"oz" consistently means strength/power/might throughout the old testament, as well as in other semitic texts such as Ugaritic. In no text does it mean "praise". In fact the root, עזז, is never translated as anything other than: strength, refuge, mighty, stronghold, and proper names. No child of this root is ever used as praise.
Contra Genesius, HALOT gives only two senses, not four, and these are "strength/might" and "refuge" (see Details). So does BDB, TDOT, NIDOTTE and other modern dictionaries (see Details).
However, when used as an adjective, it can mean "loud", from the Lexham Research Lexicon
Adjective Usage
1. loud — characterized by or producing sound of great volume or
intensity. See also רום. Related Topic: Noise.
2 Ch 30:21 וּֽמְהַלְלִ֣ים לַ֠יהוָה י֣וֹם׀ בְּי֞וֹם הַלְוִיִּ֧ם וְהַכֹּהֲנִ֛ים בִּכְלֵי־עֹ֖ז
Brannan, R. (Ed.). (2020). Lexham Research Lexicon of the Hebrew Bible. Bellingham, WA: Lexham Press.
Looking at Gesenius' other examples:
Ps. 8:2: (to be covered later)
Ps. 29:1: Ascribe to Yahweh, O sons of God, ascribe to Yahweh glory and strength.
Ps. 68:35: Awesome are you, O God, from your sanctuary. The God of Israel, it is he who gives strength and might to the people. Blessed be God.
Ps. 99:4: And the strength of the king loves justice. You have established equity; you have executed justice and righteousness in Jacob.
Ex. 15:2: Yah is my strength and song, and he has become my salvation; this is my God, and I will praise him—the God of my father—and I will exalt him.
(LEB translation)
In the sense of Psalm 8.2 it is a figurative reference to praise. That is, Psalm 8.2 equates praise coming from infants as the strength/power of God:
From the mouth of children and infants you have founded/ordained strength on account of your enemies, to silence the enemy and the avenger.
Unless you believe that the children and infants are shooting death rays out of their mouths, then it is the praise that is coming from their mouths (this is, after all, a song) and this praise is referred to as the power that God has ordained to silence the enemy and avenger.
Thus figuratively, praise could be strength as could prayer, faith, fasting or anything that is a source of power or strength, and thefore in some interpretations you can use a different word to get the best meaning across, but in hebrew the word oz means only strength or refuge.
It is in this sense that Jesus says:
"And they said to him, “Do you hear what these children are saying?” So Jesus said to them, “Yes, have you never read, ‘Out of the mouths of children and nursing babies you have prepared for yourself praise’?”"
And this should be viewed as a religious argument about whether children should be allowed in the Temple courts, Jesus cites the Psalm that God has ordained ("prepared") the praise of children, which is what the Psalm says, even though it (figuratively) refers to the praise of children with the word "oz".
Details
HALOT citation:
I עֹז, עוֹז Pr 24:5 31:17 †; SamP. ʿaz, sf. bazzåk Ex 15:13; Sec. οζ
(Sperber 246; Brönno 122f): עזז, Bauer-L. Heb. 455g; Ug. ʿz (Gordon
Textbook §19:1835; Aistleitner 2021; Ug. 5 p. 553 line 9, cf. p. 602a,
see de Moor UF 1 (1969):179; Craigie VT 22 (1972):145f); Ph. עז
(Jean-H. Dictionnaire 205): עֹֽז Ju 5:21 Jb 26:2, עָז־ in abs. Js.
26:1, עֹז־וְ Pr 31:25; עָֽז Gn 49:3 as by-form → *עַז (→ SamP. !); cs.
