Science
Science assumes the scientific method as its foundational approach to understanding the natural world. However, it is logically impossible for science to prove its own validity because such an attempt would involve circular reasoning, where the method relies on itself for justification.
Causality
Science presupposes the principle of causality, which states that every effect has a cause, and that these causes can be identified and studied. Science cannot use its methods based on causality to prove the principle of causality itself, as this principle underlies all of reality and thus the entire scientific endeavor.
Reality
Science presupposes the existence of an external, objective reality that exists independently of human perception and can be studied through observation and experimentation. Science cannot use its methods to prove the existence of this objective reality while assuming inquiry according within objective reality. Such is another example of circular reasoning by assuming what one seeks to prove.
Reliability of the Mind
Science presupposes that the human mind and its cognitive processes are reliable for interpreting data, forming hypotheses, and drawing conclusions. People cannot use scientific methods to prove the reliability of the mind itself, as such a proof would require assuming the very cognitive faculties being questioned.
Laws of Logic
Science presupposes the laws of logic, such as the law of non-contradiction and the law of excluded middle, to structure and evaluate arguments and observations. Science cannot use itself to prove the validity of these logical principles because they are fundamental to any rational process, including scientific inquiry.
Inductive Reasoning
Science depends on inductive reasoning to make generalizations from specific observations, such as deriving theories from experimental results. The validity of inductive reasoning is assumed, but science cannot use reasoning to prove this validity, as doing so would involve assuming the very reasoning process being evaluated.
Mathematics
Science relies on mathematics to model and explain natural phenomena, assuming that mathematical relationships and structures accurately describe aspects of the physical world. Science cannot use the applicability of mathematics to prove mathematics is reliable because the proof would inherently rely on mathematical principles.
Moral Absolutes
Science presupposes moral values and ethical guidelines to conduct research responsibly and interpret results with integrity. It cannot use its methods to prove the existence of moral absolutes because ethical principles are foundational to the practice of science rather than derived from it.
Love
Science presupposes the virtue of love as good and useful and so value truth and seek knowledge for the betterment of humanity. Science cannot prove the virtue of love while assuming it is a derive concept of humanity’s survival instinct. The plea that love should underpin the motivation and ethical conduct in scientific inquiry is not itself a product of scientific methods.
Meaning and Purpose
Science presupposes that human life and the pursuit of knowledge have inherent meaning and purpose. Science cannot prove the existence of ultimate meaning and purpose for knowing and understanding the natural world. Meaning of purpose for human life provides the motivation for scientific inquiry but are not established by scientific methods.
The Breath of God 
“Science presupposes the existence of moral values and ethical guidelines to conduct research responsibly and interpret results with integrity. It cannot use its methods to prove the existence of moral absolutes”
You’ve assumed that moral absolutes exist. Do they? I see plenty of morality but just the regular kind as defined in the dictionary, not absolute/objective morality.
Yeah well, people act like moral absolutes exist by judging the morals of others. People live and discern life as though they know what a crooked path is so they judge as though there is only one straight path. Whether you accept moral absolutes or not, you live as though moral absolutes do exist when you say the abuse of the innocent is always wrong or when you judge any act is always evil. People still act as moral absolutes exist when they apply morality to science.
“Radioactive decay is still caused no matter how far back you want to go to the origin of entropy.”
Show us. Take a nucleus that just decayed—what was the cause? Was it heat? Pressure? The presence of an electromagnetic field?
To be clear, causeless events isn’t universally accepted within the science community, but my understanding is that it’s the prevailing view.
“The faith stands on the best explanation of an intelligible universe allowing intelligent observers to observe it — the intelligent Creator rather than an unintelligent cause.”
And yet the people who understand such things—cosmologists and scientists in similar fields—disagree. I think I’ll follow the science.
“it is logically impossible for science to prove its own validity”
Suppose we hypothesize that following the evidence gives more reliable conclusions than believing things on faith. We could test this hypothesis.
So where’s the problem?
“every effect has a cause”
Does it? If anything, this would probably be a philosophical declaration, not a scientific conclusion.
But at the subatomic level, things happen without a cause all around us. When the nucleus of a radioactive isotope decays, we can understand that statistically (how likely that atom is to decay in the next minute, say), but that’s it. There is no cause.
You could test the hypothesis based on your own mind’s conclusion, but again that’s circular to trust your own mind’s conclusion or trust what you perceive is the conclusion of others.
Yes, underlying science is the philosophy of science and philosophy of science requires an ultimate axium to trust one’s intelligence.
Causality is still the basis of all reality. Radioactive decay is still caused no matter how far back you want to go to the origin of entropy.
Assuming the possibility that causality is not always true is an appeal to possibility which we all know is a logical fallacy.
Lastly, the Christian faith is not defined by unbelievers. The Christian faith is evidence based throughout the Scriptures relying on the legal-historical method applied to prophecies and witnesses. The faith stands on the best explanation of an intelligible universe allowing intelligent observers to observe it — the intelligent Creator rather than an unintelligent cause.