According to Aquinas, in the conversion of the bread into the flesh of Jesus, the substance of bread is changed into the flesh of Jesus but the accidents (like the smell, taste, color, quantity) of the bread remain the same. This is considered a mystery; however, for certainty the substance of the bread does not remain the same, he thinks. Accordingly,
Some have held that the substance of the bread and wine remains in this sacrament after the consecration. But this opinion cannot stand: first of all, because by such an opinion the truth of this sacrament is destroyed, to which it belongs that Christ's true body exists in this sacrament; which indeed was not there before the consecration.....One view contrary to Aristotelian realism is nominalism (with its various sub-views). Nominalism basically rejects the doctrine of substance and accidents and the idea that properties exist independently as universal or abstract objects. It considers these properties as just names that humans give to things or ideas or appearances in order to be able to speak of the world. For instance, when Adam gave names to animals, he didn't give particular names but universal names: Thus, Elephant is a generic name for a class of animals that are elephants. Similarly, when he called his wife, Woman, it was a name by which all women in history were going to be known. Later, he gave her the specific name Eve. The idea of "man" or "woman" does not exist apart from men and women. To abstract the idea from the particulars and treat it as a separate entity in itself (though perfect as it could seem) is the error of Platonic realism. Aristotle rejected Platonic realism; however, his own idea of substance and accident in which accidents are realities that are instantiated in substances found entry in Catholic theology. Of course, religious language can often get riddled with confusion of treating metaphors and symbols as literal realities. The doctrine of transubstantiation is one such example among many.
Secondly, because this position is contrary to the form of this sacrament, in which it is said: "This is My body," which would not be true if the substance of the bread were to remain there; for the substance of bread never is the body of Christ. Rather should one say in that case: "Here is My body."
Thirdly, because it would be opposed to the veneration of this sacrament, if any substance were there, which could not be adored with adoration of latria.
Fourthly, because it is contrary to the rite of the Church, according to which it is not lawful to take the body of Christ after bodily food, while it is nevertheless lawful to take one consecrated host after another. Hence this opinion is to be avoided as heretical.
It is evident to sense that all the accidents of the bread and wine remain after the consecration. And this is reasonably done by Divine providence. (Summa III.75)
In the Council of Trent in 1545, the division between Catholic Thomistic realism and Protestant nominalism became evidently clear. Affirmation of Thomistic realism made it possible for the Catholic church to explain how it was possible that the bread and wine appeared to have all the properties they had earlier and yet had converted to the body and blood of Jesus. Catholicism rejected nominalism. Some think that nominalism (in the legacy of William of Ockham) was the cause of increasing skepticism, individualism, and secularism in Western civilization.[See Olson, What's in a Name]. Of course, that has to be justly established.
It certainly is evident that treating concepts as abstract realities independent of concrete being only create more confusion. For instance, while we can talk of love, grace, anger, justice, and peace objectively and abstractly (as in "love is patient", "love is kind"), it is erroneous to suppose that the love of God is an object in itself independent of God (as in Platonism) or even that love is instantiated in God (Aristotelianism). In contrast, the Bible declares that God is love (1John 4:8).