A logical chain argument, or, a Categorical Sorites.
Rom. 8:28-30 LEB
- And we know that all things work together for good for those who love God, for those who are called according to his purpose,
- because those whom he foreknew [i.e. Foreloved], he also predestined to be conformed to the image of his Son, so that he should be the firstborn among many brothers.
- And those whom he predestined, these he also called, and those whom he called, these he also justified, and those whom he justified, these he also glorified.
[Author’s Note: the ordering below is a combination of logical ordering, (terms 1, and 2), and then historical order of the decrees. I normally do not do this when making a syllogism, because of the added complexity when teaching, but used it this way for the use of the predicate logic. See end note below for more information.
For more see my post, The Order of the Decrees]
The logical deduction Paul uses here is called a Sorites. This is simply a normal bullseye syllogism (i.e. A.A.A, where A is a proposition that = All Subject is in the Predicate), but it continues to add additional categories, where the previous category is placed inside the next one. (All A is inside of B, and all B is inside of C; Thus, all A is inside the category of C.) What needs to happen is that the predicate of the previous proposition needs to be the subject of the next with affirmative propositions. This will create a circle diagram where one circle will be placed in the next. The circles do not lie; they give a visual demonstration of the deduction; to show if it is invalid or not. In this case, it is valid. Because this is a normal AAA bullseye type syllogism but only longer (i.e. A.A.A.A.A.), one is able (if the sorites is done correctly) to take any two premises and form an independent AAA syllogism.
There are exceptions for a particular premise, for a negative one, and when it is stated in the form of a hypothetical (If P, then Q) but that is for another time. Also, this type of syllogism may be stated in a reverse format. 
The form looks like this with a 6 premise sorites.
All A is inside the category of B
All B is inside the category of C
All C is inside the category of D
All D is inside the category of E
All E is inside the category of F
Thus, All A is inside the category of F.
I see examples of other people mentioning this sorites in Romans 8:30, however, they are prone to leave out verse 29, and thus only make this a 4-premise syllogism. This is a mistake, because the first premise comes from verse 29; and thus, the syllogism is in fact 5 premises.
At any rate, the first premise starts with, Those whom God foreloved are those He predestined.” The rest of the verse gives us extra insight as to what this predestination results in for both Jesus and for the ones predestined; however, this is not relevant for the immediate syllogism being made by Paul, because the next verse simply picks up at the category of, “whom He predestined … .” The predicate of premise is the subject of the starting premise in verse 30. Paul does not give the conclusion of this syllogism. However, in my experience of reading Paul he normally does gives the conclusion. I suspect that he does not here simply because he so exactly spells out the rest of this enthymeme sorites that the conclusion it is not needed, for it is obvious.
In summary, we are told all things work for our good who are called by God in verse 28. Paul then gives a sorites to show the undeniability of this reality. We are told from the initial love of God to glorification the saints are directed by God’s decree to love them, and that this decreeing leads to a good end, without any falling through the cracks or mishaps. Whom God foreloves He glorifies. God direct and absolute sovereignty is the totality of all Christian metaphysics and ontology. Soteriology is in fact a sub-category under metaphysics. That is, it is how God uses existence and causality toward this particular group of elect persons.
Also, it is in this syllogism that Paul shows the reality of verse 28’s category of “the called.” Paul shows us that this category needs to be seen in the larger logical and metaphysical reality of God’s decrees. He desires for them to see it all put together in a chain argument. Here we find being “Called” is in the middle of the decreeing, and that the decree starts with being foreloved first, and then finally ends –without fail—being glorified with Christ.
See my article called, “The Order of the Divine“ decrees to see how this fits together in an even larger view of the Divine Decrees. Foreloved would be in decree 2. Predestination would be decree 3. Called would be 8. Justification would be 9. And Glorification would be point 10.
(A) Those whom God foreloved are (B) those whom God predestined.
(B) Those whom God predestined are (C) those whom God called.
(C) Those whom God called are (D) those whom God justified.
(D) Those whom God justified are (E) those whom God glorified.
Therefore, (A) those whom God foreloved are (E) those whom God glorified.
HCS = Hypothetical Chain Syllogism rule for Natural Deduction. (see pic)
L = Foreloved. g = God. P=predestined. C = Called. J = Justified. G = glorified. s = Sally.
For every x, if x is fore-loved by God, then x is predestined by God; and, if x is predestined by God, then x is called by God; and if x is called by God, then x is Justified by God; and if x is Justified by God, then x is glorified by God.
