Having given this topic further thought, I think I can explain all the imperatives I have encountered to my satisfaction and so want to give an answer that might help others and is what I would have liked to read when first learning about this aspect of Greek.
First, let me outline the original problem again. There are fairly good descriptions in grammar books about how the aorist and imperfect tenses differ in narrating past events and how they differ in participles. There is less said about how the aorist and present stems differ in infinitives, apart from usages that parallel the difference in participles, such as in indirect statement. The grammars say next to nothing about imperatives and do not give enough information to predict what form to use or what the nuances of each form might be.
Some materials that teach Koine Greek say things like the aorist is used to express urgency. Whether this is true or not, this notion really describes a pragmatic use of the aorist and a secondary implication of its use, rather than fully explaining the semantics. In any case, I think urgency is not really a factor in choosing between the two forms.
In considering past events, any focus on a change in the situation tends to imply the use of the aorist; however, almost all imperatives imply a change in the situation. I now see that this notation of change is actually different in the two forms.
One could also equate the aorist stem with expressing telic events and the present stem with atelic events; however, I now see that this is not the case. The mere fact that an event is telic does not indicate that the imperative use expresses the necessity of reaching the endpoint that makes the expression telic. This is even more obvious when you consider that for the present tense, there is only one general choice of stem to use (i.e., the present stem) regardless of whether an event is telic or atelic.
The semantic difference I propose for imperatives is that the aorist stem presupposes that the speaker is focusing only on a result as necessary to satisfy the implied conditions; whereas the use of the present stem focuses on the importance of engaging in or initiating the action commanded, with whatever additional goal to be accomplished in due course.
The present stem is the default, so that if engaging in the action is the result wanted, the present stem will be used. Also, you have to look beyond the meaning of the verb in isolation, but consider any arguments used with it and any previous or follow-up actions described.
Here are 10 specific cases to illustrative the differences mostly with my translations to illustrate the difference in meaning. I tried to choose either well-known passages or passages where the same verbs are used in different forms:
- The first verse of Homer's Odyssey begins as follows:
Ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον,...τῶν ἁμόθεν γε, θεά, θύγατερ
Διός, εἰπὲ καὶ ἡμῖν.
Speak to me, O Muse, of that twisty and twisting one,... Bring us up
to speed about these things, o goddess, daughter of Zeus, from some
point in the story.
The form ἔννεπε is an present imperative and εἰπὲ is an aorist imperative. The first form, ἔννεπε, uses the present stem because it calls on the Muse to begin the tale. The idea is not "get the tale told" and so the present stem is appropriate.
Τhe second imperative form, εἰπὲ, is an aorist imperative. This form is used because the bard has gone on at some length to give the particulars of the tale the Muse should sing about, but then makes a specific request to orient the audience from some point or another before launching into the full tale. "Getting the audience informed" is a focus on a result and so makes the use of the aorist form appropriate. If you just translate both verbs as "tell," this difference in meaning is lost.
- the Iliad 1.32:
ἀλλ᾽ ἴθι μή μ᾽ ἐρέθιζε σαώτερος ὥς κε νέηαι.
So get going and don't be bothering me so you can return home more
Here, both ἴθι and μή μ᾽ ἐρέθιζε are present imperatives, though the command is given with urgency and menace. King Agamemnon does not care where the priest goes, but just wants him to get going, so a present imperative is appropriate. The action actually is the result wanted. As for ἐρέθιζε, Agamemnon is already angry and upset with the priest's request and wants him to stop asking for his daughter back and stop his extended pleas. Not continuing to be bothersome calls for the present imperative.
- Odyssey 3.380:
ἀλλά, ἄνασσ', ἵληθι, δίδωθι δέ μοι κλέος ἐσθλόν, αὐτῷ καὶ παίδεσσι καὶ
But, queen, be gracious and give good renown to me and my children,
and also to my honored companion.
It totally makes sense here that Homer doesn't use the aorist, because
this is a request that can't possibly be carried out immediately but
rather a request to do something in general in the future.
This is from user3597's answer and makes perfect sense. The requests are to engage in habitual action. The actions are the result desired, so the present imperatives are appropriate here.
- Gospel According to Matthew 2:20
“Ἐγερθεὶς παράλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ καὶ πορεύου εἰς γῆν
"Arise and then take the child and his mother and head to the land of
Here the Angel is telling Joseph that it is no longer necessary to stay as a refugee in Egypt because the danger has passed and so he is to get up, take his family and head to Israel.
There are three verbs to consider: Ἐγερθεὶς, παράλαβε, and πορεύου.
Ἐγερθεὶς is an aorist participle, but is translated in English with an imperative. In a combined action or imperative, English tends to use two verbs, but Greek often prefers a participle followed by the main verb. Another good example of this structure is the famously laconic answer King Leonidas gave to the Persians asking for earth and water in submission: μολὼν λαβέ (come and take (them)).
If used separately, this would have been Ἐγέρθητι, an aorist imperative. Both forms are aorist to background them as actions prior to the main command, which in this case is to take the child and mother.
In the phrase παράλαβε τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ, παράλαβε must be aorist for us to envision the result of reaching for the family members and not just the process.
The last imperative, πορεύου, is present imperative because what is desired is for Joseph to leave. The arrival in Israel is not the focus. Here the process is the result desired, requiring the present imperative.
