After posing the question regarding the alternate theories/ formulations on justification in my last post here, I would like to answer the question here. I was hoping that more people would chip in to attempt to answer, but oh well...(I mean.... saying that regeneration precedes faith doesn't quite answer the question)
Anyway, as I said in the comments section, both of the formulations are false. Here is the correct formulation:
Salvation = Justification → Sanctification
Justification = Faith → Works
(The arrow "→ " means "leads to")
Here are the two false formulations again:
Justification = Faith + Works
Faith = Justification + Works; & Salvation is by faith alone
The first formulation states that justification is by faith and continuation in a life of good works. This is actually Rome's view of Justification, as can be seen in the following statements from the Council of Trent:
CANON I.-If any one saith, that man may be justified before God by his own works, whether done through the teaching of human nature, or that of the law, without the grace of God through Jesus Christ; let him be anathema
CANON XII.-If any one saith, that justifying faith is nothing else but confidence in the divine mercy which remits sins for Christ's sake; or, that this confidence alone is that whereby we are justified; let him be anathema.
CANON XXIV.-If any one saith, that the justice received is not preserved and also increased before God through good works; but that the said works are merely the fruits and signs of Justification obtained, but not a cause of the increase thereof; let him be anathema.
We can see from Canon I On Justification in the Sixth Session of the Council of Trent that the Roman Catholics do not believe in justification by works, contrary to what many ill-informed Protestants believe. Granted, practically speaking, many if not all Roman Catholics behave as though they believe in salvation by works, but this is not what Rome technically believes, and any informed Roman Catholic knows that. Rome believes in salvation through faith PLUS the continuation in a lifetime of good works, which can be seen in Canons XII and XXIV as quoted above.
The problem with Rome's view, besides the serious and obvious fact that it is unscriptural and thus anathemized by Scripture, is in its practical outworking. People ensnared by Rome's theology could not be certain of their salvation, since even though they initially 'believed in Christ', they are always in danger of losing their salvation if they stop doing good works and commit grave and serious sins (mortal sins). The person who is thus supposed to be saved thus has no peace and rest in Christ. More serously, unless he turn to Christ alone, he is in serious danger of damnation for believing in false doctrines and a false Christ.
The first alternate formulation is thus heretical since it denies the doctrine of salvation and justification by grace alone through faith alone, which the Bible teaches in Romans and especially in Eph. 2:8-9. With that, let us look at the second formulation.
The second formulation looks rather orthodox. It basically says that faith caused one to be justified before God and to have good works. Put together with the orthodox formulation of salvation by faith alone and we get the idea that salvation involves one being justified before God and doing good works. In fact, if I am not wrong, this phrase is accepted by quite a few 'Reformed' people. However, notwithstanding this fact, this phrase is in error, although its error is not easily discerned. Let us now look more closely at this phrase.
Before we look closely, we must always keep in mind that salvation is by grace alone through faith alone. Anything which undermines this great and glorious doctrine is heresy. Grace and salvation is free to all who will believe, and justification and salvation is by God's grace 100% from the beginning to the end.
Now, if faith = justification + works, then faith includes some measure of works; or rather a life of continuation in good works. If that were so, then someone who does not show a lifetime of good works do not have faith. So far, so good. But then, it becomes tricky. Does this formulation then thus mean that somehow works are meritorious in being part of faith? Can the Tridentine formula of saying that 'the justice received [justification] ... is ... increased before God through good works' be somehow subscribed to? After all, we are not saying that works are to be counted on to save us, but they could be part of the salvific process as the practical expression of faith?
Note that I use and bold the word expression in the last statement. It is this word which shows the problem with the whole formulation. With such a formulation, the whole idea of works-salvation is smuggled in and a step back to Rome is taken. With the usage of the word 'expression', works is not meritorious in securing salvation (thus seemingly orthodox), but IT IS shown to be meritorious in practically proving salvation. Thus, the assurance of salvation for a person would lie NOT in faith but in a life of continuation in good works. Thus, such a person would live in conscious fear of being shown that his/her faith is false IF he/she stops doing good works and thus is not saved. Practically speaking, such a life consistently lived with its professed doctrine would leave one in no better state than Roman Catholics. I would hope, however, that the people who believe in it cannot discern its deadly error and thus are inconsistent with regards to their doctrine.
Now, I definitely share the concern of people who wants to guard against the heresy of Antinomianism, otherwise known as 'cheap grace', 'anti-Lordship' position, or 'Zane Hodge-ism', which I hope what people who subscribe to or are symphathetic to the second formulation are concerned about. However, we should not guard against Antinomianism by smuggling in works-salvation through the back door! Let us gaurd against works-salvation in ANY and EVERY form by removing works from soteriological formulations altogether. Similarly, we should guard against Antinomianism by emphasizing the reality of regeneration (which precedes faith and justification), and the reality of the presence of good works which is the fruit of justification and NOT part of the justification process itself; it is part of sanctification (post-justification) which is always coupled to and occurs immediately after the process of justification. Thus, the formulation which I have used is definitely better, since the arrow sign "→" shows that the thing which is implied (right hand side) is caused by but is not meritorious nor contributes anything whatsoever to the thing which implies it (left hand side).
With all this said, let us continue to emphasize and re-emphasize the glorious doctrine of salvation and justification by faith alone as the alone meritorious agent (which is in turn caused by God's grace alone) which contributes to our being made right and righteous (justification) before our most holy God and thus saving us. Let us guard against neolegalism and all forms of work-righteousness on one hand, and Antinomianism on the other hand.
NOTE: Justification ≠ Salvation. However, the point of time at which a sinner is justified before God is the point of time at which the sinner is saved. Thus, being justified can be used in certain situations to mean the same thing as being saved, especially when discussing on the temporal relation of events.