# Logic

The science of valid reasoning. An essential part of instruction at every level of formal education, logic dates back to ancient Greece, when ARISTOTLE formulated the rules of syllogistic reasoning, based on four forms of argument: universal affirmatives (All As are Bs), universal negatives (No As are Bs), particular affirmatives (Some As are Bs) and particular negatives (Some As are not Bs). A syllogism consists of two premises and a conclusion, each with one factor in common. Thus, “all mammals nourish their young with milk from mammary glands; all humans nourish their young with milk from mammary glands; therefore, all humans are mammals.”

Logic is not, however, designed to produce truth—but only a valid argument. A valid argument based on one or more false premises usually produces a false, albeit valid conclusion. Thus, “all dogs are carnivores; all humans are carnivores; therefore, all humans are dogs.” The range of classical, Aristotelian logic expanded beyond the syllogism in the early 20th century with the introduction of more complex types of assumptions and connections, but both modern and classical logic continued to be based on deductive reasoning, whereby a true conclusion can be drawn with certainty from true premises. Logic is not, however, designed to produce truth—but only a valid argument. A valid argument based on one or more false premises usually produces a false, albeit valid conclusion. Thus, “all dogs are carnivores; all humans are carnivores; therefore, all humans are dogs.” The range of classical, Aristotelian logic expanded beyond the syllogism in the early 20th century with the introduction of more complex types of assumptions and connections, but both modern and classical logic continued to be based on deductive reasoning, whereby a true conclusion can be drawn with certainty from true premises.

the founding of the first schools in the colonial era. Taught informally or formally, depending on the age of each student group, it disappeared from the curriculum in the 1950s, 1960s and 1970s in favor of so-called life adjustment education. According to U.S. Department of Education studies, in the 1980s it was clear that “public school students of all ages [were] . . . deficient in higher order thinking skills.” Such thinking skills are the result of formal or informal instruction in logic.

Many public elementary and middle schools subsequently reintroduced informal instruction in logic, integrating it into mathematics, science and other classes. Typical logic instruction asks students to read a question first, then to identify the problem in their own words and determine specifically what information is relevant to the problem and what is irrelevant. Students are then asked to generate possible paths to a solution, evaluate them all, select one and explain the reasoning for that selection. The solution is then implemented. It is the generation and evaluation of alternative solutions that converts the exercise from problem solving into logic-based decision making.