In English, “a double negative equals a positive.”1 In Greek,
Similar negatives as a rule strengthen each other, or the second is only the continuation of the first.
Cases may occur, however, in which two similar negatives destroy each other, inasmuch as both the sense and the natural position of the words exclude all ambiguity. In the N.T. there is only one passage where similar negatives destroy each other in one and the same sentence: 1 Cor. 12:15...
August Heinrich Matthiae:3
Two negatives of the same kind cancel one another, as in Latin, and then oὐ often negatives not only the first clause, but also the following negative clause.
Sometimes two negatives strengthen one another...
But in general both the simple and compound negatives in one and the same sentence strengthen one another.
Also μὴ οὐ and οὐ μή do not mutually cancel each other.
Christian Gottlob Wilke:4
The particles οὐ μή in combination augment the force of the negation, and signify not at all, in no wise, by no means...
Friedrich Wilhelm Blass:5
The most definite form of a negative assertion about the future is that with οὐ μή...
George Benedikt Winer:6
Two negatives employed together in one principal clause either
a. Produce an affirmation
b. They both produce a single negation (which is the more frequent case), and serve (originally) only to make the principal negation which would have sufficed alone more distinct and forcible, and to impart to the sentence a negative character throughout.
George Benedikt Winer (in another work):7
The intensive οὐ μή (of that which in no wise will or shall happen)...
Gerald L. Stevens:8
Emphatic Negation (οὐ μή)
English considers a double negative improper... Greek allows a double negative. Using οὐ and μή together as οὐ μή (notice the order) is equivalent to strong emphasis.
When a negative sentence contains indefinite pronouns or adverbs, e.g. any one, any how, any where, at any time, ever, etc., these are all expressed negatively.
Hence οὐ μή is used, when the idea to be expressed is...this CERTAINLY will not happen.
Rodney J. Decker,10
οὐ μή + aorist subjunctive: the strongest way to say “No!”
In English a double negative cancels itself (“I am not not going to study” means “I am going to study”), but in Greek double negatives intensify the negation rather than cancel it.
The construction οὐ μή followed by the aorist subjunctive is a strong negation of a future situation, stronger than simply saying οὐ. The two negatives do not negate each other; they strengthen the construction to say “No!” more emphatically.
William Watson Goodwin:12
The subjunctive (generally the aorist) and sometimes the future indicative are used with the double negative οὐ μή in the sense of an emphatic future indicative with οὐ.
1 American Heritage, p. 14
2 Buttman, p. 354, §148
3 Matthiae, p. 1081–1082
4 Wilke, p. 410, μή, IV.
5 Blass, p. 209, §64.5
6 Winer, p. 498–499, §55, 9., a.–b.
7 Winer, section LVI., p. 634, 3.
8 Stevens, Ch. 12, p. 181
9 Kühner, p. 261, 6. & p. 262, 9.
10 Decker, p. 627, 29.15
11 Mounce, p. 296, 31.18
12 Goodwin, p. 289, §1360
The American Heritage Book of English Usage: A Practical and Authoritative Guide to Contemporary English. Boston: Houghton Mifflin Harcourt, 1996.
Blass, Friedrich Wilhelm. Grammar of New Testament Greek. Trans. Thackeray, Henry St. John. 2nd ed. London: Macmillan, 1905.
Buttmann, Alexander. A Grammar of the New Testament Greek. Trans. Thayer, Joseph Henry. Andover: Draper, 1873.
Decker, Rodney J. Reading Koine Greek: An Introduction and Integrated Workbook. Grand Rapids: Baker, 2015.
Goodwin, William Watson. A Greek Grammar. Boston: Ginn, 1895.
Kühner, Raphael. An Elementary Grammar of the Greek Language. New York: Ivison, 1857.
Matthiae, August Heinrich. A Copious Greek Grammar. 5th ed. Vol. 2. London: Murray, 1832.
Mounce, William. Basics of Biblical Greek Grammar. 2nd ed. Grand Rapids: Zondervan, 2003.
Stevens, Gerald L. New Testament Greek Primer, Third Edition: From Morphology to Grammar. 3rd ed. Eugene: Cascade, 2010.
Wilke, Christian Gottlob. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Trans. Thayer, Joseph Henry.Ed. Grimm, Carl Ludwig Wilibald. Rev. ed. New York: American Book, 1889.
Winer, George Benedikt. A Grammar of the Idiom of the New Testament. 7th ed. Andover: Draper, 1892.
Winer, George Benedikt. A Treatise on the Grammar of New Testament Greek. 3rd ed. Trans. Moulton, William Fiddian. Edinburgh: Clark, 1882.