Featured Article Summary #36

Logic is the study of correct reasoning and includes both formal and informal logic. Formal logic focuses on deductive valid inferences and logical truths, while informal logic examines fallacies, critical thinking, and argumentation theory. Logic plays a central role in fields such as philosophy, mathematics, computer science, and linguistics. In logic, arguments consist of premises and a conclusion, with propositions or claims that can be true or false. Complex propositions are made up of simpler propositions linked by logical vocabulary. Logical truth propositions are true due to their logical structure and not the specific meanings of its parts. Arguments can be correct or incorrect, with deductive arguments having the strongest form of support. Ampliative arguments are not found in the premises and are divided into inductive (statistical generalizations) and abductive (inferences to the best explanation). Fallacies often arise from arguments that fall short of correct reasoning. Logic has been studied since antiquity, with early approaches including Aristotelian logic. Modern formal logic, rooted in the work of late 19th-century mathematicians, replaced Aristotelian logic as the main system of logic. Classical logic is the most used system today, consisting of propositional and first-order logic. Extended logics extend classical logic to other fields, while deviant logics reject certain classical intuitions. The word "logic" comes from the Greek word "logos" and is defined as the study of correct reasoning or the laws of thought. Logic focuses on arguments and inferences, determining whether the premises support the conclusion. There are two types of logic: formal and informal, with formal logic being the more dominant field. Formal logic, also known as symbolic logic, is a method of studying reasoning by using abstract symbols instead of concrete expressions. It focuses on the structure of arguments rather than their specific content. Formal logic is interested in deductively valid arguments, where the truth of the premises guarantees the truth of the conclusion. It uses formal languages with precise rules to express and analyze arguments. Natural language arguments need to be translated into formal language before their validity can be assessed. There are different types of logics with varying rules of inference and formal languages. Informal logic is the study of arguments in everyday discourse using non-formal criteria. It addresses problems that formal logic cannot, such as ambiguity and context-dependence in natural language. There is no agreed-upon definition for informal logic, but it can be seen as the normative study of argumentation standards and procedures, the study of non-deductive arguments, or the study of informal fallacies. Premises and conclusions are the basic elements of arguments. In valid arguments, the conclusion is supported by the premises. Premises and conclusions can be seen as either propositions or sentences, but each approach has its own problems. Another approach is to understand them as thoughts or judgments, but this position is not widely accepted.