"Does philosophy and science work together to offer compelling evidence for the existence of God?"

We would like to address your first main point. You mentioned how "there can be an infinite number of events since any finite interval can be divided infinitely, and each division can be considered an event." However, in Dr. Craig"s On Guard, he mentions that this is committing the fallacy of composition which confuses a property of a part with the property of a whole. For example, one part of an elephant can be light in weight, but that doesn"t mean the whole elephant is light in weight. In the same way, every finite interval can be counted but it doesn"t mean the infinite number of events can be counted. You have confused finite as the whole when it is in the infinite. Now that we understand this concept, the analogy of Hilbert"s Hotel is absurd because you cannot have an infinite of anything including events. With the explanation that the finite is part of the infinite, we can conclude that the universe has a beginning. This brings us back to the Kalam Cosmological Argument which states: Whatever begins to exists has a cause The universe began to exist Therefore, the universe has a cause Recognizing that the universe has a beginning, we can come to a conclusion that the universe has a cause which leads to a designer/creator. +++++++++++++++++++++++++++ Assuming that we have agreed on what the cause of the universe must not be. What, then, does that leave us with? Dr. Craig also argues that there is only a short list of things that fit the traits of the First Cause. The only two things that can be described as "immaterial, timeless, and spaceless" are abstract objects or an unembodied mind." However, as abstract objects do not have causal powers, the only option left is an unembodied mind. If the universe was not caused by a consciousness, it would be brought into being by a set of impersonal necessary and sufficient conditions. One of the arguments of why the cause of the universe must be personal/conscious is: how we can have an origin of a temporal effect with a beginning from a cause which exists timelessly and hence eternally. "If the cause of the universe was simply an impersonal [and unconscious), mechanically operating set of necessary and fixed conditions, then if the cause is given permanently and timelessly, why isn't the effect then permanently given?." In order for the First Cause to be timeless yet have its effect obtain the ability to bring about a changing effect, is for the cause to be a conscious and personal agent. The idea of agent-causality is presented. Wikipedia describes it as an idea in philosophy which states that an agent can start new causal chains not determined by prior events. Your analogy of the rock is contingent upon three things: time, space, matter. How would you actually prove that the existence of all things is contingent upon these three things? You are taking a very naturalistic approach to the topic and it seemed to have led you astray. Take for example, the laws of reason. We understand that 1 + 1 must equal 2 but it"s truth is not contingent upon the three things mentioned earlier. Yet, we know for certain that 1 + 1 must equal 2. Similarly, when we argue for the existence of God, we argue not for an existence contingent upon the universe but rather an incontingent existence beyond the universe itself. A logical necessity if you will. That is not to say that empirical findings are obsolete. Both metaphysical demonstrations and empirical findings can go hand in hand. As discovered, the properties of the universe show that it is finite because science proves that it is decaying or moving towards a state of entropy.(2nd Law of Thermodynamics) This is evidence of a cause for the universe, before matter,time and space. It gives us proof of the universe coming into being from a something that is out of time,matter,and, space. Science and Philosophy can go hand in hand because science itself proves the existence of being that created the universe. Philosophy uses the empirical evidence that science gives us to solidate the premises and basics of itself. It is only needed when there needs to be answers for something beyond the naturalistic world. The assumption that something, regardless if it is the universe, does not have a cause is unreasonable and can not be defended. Through an argument given by Surrendra Gangadean, in his book Philosophical Foundations, an uncaused event or being is not rational. 1. Contradictory statements cannont both be true and both be false. 2. The contradiction of "some is eternal" is "none is eternal." 3. If "none is eternal" then: All is temporal All had a beginning All came into being 4. If all came into being then being came into existence from non-being. 5. Being from non-being is impossible. 6. Therefore, the original "none is eternal" is not possible. 7 Therefore, its contradiction "some is eternal" must be true. Premise 5 states that "being from non-being is not possible." This means that everything has a cause and can not "just be", chance is extremely improbable. If you were to hold to the claim that the universe is uncaused, it is equivalent to seeing an elephant randomly appear in the room and be logically okay not knowing where or how it came to be. The universe can not come from nothing, it had to have a cause for its existence because something can not come from nothing. After this, concluding that the universe exists, through the Kalam cosmological argument we can conclude that the universe must have a cause. The cause of the universe must be a conscious mind, spaceless, timeless being outside of our time that is able to bring the universe into existence. The only thing that fits these criteria is God.