronger or weaker. An inductive argument is strong when, if its premises are true, the conclusion is probably true, and cogent when it is strong and its premises really are true. Even a cogent inductive argument can have a false conclusion. For centuries, every swan Europeans had seen was white, and "all swans are white" seemed safe. In 1697 the Dutch explorer Willem de Vlamingh's crew saw black swans in western Australia. Figure 2.4 compares the two kinds of argument.

Because many of them feel like good ones. A fallacy is a mistake in reasoning that can still seem persuasive. Formal fallacies, such as affirming the consequent, are flaws in the form. Informal fallacies are flaws in content or context: the premises are irrelevant, too weak, or quietly assume what they claim to prove (Dowden, n.d.). Aristotle catalogued thirteen of them in a short book, Sophistical Refutations. Figure 2.5 is a field guide to eight that show up most often, each with a question that exposes it.

A warning that runs the other way: calling out a fallacy does not prove the conclusion false. A bad argument can be offered for a true conclusion. Deciding that a claim must be false because someone defended it badly is itself a fallacy, sometimes called the fallacy fallacy.

A rule philosophers call the principle of charity: before you criticize an argument, restate it in its strongest reasonable form, the version its best defender would recognize. Some people call that steelmanning, the opposite of building a straw man. Charity is fair to the other person, and it is also smart. If you defeat only the weakest version of a view, you have learned nothing about whether the view is true.

Socrates, in Lesson 1, asked questions before he objected. Charity is the same habit in logical form: understand first, then test. Disagreement done this way stays respectful, and it is far more likely to change a mind, including your own.

• Find the conclusion first. Ask: what exactly am I being asked to believe?
• List the premises. Put the reasons on separate lines, including any the speaker left unstated.
• Test the form. If every premise were true, would the conclusion have to follow, or only probably follow?
• Test the premises. Which one is most likely false, and how would you check it?
• Be charitable. Fix the argument's easy flaws yourself before you judge it.