Was Epaphroditus sent off sick by the apostle Paul in Phil 2:26, implying no one could heal him?
The word used here is ασθενεια, which is a combination of α-, which means "without," and "σθενος," which means "strength" or "vigor," so the combination means "without strength/vigor." That can be physical or non-physical, depending on the context. So, it can be translated "weakness" or "infirmity." Sickness or some other physical affliction would be one type of ασθενεια, but ασθενεια can mean physical or non-physical infirmity or weakness (un-firmness), not necessarily just sickness, and not necessarily even physical weakness/infirmity.
In Phil 2:26 it is the verb form. It and the accompanying verbs are in the Greek aorist tense, which expresses fact, not act, leaving context to determine time frame and completion, yet translators unfortunately habitually translate it as English past tense when it is not called for. Likewise there is a Greek imperfect tense, which only denotes incompletion of an activity, not time frame.
Taking the "past tense-ness" out of it, we have,
" Yet I deem [aorist] it necessary to send [aorist] to you Epaphroditus, the brother and together-worker and together-war-er of me, of you yet apostle and servant of the need of me,  since-necessarily longing-for [present participle] all he has-been-being [imperfect] and/also being-dismayed [present participle], you hear [aorist] that he lacks-strength/vigor [aorist],  for also he lacks-strength/vigor [aorist] near to death, but the God is-merciful [aorist] to him, yet not only to him but also to me, in order that no sorrow upon sorrow I should-have [aorist].  more expediently then, I send [aorist] him, in order that beholding [aorist participle] him again you may rejoice [aorist] and I may-be-being [present tense] without sorrow."Well, obviously it gets awkward translating so hyper-literally into English, but without the presupposition of "past tense," and given the present tense verb participles "longing for" and "being dismayed," you now see that it is a situation playing out in the present. Whatever weakness Epaphroditus has is to be remedied by sending him to Philippi. We aren't told what it is, but for all we know it could just be weakness from exhaustion or something like that. If he was really that sick, how could he travel? No cars, trains, airplanes, ambulances, medical airlift... he would be traveling some distance. Also note that in verse 19 he also "is expecting" to send Timothy to them "swiftly," but that is an "expectation" and not that Timothy is going right then at the time of his writing. By contrast, Epaphroditus is being sent "more expediently."
Also, note that the aorist tense would, in context, have us render "God is-merciful to him," not the traditional past tense "but God had mercy on him." Translating using the English past tense would not make much sense in light of the New Covenant and principles of the New Man.
Finally, keep in mind where Paul is: In prison (Phil 1:12-14). Wherever Epaphroditus is, he is not with Paul, because Paul was in prison and, if Epaphroditus was there, he wouldn't be able to be sent back to Philippi by Paul. So, these are instructions by Paul of what to do with Epaphroditus.
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