Those who deny that natural theology teaches anything reliable concerning God, ... (Charles Hodge, Systematic Theology, 1:22)
The Scriptures clearly recognize the fact that the works of God reveal his being and attributes. This they do not only by frequent reference to the works of nature as manifestations of the perfections of God, but by direct assertions. (1:24)
Not only the act of this revelation, but its clearness is distinctly asserted by the Apostle [Paul] ... It cannot, therefore, be reasonably doubted that not only the being of God, but also his eternal power and Godhead, are so revealed in his works, as to lay a stable foundation for natural theology (1:25)
Natural theology. It seems strange to me that people think that natural theology is actually a biblical and worthwhile endaevor, as opposed to just staying with a Biblical Theology of Nature. Natural theology, in its Reformed variant, is limited in scope yet it seeks truths from nature about God. Using Romans 1:20-21 as one of its base texts, it declares that Man can from nature know something about God, namely His eternal power and divine nature. The basic Biblical Theology of Nature, or Doctrine of Created things, on the other hand, tells us what God intends Nature to convey to us. The former (Natural Theology) looks to nature for God's revelation in nature, while the latter (Biblical Theology of Nature) looks to Scripture for God's revelation in nature.
Hodge, as part of his background in some form of Scottish Common-Sense Realism, believes that one can just trust one's senses as they are. Thus, he claims that Nature's revelation is plain enough on its own to give us a natural theology. But it is one thing to believe, with Scripture, that General Revelation is enough to condemn people through some knowledge of God, and another to claim that Nature itself reveals those aspects of Nature. The two propositions are not the same, and in my opinion it is a leap to jump from the biblical teaching that God reveals in General Revelation through Nature, to God reveals in Nature. Of course, it might be argued that the first leads to the second, but that is what is under dispute here.
General Revelation is what Scripture teaches. But the mode is not explicitly mentioned. Relying on empirical data and sense experiences, or even cognitive experiences, presupposes that these are necessarily reliable for the perception of truth. But if that is the case, why is it that none of the theistic arguments are foolproof? Even the teleological argument, or the argument from design, merely proves the existence of a cosmic designer(s). Now God is certainly who we believe the designer is, but I don't think it is clear enough from that argument that there is one Designer who is the Christian God.
Hodge claims the "most obvious" and "most effective" argument "in support of the truths of natural religion" comes from "the constitution of our own nature." (1:22). But what does this even mean, since there is no consensus on the constitution of Man in philosophy? Of course, if one interprets reality through Christian lenses, then the Imago Dei certainly shows us an aspect of General Revelation, but what if one does not interpret through Christian lenses?
Hodge lives in a much more Christian environment, but for those of us who have been exposed to non-Christian thought from cultures that never had Christian influences until the modern time, we can see how pervasive Christian theological and philosophical thought patterns have pervaded the West such that even much of Western unbelief borrows from the conceptual world of the Christian worldview. What Hodge thinks are "obvious" are not actually obvious to everyone. It is not so much that the arguments are inconclusive, as that the axioms undergirding the arguments are disputed as well. Therefore, it seems to me that arguments for natural theology are undermined at the conceptual level. For example, the ontological argument assumes that perfection of being in all aspects is possible, or that just because something can be mentally conceived means that it could exist in a possible world. All such assumptions can be questioned, and it seems that unless one brings in the Christian worldview, there is no way to establish the arguments for natural theology at all.
God does reveal aspects of Himself, His eternal power and divine nature, through General Revelation. At the same time, I deny that there is actually Natural Theology of any kind. It would seem that General Revelation is mediated by daily living as opposed to philosophical arguments, for after all General Revelation is accessible to everyone including the non-philosopher. The man on the street watches the stars, and encounters God's General Revelation there, without the necessity for analysis. General Revelation therefore is by intuition through daily living in God's world, and not by philosophical arguments and empiricism or science.