Logic

Logic is a field of philosophy that deals with the nature and application of logic, and is related with many other fields such as language or epistemology. The term is derived from the greek word ‘logos’ - which mainly refers to reasoning and language. Logic can generally be divided into two categories: formal and informal. Formal logic is used to define and explore the nature of logic and propositions (a true or false statement). In an argument (or proof or demonstration), both the form and content matter must be examined. For example, take the following syllogism:
1. If A, then B
2. A
3. Thus, B
The syllogism has a proper form in which each premise (points 1-2) follow necessarily and lead to the conclusion (point 3). This argument is said to be a valid one. Often, however, logical demonstrations are a little more complex than a 3-point syllogism - and require more advanced logical tools. This is where symbolic logic plays a role, to clear vagueness and to clearly define what the argument is (this allows logicians to better understand and critique a claim). The symbols used not any random symbols, but rather ones of standard mathematical notation, such as: ∀, Ǝ, or ∪. Content matter is also of importance in logic, and will determine whether or not the argument is sound or not. A sound argument is not only valid (having correct form), but also must have true premises, and thus a necessary conclusion. While it may seem daunting to see mathematical notation used in philosophical papers, or in general logic - these tools allow an individual to not only understand an argument in clearer terms, but also to correctly infer conclusions. Lastly, there is the category that is termed ‘informal logic’. Informal logic primarily refers to the every-day application of logic emphasizing proper forms of reasoning, common argumentative fallacies, and critical thinking skills. However, plenty of more categories can be derived from simply formal logic, such as: propositional logic, predicate logic, semantics, etc. This is a field that was most developed during the explosion of interest in Analytic philosophy (separate entry).