Aionios primarily refers to something that occurs during age(s) (which is a major theme of the new testament; multiple ages), which by definition occur inside a restricted time frame. Otherwise, you get nonsensical translations of certain passages which when translated literally would mean something like “to the eternity of eternities” or “forever and evers”, meaning multiple eternities. Or “in eternities past” or some other illogical nonsense like that.
It’s true that aionios can be applied TO eternal things, and can apparently be used to imply that in other respects, but it doesn’t have that intrinsic meaning in and of itself. If it did, it would work that way in every instance it is used, but it doesn’t.
Another reason that aionios cannot mean eternal (in the strictest sense) is that in order for something to truly be eternal, it must have no beginning as well as no end. If something has a beginning, then there had to be a point in time in which it started, which would automatically make it pertain to time.
Strong’s is amusingly self-contradictory on the point:
aiónios: agelong, eternal (how the hell can it mean age-long AND eternal? Those two concepts are not equivalent)
Original Word: αἰώνιος, ία, ιον
Part of Speech: Adjective
Phonetic Spelling: (ahee-o’-nee-os)
Short Definition: eternal, unending (But wait for it…)
Definition: age-long, and therefore: practically eternal, unending; partaking of the character of that which lasts for an age, as contrasted with that which is brief and fleeting.
(Er, hang on; ACTUAL DEFINITION is age-long, yet this somehow means “practically eternal”? Give me a break. Also “Partaking of the CHARACTER of that which LASTS FOR AN AGE.” That sounds blatantly qualitative to me.)
Cognate: 166 aiṓnios (an adjective, derived from 165 /aiṓn (“an age, having a particular character and quality”) – properly, “age-like” (“like-an-age”), i.e. an “age-characteristic” (the quality describing a particular age);
(figuratively) the unique QUALITY (reality) of God’s life at work in the believer, i.e. as the Lord manifests His self-existent life (as it is in His sinless abode of heaven).
(Again, sounds qualitative to me.)
"Eternal (166 /aiṓnios) life operates simultaneously outside of time, inside of time, and beyond time – i.e. what gives time its everlasting meaning for the believer through faith, yet is also time-independent. See 165 (aiōn).
(I’m sorry, but this is gibberish. It’s independent or outside of time but also occurs within it?)
[166 (aiṓnios) does not focus on the future per se, but rather on the QUALITY of the age (165 /aiṓn) it relates to.
(Yeah, I’m pretty sure this was basically a point I raised. It pertains to a finite period of TIME. So how does it mean eternal or endless again?)
Thus believers live in “eternal (166 /aiṓnios) life” right now, experiencing this QUALITY of God’s life now as a present possession. (Note the Gk present tense of having eternal life in Jn 3:36, 5:24, 6:47; cf. Ro 6:23.)]
This last note is interesting as well. The Greek in all of those passages referenced is in present tense when referring to “eternal” life. Again, time-bound.
Even Strong’s is clearly at odds with (some of) it’s own definition here. It’s self-contradictory rubbish. It can’t mean truly eternal, unless it is applied to something that is intrinsically eternal.