Summary

Logic is the study of reasoning and is a key tool for discovering truth in philosophy and other disciplines. Early philosophers used dialectics—reasoned debates with the goal of getting closer to the truth—to practice and develop reason. Dialectics usually start with a question. An interlocutor offers an answer to the question, which is then scrutinized by all participants. Early forms of arguments are evident in written dialogues. Arguments are reasons offered in support of a conclusion. We use logic to test hypotheses in philosophy and other domains. There are laws of logic—the law of noncontradiction and the law of the excluded middle. Laws of logic can be thought of as rules of thought. Logical laws are rules that underlie thinking itself. The rules or laws of logic are normative—they describe how we ought to reason.

Logical statements can be conditionals or universal affirmative statements. Both are important since they express the important logical relations (also called “conditions”) of necessity and sufficiency. If something is sufficient, it is always sufficient for something else. And if something is necessary, it is always necessary for something else. If you want to prove that a conditional or universal affirmative statement is false (which is to also prove that the necessary and sufficient conditions they express do not hold), then you must offer a counterexample.

An argument is a set of reasons offered in support of a conclusion. The reasons are called premises, and they are meant to logically support the conclusion. Identifying the premises involves critically identifying what is meant to be evidence for the conclusion. Both the premises and conclusion can be indicated by phrases and words. Evaluations of arguments take place on two levels: assessing truth and assessing logic. Logic and truth are separate features of arguments. Logical assessment involves determining whether the truth of the premises do support the conclusion. Logically good arguments contain inferences—a reasoning process that leads from one idea to another, through which we formulate conclusions—where the inference does support the conclusion.

There are three different types of inferences: deductive, inductive, and abductive. Deductive inferences, when valid, guarantee the truth of their conclusions. Inductive inferences, when strong, offer probable support for the conclusion. And good abductive inferences offer probable support for their conclusions. Deductive inferences that cannot guarantee the truth of their conclusions are called invalid. A counterexample can be offered to prove that a deductive inference is invalid. Inductive inferences involve using observations based on experience to draw general conclusions about the world. Abductive inferences involve offering explanations for accepted evidence. Abduction is sometimes called “inference to the best explanation.”

A fallacy is a poor form of reasoning. Fallacies that cannot be reduced to the structure of an argument are called informal fallacies. There are many types of informal fallacies, which can be sorted into four general categories according to how the reasoning fails. These categories are fallacies of relevance, fallacies of weak induction, fallacies of unwarranted assumption, and fallacies of diversion. A fallacy of relevance occurs when the arguer presents evidence that is not relevant for logically establishing their conclusion. The fallacies of weak induction occur when the evidence used is relevant but is too weak to support the desired conclusion. The fallacies of unwarranted assumption occur when an argument assumes, as evidence, some reason that requires further justification. The fallacies of diversion occur when the arguer attempts to distract the attention of the audience from the argument at hand.