Owen's basic argument is as follows:
The first argument may be taken from the nature of the covenant of grace, which was established, ratified, and confirmed in and by the death of Christ; that was the testament whereof he was the testator, which was ratified in his death, and whence his blood is called “The blood of the New Testament,” Matt. 26:28. Neither can any effects thereof be extended beyond the compass of this covenant. But now this covenant was not made universally with all, but particularly only with some, and therefore those alone were intended in the benefits of the death of Christ.[16] (Book III, chapter 1)
The Two Classes of Men (Arg. IV)
Owen's argument here is that since the Bible separates people into two categories, namely, believers and unbelievers, and various other designations of the groups, therefore, when Christ is said to die for one, it is implicit that He did not die for the other. In his own words:
If all mankind be, in and by the eternal purpose of God, distinguished into two sorts and conditions, severally and distinctly described and set forth in the Scripture, and Christ be peculiarly affirmed to die for one of these sorts, and nowhere for them of the other, then did he not die for all; for of the one sort he dies for all and every one, and of the other for no one at all.[17] (Book III, chapter 2)
The elect are designated also as:
those whom he “loves”…Rom. 9:13; whom he “knoweth,”...John 10:14, “I know my sheep;” 2 Tim. 2:19, “The Lord knoweth them that are his;” Rom. 8:29, “Whom he did foreknow;” chap. 11:2, “His people which he foreknew;” “I know you not,” Matt. 25:12: so John 13:18, “I speak not of you all; I know whom I have chosen.” Those that are appointed to life and glory, and those that are appointed to and fitted for destruction, — “elect” and “reprobate;” those that were “ordained to eternal life,” and those who “before were of old ordained to condemnation:” as Eph. 1:4, “He hath chosen us in him;” Acts 13:48, “Ordained to eternal life;” Rom. 8:30, “Whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.” So, on the other side, 1 Thess. 5:9, “God hath not appointed us to wrath, but to obtain salvation;” Rom. 9:18–21, “He hath mercy on whom he will have mercy, and whom he will he hardeneth. Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will? Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus? Hath not the potter power over the clay, of the same lump to make one vessel to honour, and another to dishonour?” Jude 4, “Ordained to this condemnation;” 2 Pet. 2:12, “Made to be taken and destroyed;” “Sheep and goats,” Matt. 25:32; John 10 passim. Those on whom he hath “mercy,” and those whom he “hardeneth,” Rom. 9:18. Those that are his “peculiar people” and “the children of promise,” that are “not of the world,” his “church;”[18] (Book III, chapter 2)
All these things are true only of the redeemed, the elect of God from all eternity. But this is not the only group which Scripture knows. On the other hand, Scripture designates the reprobates in the following words:
...in opposition to them, are “the world,” “not prayed for,” “not his people:” as Tit. 2:14; Gal. 4:28; John 15:19, 17:9; Col. 1:24; John 11:52; Heb. 2...