Here is how Richard Muller introduces the topic of “Proofs for the existence of God”:
An example that will be addressed at the very outset of the topical section of this study is the use of arguments for the existence of God where, contrary to much received opinion, the Reformers did not scorn the issue and the later orthodox did not revert to a purely Thomistic exposition of the five ways. Rather both the Reformers’ and the later orthodox writers’ use of these arguments offers evidence of the changing patterns of logic and rhetoric characteristic of the movement from the later Middle Ages into the Renaissance—parallel to the relative shift from the demonstrative mode of the medieval disputation and quaestio to the more rhetorically-couched form of loci communes.
Muller, R. A. (2003). Post-Reformation Reformed Dogmatics: The Rise and Development of Reformed Orthodoxy; volume 3: the divine essence and attributes (p. 32). Grand Rapids, MI: Baker Academic.
Later, he has a longer selection, which I tend to think is less useful than Bavinck’s commentary on the “Proofs”.
While Aquinas gave the “five ways” (“First Cause”, “Argument from Motion”, “Necessity”, “Superlative”, and “Design”). John Frame notes that these “five ways” do not necessarily point to the Christian God.
Other theologians have given other “proofs”. Earlier than Aquinas was Anselm’s “Ontological Argument”. Charles Hodge reviewed a number of these: the Ontological Argument, the Cosmological Argument (“Causation”), the Teleological Argument (“Design”), and the Moral Argument.
Bavinck also (Vol 2, pg 77 ff) also reviews some of these, and provides long list of other thinkers who have made attempts, and he even notes that Kant “attempted to establish the existence of God as a postulate of practical reason”.
Assessing these, Bavinck says:
It is regrettable that in theology these arguments for the existence of God are called “proofs”. Not, however, for the reason cited by Jacobi: Although the verb “to prove” means to infer one proposition from another, proving the existence of God is not for that reason a contradiction in terms. Dependence in a syllogism is something very different from dependence in reality. A “ground of knowledge” is far from being a “ground of existence.” Although in a syllogism the existence of God may be the conclusion—just as, generally speaking, one may infer the existence of a worker from the existence of a piece of work—that existence in reality is still in fact the origin and ground of the existence of all things; indeed, it is even posited as such in the conclusion.
But the term “proofs” for these arguments is infelicitous. The reason is that the term transfers the arguments to a category in which they do not belong, the category, that is, of logical, mathematical, exact, compelling arguments, and thereby deprives them of their ethical and religious character.
Now it appears as if belief in the existence of God is based on these proofs and has no foundation apart from them. And surely it would be “a wretched faith that first has to prove God’s existence before it prayed to him.”
The contrary, rather, is the case. There is not a single thing whose existence is certain to us only on the basis of proofs. We are fully convinced—prior to any argumentation—of our own existence, the existence of the world around us, the laws of logic and morality, simply as a result of the indelible impressions all these things make on our consciousness. We accept that existence—without constraint or coercion—spontaneously and instinctively. And the same is true of God’s existence.
The so-called proofs may introduce greater distinctness and lucidity, but they are by no means the final grounds on which our certainty regarding God’s existence is ultimately based. This certainty is solely determined by faith, that is, the spontaneity with which our consciousness bears witness to the existence of God that urges itself upon us from all directions. The proofs, as proofs, are not the grounds but rather the products of faith.
The situation is this: Faith attempts to give an account of the religious impressions and feelings that we humans receive and carry with us in our soul. That faith also exerts its influence on the intellect, which in turn seeks little by little to introduce some order in that chaos of impressions and notions. It classifies them and reduces them to a few categories.
Impressions come to us from the world of ideas (the ontological argument); from the world of finite, contingent, and mutable things (the cosmological argument); from the world of beauty and harmonious design (the teleological argument); from that of moral order (the moral argument); from the speech and history of all humankind (the universal consent and the historical argument).
However, although these impressions may be so classified, no one should ever think that these six proofs are the sole, isolated testimonies God sends to us. On the contrary, to the believer all things speak of God; the whole universe is the mirror of his perfections. There is not an atom of the universe in which his everlasting power and deity are not clearly seen.
Both from within and from without, God’s witness speaks to us. God does not leave himself without a witness, either in nature or history, in heart or conscience, in life or lot.
This witness of God is so powerful, accordingly, that almost no one denies its reality. All humans and peoples have heard something of the voice of the Lord. The consent of all peoples is confirmation of the fact that God does not leave himself without a witness; it is humanities response to the voice of God (Bavinck, “Reformed Dogmatics”, Vol 2, pgs 89-90).