Formal equivalence is sometimes called "literal" or "word-for-word" translation. A formally equivalent translation is relatively transparent to the source language reflecting, to the extent that it is possible, the grammatical structure and even word order of the original.
Strict formal equivalence is not really possible. Wtords in the source language may not have a precise equivalent in the target language. That is, words in different languages have different ranges of meaning. Some words are untranslatable. In Greek there are little words called "particles" that add emphasis, for example, or "iffy-ness" o a sentence but which cannot be reproduced in English. Greek also employs double negatives which, if rendered literally, result in ungrammatical English. Word order is also used very differently in Greek than in English.
As an example, here is a very literal rendering (it can't really be called a translation) of Romans 12:9-10 from the Greek:
The love unhypocritical. Loathing the evil, sticking-like-glue to the good, in brotherly-love to one-another persons-with-familial-affection; in honor one-another persons-who-go-before....
Dynamic equivalence is sometimes described as thought-for-thought translation. The idea of dynamic equivalence is to render the meaning of the source text into the target language with less concern for the actual words and grammar of the original. Dynamic equivalence translations tend to be freer, more idiomatic and more natural than formally equivalent translations. I think it is safe to say that they are also more interpretive. The success of a dynamic equivalence translation depends in large measure on the translator's understanding of the source text.
Here is Romans 12:9-10 from the New American Standard Bible, a high formal equivalence translation:
Let love be without hypocrisy. Abhor what is evil; cling to what is good. Be devoted to one another in brotherly love; give preference to one another in honor....
And for comparison, from the Common English Bible, a much more dynamically equivalent translation:
Love should be shown without pretending. Hate evil, and hold on to what is good. Love each other like the members of your family. Be the best at showing honor to each other....
The translation philosophies of formal and dynamic equivalence both have their strengths and weaknesses. English readers, with hundreds of versions available to them, are probably fortunate that they don't have to choose a single type of translation. When I teach my New Testament class in the Diakonia program, I require my students to write paper explaining a passage of Scripture. I always tell them to compare the passage in several versions.
Some of the more formally equivalent English translations of the Bible include the King James Version, the American Standard Version, the Revised Standard Version, the New American Standard Bible and the New King James Verson.
Dynamic equivalence translations include the Good News Translation, the Contemporary English Version, the New Living Translation and the Common English Bible.
The New Revised Standard Version and the New International Version steer a middle course, with the NRSV leaning toward formal equivalence and the NIV family favoring dynamic equivalence.
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