In classical

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

, propositions are typically unambiguously considered as being true or false. For instance, the proposition ''one is both equal and not equal to itself'' is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition ''one is equal to one'' is regarded as simply true, by the

Law of Identity In logic, the law of identity states that each thing is identical with itself. It is the first of the traditional three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are b ...

. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be ''more or less'' true, rather than wholly true or wholly false. Consider ''My coffee is hot''. In

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, this idea can be developed in terms of

fuzzy logic Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely ...

. In

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, it has found application in

artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

. In

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

, the idea has proved particularly appealing in the case of

vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word " prime" ...

. Degrees of truth is an important concept in law. The term is an older concept than

conditional probability In probability theory, conditional probability is a measure of the probability of an Event (probability theory), event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This ...

. Instead of determining the objective probability, only a subjective assessment is defined. Especially for novices in the field, the chance for confusion is high. They are highly likely to confound the concept of probability with the concept of degree of truth. To overcome the misconception, it makes sense to see probability theory as the preferred paradigm to handle uncertainty. In adjudicative processes, 'substantive truth' is distinct from 'formal legal truth' which comes in four degrees:

hearsay Hearsay, in a legal forum, is an out-of-court statement which is being offered in court for the truth of what was asserted. In most courts, hearsay evidence is Inadmissible evidence, inadmissible (the "hearsay evidence rule") unless an exception ...

balance of probabilities In a legal dispute, one party has the burden of proof to show that they are correct, while the other party has no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts ...

, proven beyond

reasonable doubt Beyond (a) reasonable doubt is a legal standard of proof required to validate a criminal conviction in most adversarial legal systems. It is a higher standard of proof than the standard of balance of probabilities (US English: preponderance of ...

and absolute truth (

knowledge Knowledge is an Declarative knowledge, awareness of facts, a Knowledge by acquaintance, familiarity with individuals and situations, or a Procedural knowledge, practical skill. Knowledge of facts, also called propositional knowledge, is oft ...

reserved unto

God In monotheistic belief systems, God is usually viewed as the supreme being, creator, and principal object of faith. In polytheistic belief systems, a god is "a spirit or being believed to have created, or for controlling some part of the un ...

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Fuzzy logic Logical truth {{logic-stub

See also

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