This word da`at is in Hebrew simply the infinitive of the verb yada` “know”. Claude explains well the meaning of the Hebrew phrase da`at ‘elohim, traditionally translated “knowledge of God”:
an expression used to describe the special relationship between God and Israel that comes out of the covenant relationship.
As such he is right to reject the rendering “acknowledgement of God”, found at Hosea 4:1, 6:6 in NIV and TNIV. Similarly wrong is the NET Bible rendering at Proverbs 9:10 “acknowledging the Holy One” (and similarly in Hosea). This phrasing means to me no more than affirming the existence of God or perhaps his activity in some situation.
The problem is that “knowledge of God”, or “knowledge of the Holy One”, is just as misleading, and as so has been rightly discarded by the NET Bible translators, and in part by the NIV and TNIV translators. For to me this phrase implies knowing facts about God, i.e. theology. But this is not the meaning of the Hebrew phrase either.
Even worse is “the knowledge of God”, as in Hosea 6:6 KJV and RSV, which implies to me the knowledge which God has.
What is needed is a phrase which clearly expresses relational knowledge, not that we know about God but that we know him and have a relationship with him. To find a better phrase, I take a tip from NET Bible’s use of a verbal gerund rather than a noun, and suggest “knowing God”.
This is of course the title of JI Packer’s classic book. Sadly the book concentrates on knowing about God rather than having a relationship with him. But its title is an excellent one, and deserves to find its way into the Bible.