[S]omething must be said about the term ‘rebaptism’… Strictly speaking such a word begs the whole question at issue. Orthodox believe, just as firmly as Roman Catholics, that Baptism is conferred once for all, and cannot be repeated without grave sacrilege and blasphemy. Thus when Greeks and Russians intended on baptizing converts, they did not think of this as a second Baptism, but argued that the converts in question had never been truly baptized in the first place. They would have said that they were not ‘rebaptizing’ but ‘baptizing’ them.
But on what grounds did [Ecumenical Patriarch] Cyril V and his party reject all western baptisms as null and void? Their basic position is clearly stated in the Definition of 1755… “We know only One, our own, Holy, Catholic, and Apostolic Church, and acknowledge only her sacraments, and consequently only her divine Baptism.’ The line of thought is evident: there is only one Church — the Orthodox Catholic Church; the sacraments are God’s gift to the Church, and therefore cannot be conferred by any who are outside her; heretics and schismatics are outside the Church, and so cannot possess the sacrament of baptism or any other. Since, then, their previous Baptism is invalid, converts from the west on embracing Orthodoxy must undergo the true Baptism of the Church.
This view of sacramental validity is usually termed the Cyprianic, for it finds its classic expression in the works of Saint Cyprian of Carthage. Some fifty years before Cyprian, the same view had already been expounded by another African writer, Tertullian, in the De Baptismo (a work belonging to his Catholic period, probably composed around 198-200): For us there is one, and only one Baptism, since there is only one God and one Church in the heavens… But the heretics have no participation in our teaching: the very fact that they are excluded from communion proves them to be outsiders… We and they do not have the same God, nor the one — that is to say the same — Christ; and so we cannot both have the one Baptism, for it is not the same. (De Baptismo, 15)
So Tertullian draws his conclusion: since heretics do not possess the one Baptism, they lack the power to confer Baptism on each other.
Tertullian is closely followed by Saint Cyprian: Baptism cannot be common to us and the heretics, for we do not have God the Father in common, nor Christ the Son, nor the Holy Spirit, nor the faith, nor the Church itself. Therefore those who come from heresy to the Church ought to be baptized, so that they may be made ready for the Kingdom of God by divine regeneration in the lawful, true, and unique Baptism of the Holy Church. (Epistle 73.21)
‘The Church is one,’ Cyprian argues, ‘and only those who are in the Church can be baptized (Epistle 69.2); ‘we say that no heretic or schismatic whatsoever has any power or right (nihil habere potentates ac iuris). (Epistle 69.1). ‘No heretic or schismatic whatever possesses the Holy Spirit… and he who does not possess the Holy Spirit cannot in any sense baptize… All without exception who come over to the Church of Christ from the adversaries and the antichrists are to be baptized with the Baptism of the Church’. (Epistle 69. 10-11)
Such was the sacramental theology which lay behind Cyril’s Definition of 1755. The Cyprianic view can be summarized in a syllogism:
True sacraments cannot exist outside the Church; Heretics and schismatics are outside the Church; Therefore, heretics and schismatics do not possess true sacraments.
But the west since the time of Augustine has normally adopted a somewhat different position. Augustine accepted Cyprian’s minor premise but denied his major. Unlike Saint Cyprian, he distinguished between validity and regularity: a sacrament performed by heretics or schismatics, while irregular and illegitimate, is nonetheless technically valid provided that certain specified conditions are fulfilled. Whereas Cyprian denied heretics both ius and potestas to perform sacraments, Augustine denied them the first, but not necessarily the second. A number of Orthodox theologians, particularly in Russia during the past three centuries, have inclined towards the Augustinian view; but in general the position of the Orthodox Church has been Cyprianic and non-Augustinian. The Cyprianic view was taken for granted by most Greek writers of the 18th century… and the Cyprianic view is still followed by the standard Greek manuals of theology in use today.
Two qualifications must be added here. First, although the Augustinian theory predominates in the west, it is not accepted universally: in some Roman Catholic writings an approximation can be found to the Cyprianic position. (see F. Clark, Anglican Orders and Defect of Intention, London, 1956, p. 10, note 1.) Secondly, while most Orthodox continue in the main to hold the Cyprianic theory, many of them today would slightly modify the austerity of Cyprian’s conclusion. Augustine accepted Cyprian’s minor premise but denied his major; it is equally possible to accept the major and deny the minor, and it this that many Orthodox at the present moment have chosen to do. They continue to claim that the Orthodox Church is the one, true Church; they still uphold the basic Cyprianic principle that outside the Church there can be no sacraments; they make no use of the Augustinian distinction between validity and regularity. But they would yet add that many non-Orthodox Christians are still in some sense members of the Church, so that it is possible that in certain cases these non-Orthodox possess true sacraments. But Greek Orthodox in the eighteenth century… were less lenient in their reasoning: like Cyprian — and for that matter, like most of the Fathers — they would simply have said that heretics and schismatics are outside the Church, and left the matter at that. (Eustratios Argenti: A Study of the Greek Church Under the Turkish Rule by Kallistos Ware, pp. 80-82)
also see: http://classicalchristianity.com/2013/12/20/on-the-reception-of-the-heterodox/