עָז־ (Bauer-L. Heb. 562v) עֻזּוֹ/ה, עֻזְּכָ/זָּֽךְ, עֻזֵּךְ, עֻזִּי,
also עָזִּי/זְּךָ (Bl 559i), Or. עֹזְךָ and עֹזוֹ (Kahle Text 73),
Sec. οζει (Sperber and Brönno 122f); עוּזֵּנוּ (Ps 81:2, BHS),
עֻזְּכֶם, עֻזָּמוֹ (Bauer-L. Heb. 252o), THAT 2:252ff. —1. might,
strength: a) 1S 2:10 Is 51:9 52:1 Ezk 19:12 Ps 138:3 Jb 41:14 Pr 21:22
31:17, 25; בְּכָל־עֹז with all his might 2S 6:14 cj.5 for בְּכָל־עֲצֵי
בְרוֹשִׁים prp. with 1C 13:8 בְּכָל־עֹז וּבְשִׁירִים; cj. 2C 30:21 for
בִּכְלֵי־עֹז prp. בְּכָל־עֹז; b) adv. (Bauer-L. Heb. 632m) in strength
Ju 5:21; c) in phrases, means fortified, strong, well founded:
מִגְדַּל־עֹז Ju 9:51 Ps 61:4 (יהוה), Pr 18:10; עִיר עֹז Is 26:1,
קִרְיַת עֹז Pr 10:15 18:11, 19, מַטֵּה עֹז Jr 48:17 Ps 110:2, מַטּוֹת
עֹז Ezk 19:11, sg. 19:14, מַצְּבוֹת עֹז 26:11, קוֹל עֹז Ps 68:34,
הַרְרֵי עֹז Ps 30:8, מְרוֹם עֹז Jr 51:53; רְקִיעַ עֻזּוֹ Ps 150:1 →
under 3, מִבְטַח־עֹז Pr 14:26, מַחֲסִי־עֹז Ps 71:7 → under 3; גְּאוֹן
עֹז proud strength Lv 26:19 Ezk 24:21 30:6, 18 33:18, 28 cj. 7:24 (rd.
עֻזָּם → עַז); עֹז פָּנָיו his hard face Qoh 8:1; לֹא־עֹז without
strength Jb 26:2. —2. the fortifications of a town, ramparts (Hamp
BZ NF 16 (1972):117ff): with יִסַּד Ps 8:3 (Donner ZAW 79 (1967):326:
עֹז = firmament :: trad. Versions, praise), with הוֹרִיד Pr 21:22 Am
3:11 (cj. הוּרַד BHS). —3. God’s might (cf. II !): הָבוּ לי׳ כָּבוֹד
וָעֹֽז Ps 29:1, cf. ἐνισχυσάτωσαν αὐτῷ πάντες ἄγγελοι Θεοῦ Dt 32:43
Sept. (BHS); Ps 59:17; עֹז יהוה Mi 5:3, cj. Ps 68:29 for עֻזֶּךָ
עוּזָּה אֱלֹהִים prp. עֻוְּךָ עֹז הָאֱ׳ (BHS); God acts בְּעֻזּוֹ Ps
78:26, cj. Dt 33:26 for בְּעֶזְרָֽךָ prp. בְּעֻזֶּךָ (Seeligmann; see
also BHS); בְּעֻזְּךָ Ex 15:13 Ps 21:14 74:13, זְרוֹעַ עֻזּוֹ Is 62:8
Ps 89:11, חֶבְיוֹן עֻזֹּה Hab 3:4 → חִבָּיוֹן; רֹב עֻזְּךָ Ps 66:3,
אֲרוֹן עֻזֶּֽךָ Ps 132:8 2C 6:41 = Ps 78:61, עֹז אַפֶּֽךָ Ps 90:11;
cj. 76:8 for מֵאָז אַפֶּֽךָ prp. מֵעֹז אַ׳; עֻזּוֹ וְאַפּוֹ Ezr 8:22,
רְקִיעַ עֻזּוֹ Ps 150:1; in יהוה is עֹז to Is 45:24 Ps 29:1/1C 16:28
Ps 62:12 63:3 68:29, 35 93:1 96:7 Jb 12:16 1C 16:27; יהוה וְעֻזּוֹ Ps
105:4 1C 16:11; יהוה is עֹז strength (if I עֹז is equivalent to II
עֹז, where see further); God gives עֹז Ps 68:36 86:16; God allows his
עֹז to be experienced Ps 77:15; God is מַחֲסִי־עֹז Ps 71:7, תִּפְאֶרֶת
עֻזָּמוֹ 89:18; with God is עֹז יְשׁוּעָתִי Ps 140:8 and עֹז
וְתוּשׁיָּה Jb 12:16 and עֹז וְחֶדְוָה 1C 16:27; the righteous find
עוֹז בָּֽךְ Ps 84:6; עֹז וְתִפְאֶרֶת are in the מִקְדָּשׁ Ps 96:6.
—4. strength, might of the king: Ps 99:4: cj. ? for עֹז מֶלֶךְ prp.
מֶלֶךְ עָֽז (Gunkel Ps. 431) or וְעַז מָלַךְ (Kraus BK 155:580).
