In his book The Difficult Doctrine of the Love of God (pp73-78), D.A. Carson argues as follows.

Carson begins by noting that the term ‘limited atonement’ is unfortunate.  For one this, ‘it is a defensive, restrictive expression’, and for another thing, it obscures that fact that all non-universalists ‘limits’ the atonement in some way: the Arminian, by regarding it as potentially for all, but certainly effective for none; the particularist, by teaching that Christ died only for the elect.

Let’s use the terms ‘general atonement’ and ‘definite atonement’, then.

Those who hold to definite atonement argue that the doctrine of election forces us to distinguish a particular group of people ‘the elect’ for whom Christ died in order to secure their pre-ordained salvation.  Moreover, various texts indicate the existence of just such a group of people:-

Those who believe in general atonement’, on the other hand, respond with another set of texts that teach that Christ died for ‘the world’ (Jn 3:16; 1 Jn 2:2, and so on).

Is there a way forward from this impasse?

If we can agree that the Bible speaks of God’s love in various ways:-

(1) God’s intra-Trinitarian love,
(2) God’s providential love,
(3) God’s general love, expressed as an invitation to all to repent and believe,
(4) God’s particular love toward the elect’,
(5) ‘God’s conditional love toward his covenant people as he speaks in the language of discipline.’

It would be quite wrong to absolutise any one of these, for to do so would force our theology out of shape and distort our vision of God.

If we accept that both (3) and (4) are true, then we avoid the dangers of both particularism (which tends to ignore or underplay those texts which speak of God’s love for everyone) and generalism (which tends to do the same with those texts which speak of God’s special love for his own people).

Let us not seek to divide what God has joined together.  Let us, rather, affirm that the atonement is sufficient for all and effective for the elect.  Even if 1 John 2:2 (often cited in this debate) teaches that Christ died not just for some (proto-gnostic) elite, but for people of all types (i.e. even if this text means that Christi died potentially for all without distinction, rather than actually for all without exception), there are plenty of others that allow for sense (3) above.

This approach should (a) allow preachers in the Reformed tradition to speak, in evangelistic settings, more freely of God’s love than they sometimes fear is permissible.  On the other hand, (b), a commitment to the biblical doctrine of election will preserve the understanding that, ultimately, our salvation is not dependent upon our own decision or will, but upon God’s gracious choice.

Note: although Carson explicitly ‘lumps together’ the Arminian and the Amyraldian in this discussion, it appears that he is actually arguing for a ‘multiple-intentions’ view of the atonement, such as is advocated by the latter group.