Deductive logic

Deductive logic is a category of reasoning that is fundamental to the sciences and technology and, therefore, especially important for science communicators and others concerned with understanding science. In fact, deductive logic is important anywhere computers are used. Deductive logic forms the basis of all computer code and is often taught in computer science curricula, not just in philosophy departments.

Logic itself is commonly understood as the relationships and principles of reasoning. The phrase “the process of reasoning” generally refers to the way in which one or several sentences give reason to believe some conclusion, which is itself another statement. For instance, when Jack is taller than Tom and when Tom is taller than Allen, someone can know from these two premises that Jack must be taller than Allen. This example is an instance of deductive logic.

Deductive logic is generally contrasted with inductive logic. Inductive logic is the kind of reasoning that is founded upon premises that support a conclusion with a degree of likelihood or probability, not with necessity. For example, when Jill sees clouds outside, she reasons that it will rain. She does not know this with certainty, but this is not her fault. Until a sign appears that implies there will necessarily be rain, something that is not yet the case, Jill cannot know for sure what the weather will do. By contrast, consider that when there is fire, there must be oxygen present. This is true because fire itself is a process that requires oxygen. So wherever there is fire, there is at least some oxygen.

Arguments that involve necessity, such as the kind involving fire and oxygen, are different in kind from inductive arguments. It is important not to assume that in all deductive arguments the conclusion necessarily does follow from the premises, however. That is because the argument can simply be a bad one, called invalid. Take the following as an example: Jack is a bachelor; therefore, Jack is married. This is an example of a deductive argument, but it is one in which the necessary characteristics of bachelorhood are mistakenly related to being married. In fact, to be a bachelor implies that one is not married. This argument would be called deductive, but invalid. The valid version looks like this: Jack is a bachelor; therefore, Jack is not married.

There are several different kinds of deductive argumentation. The simplest kind is an argument from definition. The example of bachelorhood is one of these. How terms are defined bears important consequences, however, since the definitions used imply consequences than can be better or worse for particular purposes. Controversies can arise over the proper way to define terms. Some controversial examples have included terms such as planet, marriage, or enemy combatant.

Another kind of deduction is called natural deduction. Natural deduction generally refers to the forms that arguments take. There are certain shapes that our arguments frequently form. When someone substitutes other terms and categories into well-designed deductive arguments, some forms never lead to false conclusions. Those are the arguments that are called valid. For example, one argument form, called modus ponens, is especially common and important to the study of logic. In modus pon-ens, the arguer says that if some condition P is true, then condition Q is also true. He or she then claims that P is true. Therefore, according to these reasons, it must be that Q is also true. This form of argument has been shown time and time again to be irrefutable. There could be mistakes made in filling in the details, but the form itself cannot lead someone from true premises to a false conclusion. When an argument has proper form but has premises that are not true, the argument is called valid but unsound. In fact, all deductive arguments that are either invalid or that have one or more false premises are considered unsound. Therefore, a sound argument, technically speaking, is a valid, deductive argument in which the premises are true.

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