In the first place, the holy Synod teaches, and openly and simply professes, that, in the august sacrament of the holy Eucharist, after the consecration of the bread and wine, our Lord Jesus Christ, true God and man, is truly, really, and substantially contained under the species of those sensible things. For neither are these things mutually repugnant,-that our Saviour Himself always sitteth at the right hand of the Father in heaven, according to the natural mode of existing, and that, nevertheless, He be, in many other places, sacramentally present to us in his own substance, by a manner of existing, which, though we can scarcely express it in words, yet can we, by the understanding illuminated by faith, conceive, and we ought most firmly to believe, to be possible unto God: for thus all our forefathers, as many as were in the true Church of Christ, who have treated of this most holy Sacrament, have most openly professed, that our Redeemer instituted this so admirable a sacrament at the last supper, when, after the blessing of the bread and wine, He testified, in express and clear words, that He gave them His own very Body, and His own Blood; words which,-recorded by the holy Evangelists, and afterwards repeated by Saint Paul, whereas they carry with them that proper and most manifest meaning in which they were understood by the Fathers,-it is indeed a crime the most unworthy that they should be wrested, by certain contentions and wicked men, to fictitious and imaginary tropes, whereby the verity of the flesh and blood of Christ is denied, contrary to the universal sense of the Church, which, as the pillar and ground of truth, has detested, as satanical, these inventions devised by impious men; she recognising, with a mind ever grateful and unforgetting, this most excellent benefit of Christ. . . .
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 peculiar thing, that the other sacraments have then first the power of sanctifying when one uses them, whereas in the Eucharist, before being used, there is the Author Himself of sanctity. For the apostles had not as yet received the Eucharist from the hand of the Lord, when nevertheless Himself affirmed with truth that to be His own body which He presented (to them). And this faith has ever been in the Church of God, that, immediately after the consecration, the veritable Body of our Lord, and His veritable 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 connexion and concomitancy whereby the parts of Christ our Lord, who hath now risen from the dead, to die no more, are united together; and the divinity, furthermore, on account of the admirable hypostatical union thereof with His body and soul. Wherefore it is most true, that as much is contained under either species as under both; for Christ whole and entire is under the species of bread, and under any part whatsoever of that species; likewise the whole (Christ) is under the species of wine, and under the parts thereof. . . ,
And because that Christ, our Redeemer, declared that which He offered under the species of bread to be truly His own body, therefore has it ever been a firm belief in the Church of God, and this holy Synod doth now declare it anew, that, by the consecration of the bread and of the wine, a conversion is made of the whole substance of the bread into the substance of the body of Christ our Lord, and of the whole substance of the wine into the substance of His blood; which conversion is, by the holy Catholic Church, suitably and properly called Transubstantiation.
So the idea is that in a physical object we have two things: the substance and the species. The species refers to the empirical characteristics or qualities of the object--extension, texture, color, smell, taste, elemental make-up, effects on and from other physical elements and objects, etc. The substance refers to the "essence" or the "core identity" of the object--what it truly is at the level of fundamental identity. The Catholic position is that in transubstantiation, the substance of the bread and the wine becomes the substance of Christ (body, blood, soul, and divinity--that is, the whole Christ), while the species remains the same. So before we had the substance of bread under the species of bread, and now we have the substance of Christ under the species of bread.
Now, here's a little more on this seasoned with a little of my own philosophical point of view: I would argue that what "bread" fundamentally is is an empirical object. It is nothing less nor more than this. This means that the empirical qualities of the bread (the species), including the permanence and consistency of these qualities in their context in the rest of the empirical universe, constitute the very substance of the bread. That is, what the object fundamentally is is an object made up of the empirical qualities of bread and nothing more, and we call this object, in terms of its essence or substance, "bread". To put it another way, because what we have before us in a piece of non-consecrated bread is an object made up of the empirical qualities of bread and nothing more, we should say that its substance, or what it fundamentally is in its core, essential identity, is "bread". When transubstantiation occurs, Christ comes and places his substantial presence in the "place" of the bread. That is, Christ manifests his presence in a special and substantial way where the bread is when the bread is consecrated. The result of this is that we no longer have before us merely the empirical qualities (the species) of bread. We do still have those qualities before us, but we now also have the substantial presence of Christ. Because of this, we should say that the essential identity of the object (its substance) has changed. Before, it was "bread". Now, it is "Christ along with and under the species of bread". It is fundamentally or essentially a different object now than it was before (transubstantiation). But it is not entirely different, for the species of bread continue to be there. (And all this goes the same for the wine as well, of course.)
Note, then, that there is nothing illusory going on here, no false appearances. All we ever experience empirically of a physical object are, not surprisingly, its empirical characteristics. We name and identify a physical object based on those characteristics. We cannot tell merely by our observation of the empirical qualities that there is nothing in the object besides the empirical qualities, for, by definition, if there was something else there, that something else would not be empirically observable because it would not be empirical. So non-consecrated bread and consecrated bread are going to be the same in terms of empirical observation, because all we observe are the empirical qualities, and those qualities are truly there in both kinds of bread. It is not that they appear to be there but really aren't, but that they are really there. This is why it was silly for a group of Atheists to do a DNA analysis on a consecrated host to determine if it really had been changed into the body of Christ. They concluded that "[r]esults showed unequivocally that the rituals performed by the priests during the Eucharist sacrament have no detectable effect on the substance of altar bread at the DNA level." The error here is that they are using the term substance differently from the way it is used in Catholic theology. By the word "substance," these Atheists obviously mean "empirical qualities," because they are talking about what they observe through empirical observation. They conclude that these qualities have not changed. This is not surprising to Catholics, who have never asserted that the empirical qualities (the species) of the bread are changed in the consecration of the bread. When they say that the substance has changed, they aren't talking about the empirical qualities but the core, fundamental identity of the bread, which has indeed changed because now Christ is substantially present in a way he wasn't before. The bread has gone from being essentially "bread" to being "Christ along with and under the empirical qualities of bread". But this change will not be empirically detectable, because it does not take place on the empirical level but underneath that level, so to speak. It is not that there is an empirical change that we can't see (because we don't have the right equipment, etc.) but that there is no empirical change at all. There is a change, but it is not empirical in nature.
There are Protestants who believe in the real, substantial presence of Christ in the Eucharist. The Lutherans, for example, believe that Christ is present in the Eucharist along with the bread, so that what we have is both bread and Christ. This is usually seen as a view substantially different from the Catholic view, because Catholics say rather that the bread is changed into Christ and so is no longer there (except for its empirical characteristics). But I wonder if, when both views are explained in such a way as to remove certain misconceptions, they need necessarily be seen as at odds. If all the Lutherans are saying when they say that the "bread" is still there after the consecration is that the empirical qualities of the bread are still there--and these can be called "bread" since they constitute what we ordinarily call "bread" and are what originally draw forth that label from us--then Catholics can agree with that. And if Catholics clarify that those qualities which ordinarily draw forth from us the label "bread" are still there after the consecration, then it can be said, in some sense, and perhaps in a sense satisfying to Lutherans, that the "bread" is still there after the consecration. Maybe both sides could agree that while the fundamental essence of the object has changed because now Christ is there in addition to the empirical qualities of bread (so that we cannot anymore label the object simply and merely "bread"), yet the empirical qualities we ordinarily label "bread" are still there as well along with Christ. I don't know if speaking this way would help to manifest greater agreement or not. Perhaps this sort of thing has already been discussed in Lutheran-Catholic dialogue. I'm curious now to read further in this field and find out.
To read more about the Catholic doctrine of the Eucharist, see here.
Published on the feast of St. Raymond of Penyafort