Essentially the answer to, “How do we know that the last verses of Ps 102 are referring to Jesus, rather than to God the Father?” is, that is what writer of Hebrews states:
And: “You, LORD, in the beginning laid the foundation of the earth, And the heavens are the work of Your hands. (1:10) [NKJV throughout]
The writer also employed other techniques to accomplish this and show it was their intent.
To begin, the principle of Sola Scriptura is at work because the writer is explaining how a specific text from Psalm 102 applies to Jesus. Two sources of the Psalm were available to the writer: one in Hebrew and one in Greek. To compare the letter to the Psalm requires the reader to compare it to the two sources. If the Hebrew text of the Psalm was used, then the writer chose to interpret the source text by adding “Lord” (implying YHVH, the Name of the LORD in Hebrew):
Translation based on Hebrew of Masoretic Text (MT): Of old You laid the foundation of the earth, And the heavens are the work of Your hands.
If the Greek translation (LXX) of the Psalm was used, the writer retained the added "Lord":
Translation based on Greek text of Septuagint (LXX): At the beginning it was you, O Lord, who founded the earth, and the heavens are works of your hands. [NETS]
Regardless of which source the writer used, it is apparent they saw it necessary to write "Lord" in their letter to explain how the Psalm text applied to Jesus and a reader would recognize the Sensus Plenior present in the Hebrew text. As Richard quotes Raymond Brown:
The sensus plenior is that additional, deeper meaning, intended by God but not clearly intended by the human author, which is seen to exist in the words of a biblical text (or group of texts, or even a whole book) when they are studied in the light of further revelation or development in the understanding of revelation.
Raymond E. Brown, The Sensus Plenior of Sacred Scripture (Baltimore: St. Mary's University, 1955), p 92
In the source text, the Psalmist is lamenting the destruction of Jerusalem and praying for its restoration 1 yet has written prophetically to include a deeper meaning which the writer of the letter can recognize after God speaks to people through Jesus:
God, who at various times and in various ways spoke in time past to the fathers by the prophets, has in these last days spoken to us by His Son... (Hebrews 1:1-2)
Next since the NT writer appears to be using the LXX, the logical comparison would be to the English translation of the LXX. Yet when the LXX text of the Psalm is compared to its citation in the letter, it is obvious the writer of the letter also deviated from the LXX:
Hebrews 1:10 σὺ κατ’ ἀρχάς κύριε
LXX 101:26 κατ᾽ ἀρχὰς σύ, κύριε
Hebrews 12 καὶ ὡσεὶ περιβόλαιον ἑλίξεις αὐτούς ὡς ἱμάτιον καὶ ἀλλαγήσονται
LXX 101:27 καὶ ὡσεὶ περιβόλαιον ἀλλάξεις αὐτούς, καὶ ἀλλαγήσονται
Therefore, regardless of source, it is clear the writer modified what they started from in order to use it to describe Jesus. It is presumptive to assume a reader can use other portions of the Psalm and apply them to the Messiah. Rather, one must acknowledge the writer of Hebrews understood a sensus plenior aspect of the Psalm, which, when modified described the Messiah. If the entire Psalm is studied for additional Messianic allusions, it should be done by applying the NT understanding of the Messiah to the Psalm and not by attempting to define the Messiah by using the Psalm.
The “Preface” Effect
The proper orientation is for a reader to approach the OT passage from the context established in the letter. For example, consider how Psalm 2:7 is introduced and used in the letter:
Hebrews 1:5 Psalm 2:7
For to which of the angels did God ever say, The LORD said to me,
You are my Son, You are my Son;
today I have begotten you. today I have begotten you.
The preface to the quote effectively restates the first part of the Psalm. "The LORD said to me..." in the Psalm becomes "For to which of the angels did God ever say..." in the letter. The preface reorients the reader away from the original text of the Psalm to make the point the Messiah is not an angel. From the perspective of the letter writer, the Messianic portion of the Psalm is only: "You are my Son; today I have begotten you." 2 If one is to (re)read the Psalm understanding there is a Messianic component, it must be done seeing the Psalmist as making a personal appeal (“The LORD said to me…”) which has a prophetic (sensus plenior) Messianic component (“You are my son [Son]; today I have begotten you”).
There is no basis for presuming the use in the letter means the entire verse without modification can be applied to the Messiah. Rather, the letter writer has eliminated the potential for misunderstanding the identity of "the LORD" and "me" by effectively restating part of what the Psalmist wrote, before using it in the letter.
