Karl Barth is famous for his rejection of natural theology, as he should be! A naked natural theology might be the kind wherein a person attempts to think God from a rationalist reflection upon the pressures and attributes present within nature. And from this reflection, and its absolute form, the categories for how God must be are derived and imposed upon God as the grammar by which the natural theologian begins to speak about God. Most people, most Christian people, upon hearing about the natural theologian would or should immediately recognize the dangers associated with thinking God as a natural theologian.
But there is a different way to engage with nature as a Christian theologian, a way that eludes the pitfall of using nature to conceive of God. It is possible, as John Calvin thought, to know God through nature, but not without revelation first. It was upon this basis that Calvin articulated his idea of the sensus divinitatis and his two-fold knowledge of God (duplex cognitio Domini); that we can know God as Creator and Redeemer, but the latter must now be the lens for the former. And Scripture becomes the spectacles by which we know God as Creator, as Father, as it reveals to us knowledge of God as Redeemer in Christ alone.
Besides John Calvin, Thomas Torrance also had a unique approach to viewing God in nature, but not by placing a primacy on nature, instead, like Calvin, a primacy on Christ is given over nature in a way that allows nature to have an ontology and thus a theological place of its own; a place wherein we as Christian thinkers can know God in all of his magnificent glory. Alongside Torrance, and Calvin, there is another Reformed theologian who also gives place, not to a ‘natural theology,’ but instead what we might term a theology of nature. This other Reformed thinker is Dutch theologian, and neo-Calvinist, Herman Bavinck. Bavinck writes:
Admittedly, article 2 of the Belgic Confession states that God is known by two means–nature and Scripture–and natural theology is upheld in its truth and value by all Reformed theologians. But in that first period, before rationalism infected Reformed theology, it was clearly seen that nature and Scripture are not detached and independent entities, any more than natural and revealed theology are. Calvin incorporated natural theology into the body of Christian dogmatics, saying that Scripture was the spectacles by which believers see God more distinctly also in the works of nature. Originally natural theology was by no means intended to pave the way, step by laborious step, for revealed theology. In adopting it, one was not assuming the provisional stance of reason in order next, by reasoning and proof, to mount to the higher level of faith. But from the very outset the dogmatician took a stand on the ground of faith and, as a Christian and believer, now also looked at nature. Then, with his Christian eyes, armed by Holy Scripture, he also discovered in nature the footprints of the God whom he had come to know–in Christ by Scripture–as Father. From a subjective point of view, in dogmatics it was not therefore natural reason that first took the floor, after which faith in the Word had its say. On the contrary, it was always the believing Christian, who, in catechism, confession, and in dogmatics, gave voice to his faith. And in the same way, speaking objectively, nature did not stand on its own as an independent principle alongside of Holy Scripture, each of them supplying a set of truths of their own. Rather, nature was viewed in the light of Scripture, and Scripture not only contained revealed truth (in the strict sense) but also the truths that a believer can discover in nature. Thus Alsted did indeed acknowledge the existence of a natural theology in the unregenerate, but a confused and obscure natural theology. By contrast, for the believer the principles and conclusions of natural theology are replicated clearly and distinctly in Scripture.
I think it would be better for Bavinck to call what he is discussing a theology of nature instead of ‘natural theology,’ which can become confusing given the passing of time and the negative connotations that have accrued to the language of natural theology. Clearly Bavinck, by way of method, is not giving ground to a brute or pure nature, as if it has the capacious resource to supply the categories for knowledge of the true God. Instead Bavinck sees faith, the faith of Christ as evoked by the Spirit in the illumination of Holy Scripture, as the lenses by which we can know God, even in his creation. I think, again, that it would be better for Bavinck to use the language of a ‘theology of nature’ here.
Furthermore, to compare Bavinck and Barth at this point: I think is a false parallel. Remember, Karl Barth’s context, he was writing within a world on Nazi-fire; a world that had used a Christian pretext to reinforce its villainous march forward into the halls of barbaric genocide against the least of these, which of course included the Jewish people. Barth (like in his drafting of the Barmen Confession), was explicitly taking away any resource for the Nazi church to use the categories of a natural theology informed by a Darwinian ethic to justify their rapacious march forward against humanity. In other words, the context of Barth, and his adamant stance against natural theology, needs to be taken into consideration when attempting to use his stance against all ostensible natural theologies, such as Herman Bavinck’s.
Does this mean that Barth’s theology against natural theology has no de jure or principled force? Does this mean that Barth’s theology against natural theology is marginalized by its de facto place and origin within his own German/Swiss context? God forbid it! What it means though, is that we shouldn’t necessarily read Barth against people like Bavinck without careful nuance between their respective contexts. They might actually reinforce each other more than they ameliorate.
 Herman Bavinck, Reformed Dogmatics. Prolegomena, Vol. One (Grand Rapids, Michigan: Baker Academic, 2003), 87-8.