"He makes this favor common to all, because it is propounded to all, and not because it is in reality extended to all; for though Christ suffered for the sins of the whole world, and is offered through God's benignity indiscriminately to all, yet all do not receive him." John Calvin on Romans 5:18
1) Calvin says that the gospel call is an "offer."
Some may object to the notion that the gospel is an "offer" or an "invitation," but not Calvin. He understood the conditionality of the gospel call and/or man's responsibility to believe. Though Christ died for you, he must be voluntarily "received" through faith in order to be justified.
2) Calvin says that the gospel is offered "through God's benignity."
God's offer of Christ to all that hear the gospel call is grounded in his goodness, kindness and love (or benignity). In other words, according to Calvin, it's a well-meant or sincere offer.
3) Calvin says that God benignantly offers Christ "indescriminately to all."
It's not merely the case that WE, in our ignorance of who is elect and who is not, are to offer Christ indescriminately to all, but that God himself offers Christ through our gospel call in an indescriminate fashion (to both elect and non-elect). God is not ignorant of his chosen ones, but he still offers Christ to all indescriminately, i.e. even to the non-elect.
See this R. B. Kuiper quote for more on this subject.
4) Calvin says that Christ suffered "for the sins of the whole world."
Some may try to escape what Calvin is saying here, but the honest mind can see that the "all" who "do not receive him" are a subset of the "world." Calvin does not equate the "world" with the elect scattered abroad here. He clearly says that Christ suffered for the sins of some who do not receive him (i.e. the non-elect). One can find other quotes from Calvin where he says that Christ died for some who finally perish.
It does not follow that he thinks that Christ suffered for all with an equal intent to save all, so let not that straw man be erected. There are more options other than 1) Christ suffered ONLY for the salvation of the elect or 2) Christ suffered for all with an EQUAL intent to save all. The tertium quid is 3) Christ intended to suffer for the whole world sufficiently, but he especially (unequal intention) suffered for the elect. This is why Charles Hodge says in his Systematic Theology that, "it has in all ages been customary with Augustinians to say that Christ died 'sufficienter pro omnibus, efficaciter tantum pro electis;' sufficiently for all, efficaciously only for the elect. There is a sense, therefore, in which He died for all, and there is a sense in which He died for the elect alone." Richard Baxter rightly says in his work on Universal Redemption that:
"When God saith so expressly that Christ died for all [2 Cor. 5: 14-15], and tasted death for every man [Heb. 2: 9], and is the ransom for all [1 Tim. 2: 6], and the propitiation for the sins of the whole world [1 Jn. 2: 2], it beseems every Christian rather to explain in what sense Christ died for all, than flatly to deny it."
My Concluding Remarks:
The righteousness of Christ propounded in the gospel is only efficaciously "extended" to the elect because they are morally enabled to believe by the renewing work of the Holy Spirit, and thus they alone appropriate Christ's merit unto justification. This is the result of God's special, efficacious and eternal decree. There is a limitation in God's special intent (but this special intent does not negate the other intent to satisfy for all) that concerns the elect and also in the application of Christ's satisfaction, but there is no limit in the expiatory satisfaction itself.
He who does not speak according to the 4 doctrines above has departed from classical Calvinism. Does that make them wrong in their biblical interpretations or in their systematic theology? No, not on that basis. It will only make them historically wrong if they claim that Calvin said something different than the above. God requires that we be honest in all things, and that at least includes our interpretation of writings throughout church history.
This is one of my favorite Calvin quotes because it ties together the concepts of common grace/love, the ground of the well-meant gospel offer, and duty-faith. These are a cluster of biblical truths that stand or fall together, and the undermining of them (however subtle and gradual) besmirches the very heart and character of God as revealed in the gospel.