Modern Biblical Scholarship: The Documentary Hypothesis and its Discontents

I willingly agree that, in consequence of the foundation of my belief, I am unable to arrive at the conclusion that the Pentateuch was written by anyone other than Moses ... We believe that the whole Bible is true, holy, and of divine origin. That every word of the Torah was inscribed by divine command is expressed in the principle Torah min Ha Shamayim ... We must not presume to set ourselves up as critics of the author of a biblical text or doubt the truth of his statements or question the correctness of his teaching ... The Jewish commentator must (therefore) constantly be on guard against interpreting the passage in such a way as to appear to be in conflict with traditional Halachah. Just as the Torah as a divine revelation must not contradict itself, in the same way it must not contradict the Oral Law which is of divine origin.
Rabbi David Zvi Hoffmann (1843 – 1921) quoted in "Scholarship and faith: David Hoffman and his relationship to Wissenschaft des Judentums"

[The Bible’s] means of representation may be termed the semi-poetic or dichotomistic. It proceeds like poetry, but without its strict measure [i.e., meter], employing instead paired thoughts, patterns of words and clauses and syntax, in doublets, parallels and contrasts; it is rooted, when all is said and done, in the Semitic [way of thought], which grasps matters dichotomously. This manner of seeing, conceiving and representing dominates the Hebrew language and literature in its entirety, to its subtlest manifestations.
Rabbi Benno Jacob (1862–1945), quoted in "The Rebirth of Omnisignificant Biblical Exegesis in the Nineteenth and Twentieth Centuries"

[W]e must clarify, to the best of our ability, why just in certain sections or verses the Torah narratives have the Tetragrammaton and in others ’Elohim. Is it possible to formulate rules with regard to the use of the Names in proximity to each other? I believe that we are able to answer this question affirmatively. On the basis of what we have stated so far, we may assume that in each case the Torah chose one of the two Names according to the context and intention, precisely as follows:
It selected the name YHWH when the text reflects the Israelite conception of God, which is embodied in the portrayal of YHWH and finds expression in the attributes traditionally ascribed to Him by Israel, particularly in His ethical character; it preferred the name ’Elohim when the passage implies the abstract idea of the Deity prevalent in the international circles of ‛wise men’—God conceived as the Creator of the physical universe, as the Ruler of nature, as the Source of life.
The Tetragrammaton is used, when expression is given to the direct, intuitive notion of God, which characterizes the simple faith of the multitude or the ardour of the prophetic spirit; the name ’Elohim, when the concept of thinkers who meditate on the lofty problems connected with the existence of the world and humanity is to be conveyed.
The name YHWH occurs when the context depicts the Divine attributes in relatively lucid and, as it were, palpable terms, a clear picture being conveyed; ’Elohim, when the portrayal is more general, superficial and hazy, leaving an impression of obscurity.
The Tetragrammaton is found when the Torah seeks to arouse in the soul of the reader or the listener the feeling of the sublimity of the Divine Presence in all its majesty and glory; the name ’Elohim, when it wishes to mention God in an ordinary manner, or when the expression or thought may not, out of reverence, be associated directly with the Holiest Name.
The name YHWH is employed when God is presented to us in His personal character and in direct relationship to people or nature; and ’Elohim, when the Deity is alluded to as a Transcendental Being who exists completely outside and above the physical universe.
The Tetragrammaton appears when the reference is to the God of Israel relative to His people or to their ancestors; ’Elohim, when He is spoken of in relation to one who is not a member of the Chosen People.
YHWH is mentioned when the theme concerns Israel’s tradition; and ’Elohim, when the subject-matter appertains to the universal tradition.
Rabbi Umberto Cassuto (1883 - 1951), The Documentary Hypothesis and the Composition of the Pentateuch, 30 - 32

[T]he verses in the narrative of the Flood in which the Tetragrammaton occurs conform exactly, as I have already indicated, to our rules. The name YHWH appears when the moral motive, which extends indeed through the whole story, is accorded special prominence and emphasis, as in the punishment of the wicked on account of their wickedness and in the prosperity of Noah because of his righteousness (vi 5–8; vii 1); so, too, when reference is made to the sacrifices, or to the clean animals that Noah was commanded to take with him into the Ark for the purpose of bringing oblations from them after the Flood (vii 5; viii 20–21); likewise when it is intended to express a direct—as it were, palpable— relationship between God and Noah, the relationship of a father full of compassion towards his son, who is dear to his heart (vii 16: and YHWH shut him in); similarly when Scripture reverts to the curse upon the ground (viii 21), which is mentioned in the section that uses the Tetragrammaton. In these verses we find the name YHWH; in the rest of the account of the Deluge, ’Elohim occurs for the reasons given.
Rabbi Umberto Cassuto (1883 - 1951), The Documentary Hypothesis and the Composition of the Pentateuch, 36

This is the position that we have staked out. God, who is beyond the limitations of time and space, prepared the Torah, declaring in one utterance what man can comprehend only as a combination of differing sources. Before the world was created, God redacted one document characterized by justice and one characterized by mercy, synthesized them with the quality of harmony. After a thousand generations this Torah, "black fire on white fire," descended to earth. Moses, the faithful shepherd, was summoned to the upper realm, and brought it down to the terrestrial sphere.
Rabbi Mordechai Breuer (1921 - 2007), "The Study of Bible and the Primacy of the Fear of Heaven: Compatibility or Contradiction?", 170 - 171