—Emendations: cj. Jb 37:6 for עֻזּוֹ prp. עֹזּוּ (עזז impv.); Pr 24:5
rd. מֵעָֽז → עַז II 1; → II עֹז. †
II עֹז, SamP. ʿaz, with sf. ʿazzi: עוז, Bauer-L. Heb. 451n; textual
confusion with I; עֻזִי (so BHK3; Bomberg and BHS עֻזִּי) is apparent
in Ps 59:18 and this word (or עֹזִי, see R. Meyer Gr. §23, 1c) is to
be substituted for עֻזִּי Jr 16:19 Ps 28:7 62:8 and for עָזִּי Ex 15:2
(:: Barr Philology 29), Is 12:2 Ps 118:14 and correspondingly
עֹ/עֻזְךָ for עָזְּךָ Ps 21:2 עֹ/עֻזֵנוּ for עוּזֵּנוּ Ps 81:2 (THAT
2:221f): refuge, protection (always God) = II מָעוֹז: Yahweh is עֹז Ps
28:8 29:11;מַחֲסֶה וָעֹז 46:2; with sf., my protection Is 49:5 Jr
16:19 Ps 28:7 59:18 cj. 10 for עֻזּוֹ prp. עֻוִּי (< עֻזִי), ע׳
וְזִּמְרָתִי Ex 15:2 Is 12:2, your protection Ps 21:2, our 81:2; I עֹז
still remains a possibility, except for Ps 62:8 צוּר־עֻזִּי, see Hamp
BZ (new series) 16 (1972):117ff. †
Koehler, L., Baumgartner, W., Richardson, M. E. J., & Stamm, J. J. (1994–2000). The Hebrew and Aramaic lexicon of the Old Testament (electronic ed., pp. 805–806). Leiden: E.J. Brill.
NIDOTTE citation:
עָזַז (ʿāzaz), q. be or prove oneself strong; prevail over, overpower;
give or impart strength; pi., establish; ni., be insolent, impudent,
bold; hi., (make strong [the face] =) be insolent, impudent, bold,
brazen, shameless (#6451); עַז (ʿaz), adj. strong; fierce/cruel;
defiant, shameless; hard, stern, severe, grim, brazen; turbulent
(#6434); עָז (ʿāz), nom. strength (hapleg.; #6435); עֹז (ʿōz), nom.
strength, power (#6437 [HALAT distinguishes between עֹז, strength,
power; and עֹז, refuge, shelter; defence, protection (derived from
עוּז, take or seek refuge]); עֱזוּז (ʿezûz), nom., strength, power
(#6449); עִזּוּז (ʿizzûz), adj. powerful (#6450).
ANE Cognate forms are found in Ugar., ʿz; OSA, Eth., azaza; Akk.
ezēzu, be annoyed or angry, fall into a rage; Sam. ʿaz (with suff.
bazzåk); Aram. עָזַז, be strong; Syr. ʿaz, be powerful; Phoen. ʿz,
power, force.
VanGemeren, W. (Ed.). (1997). New international dictionary of Old Testament theology & exegesis (Vol. 3, pp. 365–366). Grand Rapids, MI: Zondervan Publishing House.
TDOT citation:
- Etymology, Occurrences, and Meaning. The root ʿzz is common Semitic. Ugaritic uses it as a verb, noun, and adjective in the sense
of “be strong,” “strengthen,” “strong,” “strength,” etc. Akk.
ezēzu/ezzu means “be angry,” “be powerful,” “be(come) enraged.” OSA
ʿzz means “fortify, strengthen,” and ʿzt means “strength.” The meaning
of Old Aram. ʿzz/ʿzyz corresponds to Ugaritic usage. The root occurs
also in Jewish Aramaic, Mandaic, and Ethiopic. The Qumran Scrolls use
both verbal and substantival forms of ʿzz. The meaning is essentially
constant: “be/become/make strong, powerful,” “strength, power.” There
are 11 occurrences of the verb in the OT, all in the qal or hiphil.
Intensive stems are found in other Semitic languages. In Hebrew a
number of nouns derive from ʿzz: ʿezûz, “strength, power” (3 times);
ʿizzûz, “powerful” (twice); ʿaz, “strength,” “strong” (22 times); and
ʿōz, “strength, power, might” (94 times), which can sometimes take on
the meaning “(strong) defense,” “(great) security,” “refuge,”
“protection.” The derivation from ʿwz of forms having this meaning has
been suggested frequently but is difficult to prove etymologically.
The same is true of māʿôz (36 times), which means “refuge, fortress,”
but also “strength” (Ps. 27:1). Several proper names appear in
extrabiblical texts;7 in the OT we find: ʿuzzāʾ, ʿuzzâ, ʿāzāz,
ʿazazyāhû, ʿuzzî, ʿuzzîyāʾ, ʿuzzîyāh(û), ʿazîʾēl, ʿuzzîʾēl, ʿazîzāʾ,
ʿazzān, and maʿazyâ. We also find yʿz, a by-form of ʿzz, in the niphal
ptcp. nôʿāz (Isa. 33:19).
