All the articles I've read on this fall into two groups:
The "ki" is translated as "if" (which is dubious from a literal point of view, but not necessarily from an overall translation perspective) meaning "Do you know?"
The "ki" is translated as "surely", but the overall line is interpreted as being sarcastic, meaning "Surely, you know!"
The reason is that these questions are rhetorical in nature, and follow the famous "who shall ascend" in Deuteronomy, where it is clearly meant rhetorically, and this phrasing would be familiar to all jewish readers:
For this commandment which I command thee this day, it is not hidden
from thee, neither is it far off. It is not in heaven, that thou
shouldest say, Who shall go up for us to heaven, and bring it unto us,
that we may hear it, and do it? Neither is it beyond the sea, that
thou shouldest say, Who shall go over the sea for us, and bring it
unto us, that we may hear it, and do it? But the word is very nigh
unto thee, in thy mouth, and in thy heart, that thou mayest do it.
It also bears similarity to the sarcasm of God when he questions Job in chapter 38:
Hast thou entered into the springs of the sea? Or hast thou walked in
the search of the depth? Have the gates of death been opened unto
thee? Or hast thou seen the doors of the shadow of death? Hast thou
perceived the breadth of the earth? Declare if thou knowest it all.
Where is the way where light dwelleth? And as for darkness, where is
the place thereof, That thou shouldest take it to the bound thereof,
And that thou shouldest know the paths to the house thereof? Knowest
thou it, because thou wast then born? Or because the number of thy
days is great? v16-21
For just a sample of commentaries:
By two sets of rhetorical questions, a form of strong assertion (cf.
Ruth 3:1), Agur challenges his audience to bridge the “unbridgeable”
gulf between the LORD’s knowledge of wisdom and human helplessness by
personally identifying itself as a “son” of the Holy One. In verset A,
he employs in an anaphora the animate interrogative pronoun, who (see
23:29), four times, and in verset B, the inanimate interrogative
pronoun, what (vis-à-vis, “is his and his son’s name?” see 20:24). The
answer to the first question is, “No human being, but only God.” All
brings the “who” questions to their climatic conclusion (see 3:15,
17). The answer to the “what: questions are “the LORD” and “Israel.”
The “who” questions exhibit a chiastic pattern. The outer core
presents the merism “heaven” (4aα1) and “earth” (4aβ2) to denote the
cosmos (see 3:19). To ascend to heaven represents its vertical axis
and “ends of the earth,” its horizontal axis. The inner core presents
the two parts of a thunderstorm, “wind” (4aα1) and “water” (4aβ2) that
sustains life on earth (see 3:20). By restraining them the Lord
inflicts a drought (cf. 26:8; 28:25). The answer to these questions,
standing between humanity’s inability to know wisdom (vv. 2–3) and the
presence of God’s word with his people (vv. 5–6), unravels the paradox
of how inaccessible wisdom becomes accessible to earthlings.
Waltke, B. K. (2005). The Book of Proverbs, Chapters 15–31 (pp. 471–472). Grand Rapids, MI: Wm. B. Eerdmans Publishing Co.
Four questions (vv 4a, 4b, 4c, 4d) are reprised by a double question
(v 4e) and a challenge to respond to them (v 4f). The questions are
really the same and have a single response, as the singular “his”
(“his name,” “his son”) in v 4e shows. Three responses to these
questions are possible: (1) someone; (2) God; (3) no one.
“No one, of course.” This is the intended response. (The rhetorical
question in Qoh 7:24 is also to be answered this way.) The scope of
the questions is implicitly confined to humanity, because Agur is
speaking about the inadequacy of human wisdom. When Gilgamesh asks
“Who can go up to heaven, my friend?” (see below), the question
clearly pertains only to mankind, for gods regularly do this. No human
has the capability of doing godlike things: traversing the universe,
controlling the elements, creating the world. This is a fact known to
all, and Agur adduces it to remind the readers of their own ignorance.
Humans must always be aware that they are infinitely less powerful and
wise than God. Therefore they must rely on him and his word (Prov
Fox, M. V. (2009). Proverbs 10–31: A New Translation with Introduction and Commentary (Vol. 18B, p. 856). New Haven; London: Yale University Press.
In a series of rhetorical questions (v. 4), he first challenges the
reader to admit that no one has achieved direct understanding of the
world and the truth behind the world. To “go up to heaven and come
back down” is to attain and bring back direct knowledge of eternal
truth. Then, with three questions that allude to the creative power of
God (and human lack of that power), he implies that no one can explain
the metaphysical powers behind the visible creation. This language
recalls both Qoheleth’s confessions (Eccl 7:24) and God’s
confrontation of Job (Job 38:8–11). Finally, he ironically demands
that the reader produce such a sage if he can.
Garrett, D. A. (1993). Proverbs, Ecclesiastes, Song of songs (Vol. 14, pp. 236–237). Nashville: Broadman & Holman Publishers.