I must admit, I am a bit surprised I have never seen Karl Barth (or Thomas Torrance) compared to 17th century “Reformed” thinker Pierre Poiret; at least by those who are in the know in regard to the history of ideas in the development of Post Reformed Orthodox theology. I mean, yes, Barth is often called a heretic by contemporary after-Westminster theologians of today, but they never really get that specific; it’s just like an appeal to their people, and an announcement to their choir. As I am continuing my trek through Richard Muller’s four volumes (apparently vols. 5–8 are coming out in 2018), in volume three I came upon this following reference to, indeed, Pierre Poiret. I find it interesting, because the way Muller describes Poiret’s Cartesian inspired theology, relative to knowledge of God and what that implicates, one might conclude that Poiret could serve as the poster-boy and precedent for Barth’s later and ostensible heretical theology (at least as many of the classically Reformed of today think of Barth i.e. largely those who follow Van Til’s influence out of Westminster Theological Seminary in both Philly and California). Let me share the quote, and you can take a look and see what you think. I’m sharing this also for future reference purposes. Here’s Muller on Poiret:
An example of the impact of Cartesian thinking on an entire system of nominally Reformed theology is Poiret’s L’Oeconomie divine, ou système universal (1687): in its subtitle, the work indicates that it demonstrates and explains the origin of Christianity and offers metaphysically certain statements of the “principles and truths of nature and grace, philosophy and theology, reason and faith, natural morality and Christian religion” together with a resolution of “the great and thorny difficulties of predestination, freedom, universal redemption, and providence.” Here we actually have a theology that begins with the problem of Pyrrhonistic skepticism, asserts the certitude of self-existence on the ground of the Cartesian cogito, and proceeds from the existence of certainty to the existence of God. From these arguments, Poiret passes on to a discussion of “the fundamental idea of the divine essence” and “the nothingness of ideas by themselves,” to a positing of “the origin of ideas through the decree of God in his discretionary understanding.” The eternal decree, according to Poiret, is the firm resolve of God “to give birth to ideas in his understanding, and beyond himself to things corresponding to his ideas.” The doctrine of the Trinity is to be understood by inference from the tripartite character of the soul — with the Father as “infinitely living Thought,” the Son as “image” and “light,” and the Spirit as “joy” and activity. The problem of predestination is resolved in the declaration “that all those who have and who will participate in human nature are all predestined by god to life eternal” on the ground that the god who is infinite thought and who, in the execution of his decree, has realized his own ideas in the finite order, could not decree to create the most admirable creature in his own image and then consign it to eternal death. The irony of Poiret’s formulation is that this sole “decretal” system produced in the seventeenth century rests on Cartesian, not Aristotelian, principles and deduces apokatastasis from the eternal counsel of God! And, by Reformed orthodox standards, Poiret’s decretal Cartesianism had certainly produced heresy.
Obviously there isn’t going to be univocal correspondence between Poiret and Barth, but there is enough there that I am very surprised that some of the proponents of Reformed orthodox theology of today haven’t ever pulled this type of Poiret card out when they are lambasting Barth as a heretic.
If anyone knows of Barth’s actualism, being-in-becoming theology you might see some similar contours of thought between Poiret and Barth, at least in tone and trajectory; particularly when it comes to predestination and its resolution in a Christian universalism (e.g. apokatastasis)—even though Barth rejected universalism as he believes it challenges God’s freedom. Insofar as Anselm’s ontological argument helped to fuel Descartes’ thought, as well as Barth’s, we can also see this in Muller’s portrayal of Poiret’s theology; maybe another point of contact between the respective trajectories. Barth’s theology is also typically aligned with the existentialism of his modern day; in Muller’s description of Poiret’s thinking, we see a type of that in his trajectory in conformity with his own period.
In the end, Barth was not a Cartesian, he was not a Kantian dualist, nor a Hegelian dialecticist (even if the latter two were reified by Barth under the pressure of God’s Self revelation in Jesus Christ). As George Hunsinger has rightfully noted, Barth followed a Chalcedonian Pattern in all of his thinking where Christ was the key and principial reality by which all else was regulated in his theological œuvre.
 Richard A. Muller, Post Reformation Reformed Dogmatics: The Divine Essence and Attributes, Volume Three (Grand Rapids, Michigan: Baker Academic, 2003), 125.