failing the test and so rejected: unfit, worthless, or disqualified after being weighed and found wanting
TranslatabilityPartialCertaintySettled
The picture behind this word comes from testing metal and coins. Ancient assayers weighed silver to see whether it was genuine; what passed was called "approved" (δόκιμος), and what failed was counterfeit or debased and thrown out. This word is the exact negative of that "approved," and every New Testament use carries the image of something weighed and found wanting.
The same word covers both people and things, because the test can be run on either. Of a person it means "disqualified," failing to prove genuine, the way an athlete is ruled out of the games or the way Paul tells the Corinthians to examine whether their own faith stands up. Of a thing or a state of mind it means "worthless" or "unfit": land that grows only thorns, a mind that can no longer tell right from wrong, a life that comes up empty at every good work.
Romans turns on a play that English hides. Because people did not see fit to keep God in mind, God handed them over to a mind that cannot see fit, a failed instrument for judging good and evil. The refusing and the being refused are the same root.
Nuances
1adisqualified: a person who fails the test of genuineness and is ruled out
1Co 9:272Co 13:52Co 13:62Co 13:7
1bunfit or worthless: a thing, mind, or character that fails to meet the standard and is rejected
Names the FAILING verdict: after examination the person or thing does not pass, so it is rejected, disqualified, or thrown out as worthless.1Co 9:272Co 13:5Heb 6:8
Extends to a mind or character gone corrupt and useless, unfit for any good work and hollow even in its claim to faith.Rom 1:28Tit 1:162Ti 3:8
Both
Both come from the same picture of testing metal or coin for genuineness, and both name the RESULT of the assay rather than the testing itself. In the one verse where they stand together they are set as exact opposites: the hope of being found approved against the dread of being found rejected.2Co 13:7
Names the PASSING verdict: after examination the person comes through proven genuine, approved, and openly commended.Rom 16:102Co 10:182Ti 2:15
Carries a standing that God accepts and other people recognize: acceptable, well regarded, shown to be the real thing once trial has done its work.Rom 14:181Co 11:19Jas 1:12
ἀχρεῖος"useless, unprofitable": names a lack of usefulness, where this word names failure under testing, though the two overlap in the sense of "worthless"
The verdict follows a test: this is the exact opposite of "approved," so it names something put to the proof and found wanting. Paul rules himself out like an athlete disqualified from the games, and tells the Corinthians to examine themselves lest they fail the test.1Co 9:272Co 13:5
Used of people weighed against God's standard and rejected as counterfeit: a mind God hands over as debased, and men whose faith does not stand up to scrutiny.Rom 1:282Ti 3:8
Both
Both can be rendered "worthless" and mark something fit only to be discarded: a plot of ground that yields thorns and is near to being cursed, and a servant cast out into the dark.Heb 6:8Mat 25:30
The problem is uselessness, not a failed exam: built on the idea of "need" or "use," it measures a thing by the profit it returns, and the servant who returns none is thrown out.Mat 25:30
Can be said humbly of oneself: obedient servants call themselves "unprofitable" for merely doing their duty, claiming no merit, with no hint of having been tested and found faulty.Luk 17:10
adokimos in the other biblical languages
מָאַסHebrew“to reject”the Hebrew "to reject, refuse," used of "rejected silver" that failed the assayer in Jeremiah 6:30, the same image of tested-and-refused metal that stands behind the Greek word
Presupposes an examination: the verdict falls only after the thing has been tried. Paul disciplines his body so that, having preached to others, he will not himself be found failing (1 Corinthians 9:27), and he tells the Corinthians to test themselves lest they turn out to be the ones who do not pass (2 Corinthians 13:5). The rejection is the outcome of an assay, the flip side of δόκιμος, "approved after testing."1Co 9:272Co 13:5
Works as an adjective naming a settled condition, what a person or thing has become rather than an act done to them: a mind God hands over so that it can no longer judge rightly (Romans 1:28), opponents "corrupt in mind, rejected concerning the faith" (2 Timothy 3:8), people who profess to know God yet are "unfit for any good work" (Titus 1:16).Rom 1:282Ti 3:8Tit 1:16
Both
Both converge in the picture of metal that fails the assay and is thrown out. Jeremiah calls faithless Judah "rejected silver," because the LORD has rejected them (Jeremiah 6:30), and that Old Testament image of ore weighed and found worthless is just what the Greek word pronounces when Paul warns the Corinthians they may prove to be the ones who fail the test (2 Corinthians 13:5). The Hebrew names the act of rejecting that produces the very failed-assay verdict the Greek word carries.Jer 6:302Co 13:5
Names a deliberate act of the will, to refuse, spurn, or reject what is set before you, with the focus on the choosing rather than any resulting condition. It runs in both directions within the covenant relationship: God spurning a faithless people or king (2 Kings 17:20;1 Samuel 16:1), and people spurning the LORD's word, his statutes, or his rule (1 Samuel 8:7;1 Samuel 15:23;Leviticus 26:15).2Ki 17:201Sa 16:11Sa 8:71Sa 15:23Lev 26:15
Stretches from plain refusal to loathing and contempt, carrying the scorn behind the rejection and not merely a failed test: spurning correction (Proverbs 3:11;Proverbs 15:32), recoiling from oneself in self-disgust (Job 42:6), or the builders throwing away the very stone that becomes the cornerstone (Psalm 118:22).Pro 3:11Pro 15:32Job 42:6Psa 118:22
Carries no metallurgical picture at all: it is the abstract verdict that something has failed a test and is rejected. A mind, a faith, or a worker is put to the proof and does not stand, so it is disqualified as unfit.Rom 1:282Co 13:52Ti 3:8
Both
Both deliver a verdict of worthlessness on what should have been valuable. The Hebrew pictures silver debased into castoff waste, fit only to be discarded; the Greek pronounces the same failed-and-rejected sentence on a person or their work. What the furnace does to bad metal, the test does to the unfit.Isa 1:22Tit 1:16
Names a concrete substance: the dross, the worthless refining waste skimmed off molten silver in the smelter's furnace. The word paints a physical picture of impurity separated from precious metal, whether the slag itself or a people who have become that slag.Pro 25:4Ezk 22:18Psa 119:119
What scholars say about adokimos
The word is the alpha-privative of δόκιμος and belongs to the δοκιμ- word group treated in TDNT (Grundmann): the vocabulary of testing metals and coins to prove them genuine. BDAG divides the New Testament usage into two applications of one sense: unqualified or worthless of things (Hebrews 6:8; the νοῦς of Romans 1:28), and disqualified or failing the test of persons (1 Corinthians 9:27;2 Corinthians 13:5-7). Moulton-Milligan document the adjective in the papyri of debased or counterfeit coinage, the concrete background Spicq (TLNT) draws on to argue that the term consistently connotes what has been tested and found spurious rather than merely bad. The Romans 1:28 occurrence is widely read as a deliberate paronomasia with ἐδοκίμασαν in the same verse.
Sources
BDAG, s.v. ἀδόκιμοςlexicon
W. Grundmann, "δόκιμος, ἀδόκιμος, κτλ.," TDNT 2:255-260dictionary
C. Spicq, Theological Lexicon of the New Testament, s.v. δόκιμος, ἀδόκιμοςdictionary
J. H. Moulton and G. Milligan, The Vocabulary of the Greek Testament, s.v. ἀδόκιμοςlexicon