Having looked at this topic from a couple of different perspectives there has been one part of this that we haven’t looked at too closely. That is the intention of the minister of the sacrament. In Pope Leo’s encyclical he declared Anglican orders were invalid because of defect in both form (rite) and intention.
In general, an act of the will by which one determines to do something: in the case of the minister, the will to administer the sacrament.
The minister, being human, is a free instrument,(contra Luther who declared that by original sin human reason has degenerated and free will no longer exists), and that is the real reason why his intention, at least virtual, to act as the representative of Christ in the administration of the sacrament, is absolutely necessary - whereas the moral dispositions (faith and the state of grace) are not required - in order that the sacrament produce the grace. It depends, in fact, on the free act of will of the animated agent, as man is, that in each and all cases he commit himself as an instrument in the hands of Christ. Besides, only the intention of acting ministerially can determine ad unam the sacramental meaning of the external rite, susceptible per se of multiple significations.
The Council of Trent in defining against Luther and Calvin the necessity of intention in the minister (Denzinger 854) determines also its object: “The minister must intend to do what the Church does”. In this expression, which sums up and sanctions a century-old theological formula, is indicated the relationship of dependency of the minister on the Church. The harmony of the plan of salvation chosen by Christ, the manifestation of the spiritual in the corporal (“the flesh is the hinge of salvation” - Tertullian), demanded that the activity of the minister be in direct relationship of dependency on the visible society,(once again, contra Luther), the Church which is the perennial manifestation of Christ (the doctrine of the Mystical Body of Christ), indefectibly faithful to the mandate of its Founder, do men of all times and places find the guarantee of the continuity of the means of salvation established by the Redeemer.
The Church, moreover, is a well organized body, in contrast to all Reformation sects, in which every vital movement, linked to an external rite, must depend in some way on the visible head (again the doctrine of the Mystical Body of Christ). It is necessary, therefore, that every infusion of new vital energies, caused by the sacraments, be in some way dependent on the visible head of the Church and on her hierarchy, which is the Pope’s co-adjutor " in ministering the blood of the Lamb for the universal body of the Christian religion" (St. Catherine of Siena).
It is purposely said “it must depend in some way,” because this dependency can be various and from a maximum can descend to a minimum necessary to preserve the bond of reference. In fact, it can be explicit, as in the Catholic priest who absolves the penitent, and implicit as in the infidel who, ignorant of the Church and her rites, is induced to administer baptism according to the intention of the one asking; it can, moreover, be direct, as in all ministers having communications with the Apostolic See, or indirect, as may be found in heretics and schismatics, who by the very fact that their respective sects or churches keep and repeat what Rome did when they separated from her, indirectly put themselves in a position of dependency on, and connection with, the Catholic Church.
) but I do attend the Novus Ordo through the week. Thankfully, our pastor and his associate have never referred to the altar as a table at the our Novus Ordo parish. I know both you and I see the significance here.