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Disclaimer: In this OP, I am not arguing whether or not the Father draws everyone. I am discussing the logical usage of the word "unless".
John 6:
There exists a person who does not have eternal life.
Therefore, the Father does not draw him.
According to the strong sense of the word "unless", the Father does not draw everyone. In either case, John 12:
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Appendix 1
Sometimes the context tells us which sense is being used. Let's apply these two senses to 2 Timothy 2:
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Appendix 2
Young's Literal Translation, John 6:44
if not
draws
ἑλκύσῃ (helkysē)
Verb - Aorist Subjunctive Active - 3rd Person Singular
Strong's 1670: To drag, draw, pull, persuade, unsheathe. Or helko hel'-ko; probably akin to haireomai; to drag.
BDAG:
John 6:
Let's try to translate the above to the first-order logic language. The trouble is that there is more than one way to express the English concept of unless. The word carries two senses.44 No one can come to me unless the Father who sent me draws him.
- the weak sense: If the Father does not draw him, he cannot come to Jesus.
⇒ If he comes to Jesus, then the Father draws him.
The Father's drawing of a person is a necessary condition. At this point, I don't know whether the Father draws everyone. - the strong sense: The Father does not draw him if and only if he cannot come to Jesus.
⇒ He can come to Jesus if and only if the Father draws him.
The Father's drawing of a person is both necessary and sufficient.
Jesus raises him up on the last day iff the Father draws him.44 No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day.
He has eternal life iff the Father draws him.40 For my Father’s will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day.”
There exists a person who does not have eternal life.
Therefore, the Father does not draw him.
According to the strong sense of the word "unless", the Father does not draw everyone. In either case, John 12:
By the Cross, Jesus does draw all people to himself.32 And I, when I am lifted up from the earth, will draw all people to myself.”
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Appendix 1
Sometimes the context tells us which sense is being used. Let's apply these two senses to 2 Timothy 2:
5 An athlete is not crowned unless he competes according to the rules.
- If he does not compete according to the rules, he is not crowned.
Method 1 (weak sense of unless) is a valid interpretation. - He does not compete according to the rules if and only if he is not crowned.
⇒ If he is not crowned, then he does not compete according to the rules.
⇒ If he competes according to the rules, then he is crowned.
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Appendix 2
Young's Literal Translation, John 6:44
ἐὰν μὴno one is able to come unto me, if the Father who sent me may not draw him, and I will raise him up in the last day;
if not
draws
ἑλκύσῃ (helkysē)
Verb - Aorist Subjunctive Active - 3rd Person Singular
Strong's 1670: To drag, draw, pull, persuade, unsheathe. Or helko hel'-ko; probably akin to haireomai; to drag.
BDAG:
Biblehub listed 30 translations out of 51 use the word "unless" to translate ἐὰν μὴ with aorist subjunctive. In this case, it is not just ἐὰν μὴ; it is ἐὰν μὴ followed by an Aorist Subjunctive verb. This pattern has been observed frequently enough that some experts believe that this pattern is the equivalent of the English concept of "unless".ⓒ w. other particles
α. ἐὰν καί even if Gal 6:1; likew. ἐὰν δὲ καί (POxy 472 II, 7) but if 1 Cor 7:11, 28; 2 Ti 2:5. ἐὰν δὲ καὶ παρακούσῃ but if the pers. refuses to listen Mt 18:17.
β. ἐὰν μή if not, unless w. pres. subj. ἐὰν δὲ μὴ ᾖ ἀξία Mt 10:13; cp. Lk 13:3; J 3:2f, 5, 27. Mostly w. aor. subj. ἐὰν μὴ περισσεύσῃ Mt 5:20; 6:15; 12:29; 18:3; 21:21; Mk 3:27; 4:22 (s. KBeyer, Semitische Syntax im NT, ’62, 131); J 4:48; 6:44; 7:51; Ro 10:15; 1 Cor 9:16; 14:6; unless, without ἐὰν μὴ αὐτὸ πίω Mt 26:42. W. fut. ἐὰν μὴ μετανοήσουσιν Rv 2:22.