Although there is no separate Greek word that literally means “might,” the Greek construction in 2 Thessalonians 2:10 requires English to use the word “might” because of the way Greek expresses purpose and potential outcome. The phrase “that they might be saved” corresponds to the purpose clause εἰς τὸ σωθῆναι αὐτούς (“unto the saving of them”), which contains εἰς τὸ plus the infinitive, a grammatical form that naturally conveys intended result and conditional possibility. Greek does not insert an explicit word for “might,” but the structure itself means something like “so that they might be saved,” “in order that they might be saved,” or “for them to be saved,” which English must express with an auxiliary verb. This construction functions much like an implied if clause, indicating that salvation was a real possibility if they received the love of the truth. In other words, while “might” is not a Greek word in the text, the grammar itself communicates that they could have been saved if they had welcomed the truth, which is why the KJV correctly renders the phrase as “might be saved.” (See side note below to learn more).
In addition, when I quoted 2 Thessalonians 2:10 in the King James Bible, I was relying on a translation produced by men whose linguistic brilliance remains unmatched by modern scholarship. The KJV translators possessed an extraordinary depth of Greek knowledge, far surpassing what is commonly found among modern committees that depend heavily on lexicons and digital helps. Lancelot Andrewes was fluent in fifteen known languages and conversant in six additional archaic languages. John Bois read the Greek Old Testament at the age of five and later wrote Greek with a natural ease comparable to writing English. Henry Savile edited the complete works of Chrysostom in eight volumes, demonstrating a level of Greek expertise that few scholars living today could hope to equal. Miles Smith, who wrote the KJV preface, was proficient in Greek, Hebrew, Chaldee, Syriac, and Arabic. These men did not merely study Greek; they lived in it. Their daily reading included Greek fathers, classical literature, and ancient texts spanning more than a thousand years of linguistic development. Because of this exceptional mastery, the KJV translators could recognize the precise force of grammatical constructions such as the one in 2 Thessalonians 2:10 and express them with exactness. Their scholarship explains why the KJV captures the meaning of the Greek text so faithfully in the words “might be saved.”
Side Note:
The εἰς τὸ + infinitive construction is regularly identified as a way to express purpose or intended result. For example, grammarians note that “the preposition εἰς, combined with the definite article and the infinitive, is used to express purpose or result—‘in order that,’ ‘to,’ or less commonly, ‘so that [someone] might [do something]’”
Here is a paper you can check out:
https://www.drshirley.org/greek/textbook02/chapter48-infinitives.pdf
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