Abarim Publications' online Biblical Greek Dictionary
αγαθος
The adjective αγαθος (agathos) means good, virtuous or beneficial. It describes a tricky concept, especially since all things work for good for those who love God (Romans 8:28), but it's probably okay to assume that any movement or effort toward the inevitable and ultimate attractor of the whole of cosmic evolution (see Revelation 21:2) can be considered good, whereas any movement or effort away from that is a waste of time and energy and thus not good.
But since the inevitable and ultimate attractor of the whole of cosmic evolution is deeply akin its most fundamental principle, namely freedom (see Galatians 5:1), any restriction of movement isn't good, and goodness has rather to do with liberty than with direction. The full definition of goodness cannot easily be shoehorned into the mere handful of dimensions our language supplies, but there seems to be an arrow to liberty, just like there is one to time and in fact even complexity itself.
From our adjective comes the name Agathon, of the famous friend of Socrates and Plato — and note that the latter's name is famously parodied in Jesus' statement about the "broad" road to destruction; see πλατυς (platus), meaning broad or wide.
Our adjective is used 102 times, see full concordance, and from it derive:
- Together with the noun εργον (ergon), meaning work: the verb αγαθοεργεω (agathoergeo), meaning to do good, to act to someone's benefit (1 Timothy 6:18 only).
- The verb αγαθοποιεω (agathopoieo), meaning to do good, which is as tricky an activity as its adjective pertains. But since ultimately all souls will fully connect, the activity described by the noun αγαπη (agape) is probably a great place to start. Our verb is used a mere 11 times, see full concordance, and from it in turn derive:
- The noun αγαθοποιια (agathopoiia), meaning good-doing (1 Peter 4:19 only).
- The adjective αγαθοποιος (agathopoios), meaning good-doing. It's used only, in 1 Peter 2:14, substantially, in the sense of someone of does good.
- The noun αγαθωσυνη (agathosune), meaning goodness, that is a quality pertaining to the positive direction of liberty. It's used 4 times; see full concordance.
- Together with the adjective φιλος (philos), meaning beloved: The adjective φιλαγαθος (philagathos), meaning loving what is good or virtue-loving (Titus 1:8 only). From this word derives:
- Prefixed with the particle of negation α (a): the adjective αφιλαγαθος (aphilagathos), meaning not virtue-loving (2 Timothy 3:3 only).
βελτιων
The adjective βελτιων (beltion) means better (2 Timothy 1:18 only). It is the irregular comparative of αγαθος (agathos), good (see above). This sort of irregularity is not uncommon; a similar one appears in English: good and better.
Our word has nothing to do with the Latin bellus, beautiful (hence the familiar belle and bellisimo), but rather derives from the sparsely attested Proto-Indo-European root "bel-", meaning strength, which survives in Slavic words for "better": bolje (while, perhaps conveniently, bol means sick; bolnica means hospital, where people get better).
Note the accidental similarity with the noun βελος (belos), dart or ballistic missile, from which may stem the name Bellerophon, the hero who captured Pegasus at Corinth, and whose iconography evolved into that of Saint George (from γεωργος, georgos, earth-worker). Our word also has nothing formally to do with the widely attested Semitic term בעל (ba'al), meaning master, from which comes the theonym Bel (but see our article on the many Hebrew roots of Greek).