Kant's expression "Das ding an sich," translates to "the thing in itself." By introducing this expression, he was attempting to introduce an important epistemological issue in the classical distinction between phenomena and noumena, or, in Aristotle/Aquinas terminology, the distinction between accidents and substance.
In the classical distinction, phenomena are what are perceived, whereas noumena are what are knowable apart from perception. Thus, noumena are, by definition, knowable, albeit in some intuitive sense. By contrast, "das ding an sich" may be quite unknowable. In Kant's view, "das ding an sich" is that which exists in its very nature, apart from its observability. This gets us closer to the distinction between accidents and substance.
Substance, in its etymological root, means "that which stands under." If we think of a rock covered with sod, we may infer, or at least conjecture, the presence of the rock without actually seeing it. In the same way, we may conjecture the presence of individual quarks without actually being able to observe an isolated quark. Furthermore, we may be able to learn how the quark interacts with its environment without actually knowing what the quark is "in itself." One of the more challenging aspects of the physics of string theory (or superstring theory) is that it posits a certain 1-dimensional internal structure for elementary particles, which, in some sense, tries to get closer to what these particles are "in themselves" but the mathematics encounters difficulties in predicting interactions, particularly in the different formulations of this theory so that it becomes difficult to isolate the "winners" from the "losers" in the theory sweepstakes.
There is, however, a deeper sense in which it becomes impossible to know what something is in itself. All human knowing, apart from personal revelation, is mediated by physical interactions between the knower and what is known. God's knowledge of things is no mediated in this way. We say that His knowledge of things is "im-mediate."
All of the foregoing delves into the more general theory of knowledge, called epistemology. How do we know what we know? Epistemology is a branch of philosophy. Another branch, metaphysics, attempts to model what we know in ways that are more fundamental than physics. Aristotle attempted to do this in his theory of hylomorphism, from which we get the distinction between "matter" and "form."
In discussing philosophy, there can be a tendency to confuse the distinction between "substance" and "accidents" with the distinction between "matter" and "form." This is, in part, due to our modern knowledge of physics and chemistry, by which we recognize that matter is, for the most part, atoms (ignoring, for the moment, dark matter), and what we observe (i.e., the accidents) is largely predictable from the arrangement of atoms, i.e., the form. In a certain sense, then, at the macro scale, these distinctions tend to dissolve.
In theology, however, the difference is all important. Apart from personal revelation, what we experience is all mediated by physics. Thus, our experience of the Eucharist is mediated by physics, apart from the personal revelation that is either made known to us or remains hidden to us (i.e., our conscious awareness) even though there is an impact on our decisions and/or character.
If we ask "what is the matter and form of the Eucharist?" we may be inclined to respond with details about the physics and chemistry of bread and wine. This is all that we can know, ordinarily, through physical interaction, or, in other words, what we can know through scientific observation.
If we ask "what is the substance of the Eucharist; what is the Eucharist in itself" we are bound to answer in a very different way. We would say that, in itself, the Eucharist is Christ. What we can know through scientific observation is merely what we would call the "accidents."
These distinctions become more problematic when we encounter Aristotle's metaphysics, which analyzes all "substance" into "matter" and "form.," and Aquinas' theology, because he uses the term "form" to take the weight of spiritual natures. In the simplest terms, this makes sense, because a spirit has no matter. If all natures are analyzable into matter and form, then those natures not possessed of matter must be form alone. Yet, this completely alters our understanding of the meaning of "form." Form can no longer be thought of as the mere arrangement of component parts, even though we use it precisely in this sense in common discourse. These sorts of difficulties led to the development of a branch of metaphysics known as ontology. The naive distinctions introduced by Aristotle in his hylomorphic theory are no longer accepted as universal on their face. Something much more abstruse has taken their place. Indeed, in Catholic sacramental theology, the terms "matter" and "form" have taken on a particularly specialized meaning. See sacramental matter and form.
These problems were largely inevitable, given the history of philosophy and theology. Aristotle's usage of matter and form did not distinguish between metaphysics and the more specialized field of ontology. Indeed, he used the distinction between matter and form to explain the differences between biological species as well as the differences between individuals. Indeed, the distinction between "substantial form" and "accidental form" originally arose in the attempt to explain how different members of the same species can differ in particulars of "form." How, for example, can some men be bald and others not? Such differences were termed "accidental." This involves us in an older meaning of the word "accidental" as "non-essential," or "not of the essence." It is this meaning of the word "accidents" that was borrowed by theology to explain the fact that the appearance of the Eucharistic species does not change with consecration. It is to say, "the appearance is not of the essence."
Here, "essence" and "substance" mean the same thing. We say that the consecration, under the power of the Holy Spirit, has altered the substance of the Eucharist. We refer to this alteration by the term "transubstantiation."
There is no credible doubt that Jesus' words, as cited in the Gospel of John, chapter 6, the Eucharistic Discourse, when combined with the testimony regarding the Last Supper cited in the Synoptic Gospels and in St. Paul's 1st Letter to the Corinthians (chapter 11) require us to recognize that Jesus granted his apostles the mandate to fundamentally alter the relationship between common bread and wine and Jesus, himself, and, by implication, our relationship to those same Eucharistic elements, and to do so "in remembrance of me."
If there had been no Last Supper or no witness to the event, our reading of John 6 might have evolved differently. We might have seen Jesus' words as having a sacramental significance, to be sure, but that sacramental significance would have been isolated to the person of Jesus quite apart from any ritual. By contrast, if there had been no Eucharistic Discourse or no witness to the event, our understanding of the significance of the Last Supper event might have been very different. We might have seen Jesus' words of consecration and the mandate to "do this in remembrance of me" as having a ritual significance apart from ontological reality. The combination of the two requires us to connect the ontological reality of the Eucharistic Discourse with the ritual significance of the Last Supper.
We thus conclude that consecration brings about a transubstantiation.
The remaining task, to explain this philosophically, requires that we hang on to distinctions like "substance" and "accidents" that no longer find use, generally, in science, except perhaps in the science of taxonomy. There, of course, these distinctions become mired in the difficulty of defining precisely what a given species is in its genetic detail.
Furthermore, our common understanding of the term "substance" is confined to the distinctions of chemistry. In chemistry, what a thing is "in itself" is precisely determined by its molecular structure. The term, "substance" as used in theology, however, is far more general and abstract, where we ask what a thing is "in itself" apart from observation.
What could motivate us to hang on to these distinctions that the modern world largely rejects? Only our faith in Jesus Christ, a faith that embraces his divine and human natures, could do so. If we recognize, in Christ, the Word of God through whom all created things exist [John 1], we are bound to take the words of John 6 and the Last Supper witness with ultimate seriousness and as having an ultimate consistency and intention that is at least as deep and as significant as human nature, itself.