In classical
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
, 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
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the s ...
; while the proposition ''one is equal to one'' is regarded as simply true, by the
Law of Identity. 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 an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, 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 completel ...
. In
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, it has found application in
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech ...
. In
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...
, 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" is ...
. 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 occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occu ...
. 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.
See also
;Language:
*
Meaning (linguistics)
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
—
Semiotics
Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something ...
;Technology:
*
Artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech ...
;Logic:
*
Bivalence
*
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 completel ...
*
Fuzzy set
In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set.
At the same time, defined ...
*
Half-truth
A half-truth is a deceptive statement that includes some element of truth. The statement might be partly true, the statement may be totally true, but only part of the whole truth, or it may use some deceptive element, such as improper punctuation, ...
*
Multi-valued logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...
*
Paradox of the heap
The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a s ...
*
Truth
Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as belief ...
*
Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false'').
Computing
In some pro ...
*
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" is ...
;Books:
*''
Vagueness and Degrees of Truth''
Bibliography
*
References
Fuzzy logic
Logic
Truth
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