It is this sort of basis that Kuyper and Warfield alike maintained the basic unity of science [here understood generically as a rigorous intellectual discipline, not just what we normally mean by the empirical sciences]. God is certain to attain his end with mankind. In the face of Satan, he will cause men to develop and bring to fruition the potentialities that he himself has deposited within the universe. Whether willingly or unwillingly, whether conspicuously or inconspicuously, all men, and Satan too, contribute to the realization of the purpose of God with man and his universe. ...
... And God had determined that through Christ as Redeemer mankind would accomplish the task assigned it. Only on the basis of the work of Christ, then, does the unity of science actually exist and will it be actually consummated. True, the work of Christ must be thought of as immediately and directly effecting the salvation of men. But in saving men and in saving mankind Christ saves science. The unity of science may therefore be said to be Christological in a secondary sense.
— Cornelius Van Til, The Defense of the Faith, 4th Ed. (ed. by K. Scott Oliphant; Phillisburg, NJ: P&R, 2008), 178
Cornelius Van Til is often thought to be a giant defending the Reformed faith. The question therefore is whether Kuyperian incipient Reconstructionism will disqualify him.
In the above passage, Van Til believes that Christ came with one result being that mankind would accomplish the task assigned it. The cultural and intellectual strivings of Man will find their ultimate fulfillment when Christ finally comes again and consummate everything showing the unity of science in Christ.
What are we to make of this? The first thing we can see is the Kuyperian emphasis on the importance of the cultural and intellectual strivings of Man. However in Scripture, is there such an emphasis on such strivings? While certainly those strivings that honor God glorify Him, the focus of Scripture seem to be elsewhere.
These strivings of Man are a part of the Cultural Mandate. As such, it belongs to creation, not redemption. Christ therefore cannot "save" science, as if science however defined is a person which Christ died for. Christ died for sinners, and the elect who were and are sinners. Christ did not die for science or culture, or business or government! Christ shed His precious blood to redeem sinners, not institutions.
In a footnote, the editor K Scott Oliphant sees this as the principle "in which the work of Christ extends to the benefits of the nonelect." In other words, a Kuyperian view confusing creation and redemption; culture and the church, seems to be the basis of Van Til's idea of the well-meant offer. According to this view, Christ came to enable Man to complete the Cultural Mandate and therefore since all things will be consummated in Christ, there is a very real sense that those who are nonelect will get to partake of the benefits of Christ. From this, one could very well say that in some sense Christ died for the nonelect, and from there to the well-meant offer is not that far off.
All of this fail to differentiate between creation and redemption; between Adam and Christ. Christ died for particular people only. Christ is Savior of the Elect in redemption, but He functions differently as Creator and King of all men due to creation. Christ's role in redemption is different from creation, a truth that Van Til failed to grasp.
In this light, we have all the more reason to reject the unbiblical teaching of the well-meant offer. The Gospel offer is unconditional to and for all, but it is not well-meant. We are not to attempt to peer behind the veil at God's secret sovereign will (Deut. 29:29), or by confusing creation with redemption universalize the saving work of Christ in some fashion.