JEDP - the theory is challenges the position that Moses is the author of the first five books of the OT. JEDP asserts that there are four major strands that have been woven into the text of the Pentateuch (Five books of Moses). Usually the origins of this approach are granted to Jean Astruc (ca. 1750). Noth modified this to claim a Tetrateuch (the first four books) with Deuteronomy as the head of the following Deuteronomist school. And early critical scholars posited a Hexateuch to include the first five books and Joshua as a literary unit.
J - the material that primarily includes the name for God as Yahweh (Jehovah)
E - the material that includes the title for God - Elohim
D - the Deuteronomist, a later work that is primarily seen in Deuteronomy, but with some remarks that appear throughout the Pentateuch.
P - the priestly sections of the Pentateuch
The basic premise is that because there seem to be parallel accounts, they had to come from different sources. Three main arguments are given to support this source theory:
1. Variations in vocabulary and style: Astruc pointed to what is often considered the premier example, the use of different designations for God in Genesis 1 (Elohim) and Genesis 2 (Yahweh-Jehovah). While this seems both obvious and consistent, outside of Genesis, this particular argument carries far less weight.
A reasonable response to this is that any good writer would use alternative divine designations (so in the NT, Jesus Christ Lord Lord Jesus etc.). To use variety does not necessarily indicate different authors.
2. Doublets/Triplets: Here evidence is presented to show that two accounts of the same story are given (with contradictory material), but by different sources, and the final redactor (editor) just included both accounts. For instance, Genesis 1 and Genesis 2 are considered the classic example, each having its own sequence. Other examples are: two accounts of the flood (Genesis 6-9) - duration, number of animals on the ark, etc., Exodus 3 (E) and Exodus 6 (P) supposedly give different accounts of the divine name, the patriarchs saving themselves by claiming that their wives were their sisters (Abraham twice and Isaac once).
A reasonable response to this claim is that archaeological discoveries have demonstrated that repetition really is charcteristic of ancient writing, not different sources and authors. The finds at Ebla in northern Syria establish the interplay of Yahweh and El (shortened version of Elohim), which contradicts the JEDP position.
3. Passages that seem to imply a much later date: Some examples include: Genesis 12:6 the Canaanites were then in the land - suggesting that the composition took place when the Canaanites were not longer in the land; Genesis 14 which refers to the Danites homeland in the far north, which they did not acquire until much later (Judges 17); Deuteronomy 34:10 no other prophet has arisen since; and several others.
It is noted that this last category indicates post-Mosaic touch-up. But this is not as strong support for JEDP as first appears. Usually these items involve adjustments on the periphery, made for the sake of communicating better to later audiences.
Another support for JEDP given under # 3 is that Moses is referred to in the third person, and so cannot be autobiographical. However, the third person (and also first person plural we) is very common among ancient and modern writers, especially where the intent is not to provide an autobiography.
Note that while the initial blush at JEDP seems convincing, further inspection of the text and historical study and archaeological evidence offer alternative explanations that coincide with Mosiac authorship.
And it should be noted that there are problems with the JEDP approach. First, there is NOT ONE bit of manuscript evidence to support the JEDP theory. Second, there is the matter of chronology of the supposed sources. Third, why stop at just four sources? Why not one with the law codes? And there are other problems, but at least, it can be shown that JEDP is not the consensus of Biblical scholarship.