Rabbi Gottlieb has also written on the topic of reconciling the apparent Torah claim that the Earth is 5766 years old with the scientific evidence suggesting that it is far older than that; he suggests simply that the world was created 5766 years ago with the appearance of being much more ancient.
The following question was posed to me (unless I misunderstood it): Assume the Torah definitively states that the Earth is 5766 years old. Rabbi Gottlieb's premise in "Living Up to the Truth" is that we can use our observations of the world around us (historical records, for example) to draw conclusions regarding the veracity of the Torah. But he also proposes that we ignore the implications of our observations of the world around us when they indicate that the Earth is billions of years old, since those implications conflict with the Torah, which we have established to be factual. Would it not be equally valid to argue that we should accept the scientific evidence about the Earth's age, and ignore the evidence that the Torah is truthful, since the Torah conflicts with compelling science?
I believe the answer to the question is no, because the two sets of conclusions described in the preceding paragraph are neither equally plausible, nor logically equivalent. If we accept, based on the evidence, that the Torah is true, and, hence, that the world is 5766 years old, we must, indeed (based on our initial assumption), discard as misleading the evidence that the world is billions of years old. However, we can fall back on Rabbi Gottlieb's alternative (and logically irrefutable) approach to the age of the world, viz., that it just looks very old. If we believe what the Torah tells us about God, it's certainly within God's capabilities to make an old-looking world (no more difficult than making a new-looking one, in fact). There's no evidence that God didn't do exactly that; indeed, from a theological perspective, it actually makes sense that he would have (ask me if you want more explanation of that). The evidence is all reconcilable; we are left with no contradictions.
However, if we accept initially that the Earth is older than the Torah allows, we must then confront and discard the evidence that the Torah is true. Can we explain how that evidence came to exist? Not to the best of my knowledge. We can't say that God manufactured the evidence, because we have (as yet) no evidence that there's a God at all. The facts we know about Jewish history just sit there, crying out their contradiction of our conclusions about the world's age. This approach, unlike the last one, cannot account for the existence of all the evidence. The Torah-affirming approach discussed above may adopt a hypothesis that seems weak, or cheap, but at least it covers all the bases.
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I'd like to aver that there is, in fact, nothing weak or cheap about Rabbi Gottlieb's hypothesis. Suppose academia universally accepts the Documentary Hypothesis of Biblical authorship, and suppose, furthermore, that we all agree with its premise that it is just inconceivable that the Five Books of Moses were authored, in their entirety, by the same human being. Does that mean it's weak, or cheap, or intellectually dishonest or undesirable to ascribe the Pentateuch to God (who can write in a multiplicity of styles)? I believe not, and I believe the same is true of Rabbi Gottlieb's explanation of the world's ancient appearance. It fits the facts very nicely. There's no evidence that it's wrong. At the risk of sounding like a right-wing Haredi lunatic, academia's acceptance of a particular explanation for the existence of a body of facts does not require Jews to accept that explanation when another explanation exists, one more compatible with the sum total of our knowledge.