The "proofs" are these two arguments: 1) Since human beings have free will, they are finite beings. Finite beings need a cause, but an infinite being can be the reason for its own existence. The religions originating in the Near East call the infinite being God. One of the Chinese religions calls the infinite being Tao, which means "way." 2) If moral laws are true and not value judgments, a transcendent reality exists.
bfilx are only arguments because they are based on the assumption or hope that the universe is intelligible. If someone says the arguments are not persuasive, this does not mean they have bad judgment or don't understand the arguments. However, most atheists and agnostics don't say this. They say, "I don't know whether or not God exists." This statement implies that there are no arguments for God's existence. The arguments can be called proofs because the question of whether or not God exists is only relevant if you are deciding whether or not to believe in God and fear His wrath.
This is what Robert Spitzer, S.J., Ph.D., author of "New Proofs for the Existence of God: Contributions of Contemporary Physics and Philosophy," says of the book:

Though many sound books have been written about the 'first cause/mover' proof of Aristotle and St. Thomas, this is the most accessible and illustrative rendition I have encountered. His explanations make a heavy subject engaging and easy to read. It has outstanding pedagogical value. (Ignatius Press website)I was surprised that a Jesuit promotes arguments for God's existence based on the "first cause" argument of Thomas Aquinas rather than the metaphysical argument of Ètienne Gilson. Spitzer considers the Big Bang, the "fine-tuning" of physical constants, and the limited explanatory power of quantum mechanics evidence of God's existence. I consider this reasoning pseudoscience because there is no evidence God caused the Big Bang, "fine-tuned" the universe, or is entangled in quantum mechanics. In my opinion, this scientific knowledge is evidence that God does not exist because it is evidence that the universe is not intelligible. It is one thing to assume the universe is intelligible to answer the question of what a human being is and what causes human beings to exist. However, to make this assumption to answer scientific questions is nonsense.