This is an interesting question because it reflects the thinking of the modern day church. Prior to Darwin this question would have never been raised in the church; even in cosmopolitan circles cavemen were nothing more than myths which made interesting movie characters, and dinosaurs were creatures without explanation or significant veracity.
Let's first address "cavemen." Let’s get it straight, there is no proof of the existence of cavemen. Do we have pictures of men living a primitive life style on the walls of caves and archeological findings? Yes. Does close examination in any way reveal a creature that is half man and half ape? No. We have people today who live in caves and draw pictures on walls and live primitive life styles – it does not make them evolutionary creatures.
The premise of the "caveman" (half man half ape) is based on the theory of evolution. If evolution had any credibility at all we would have in existence TODAY, caveman (and other evolving creatures). In fact, show me one "evolving creature!" They can't be found, just as the cavemen purported by Evolutionists can't be found. The latest evolutionary find was supposedly the speckled moth – it too was found to be a sham. One cannot prove evolution because evolution is a lie from the mouth of Satan to circumvent mans' need for a Saviour. Circumvent man's need for a Saviour and man can be his/her own God. Even Darwin himself recanted his own theory embracing the creation account of the Bible.
God is definitive in the creation process: "each seed will produce after its own kind." Genesis 1:12. Fruit trees produce fruit trees, dogs dogs, cats cats, fowl fowl, apes apes, man man, etc.. There are no mixed species. A species can, through man's creative resources (which is the "image of God") and selective breeding, produce a hybrid, but it is still its own kind. There is nothing evolutionary about it. An ameba does not become a fish that millions of years later becomes a four legged creature, that after another million years becomes an ape which later becomes a half-man and eventually a man.
The caveman of the movie world and today's science text book does not exist and has never existed. He/she has no place in God's timetable. The only man in God's timetable is the one created in His image and likeness -- a brilliant man who named each animal, invented musical instruments and tools for building. (Genesis 4) If man through perversion chooses to distort the image of God that is in him he has that option, but the man of Creation was never intended to live any other way than in the Eden of God's world.
As to the question "What happened to the dinosaurs?'', most Bible scholars believe they were annihilated during the flood. However, even here most of the creatures classified dinosaurs are in question. An entire dinosaur is projected from one or two supposedly "pre-historic" bones. Who really knows? Could there have been dinosaurs? Archeological findings certainly indicate "yes." When you read the book of Job, the creature described in chapter 41, verses 1-34 certainly seems dinosauric.
Back to the question: "Where do they fit in God's timetable?" If you believe in the gap theory – a time span between Genesis 1:1 and Genesis 1:2 where Satan, when cast out of heaven, destroyed the Pre-Adamic earth and made it a waste place (Jeremiah 4:23-26) then the dinosaurs could well have been destroyed then. Whatever the case, dinosaurs were not an evolutionary process – again, if they were we would see them today evolving into something more domesticated. Dinosaurs, if indeed they did exist, did so as a part of God's creation. For whatever the reason, God saw fit in His wisdom to remove them from the earth.
(Suggested reading: Evidence that Demands a Verdict by Josh McDowell; Teaching Creation Science in Public Schools by Duane T. Gish; The Question of Origins – Institute for Creation Research; The Argument – Evolution vs Creation by Wilbert H. Rusch, Sr.; Dinosaurs and Creation by Don DeYoung; Evolution the Fossils say No! by Duane T. Gish)
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