My people are destroyed for lack of knowledge. Because you have rejected knowledge, I will also reject you, That you may be no priest to me. Because you have your God's law, I will also forget your children.
"Law of thy God" is a clear and positive reference to the Decalogue and related commandments which formed a basic part of the holy Covenant between God and Israel.  The word here is "Torah," and, despite the efforts of Mauchline and others to read this as teachings delivered to people by their priests, the technical and specific meaning of the term is apparent.  In a word, it is a reference to the Pentateuch.  A book like Hosea could not possibly have been written except in the shadow of the first five books of the Old Testament.