section_path: Formal theories/Logic
section_name: Logic
paragraph_text: Logic
  
  Logic is concerned with the patterns in reason that can help tell if a proposition is true or not. Logicians use formal languages to express the truths they are concerned with, and as such there is only truth under some interpretation or truth within some logical system.
  
  A logical truth (also called an analytic truth or a necessary truth) is a statement that is true in all possible worlds or under all possible interpretations, as contrasted to a fact (also called a synthetic claim or a contingency), which is only true in this world as it has historically unfolded. A proposition such as "If p and q, then p" is considered to be a logical truth because of the meaning of the symbols and words in it and not because of any fact of any particular world. They are such that they could not be untrue.
  
  Degrees of truth in logic may be represented using two or more discrete values, as with bivalent logic (or binary logic), three-valued logic, and other forms of finite-valued logic. Truth in logic can be represented using numbers comprising a continuous range, typically between 0 and 1, as with fuzzy logic and other forms of infinite-valued logic. In general, the concept of representing truth using more than two values is known as many-valued logic.