[...]
- ʿōz. a. Psalms. Of the 94 occurrences of ʿōz, 44 are in the Psalms. The range of meanings is wide: “strength,” “power,” “might,” but also
“refuge.” The noun appears occasionally in parallel with māʿôz (Ps.
28:8). It can be used both literally and figuratively. Creation hymns
and texts that allude to the theology of creation extol Yahweh’s
creative power: it can bring to pass works of power and might and lend
strength to both the people and the individual believer, making them
strong. Somewhat obscure is the “founding” (ysd piel) of ʿōz from the
mouths of babes and infants (8:3[2]), an ʿōz that prevails against
enemies like a bulwark. The praise that resounds in the sanctuary
takes place at the point of contact between heaven and earth, so that
we hear the summons hallelûhû birqîaʿ ʿuzzô, “praise him in the
firmament of his power” or “praise him in his mighty firmament”
(150:1). With his might (beʿozzeḵā) he divided the sea in the act of
creation (74:13); with his mighty arm (bizrôaʿ ʿuzzeḵā) he scattered
the forces of chaos (89:11[10]). His commanding voice is “a mighty
voice” (qôl ʿōz, 68:34[33]; cf. Ps. 29). Power over nature and power
over history are based on power in the skies, inaccessible to mortals
(68:35[34], par. gaʾawāṯô, “his majesty”). This universal power he
gives (nāṯan) to his people (68:36[35], ʿōz par. taʿaṣumôṯ, as in
29:11). All creatures in heaven and earth are called on to acknowledge
(by worshiping) this mighty God: hāḇû leyhwh kāḇôḏ wāʿōz, “ascribe to
Yahweh glory and strength” (29:1; cf. 96:7; 1 Ch. 16:28; Ps.
68:35[34], tenû ʿōz lēʾlōhîm). This figure of speech probably does not
refer to a cultic investiture of Yahweh but to confession and
affirmation of the power and glory Yahweh inherently possesses. This
affirmation (learned or heard, 62:12a [11a]) is common knowledge: ʿōz
belongs to Yahweh (v. 12b[11b]). Nevertheless, a hymn to Yahweh as
king can say that Yahweh has robed himself (lāḇēš) in majesty and
girded himself (ʾzr hithpael) with ʿōz (93:1). The worshiper pouring
out a lament in the sanctuary can look on God there and behold
(physically) God’s power and glory (63:3[2], lirʾôṯ ʿuzzeḵā ûḵeḇôḏeḵā;
cf. 96:6, ʿōz weṯip̱ʾereṯ bemiqdāšô; also 1 Ch. 16:27), so that it is
reasonable to think of a visual representation. But the possibility of
individual ceremonial acts cannot alter the fact that no one can give
or bring Yahweh anything that he does not already have. In laments the
motif of trust leads to affirmation of Yahweh’s greatness and power,
on which one can rely; the poet also prays for a demonstration of
God’s power to save. In 62:8(7) the meaning of ʿōz modulates to the
equivalent of Eng. “refuge,” since the beset psalmist finds in Yahweh
ṣûr-ʿuzzî, the “rock of my might” (or “my mighty rock”). In parallel
are words like “salvation,” “honor,” and “refuge” (vv. 3, 12[2, 11]).
The psalmist miraculously experiences Yahweh as a “strong refuge”; in
this experience he himself is a kind of portent to many (71:7,
kemôp̱ēṯ hāyîṯî lerabbîm weʾattâ maḥasî-ʿōz). Another psalmist
confesses: “You are my refuge (maḥseh), a strong tower (mig̱dal-ʿōz)
against the enemy” (61:4[3]). The persecuted supplicant sees in Yahweh
a strong deliverer (140:8[7], ʿōz yešûʿāṯî). Finally, the psalmist can
pray for Yahweh to give his strength (tenāh-ʿuzzeḵā) to his servant
(86:16). Yahweh can be addressed directly as “my strength” (59:10,
18[9, 17]; in v. 10[9] ʿuzzô should be emended to ʿuzzî with LXX,
Targ., and Heb. mss., as well as the analogy of v. 18[17]; in both
verses the parallel is miśgāḇ). At the same time, in the oath section
of the lament ʿuzzeḵā can be objectified as the subject of praise
(59:17[16], with mānôs and miśgāḇ in parallel). The speaker of a
lament remembers the great and wonderful acts of Yahweh in nature and
history (77:12[11]), acts that imbue the worshiper with confidence and
trust. The psalmist also knows that Yahweh has made known (ydʿ hiphil)
his ʿōz among the peoples (v. 15[14]). Lament and petition (and the
supposed priestly oracle of salvation) are followed by praise and
thanksgiving, in which God’s saving power is proclaimed (e.g.,
28:7–8[6–7]). In Ps. 30:8(7) the text should probably be emended to
leharerê ʿōz (with Targ.) and the verb read as heʿemaḏtānî: “By your
favor, O Yahweh, you have established me on a strong mountain [or:
‘firm ground’].” Here ʿōz describes the nature of the firm foundation
on which Yahweh has set the psalmist, whose life was threatened. The
use of ʿōz in 138:3 is not without its problems. Aquila (see also
Jerome) has probably preserved the correct interpretation: tarḥîḇēnî,
“you give me great space, in my soul [or: ‘life’] there is strength.”