- The Gospel According to Luke 5:24:
“Σοὶ λέγω, ἔγειρε καὶ ἄρας τὸ κλινίδιόν σου πορεύου εἰς τὸν οἶκόν
σου.” "I tell you, arise, take your bedding and head home."
This sentence appears like number 4, but uses a different mix of forms. The setting is that Jesus is commanding a paralyzed person to get up and walk home despite his paralysis.
The first imperative, ἔγειρε, is present-stem to focus on the surprising action. It is foreground, not background as in number 4. In effect, Jesus is showing that with God's power the person can actually get up on his legs despite the paralysis.
The participle ἄρας is like Ἐγερθεὶς in number 4. It is a backgrounded aorist participle and the first part of a two part action.
The imperative πορεύου is the second part of the action. It is a present imperative because the emphasis is not on what happens when the man gets home, but on his ability to walk home at all. The action is the result desired and so the verb is in the present-stem form.
- Luke 13:31
“Ἔξελθε καὶ πορεύου ἐντεῦθεν, ὅτι Ἡρῴδης θέλει σε ἀποκτεῖναι.” "Get
out of here and get away from here, because Herod wants to kill you"
I think this could have been said in many ways, but by using the aorist imperative Ἔξελθε, the speakers are saying that presence means death and so the desired result is not just starting to leave, but successfully vacating that place. On the other hand, the word πορεύου is present-stem because the destination is irrelevant. Once leaving has taken place, being in the process of heading away is the result desired; hence, the present imperative is good for this meaning.
- Iliad 1.33:
κλῦθί μευ ἀργυρότοξ᾽
Hear me/Hear my prayer, you of the silver bow
The word κλῦθί is aorist imperative. The meaning is not just "listen to what I am saying and consider it." The result desired is to have the prayer granted and so the aorist is needed here.
- Iliad 1.62
ἀλλ᾽ ἄγε δή τινα μάντιν ἐρείομεν ἢ ἱερῆα
Let's get going and put the question to a seer or a priest
Here, Achilles is desperate for a result, the end of plague that had been raging for 10 days, but this plea does not directly address the result. He is pleading for action, rather than just idly suffering from the wrath of some unknown god for some unreason. The action is the result desired so both verbs are in the present imperative.
- Matthew 8:9:
καὶ λέγω τούτῳ ‘Πορεύθητι,’ καὶ πορεύεται, καὶ ἄλλῳ ‘Ἔρχου,’ καὶ
ἔρχεται, καὶ τῷ δούλῳ μου ‘Ποίησον τοῦτο,’ καὶ ποιεῖ.
and I say to this one, "On with you!" And he goes. And to that one:
"Proceed!" And he proceeds. And to my slave: "Do this," and he does
From a discourse perspective, the speaker, a Centurion with a sick servant, is trying to illustrate that since he can give underlings a variety of different types of commands, he believes Jesus can too and command that his servant be healed without even having to visit him. As a result, the imperatives are of three different types and show both aorist and present-stem.
The word Πορεύθητι is aorist and so refers to a desired result. I think it is appropriate if you saw your servant starting to do something, but actually not moving fast enough. You can't just tell them to go, because they are already going. They are just dawdling. So you say, "On with you" or "Get out of here and be on your way." Don't just start doing it, get it done. This is what I think is the flavor of Πορεύθητι. It is a command to a dawdler to "be gone."
The word Ἔρχου is a present imperative. I think this is what you say to someone who is doing one thing, and you want them to do something else. Or, someone knows what to do, but is not sure whether to start yet. The particular action of Ἔρχου is the result you want, so the present imperative is appropriate.
The last imperative, Ποίησον, is an aorist imperative with an object. The idea is that you want a result, which is that the object be completed, not just worked on, so you use the aorist to express this.
By using these three different situations with underlings as examples, the Centurion is implying that surely Jesus has one of these options at his disposal with his servant angels. He can order the process of healing along as with Πορεύθητι if the boy's "guardian angel" is not taking proper care of him. If there is an angel available to take orders, Jesus can tell him to proceed and accomplish the healing as with Ἔρχου . If Jesus has to specify a particular healing procedure that needs to be accomplished, he can tell whatever "spirit messenger" is handy to complete it as with Ποίησον. With so many options to give the appropriate order, surely Jesus does not have to come in person to do the healing.
- Book of Acts. 9:11
Ὁ δὲ Κύριος πρὸς αὐτόν “Ἀναστὰς πορεύθητι ἐπὶ τὴν ῥύμην τὴν καλουμένην
Εὐθεῖαν καὶ ζήτησον ἐν οἰκίᾳ Ἰούδα Σαῦλον ὀνόματι Ταρσέα
The Lord said to him: "Get up and get to the street called "Straight"
and ask at the house of Judas for a man from Tarsus named Saul.
Hear we have three verbs, but one overall direction or command. As usual, the first, Ἀναστὰς, is a backgrounded aorist participle to show prior action. The second verb, πορεύθητι, is a full clause, but is backgrounded by being put in the aorist imperative. It is the necessary result that much be reached prior to the main action, which is to "ask for a man named Saul." The result desired is to locate Saul, not just to ask for him, so this verb, ζήτησον, is in the aorist imperative to focus on the result of the inquiry and not just the process.