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 ...

, 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''). Truth values are used in c ...

of statements in which the expressions occur. Substitution ''salva veritate'' of co-extensional terms can fail in opaque contexts. The literal translation of the

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

"''salva veritate''" is "with (or by) unharmed truth", using ablative of manner: "''salva''" meaning "rescue," "salvation," or "welfare," and "''veritate''" meaning "reality" or "truth".

Leibniz

The phrase occurs in two fragments from

Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...

'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 corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

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

Euclid Euclid (; ; 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 geometry that largely domina ...

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

truth Truth or verity is the Property (philosophy), property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise cor ...

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

Quine

W.V.O. Quine 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 Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

of necessity is dependent on context and empty otherwise; for it collapses if

essence Essence () has various meanings and uses for different thinkers and in different contexts. It is used in philosophy and theology as a designation for the property (philosophy), property or set of properties or attributes that make an entity the ...

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 ( ) is a descriptive nickname, sometimes assumed, but often given by another. A sobriquet is distinct from a pseudonym in that it is typically a familiar name used in place of a real name without the need for explanation; it may beco ...

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

References

Bibliography

Clarence Irving Lewis Clarence Irving Lewis (April 12, 1883 – February 3, 1964) was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epis ...

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

External links

Philosophical Dictionary
{{Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz Latin logical phrases Concepts in logic Willard Van Orman Quine

Leibniz

Quine

See also

References

Bibliography

External links