As we would expect, hymns also extol the strength and power of God.
Because of Yahweh’s great power (berōḇ ʿuzzeḵā), even Yahweh’s enemies
must ultimately do him homage (66:3; kḥš must be translated in this
sense). Yahweh is also praised for summoning his strength for his
people (68:29[28]). This text is not easy to translate. The MT means:
“Your God has summoned might for you [taking the suf. of ʿuzzeḵā as an
objective gen.], the strength of God, which you have done [or: ‘used’]
for us.” The phrase ʿuzzâ ʾelōhîm should be emended to ʿōz hāʾelōhîm;
the versions suggest reading ṣawwēh instead of ṣiwwâ and ʾelōheyḵā
without a suffix (“Summon, O God, your might”); but ʿuzzâ can also be
interpreted as an imperative: “Prove yourself mighty, O God, as you
have done for us before.” The introduction to a hymn may contain
predications that belong by nature in the body: “Let us sing aloud to
God our strength” (81:2[1]). A different nuance appears in 89:18(17),
which proclaims Yahweh as tip̱ʾereṯ ʿuzzāmô, “the glory of their
strength” (the suf. refers to the people). Finally, 118:14 uses
“strength” in parallel with “song” and identifies both entities with
Yahweh (ʿozzî wezimrāṯî yâ; so also Ex. 15:2; Isa. 12:2). The royal
psalms assume that Yahweh is strong; the king rejoices in that
strength (21:2[1]) and the worshipers pray Yahweh to rise up in his
strength and power to intervene against the enemy (21:14[13]). As part
of the enthronement ceremonial, the scepter (maṭṭēh-ʿuzzeḵā, “scepter
of your might” = “your mighty scepter”) is conveyed to the king
(110:2). In the historical summaries, besides the general view that
Yahweh shapes and governs history, we find certain events singled out
as being inaugurated by Yahweh, e.g., the miraculous feeding during
the wandering in the desert. For this purpose the (creative) power of
Yahweh (beʿuzzô) was invoked, bringing out the south wind (78:26),
which together with the east wind drove flocks of birds toward the
Israelites (v. 27). Ps. 78:61 says that Yahweh abandoned his sacred
ark, identified as ʿuzzô and tip̱ʾartô, to captivity and into the hand
of the foe (cf. 1 S. 4). This comports well with the description of
the ark as ʾarôn ʿuzzeḵā (“ark of your might” = “your mighty ark”) in
Ps. 132, which appears to speak of a procession with the ark (v. 8;
cf. v. 7; 2 Ch. 6:41). In another historical summary the
recapitulation of history is understood as “seeking Yahweh and his
strength” (Ps. 105:4 = 1 Ch. 16:11). In the Zion hymns the use of ʿōz
does not vary from what we have observed already. Yahweh, who dwells
on Zion, is celebrated and affirmed by the worshiping community as a
refuge, strength, and help (46:2[1]); every pilgrim is happy whose
strength is in Yahweh (84:6[5]). It is not just God’s help, mercy, and
goodness that can be associated with ʿōz; the power of God’s anger is
also a reality in the OT, and Ps. 90:11 warns against underestimating
it: “Who considers the power of your anger? Your wrath is great.” It
is therefore good to know that the strength of King Yahweh loves
justice (99:4).
Wagner, S. (2001). עזז. G. J. Botterweck, H. Ringgren, & H.-J. Fabry (Eds.), D. E. Green (Trans.), Theological Dictionary of the Old Testament (Revised Edition, Vol. 11, pp. 4–7). Grand Rapids, MI; Cambridge, U.K.: William B. Eerdmans Publishing Company.