Having had the discussion that "aionios does not mean eternal." many, many times on this forum I decided to review every occurrence of "aionios" in the NT. In the list below I show where Paul uses "aionios" synonymously with "aidios."
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[3]John 3:15
(15) That whosoever believeth in him should not perish, but have eternal [αιωνιον] life.
[4] John 3:16
(16) For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting [αιωνιον] life.
In the above two verses Jesus pairs “aionion” with “should not perish.” Believers could eventually perish in a finite period, thus by definition “aionion life” here by definition means eternal or everlasting life.
No, believers who are promised aionion life - if aionion life is a finite period such as the millenium - could not perish because they will have immortality. So your argument is not only unsound logically but also unscriptural.
For God so loved the world that He gave the only begotten Son, so that everyone believing in Him should not perish, but should have eonian (aionion) life. (Jn. 3:16).
In John 3:16 there is no question that those who are believing - shall - not perish. Even though the subjunctive "should" is used. For it is used with the hina (so that) indicating purpose or result.
Likewise, in the very next verse, Jn.3:17, the hina occurs again with subjunctive, just as it does in John 3:16:
For God did not send His Son into the world that He might judge the world, but that the world might be saved through Him. (Jn.3:17)
There we see God's reason in sending His Son, namely to save the world. That was the Diivine will of God, Who is Love Omnipotent. And notice what BDAG says about the "divine will":
“In many cases purpose and result cannot be clearly differentiated, and hence ἵνα is used for the result that follows according to the purpose of the subj. or of God. As in Semitic and Gr-Rom. thought, purpose and result are identical in declarations of the divine will…”
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More literal versions of John 3:16 say:
16 For thus God loves the world, so that He gives His only-begotten Son, that everyone who is believing in Him should not be perishing, but may be having life eonian. (CLV)
16 for God did so love the world, that His Son—the only begotten—He gave, that every one who is believing in him may not perish, but may have life age-during. (YLT)
16 For God, so loved, the world, that, his Only Begotten Son, he gave,—that, whosoever believeth on him, might not perish, but have life age-abiding. (Ro)
16 Thus for loved the God the world, so that the son of himself the only-begotten he gave, that every one who believing into him, not may be destroyed, but may have life age-lasting. (Diaglott)
Perish for how long & in what way? The same Greek word for "perish" is used of the prodigal son who was "lost" but later found. He was ruined, not annihilated.
Not everyone will get EONIAN life, which pro Endless Hell club, non universalist, versions mistranslate as "eternal life". Those who believe before they die get EONIAN life. They will live & reign with Christ for the 1000 years of the millennial EON (Rev.20). Unbelievers will not. They go to "hell" until they repent & are saved, since God becomes "all in ALL" (1 Cor.15:22-28). For Jesus is the Lamb of God Who takes away the sin of the world (Jn.1:29), "the Saviour of the world" (John 4:42), Who will draw all to Himself (John 12:32).
John 3:16 says unbelievers "perish", not that they perish endlessly. If Jesus had wanted to say "perish endlessly" there was a Greek word for "endless" He could have used (aperantos, 1 Tim.1:4). He could have also used the words "no end" (Lk.1:33) of perishing. Clearly endless punishment is not the teaching of the Word of God.
"While we are on the topic, however, I might mention that, alongside various, often seemingly contradictory images of eschatological punishment, the New Testament also contains a large number of seemingly explicit statements of universal salvation, excluding no one (for instance, John 3:17; 12:32, 47; Romans 5:18-19; 11:32; 1 Corinthians 15:22; 2 Corinthians 5:14, 19; Philippians 2:9-11; 1 Timothy 2:3-6;4:10; Titus 2:11; Hebrews 2:9; 2 Peter 3:9; Colossians 1:19-20; 1 John 2:2 … to mention only some of the most striking). To me it is surpassingly strange that, down the centuries, most Christians have come to believe that the former class of claims—all of which are metaphorical, pictorial, vague, and elliptical in form—must be regarded as providing the “literal” content of the New Testament’s teaching, while the latter—which are invariably straightforward doctrinal statements—must be regarded as mere hyperbole. It is one of the great mysteries of Christian history (or perhaps of a certain kind of religious psychopathology)."
Anent Garry Wills and the “DBH” Version
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For a response to other passages on your list:
What Does Aionios Mean? (part 2, It is wrong to define aionios based on aion)
how do people who believe in eternal torture in fire
The Restitution Of All Things A.K.A. Universalism
OTOH here we see many examples where αἰών and αἰώνιος are defined/described as being of a finite duration:
Does aionios always mean eternal in ancient Koine Greek? (paradise, Gospel, hell) - Christianity - - City-Data Forum
http://www.hopebeyondhell.net/articles/further-study/eternity/
12 points re forever and ever being a deceptive translation & being finite:
For the Lord will NOT cast off FOR EVER:
Jesus didn't use the best words & expressions to describe endlessness in regards to punishment, because He didn't believe in endless punishment:
The Restitution Of All Things A.K.A. Universalism