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Supposedly, Genesis 1 and 2 are contradictory concerning when plants were created.
And God said, “Let the earth sprout vegetation, plants yielding seed, and fruit trees bearing fruit in which is their seed, each according to its kind, on the earth.” And it was so. The earth brought forth vegetation, plants yielding seed according to their own kinds, and trees bearing fruit in which is their seed, each according to its kind. And God saw that it was good. And there was evening and there was morning, the third day.
Then God said, “Let us make man"... And there was evening and there was morning, the sixth day.
When no bush of the field was yet in the land and no small plant of the field had yet sprung up—-for the Lord God had not caused it to rain on the land, and there was no man to work the ground, and a mist was going up from the land and was watering the whole face of the ground—-then the Lord God formed the man of dust from the ground and breathed into his nostrils the breath of life, and the man became a living creature. And the Lord God planted a garden in Eden, in the east, and there he put the man whom he had formed. And out of the ground the Lord God made to spring up every tree that is pleasant to the sight and good for food. The tree of life was in the midst of the garden, and the tree of the knowledge of good and evil.
From these passages, it seems that in Genesis 1, plants are created before man, and in Genesis 2, plants are created after man. Two solutions have been proposed for this apparent contradiction, one of which is problematic and the other of which is the better solution.
The key to this solution is recognizing the difference between the plants in Genesis 1 and the plants in Genesis 2. In Genesis 2, we see the key words of the field, which do not show up in Genesis 1.
When no bush of the field was yet in the land and no small plant of the field had yet sprung up...
The key difference between the plants in Genesis 1 and the plants in Genesis 2 is that the plants in Genesis 2 are plants that are cared for by humans, or plants in a garden. Before humans were created, there would be no gardeners or gardens, so obviously these kinds of plants (plants of the field) would not be in existence yet.
Genesis 2 is not saying that wild vegetation did not exist before man was created, but rather that plants cared for by man did not exist before man was created. We can imply that while plants of the field were not created before man, wild vegetation indeed were created before man.
Since the same author wrote Genesis 1 and 2, we should assume that this author would not write such an obvious contradiction, and indeed, we find a very clear solution to the alleged contradiction.
Some people try to solve this problem by saying that the creation account in Genesis is not a genre that we should take literally or as historical. They might say that it is poetry, or that it is a "creation narrative" that has different rules for interpretation than a historical narrative.
The problem with this attempted solution is that the creation account in Genesis flows directly into what is clearly historical narrative, and it is unlikely that there is such a division between the genre of the earlier chapters of Genesis and the genre of the later chapters.
Furthermore, this attempted solution causes us to lose faith in the Bible. If the creation account in Genesis can be considered contradictory and thus not to be taken literally, then this will start to chip away at our confidence in other parts of the Bible.
The better solution presented above makes complete sense, so it should be strongly preferred over the problematic solution that was just presented.
Some people have trouble accepting possible explanations to alleged contradictions in the Bible, especially ones that they consider a stretch. For example, Dan Barker, president of the Freedom From Religion Foundation, says this:
I have received numerous replies from Christians who think that these contradictions are either trivial or easily explained. Yet not a single "explanation" has been convincing.
The fact is that there are plausible explanations for every alleged contradiction in the Bible. That there is a plausible explanation for an alleged contradiction does not mean that it is definitely the correct explanation for the alleged contradiction.
However, as long as a possible explanation has been suggested, then it has been objectively demonstrated that there is no necessary contradiction regarding the Bible verses and passages brought up.
When people like Dan Barker say that they don't find a particular explanation for a contradiction "convincing," then that is merely their opinion. A plausible explanation has been suggested that eliminates the necessary alleged contradiction. They simply don't like it, which is not at all a relevant argument against the explanation.
To read more about solutions to Bible contradictions and difficulties, check out Norman Geisler's The Big Book of Bible Difficulties: Clear and Concise Answers from Genesis to Revelation. While we do not agree with some of Geisler's theology, particularly concerning his view of predestination, this book is still an excellent resource. It is thorough and filled with research.
Another book to check out is Tim Chaffey's Demolishing Supposed Bible Contradictions: Exploring Forty Alleged Contraditions, which also answers many alleged contradictions in the Bible.