There are some within the Presbyterian Church (and, by the way, I am an elder of the PCANZ, even though my CF icon indicates something a little different), who believe that when a person is convicted of sin, they should wait until the Holy Spirit gives them the assurance they are saved. Others believe that they can receive Christ as Saviour and believe that they are saved while they are waiting on God for the assurance. This causes a major division within the Presbyterian Church in the USA in the time of Charles Finney, who identified himself as somewhere in between Calvinism and Arminianism.
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I think this is a dangerous belief. The Westminster Confession of Faith makes it clear that there are degrees of assurance (objective and subjective) and specifically says that while assurance is the expectation and normative; IT IS NOT OF THE ESSENCE OF SAVING FAITH.
This infallible assurance doth not so belong to the essence of faith, but that a true believer may wait long, and conflict with many difficulties, before he be partaker of it: (1 John 5:13, Isa. 50:10, Mark 9:24, Ps. 88, Ps. 77:112) yet, being enabled by the Spirit to know the things which are freely given him of God, he may, without extraordinary revelation in the right use of ordinary means, attain thereunto. (1 Cor. 2:12, 1 John 4:13, Heb. 6:1112, Eph. 3:17) And therefore it is the duty of every one to give all diligence to make his calling and election sure, (2 Pet. 1:10) that thereby his heart may be enlarged in peace and joy in the Holy Ghost, in love and thankfulness to God, and in strength and cheerfulness in the duties of obedience, (Rom. 5:12, 5, Rom. 14:17, Rom. 15:13, Eph. 1:34, Ps. 4:67, Ps. 119:32) the proper fruits of this assurance; so far is it from inclining men to looseness.
True believers may have the assurance of their salvation divers ways shaken, diminished, and intermitted; as, by negligence in preserving of it, by falling into some special sin which woundeth the conscience and grieveth the Spirit; by some sudden or vehement temptation, by Gods withdrawing the light of His countenance, and suffering even such as fear Him to walk in darkness and to have no light: (Cant. 5:2, 3, 6, Ps. 51:8, 12, 14, Eph. 4:30, 31, Ps. 77:110, Matt. 26:6972, Ps. 31:22, Ps. 88, Isa. 50:10) yet are they never utterly destitute of that seed of God, and life of faith, that love of Christ and the brethren, that sincerity of heart, and conscience of duty, out of which, by the operation of the Spirit, this assurance may, in due time, be revived; (1 John 3:9, Luke 22:32, Job 13:15, Ps. 73:15, Ps. 51:8, 12, Isa. 50:10) and be the which, in the mean time, they are supported from utter despair. (Micah 7:79, Jer. 32:40, Isa. 54:710, Ps. 22:1, Ps. 88)
The Westminster Confession of Faith (Oak Harbor, WA: Logos Research Systems, Inc., 1996).