Salva veritate

The literal translation of the Latin "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 of statements in which the expressions occur. Substitution salva veritate of co-extensional terms can fail in opaque contexts.[1]

Leibniz

The phrase occurs in two fragments from Gottfried Leibniz'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' and 'trilateral', for in every proposition demonstrated by Euclid concerning 'triangle', 'trilateral' can be substituted without loss of truth (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.[2] 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whole quantified modal logic of necessity is dependent on context and empty otherwise; for it collapses if essence is withdrawn.[3]

For example, the statements:

(1) Giorgione = Barbarelli,
(2) Giorgione was so-called because of his size

are true; however, replacement of the name 'Giorgione' by the name 'Barbarelli' turns (2) into the falsehood:

  Barbarelli was so-called because of his size.[4]

Quine's example here refers to Giorgio Barbarelli's sobriquet "Giorgione", an Italian name roughly glossed as "Big George."

gollark: Of course, there's no use worrying about this because I don't* have backdoors in your stuff.
gollark: And/or muck with your release pipeline accordingly (not that I did this, of course).
gollark: In the hypothetical scenario in which I had backdoors, I could theoretically just make it accept itself as valid if it was signed by potatOS keys and not your own.
gollark: It still can't verify itself.
gollark: In any case, I can neither confirm nor deny that there wouldn't be much stopping me from just sending backdoored copies into your signing process.

See also

References
  1. L.T.F. Gamut, Logic, Language and Meaning, 1991
  2. W.V.O. Quine, Quintessence: Reference and Modality, 2004, p. 378
  3. W.V.O. Quine, Quintessence: Reference and Modality, 2004, pp. 356–357
  4. W.V.O. Quine, Quintessence: Reference and Modality, 2004, p. 361

Bibliography
  • Clarence Irving Lewis, A Survey of Symbolic Logic, Appendix, Dover.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.