Degree of truth

In classical logic, 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. 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, this idea can be developed in terms of fuzzy logic. In computer science, it has found application in artificial intelligence. In philosophy, the idea has proved particularly appealing in the case of vagueness. Degrees of truth is an important concept in law.

The term is an older concept than conditional probability. Instead of determining the objective probability, only a subjective assessment is defined.^[1]^{[page needed]} 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.^[2]^{[failed verification]} 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, balance of probabilities, proven beyond reasonable doubt and absolute truth (knowledge reserved unto God).^[3]

Bibliography

L.A. Zadeh (June 1965). "Fuzzy sets". Information and control. 8 (3). San Diego: 338–353. doi:10.1016/S0019-9958(65)90241-X. ISSN 0019-9958. Zbl 0139.24606. Wikidata Q25938993.

References

^ Castell, Lutz; Ischebeck, Otfried, eds. (2003). Time, Quantum and Information. Springer Science & Business Media. doi:10.1007/978-3-662-10557-3. ISBN 978-3-540-44033-8.
^ Smith, Nicholas JJ and Dietz, Edited Richard and Moruzzi, Sebastiano (2007). "Degrees of truth, degrees of belief and subjective probabilities". To Appear in a Collection of Papers Presented at Arche. {{cite journal}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link)
^ Summers, Robert S. (1999). "Formal Legal Truth and Substantive Truth in Judicial Fact-Finding – Their Justified Divergence in Some Particular Cases". Cornell Law Faculty Publications (1186).

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[1] Castell, Lutz; Ischebeck, Otfried, eds. (2003). Time, Quantum and Information. Springer Science & Business Media. doi:10.1007/978-3-662-10557-3. ISBN 978-3-540-44033-8.

[2] Smith, Nicholas JJ and Dietz, Edited Richard and Moruzzi, Sebastiano (2007). "Degrees of truth, degrees of belief and subjective probabilities". To Appear in a Collection of Papers Presented at Arche. {{cite journal}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link)

[3] Summers, Robert S. (1999). "Formal Legal Truth and Substantive Truth in Judicial Fact-Finding – Their Justified Divergence in Some Particular Cases". Cornell Law Faculty Publications (1186).

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v t e Non-classical logic
Intuitionistic	Intuitionistic logic Constructive analysis Heyting arithmetic Intuitionistic type theory Constructive set theory
Fuzzy	Degree of truth Fuzzy rule Fuzzy set Fuzzy finite element Fuzzy set operations
Substructural	Structural rule Relevance logic Linear logic
Paraconsistent	Dialetheism
Description	Ontology (computer science) Ontology language
Many-valued	Three-valued Four-valued Łukasiewicz
Digital logic	Three-state logic Tri-state buffer Four-valued Verilog IEEE 1164 VHDL
Others	Dynamic semantics Inquisitive logic Intermediate logic Non-monotonic logic

See also

Bibliography

References