Editing Truth (section)

===Tarski's semantics===
{{main|Semantic theory of truth}}

[[Tarski's theory of truth]] (named after [[Alfred Tarski]]) was developed for formal languages, such as [[formal logic]]. Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression ''is true'' could only apply to sentences in some other language. The latter he called an ''object language'', the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.) The reason for his restriction was that languages that contain their own truth predicate will contain [[Liar paradox|paradoxical]] sentences such as, "This sentence is not true". As a result, Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates. [[Donald Davidson (philosopher)|Donald Davidson]] used it as the foundation of his [[truth-conditional semantics]] and linked it to [[radical interpretation]] in a form of [[coherentism]].<ref>{{Citation |last=Hodges |first=Wilfrid |title=Tarski's Truth Definitions |date=2022 |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/entries/tarski-truth/ |access-date=2025-04-04 |edition=Winter 2022 |publisher=Metaphysics Research Lab, Stanford University |editor2-last=Nodelman |editor2-first=Uri}}</ref>

[[Bertrand Russell]] is credited with noticing the existence of such paradoxes even in the best symbolic formations of mathematics in his day, in particular the paradox that came to be named after him, [[Russell's paradox]]. Russell and [[Alfred North Whitehead|Whitehead]] attempted to solve these problems in ''[[Principia Mathematica]]'' by putting statements into a hierarchy of [[type theory|types]], wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible [[type system]]s that have yet to be resolved to this day.<ref>{{Cite book |last=Link |first=Godehard |url=https://books.google.com/books?id=Xg6QpedPpcsC |title=One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy |date=2004 |publisher=Walter de Gruyter |isbn=978-3-11-017438-0 |language=en}}</ref>