In terms of the issue of the deity of the Messiah, the writer of Hebrews is intentional to present an OT text in a way which states the Son is God:
Hebrews 1:8 Psalm 45:6 (MT)
But of the Son he says,
Your throne, O God, is forever and ever, Your throne, O God, is forever and ever,
the scepter of uprightness The scepter of your kingdom
is the scepter of your kingdom. is a scepter of uprightness
Not only does the writer suggest the Son is God (“But of the Son he says, ‘Your throne, O God...’"), they have preserved the LXX arrangement which transposes uprightness and kingdom:
Psalm 45: 6 (LXX – NETS) Psalm 45:6 (MT)
Your throne, O God, is forever and ever Your throne, O God, is forever and ever,
A rod of equity The scepter of your kingdom
is the rod of your rule. is a scepter of uprightness
This would follow a Christian understanding of Jesus: it is the uprightness of the incarnate Messiah which results in His kingdom. In other words, where the Hebrew text of the Psalmist has God with a kingdom whose scepter is uprightness; the letter writer sees the incarnate Son as God whose uprightness is the scepter of His kingdom.
One cannot (re)read the Hebrew text of Psalm 45 as Messianic without first rearranging it: uprightness results in the kingdom and not a kingdom of uprightness. The difference is subtle yet significant. The Psalmist sees God with a kingdom having a scepter of uprightness; the writer of Hebrews sees the Messiah as incarnate God living and dying proving His uprightness which affirms, restores, and/or returns His kingdom.
The Chiasm of Hebrews 1:5-13
The writer of Hebrews has also used the prefaces to present the OT passages in a chiastic arrangement:
A: "For to which of the angels did He ever say..." [Psalm 2:7]
B: "And again…” [2 Samuel 7:14 also 1 Chronicles 17:13]
C: "But when He again brings the firstborn into the world, He says:" [Deut 32:43 (LXX)]
X: "And of the angels He says:" [Psalm 104:4]
C’: "But to the Son He says:" [Psalm 45:6,7]
B’: "And:" [Psalm 102:25-27]
A’: "But to which of the angels has He ever said:" [Psalm 110:1]
The chiastic nature of the passage is obvious when the reader follows the first and last points:
A: (1:5) "For to which of the angels did He ever say..." Psalm 2:7
Central Point: (1:7) "And of the angels He says:" Psalm 104:4
A’: (1:13) "But to which of the angels has He ever said:" Psalm 110:1
Ancient writer used chiasms to demonstrate the central point of the passage:
The use of Chiasmus in antiquity was encouraged by the fact that it provided “a needed element of internal organization in ancient writings, which did not make use of paragraphs, punctuation, capitalization and other synthetic devices to communicate the conclusion of one idea and the commencement of the next.” 3
The central point which the arrangement pivots is on what is said of (not to) the angels:
And of the angels He says: “Who makes His angels spirits, And His ministers a flame of fire.” (Hebrews 1:7)
Not only is the Messiah not an angel, He is the Creator of angels; the LORD God of Psalm 104. This central point affirms what preceded the OT citations:
has in these last days spoken to us by His Son, whom He has appointed heir of all things, through whom also He made the worlds (Hebrews 1:2)
The Son not only made the worlds (better is ages, αἰῶνας); He also made the angels.
McCoy summarizes three important aspects of the chiasm: 4
- Delineate units of thought
- Accentuate the main idea or theme the writer is concerned to convey to their readers
- Compare and contrast the interplay between textually separated but thematically paired units of thought
The delineation of units of thoughts is important to the arrangement in Hebrews: each individual OT citation is a discrete piece and the primary meaning of an individual piece is in its use to support the main point (not how this meaning should be applied to the source text).
The secondary meaning to be considered is in conjunction with the paired units of thought:
Pair 1 (A/A'):
For to which of the angels did He ever say: “You are My Son, Today I have begotten You”? (1:5a)
But to which of the angels has He ever said: “Sit at My right hand, Till I make Your enemies Your footstool”? (1:13)
Pair 2 (B/B'):
And again: “I will be to Him a Father, And He shall be to Me a Son” (1:5b)
And: “You, Lord, in the beginning laid the foundation of the earth, And the heavens are the work of Your hands. They will perish, but You remain; And they will all grow old like a garment; Like a cloak You will fold them up, And they will be changed. But You are the same, And Your years will not fail.” (1:10-12)
Pair 3 (C/C'):
But when He again brings the firstborn into the world, He says: “Let all the angels of God worship Him.” (1:6)
But to the Son He says: “Your throne, O God, is forever and ever; A scepter of righteousness is the scepter of Your kingdom. You have loved righteousness and hated lawlessness; Therefore God, Your God, has anointed You With the oil of gladness more than Your companions.” (1:8-9)
As the OP notes in their question, a linear reading of the letter presents the citation from Psalm 102 as directed to the Son: “But to the Son He says…and…” However, the reading based on the chiastic pairings shows the writer deliberately omitted any direct reference to the Son or angels in the preface to the passages from Psalm 2 and Psalm 102. In other words, the preface in 1:8 applies only to the unit of thought which follows and not the next unit of thought.
