DEFINITIONS An argument is a set of two or more statements, where one purports to follow from the others. The one that supposedly follows from the others is called the conclusion, and the statements that purport to provide support for the conclusion are called premises. A statement is a sentence that has a truth‐value, that is, a sentence that is either true or false. A sentence is a statement if and only if it has a truth value. So, for instance, 'All dogs have four legs' is a statement, while 'What time is it?' is not. A proposition is a truth or a falsehood that can often be expressed by a number of different, but logically equivalent, statements. Two statements express the same proposition if and only if they have exactly the same meaning. For instance, 'John Smith is married' and 'John Smith has a spouse' both express the same proposition. But 'John Smith is married' and 'John Smith has a wife' do not necessarily express the same proposition, since John Smith could be married to a man. A valid argument is one where the truth of the premises entails (i.e., necessitates or guarantees) the truth of the conclusion. An argument is valid if and only if, in no possible world, are its premises all true and its conclusion false. Arguments that are not valid are invalid. (Note that only arguments, and not statements or propositions, can be properly called valid or invalid. By contrast, only statements and propositions, not arguments, can be properly called true or false.) An argument is sound if and only if both of the following are true: (1) it is valid, and (2) all of its premises are true. Arguments that are not sound are unsound. A deductive argument is one in which the truth of its premises purports to establish that its conclusion is certainly true. An inductive argument is one in which the truth of its premises purports to establish that its conclusion is probably true. An inductive argument is strong if and only if the truth of its premises makes its conclusion more likely true than false. The more probable it makes the truth of its conclusion, the stronger the inductive argument is. Inductive arguments that are not strong are weak. An inductive argument is cogent if and only if both of the …