Recursive definitionIn mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs.
TrivialismTrivialism is the logical theory that all statements (also known as propositions) are true and that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance with this, a trivialist is a person who believes everything is true. In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is considered by some to be the complete opposite of skepticism.
Formal languageIn logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.
Formal proofIn logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Law of thoughtThe laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they are taken as laws that guide and underlie everyone's thinking, thoughts, expressions, discussions, etc. However, such classical ideas are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism and fuzzy logic.
Effective methodIn logic, mathematics and computer science, especially metalogic and computability theory, an effective method or effective procedure is a procedure for solving a problem by any intuitively 'effective' means from a specific class. An effective method is sometimes also called a mechanical method or procedure. The definition of an effective method involves more than the method itself. In order for a method to be called effective, it must be considered with respect to a class of problems.
ArgumentAn argument is a series of sentences, statements or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion. Arguments are intended to determine or show the degree of truth or acceptability of another statement called a conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective.
Deontic logicDeontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that A (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A, which is defined as .
Informal logicInformal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements). However, the precise definition of "informal logic" is a matter of some dispute. Ralph H. Johnson and J. Anthony Blair define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation.
