Can science prove that God could not have created our universe in six days, six thousand years ago? No they cannot. Could our All Powerful God have created our universe six thousand years ago? Yes God can.
Science cannot "prove" that the world is greater than 6000 years old, by if the standard of proof is an article of faith.
Science deals with what can be physically observed, and from Hebrews 11 we know that faith specifically rejects those things. Science cannot "prove" that the solar system is not geocentric, to the standards of religious faith; I know because I've had a few go-arounds with geocentrists. For that matter, science cannot "prove" that the moon is not made of green cheese, to the standards of religious dogma.
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Neither can religion prove to the standards of the scientific method, anything at all that is an article of faith.
Notice Hebrews 11:1
Faith is the realization of what is hoped for and evidence of things not seen.
So if you believe it in faith, that means you do NOT have physical evidence or proof, but only a belief in what you hope for, evidence of things not seen.
So you can't take science to task for not being able to prove an article of faith when the Holy Bible defines faith as things that are invisible, not seen, and hoped for. Faith is not a superset of science, nor does science claim to be a superset of faith. They work in two different realms; the observable, and the invisible-hoped for.
So to say you have faith that the universe was created in six 24-hour days, is to say "I hope it was," and "I believe it although there is no tangible evidence to support me." If you make it more than that, then you need to revisit what faith actually is.
Here are a couple short excerpts from JPII from 1979, speaking to the Pontifical Academy of Sciences about, among other things, the Galileo case. I'm not trying to get you to change your mind; it's clear that's not going to happen. What I am trying to change is your dismissal of science and its theories and conclusions, vis-à-vis based on your choice to regard literalistic interpretations of Genesis as evidence of science being wrong.
8. Another crisis, similar to the one we are speaking of, can be mentioned here. In the last century and at the beginning of our own, advances in the historical sciences made it possible to acquire a new understanding of the Bible and of the biblical world. The rationalist context in which these data were most often presented seemed to make them dangerous to the Christian faith. Certain people, in their concern to defend the faith, thought it necessary to reject firmly-based historical conclusions. That was a hasty and unhappy decision. The work of a pioneer like Fr Lagrange was able to make the necessary discernment on the basis of dependable criteria.
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9. If contemporary culture is marked by a tendency to scientism, the cultural horizon of Galileo's age was uniform and carried the imprint of a particular philosophical formation. This unitary character of culture, which in itself is positive and desirable even in our own day, was one of the reasons for Galileo's condemnation. The majority of theologians did not recognize the formal distinction between Sacred Scripture and its interpretation, and this led them unduly to transpose into the realm of the doctrine of the faith a question which in fact pertained to scientific investigation.
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Before Bellarmine, this same wisdom and same respect for the divine Word guided St Augustine when he wrote: "If it happens that the authority of Sacred Scripture is set in opposition to clear and certain reasoning, this must mean that the person who interprets Scripture does not understand it correctly. It is not the meaning of Scripture which is opposed to the truth but the meaning which he has wanted to give to it. That which is opposed to Scripture is not what is in Scripture but what he has placed there himself, believing that this is what Scripture meant".(5) A century ago, Pope Leo XIII echoed this advice in his Encyclical Providentissimus Deus: "Truth cannot contradict truth and we may be sure that some mistake has been made either in the interpretation of the sacred words, or in the polemical discussion itself".
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12. Another lesson which we can draw is that the different branches of knowledge call for different methods. Thanks to his intuition as a brilliant physicist and by relying on different arguments, Galileo, who practically invented the experimental method, understood why only the sun could function as the centre of the world, as it was then known, that is to say, as a planetary system. The error of the theologians of the time, when they maintained the centrality of the earth, was to think that our understanding of the physical world's structure was, in some way, imposed by the literal sense of Sacred Scripture. Let us recall the celebrated saying attributed to Baronius "Spiritui Sancto mentem fuisse nos docere quomodo ad coelum eatur, non quomodo coelum gradiatur". In fact, the Bible does not concern itself with the details of the physical world, the understanding of which is the competence of human experience and reasoning. There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter belong especially the experimental sciences and philosophy. The distinction between the two realms of knowledge ought not to be understood as opposition. The two realms are not altogether foreign to each other, they have points of contact. The methodologies proper to each make it possible to bring out different aspects of reality.
So you may believe what you will, but you have no basis for insisting anyone who doesn't agree is in any way deficient on the topic. And in fact an insistence that science must conform to the literal sense of scripture was considered at least by JPII to be an erroneous position.
Alan