Ver. 3.—Great is the Lord, and greatly to be praised (comp. Pss. 48:1; 96:4). And his greatness is unsearchable; literally, and of his greatness there is no search (comp. Rom. 11:33).
3. “Great is the Lord, and greatly to be praised.” Worship should be somewhat like its object—great praise for a great God. There is no part of Jehovah’s greatness which is not worthy of great praise. In some beings greatness is but vastness of evil: in him it is magnificence of goodness. Praise may be said to be great when the song contains great matter, when the hearts producing it are intensely fervent, and when large numbers unite in the grand acclaim. No chorus is too loud, no orchestra too large, no Psalm too lofty for the lauding of the Lord of Hosts.
“And his greatness is unsearchable.”
“Still his worth your praise exceeds,
Excellent are all his deeds.”
Song should be founded upon search; hymns composed without thought are of no worth, and tunes upon which no pains have been spent are beneath the dignity of divine adoration. Yet when we meditate most, and search most studiously, we shall still find ourselves surrounded with unknowable wonders, which will baffle all attempts to sing them worthily. The best adoration of the Unsearchable is to own him to be so, and close the eyes in reverence before the excessive light of his glory. Not all the minds of all the centuries shall suffice to search out the unsearchable riches of God: he is past finding out; and, therefore, his deserved praise is still above and beyond all that we can render to him.
145:3 his greatness is unsearchable. That is, past the capacity of the human mind to fully describe or comprehend. It will take many worshipers, and a long duration (forever and ever, vv. 1, 2, 21), even to begin to do justice to what the Lord deserves.
145:3 his greatness is unsearchable Emphasizes that God—along with all of His worthy qualities—is simply too much for people to comprehend.
145:3 unsearchable. God’s power and might are so great that finite human minds are unable to comprehend them fully. This verse teaches the doctrine of the incomprehensibility of God. People can have a true understanding of God, but never a complete or exhaustive one.
 Sproul, R. C. (Ed.). (2005). The Reformation Study Bible: English Standard Version (p. 865). Orlando, FL; Lake Mary, FL: Ligonier Ministries.