It is my opinion that one reason why there is so much confusion over the issue of formal and material republication of the Covenant of Works in the Mosaic Covenant is that the phrases are used in more than one sense. In an effort to add some clarity, I would like to delineate the various manners, as I understand it, in which the phrases "formal republication" and "material republication," as used of the Covenant of Works in the Mosaic Covenant, can be used.
A republication of the Covenant of Works in the Mosaic Covenant is simply to say that some aspect (form or matter) of the Covenant of Works is also found in the Mosaic Covenant which God gave ("published") to Moses especially on Mount Sinai. The trouble here is that even here we have a genitive phrase ("of __"). As anyone who has studied grammar would have known, genitives can be notoriously hard to pin down as to their exact meaning. For example, what does the phrase "love of God" mean? Is it to be taken as the subjective genitive, which is to say "God's love" (God loves X), or is it to be taken as the objective genitive, that is "X's love for God"? Normally, we decipher which sense it is from the context. Unfortunately, things get complicated when we deal with terms as big as "republication" coupled with the adjectives "formal" and "material."
On this particular topic of republication, let us see what happens when we take the phrase "republication of the Covenant of Works" as a subjective genitive. If it is a subjective genitive, then the Covenant of Works is the subject, thus we have the meaning being "the Covenant [of Works] as an oath bond being republished." If such is the case, then to claim a formal republication is to claim that the Mosaic Covenant qua covenant has the same structure or form as the Covenant of Works. To claim a material republication on the other hand is to claim that the Mosaic Covenant is essentially a Covenant of Works. Thus, if one takes the phrase as a subjective genitive, it seems to me that Formal republication in this sense is what most of those who are promoting Formal Republication are claiming, and what I see as the view of Francis Turretin for example. Material republication in this sense however must be rejected as heresy.
If one were to take the phrase as an objective genitive, then the Covenant of Works is the object, thus we have the meaning being "the republication of something within the Covenant of Works." Formal Republication in this view is to state that the form of the Law (the covenant material) seen in the Covenant of Works is the same in the Mosaic Covenant, which is to say the law in the Covenant of Works, which was given as a stipulation to be obeyed for the reward of eternal life (the form in which the Law works in the Covenant of Works) functions in the same way in the Mosaic Covenant. On the other hand, Material Republication in this view states that the material of the Law, which is in the Covenant of Works, is found in the Mosaic Covenant. Thus, we see here that, taking the phrase as an objective genitive, we affirm material republication, while formal republication in this sense is heresy.
Due to the different ways in which the genitives can be interpreted, both the phrases "formal republication" and "material republication" can be either orthodox, or heretical. If we take it as the subjective genitive, then we hold to formal republication and reject material republication, while the converse holds true if we take it as the objective genitive. In my opinion, much of the confusion over republication stems from the failure to discern and differentiate between the two ways one can interpret the genitive, resulting in massive confusion as the one attacking formal republication interpret the phrase as an objective genitive, while the defenders of formal republication interpret the phrase as a subjective genitive.
The four views are summarized as follows:
Type of Genitive Manner of republication Meaning Orthodox? Subjective Formal The outward form of the Mosaic Covenant is the form of the Covenant of Works Contended, should be Material The Mosaic Covenant is essentially a covenant of works No Objective Formal The form of the Mosaic Covenant functions just like the form of the Covenant of Works, i.e. to gain eternal life through obeying the law No Material The substance of the Covenant of Works, the Law, is the same Law published at Sinai under the Mosaic Covenant Yes