In standard mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, propositions can typically be considered unambiguously true or false. For instance, the proposition zero belongs to the set { 0 } is regarded as simply true; while the proposition one belongs to the set { 0 } is regarded as simply false. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than simply true or simply false. Consider My coffee is hot.

In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, this idea can be developed in terms of fuzzy logic

Fuzzy logic

Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...

. In computer science

Computer science

Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, it has found application in artificial intelligence

Artificial intelligence

Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

. In philosophy

Philosophy

Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, the idea has proved particularly appealing in the case of vagueness

Vagueness

The term vagueness denotes a property of concepts . A concept is vague:* if the concept's extension is unclear;* if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this...

. Degrees of truth is an important concept in law.

See also

• Artificial intelligence
  Artificial intelligence
  Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
  
  
• Bivalence
• Fuzzy logic
  Fuzzy logic
  Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
  
  
• Fuzzy set
  Fuzzy set
  Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced simultaneously by Lotfi A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to...
  
  
• Half-truth
• Multi-valued logic
  Multi-valued logic
  In logic, a many-valued logic is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values for any proposition...
  
  
• Paradox of the heap
• Truth value
• Vagueness
  Vagueness
  The term vagueness denotes a property of concepts . A concept is vague:* if the concept's extension is unclear;* if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this...