This adds clarity to the third pair of citations:
1:6 ὅταν δὲ πάλιν εἰσαγάγῃ τὸν πρωτότοκον εἰς τὴν οἰκουμένην λέγει [“when moreover again He brings the firstborn into the inhabited land He says”]
1:8 - πρὸς δὲ τὸν Υἱόν [“unto however the Son”]
The firstborn is brought into the inhabited land (not all creation). Also there is no “He says” to the preface to Psalm 45 where the actual text of the letter is: "unto however the Son, Your throne, O God is forever and ever..." In other words, the writer of the letter has deliberately omitted “He says” to establish an ambiguity to what follows: is it The Father (the implied "He" translators add) or the sons of Korah (of the Psalm) who recognize the Son as God? Given the overall sense of the letter, the ambiguity is purposeful to make the point either and both understand the Son as God.
The introduction of the first pair includes the theme of angels; the second lacks any specific referents; the third pair includes specific references, the firstborn and the Son. The reader must recognize the writer’s purposeful organization and classification of each OT text and the reader is not free to either ignore or apply an orientation from one pair to a different pair. Obviously, the passage “Let all the angels of God worship Him” applies only to the firstborn brought into the world, not to angels.
The significance of this lies in the fact the writer has no referent to the second pair (Psalm 2 and Psalm 102). So the first quote “I will be to Him a Father, and He shall be to Me a Son” is purposely ambiguous. A reader is not free to take the preface from another pair: “[To the Son He says] I will be to Him a Father…” Rather, the reader must acknowledge another meaning is possible: “[The Son] will be to Him a Father, and He [the Father] shall be to Me a Son. That is, the writer may have written to express a type of equality between The Father and The Son which is found elsewhere:
I and My Father are one. (John 10:30)
Believe Me that I am in the Father and the Father in Me… (John 14:11)
“If you had known Me, you would have known My Father also; and from now on you know Him and have seen Him.” (John 14:7)
…He who has seen Me has seen the Father… (John 14:9)
Now if the reader chooses to resolve the ambiguity by applying the traditional understanding to Psalm 2:7, and establish The Father as a referent who is speaking of, or to the Son, then that same referent should be maintained with its chiastic pair:
And again [The Father]: “I will be to Him a Father, And He shall be to Me a Son” (1:5b)
And [The Father]: “You, Lord, in the beginning laid the foundation of the earth, And the heavens are the work of Your hands. They will perish, but You remain; And they will all grow old like a garment; Like a cloak You will fold them up, And they will be changed. But You are the same, And Your years will not fail.” (1:10-12)
Thus, in the letter, it is The Father who calls The Messiah Lord and in the source text it is Psalmist who calls the Messiah, Lord. This reflects the NT understanding of how "Lord" should be used:
yet for us there is one God, the Father, of whom are all things, and we for Him; and one Lord Jesus Christ, through whom are all things, and through whom we live. (1 Corinthians 8:6)
Why does the letter writer present Psalm 102 as calling Jesus "Lord?" Because there is only one Lord and all who call upon the Name of the LORD will be saved.
Finally, those who attempt to avoid the writer's intent with respect to their use of Psalm 102 and claim in is not the Father calling the Son Lord, place themselves in a conundrum of justifying how the writer used Psalm 2 for who other than The Father can make that statement?
1. Adele Berlin and Marc Zvi Brettler, The Jewish Study Bible, Oxford Press, 2004, p. 1394
2. Psalm 2:7 is also quoted as “You are my Son, today I have begotten you” in Hebrews 5:5 and Acts 13:33.
3. Brad McCoy, "Chiasmus: An Important Structural Device Commonly Found in Biblical Literature." (quotation from John Breck , The Shape of Biblical Language, p 60). p 23 [Chafer Theological Seminary]
4. McCoy pp. 30-31