There is a helpful section in A Puritan Theology that summarizes the Quaker movement (in England around 1650) and John Owen’s criticism of it. Below is an edited summary of Owen’s critique of Quakerism found on pages 429-441 of A Puritan Theology.
1) Quaker teaching about the inner light is an attack on the work and person of the Holy Spirit. The Quakers’ lauding of the light within, which they often identify with the Holy Spirit, seems to be a subtle attempt to exalt the Spirit by the Spirit. Jesus’ statement in John 16:14 reveals that the message of the Quakers is actually an inversion of the order of the divine dispensations. That is, the role of the Holy Spirit is to glorify Christ, not himself.
2) The Quaker denial of the sacraments is unbiblical. Quaker worship is flawed by their discarding of the sacraments – baptism and the supper of the Lord – which are so great a part of the mystical worship of the church. Both of these ordinances speak about the heart of the Christian faith: the sanctifying and justifying blood of Christ. The Quakers have forsaken the gospel’s emphasis on the atoning work of Christ in order to focus on the inward light. The subjective trumps the objective in Quakerism.
3) The Quaker denial of the doctrine of the Trinity is anti-Christian. One big error in Quaker thinking is the failure to grasp the trinitarian nature of the work of redemption. Owen said, “Convince any of them of the doctrine of the Trinity, and all the rest of their imaginations vanish into smoke.”
4) The Quaker movement denies the necessity of Scripture and the doctrine of ‘sola Scriptura’ (Scripture alone). Scripture is God’s written Word, speaking of him to us. The Quakers deny that the Scriptures are the settled, ordinary, perfect, and unshakable rule for divine worship and human obedience. Owen vigorously refuted the Quakers’ insistence that Scripture is not needed once a person heeds the “inner light.” With the Reformed tradition, Owen said that the Bible is a constant aid and guide for God’s people: Scripture teaches us about salvation from sin and how to glorify God. Therefore it is necessary.
5) The Quaker doctrine of the inner light is a denial of the fall of man into sin and the consequent radical depravity of humanity. Owen said that the fall extinguished the inborn spiritual light that Adam and Eve possessed before the fall. Since Adam’s fall, his descendants are born in sin and therefore are by nature in darkness.
Here’s a summary in Owen’s own words:
“We persuade men to take the Scripture as the only rule, and the holy promised Spirit of God, sought by ardent prayers and supplications, in the use of all means appointed by Christ for that end, for their guide. They [Quakers] deal with men to turn into themselves, and to attend unto the light within them. Whilst we build on these most distant principles, the difference between us is irreconcilable, and will be eternal… Until, therefore, they [the Quakers] return unto ‘the law and the testimony’ – without which, whatsoever is pretended, there is no light in any – we have no more to do but, labouring to preserve the flock of Christ in the profession of ‘the faith once delivered unto the saints,’ to commit the difference between the word and Spirit on the one hand, and the light within on the other, unto the decision of Jesus Christ at the last day.’
Again, this is a summary of Owen’s teaching found in A Puritan Theology, pages 429-441. As a side, it would be a helpful study to compare Owen’s refutation of the Quakers to Luther’s refutation of the radical Anabaptists. There are certainly overlaps!