The dogma of transubstantiation was infallibly defined by the Council of Trent:

“The most holy Eucharist has indeed this in common with the rest of the sacraments, that it is a symbol of a sacred thing, and is a visible form of an invisible grace. But there is found in the Eucharist this excellent and unique thing, that the other sacraments have the first power of sanctifying when one uses them, whereas in the Eucharist, before being used, there is the Author Himself of sanctity….

“And this faith has ever been in the Church of God, that, immediately after the consecration, the true Body of our Lord, and His true Blood, together with His soul and Divinity, are under the species of bread and wine; but the Body indeed under the species of bread, and the Blood under the species of wine, by the force of the words; but the body itself under the species of wine, and the blood under the species of bread, and the soul under both, by the force of that natural connection and concomitancy whereby the parts of Christ our Lord, who has now risen from the dead to die no more, are united together; and the Divinity, furthermore, on account of the admirable hypostatic union with His body and soul.”

Take note of the specifics of this infallible teaching. Transubstantiation occurs in three modes, but as one and the same act of God, in one and the same instant:

(1) Change of substance

The substance of the bread only changes into the substance of the Body of Christ. The substance of the wine changes only into the substance of the Blood of Christ.

(2) Concomitancy

His blood and soul, in the case of the consecration of the bread, and His body and soul, in the case of the consecration of the wine, that is to say, the rest of His human nature, become present by the “natural connection and concomitancy” that all the parts of His human nature have with one another.

(3) Hypostatic Union

The Divine Nature becomes present by the “hypostatic union” that the Divine Nature has with the human nature of Christ. For the two natures are united as one Person.

This is the infallible dogma of the Council of Trent, and you will seldom find it taught correctly anywhere today. Most Catholics think that the consecration changes bread into all of Christ, or the substance of bread into all of Christ — which is material heresy. The substance of bread, a material thing, cannot be changed into the soul, a spiritual thing. God created two types of things in Creation, the material and the spiritual. And one does not change into the other. Then it would be absolute blasphemy to claim that mere matter, the substance of the bread, were changed into the Divine Nature. Yet that is what most Catholics, having been poorly taught, think.

Saint Thomas Aquinas

St. Thomas taught an error on transubstantiation. It is often said, correctly, that the Council of Trent took its teaching on transubstantiation from Thomas. Yes, but the Council corrected one error in his opinion. Thomas claimed that the Divine Nature becomes present in the same way as the rest of the human nature, by concomitancy.

“Because the change of the bread and wine is not terminated at the Godhead or the soul of Christ, it follows as a consequence that the Godhead or the soul of Christ is in this sacrament not by the power of the sacrament, but from real concomitance.”
http://www.newadvent.org/summa/4076.htm#article1

The Godhead is the one Divine Nature. Thomas incorrectly thought that the Divine Nature was present by concomitancy. The Council of Trent did not teach that the Divine Nature was present by concomitancy, but by the hypostatic union. Only the soul of Christ, and then the blood for the consecration of the bread, and the body for the consecration of the wine are present by concomitancy. Thomas was wrong on that point about the Divine Nature. But since he taught before the Council of Trent, his opinion was merely incorrect, not heresy. Today, to hold that same opinion would be heresy.

Heretical Teachings

It is false to say that the substance of bread, or the substance of wine, changes into the whole of Christ’s human nature, or worse still, into both natures. For the substance of bread changes only into the substance of the Body, and the substance of wine changes only into the substance of the Blood. The rest of Christ becomes present by concomitancy and the hypostatic union.

It is false to say that the substance of bread and of wine are annihilated, or return to nothingness, or cease to exist. Transubstantiation is a change of substance, one thing being transformed into another.

It is false to say that Christ is not physically present in the Eucharist. The dogma of transubstantiation requires us to believe that the whole of Christ’s human nature is present, including of course the physical part of His human nature. His presence in every host throughout the world as well as in Heaven, at the same time, is miraculous. If anyone says that true physical presence in so many places at once is impossible, I reply: “That’s why we call it a miracle.”

It is false to say that Christ is not locally present in the Eucharist. Locality is found in the accidents of a physical object, not in its substance (since locality can change without changing the nature of a thing). But the dogma clearly states that the human nature of Christ is present under the species of bread and wine. And those species have locality.

It is false to say that the accidents and the substance in the consecrated hosts are entirely separate, as if one had no connection to the other. For the dogma teaches that the substances of the bread and wine are transformed into the substances of the Body and Blood. Therefore, the latter substances retain the accidents of the former, including the accident of location.

And that is why the priest can physically pick up the host, and put it on your tongue, and that is in fact a reception of the Eucharist, by that physical act, by that change of location of the host. Therefore, Christ is physically present and locally present in the Eucharist. If not, then you could not receive him in the aforementioned physical manner, by the change of location from the priest to the communicant.

It is true to say that transubstantiation is a metaphysical change. But it is false and idiotic to claim that the molecules of bread and wine do not change at all, and that what changes is “beyond the physical”. For the term “metaphysical” does NOT mean “beyond the physical”. Metaphysics is the study of the nature of things, that is to say, the study of the substance of things. Substance refers to what is essential to the nature of a thing. If substance changes, the thing changes into something else.

Accidents refer to what is non-essential to the nature of a thing. If accidents change, and substance does not, then the thing retains its nature. Transubstantiation is a metaphysical change because it is a change of substance. Therefore, it is false to say that nothing of the physical molecules of bread and wine changes because the change is “metaphysical” supposedly meaning “beyond the physical”. The correct understanding is that bread and wine are each physical objects; they each consist of molecules. The molecules of any physical object can be divided, philosophically, into accidents and substance. In transubstantiation, the substance of the molecules change and the accidents of the molecules do not change.

The Real Presence

Most devout Catholics understand that Christ is present — body, blood, soul, and Divinity — in the Eucharist. But they also have no idea how that happens. Transubstantiation is not well understood, and many errors on the subject still prevail in the minds of the faithful.

Ronald L. Conte Jr.