Regarding esse se aequlaem Deo, we must also be clear that “equality with God” (as a noun) is misleading since it is a verbal phrase. Moreover, it’s also more than just “being equal to God.” We can’t forget that se. We’re not speaking about “to be equal with God” in general. Rather, we’re speaking about the fact of Christ’s being equal with God: “That he was equal to God,” “for him to be equal to God,” etc.

The only way to use “something to be grasped” would be if you wanted to convey the sense that Jesus did not need to grasp equality with God (because he has it). However, this does not do justice to the first part of the verse since it remains ambiguous about Christ’s status, i.e., all it says is that he won’t be grasping equality with God. The first part of the verse makes it clear that Christ’s equality with God can’t be grasped because he has it by nature. So, arpagmon should be translated as referring to something which “has been grasped” (plunder) or the act of grasping itself (robbery).

cum can be concessive without tamen or tum or the like, but context would make that obvious. Since the causal meaning is just as likely (more likely in the context of the whole canticle), I don’t see how it can be concessive without something to indicate such.

Also, let’s get that “not” in the right place since non (or “ouk”) is not negating the main verb arbitratus est but rather the noun rapinam. So, “he thought it [was] not” rather than “he did not think.”

“esse se aequalum est” is the object of “rapinum”. You are being misled by an assumption that the Latin should be translated into English in the same word order. The correct translation of the Latin is:

“He did not thing that being equal to God was a thing to be seized.”

Moreover, the Greek makes this transparently clear. The word translated “rapinum” in Latin is “arpagmon” in Greek. The Greek word does NOT mean “robbery” but rather, “a thing which ought to be seized/desired”; and that force is one possible meaning to “rapinum” as well.

And so, if you want to preserve the Latin word order, you get “He did not thing it ought to be seized/grasped to be equal to God.”

Moreover, perhaps you might read Patristic commentaries on this? Or consider context?

Fretting about the force of “cum” here, by the way, is irrelevant; the word does not show up in the Greek, which doesn’t need a conjunction because of differences in normal Greek grammar.

arbitratus est is the perfect of arbitror, which is a deponent verb. So, it means “he thought,” “he regarded,” “he esteemed,” “he judged,” etc.

Dylan, how exactly does “rapinam arbitratus” work there? The cognates are very interesting. E.g., “There would be no arbitration of rape that…”