The literal translation of the

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

"''salva veritate''" is "with (or by) unharmed truth", using ablative of manner: "''salva''" meaning "rescue," "salvation," or "welfare," and "''veritate''" meaning "reality" or "truth". Thus, ''Salva veritate'' (or intersubstitutivity) is the logical condition by which two expressions may be interchanged without altering the

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 progra ...

of statements in which the expressions occur. Substitution ''salva veritate'' of co-extensional terms can fail in

opaque context An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute "co-referential" expressions (expressions referring to the same object) without altering the truth of sentences. The expres ...

Leibniz

The phrase occurs in two fragments from

Gottfried Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...

's ''General Science. Characteristics'': * In Chapter 19, Definition 1, Leibniz writes: "Two terms are the same (''eadem'') if one can be substituted for the other ''without altering the truth of any statement'' (''salva veritate'')." * In Chapter 20, Definition 1, Leibniz writes: "Terms which can be substituted for one another wherever we please ''without altering the truth of any statement'' (''salva veritate''), are the same (''eadem'') or coincident (''coincidentia''). For example, '

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

' and 'trilateral', for in every proposition demonstrated by

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...

concerning 'triangle', 'trilateral' can be substituted ''without loss of

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 belie ...

'' (''salva veritate'')."

Quine

W.V.O. Quine Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century" ...

takes substitutivity ''salva veritate'' to be the same as the "indiscernibility of identicals". Given a true statement, one of its two terms may be substituted for the other in any true statement and the result will be true. He continues to show that depending on context, the statement may change in value. In fact, the whole quantified modal logic of necessity is dependent on context and empty otherwise; for it collapses if

essence Essence ( la, essentia) is a polysemic term, used in philosophy and theology as a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it ...

is withdrawn.W.V.O. Quine, ''Quintessence: Reference and Modality'', 2004, pp. 356–357 For example, the statements: are true; however, replacement of the name 'Giorgione' by the name 'Barbarelli' turns (2) into the falsehood: Quine's example here refers to Giorgio Barbarelli's

sobriquet A sobriquet ( ), or soubriquet, is a nickname, sometimes assumed, but often given by another, that is descriptive. A sobriquet is distinct from a pseudonym, as it is typically a familiar name used in place of a real name, without the need of expla ...

"Giorgione", an Italian name roughly glossed as "Big George."

References

Bibliography

Clarence Irving Lewis Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logic ...

, ''A Survey of Symbolic Logic'', Appendix, Dover.

External links

Philosophical Dictionary
{{Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz Latin logical phrases Concepts in logic

Leibniz

Quine

See also

References

Bibliography

External links