My wife (a Baptist) asked me last night about transubstantiation. She heard the terms “accidents” and “substance” before, but wasn’t quite sure what they meant. I explained it like this:
Your body constitutes the “accidents” of you. If you were to lose a limb, you would still be you, even though your “accidents” have changed. If you were to loose all of your limbs, your eyes, your ears, and your tongue, you would still be the same you in substance, even though your accidents have changed. This also goes for mental impairment (severe brain damage). You are still you in substance. When you die and your soul separates from your body, the accidents remain while the substance is changed - it is no longer you, it is merely the “accidents” of you.
Conversely, in transubstantiation, the accidents remain the same while the substance is changed entirely. The bread and wine still seem to be bread and wine, but the substance is Christ Himself, body, blood, soul, and divinity. Under the Lutheran consubstantiation view (as I understand it), both the substance of the bread and the substance of Christ are present. This, in my mind, is a logical absurdity. You cannot have two substances in the same thing. You cannot simultaniously have both “a person” and “not a person” in the same thing. An alligator cannot be at once an alligator and a refrigerator, for example. If it is an alligator, it is not a refrigerator. If it is a refrigerator, it is not an alligator. Similarly, if the Eucharist is the person of Christ, it cannot simultaniously be not the person of Christ.
Calvin’s view (as I understand it) denies any change in substance, but insists on a spiritual presence of Christ in the Lord’s Supper. I have yet to grasp how this is in any way different than the spiritual presence of Christ in the believer or how this is somehow more special than Christ’s presence “when two or more are gathered in [His] name”, but nonetheless this is their position.
BTW, all of the “accidents” and “substance” talk is derived from Aristotilian philosophy, which if it were taught more frequently would completely undermine the Lutheran position among sentient people (IMNSHO). Here is a link which goes into much more detail on the matter (pardon the pun), from the illustrious University of Notre Dame.