1. Ɐx (Lgx ⸧ Pgx) • Ɐx(Pgx ⸧ Cgx ) • Ɐx (Cgx ⸧ Jgx) • Ɐx (Jgx ⸧ Ggx )
2. Lgs ⸫ Ggs
3. (Lgs ⸧ Pgs) • (Pgs ⸧ Cgs ) • (Cgs ⸧ Jgs) • (Jgs ⸧ Ggs ) 1,2 UI
4. Ggs 3. HCS
  added by author.
 All A is B, All C is A, All D is C, All E is D, Thus, All E is B.
[cannibalized from the rough draft of my Systematic Theology book]
“Whom He foreknew,” is about fore-loving, and propositional understanding. When looking at where “foreknow,” is used in the bible is almost exclusively use, (if not only), for God knowing His elect chosen ones and choosing to favor/love them. Therefore, it is said, Adam knew his wife Eve. Therefore, when text says, the Father foreknew, it means God fore-loved this group of people. God pre-favored this group by choosing to conform them into the image of Christ. This is true both in respect when considering them as sinners, and as a “neutral lump of clay,” before they had done good or evil, but according to God’s choice to be establish.
The “fore-loved” and “predestined” both are referring to the first intention of “these He also glorified.” The elect are covered with the weighty value of God’s lavished goodness for them. They are predestined to obtain this. Starting with Adam, God is molding the lives and choices of the elect to obtain this purpose of God. God’s favors them so that sin does not defeat them, like it does for the reprobate. God favors them, so that even if God causes them to be born in a bad place, with bad people, God causes them to hear and believe in His revelation. God denies such favor to the reprobate.
Romans 9 and Ephesian 1 tells us God’s first plan was to bless the elect with the riches of His love, grace and mercy. Thus the doctrine of a logical order of the decrees is already established. We are making this point because what will be extracted from this argument will not work unless this is a presupposition. When reading a historical order God’s decrees executing, we know the reverse was the original logical order.
Thus, to say,
D.1. (A) Those whom God called are (B) those whom God justified.
D.2. (B) Those whom God justified are (C) those whom God glorified.
D.3. Thus, (A) those whom God called are (C) those whom God glorified.
This is a historical order. God calls and elect a person by the summons of the gospel. God then justified them, by erupting faith to believe the gospel. God then glorifies them by preserving them in this world and bringing them to Himself in heaven.
The last “C” term is the first of the logical order. The “A” is the last in logical order, but first in historical execution. Paul starts with “whom he predestined,” because He is establishing the historical execution, with the presupposition of a logical predetermined or “ predestined” goal He already has. The elect are predestined to valued with becoming the image of Christ, and their being made the image of Christ, brings value to Christ. Thus, it is perfectly fine as a chain syllogism to start with, as Paul does “whom He predestined,” because the focus is on the numerical amount of a category. When making a category truth claim the focus can be more on the attribute or the numerical number of something that belongs in that attribute. They both indirectly apply to each other, but they do not emphasis the exact same thing. Paul’s focus is on the same amount that is in the first group is in the last group. That is, Paul is emphasizing the success of God’s predetermined purposes. God has a goal of a glorified man in Christ first. God logical worked backwards in decrees to make the happen. Next, God started the history of the world to work towards that goal. Paul’s focus is on the fact that with all this planning in logical order first, and the working it out backwards in historical execution, God did not have one single mistake or failure . God does not know what failure is. All those predestined to be glorified in God’s plans, were successfully called, justified and gloried. Therefore, your faith in nothing separating you from the love of God is unshakable.
Since our focus is seeing the basics of God’s decrees, we will keep the syllogism to either a historical or logical order decree. Paul speaking on the first-born status of Christ says, “And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy,” (1 Colossian 1:18 NIV.) And so, we will use the term “supremacy” for “first born from the dead,” because this supremacy was the first purpose for Jesus that Father had.
D.1. (A) Those whom God called are (B) those whom God justified.
D.2. (B) Those whom God justified are (C) Those whom God made in Christ’s image.
D.3. (C) Those whom God made in Christ’s image, are (D) Those whom God glorified.
D.4. (D) Those whom God glorified are (E) those whom God uses to display Christ’s supremacy.
D.3. Therefore, (A) those whom God called are (E) those whom God uses to display Christ’s supremacy.
Consider our diagram of from 1 Corinthians 3:23. This looks similar. In general, when said in a historical order (in context) the circles go from small to largest, and the logical purpose starts with the largest and goes to the smallest. Creation is for man’s glory.