Much of this article is adapted from Grenier’s Cursus Philosophiae 289-290. Also, c.f., Hugon, Cosmology, Second Treatise, Third Question, Art. 3, 13-15
Recently, Byzantine Scotist, in an informal livestream, gave his thoughts on the 24 Thomistic Theses. Now, it must be noted that this was informal, giving a few thoughts to show the distinctions of Scotistic Philosophy. This was not a formal presentation and response to the 24 Thomistic Theses. In it, he questioned Thesis XII, “It is also quantity that makes a body to be circumscriptively in one place and to be incapable, by any means, of such a presence in any other place.”
In this, Gideon presented the Scotistic view of Haecceity and gave two points of objection to the thesis, 1. The bilocation of various saints, and 2. The Sacramental presence of Our Lord’s Body and Blood.
Now, this article will set forth the Thomistic view on the matter, presenting the distinctions given and proving the theses set forth. It is important to note that this article will not attempt to refute Haecceity, something which I am not prepared to do. Further, I will not be refuting the two specific objections (perhaps another time if there is popular demand, or if Gideon takes back what he said in the Discord).
Distinctions and Definitions
The first distinction which is present in the Thomistic view on the matter is between proper and improper presence. Proper presence (also called local or circumscribed presence) is that presence wherein the dimensions of a certain thing is circumscribed by the dimensions of that place. Improper presence (also called illocal or incircumscribed presence) is that presence wherein the dimensions of a certain thing is NOT circumscribed by the dimensions of that place.
Improper presence can be distinguished into three modes. The first is informative presence wherein a certain thing informs that which has a place. An example of which is the way in which a soul can be said to be “present” to a body even while not having dimensions itself. The second is operative presence wherein a certain thing operates on a place. An example of which is the way in which angels or God are said to be present by their operation. The third is sacramental presence wherein the body of Christ is said to be present in the sacrament. Grenier explains, “The Body of Christ is really present under the dimensions of bread and wine. Theologians commonly say that It has Its own internal quantity, but not external quantity. Therefore It has not, in virtue of Its own quantity, relation to place, i.e., Its dimensions are not measured by the dimensions of bread and wine, but It is in place after the manner of a substance, i.e. after the manner of a thing which of itself abstracts from place.” 
Now, bilocation, generally speaking, can be defined as the presence of a thing in two places at the same time. The presence is said to be non-definitive, i.e., that it is not restricted to a single place. One can conceive of bilocation in two ways. First, circumscriptive bilocation when a certain thing is properly present in two locations. Second, mixed bilocation when a certain thing is properly present in one location, and improperly present in another location. A third way can be conceived wherein a spiritual substance exists in multiple places at once improperly, but this is not relevant to the exposition.
Concerning the possibility of each, philosophers are divided, Alexander of Hales, Bl. Scotus, Suarez, St. Bellarmine, Valentia, Franzelin, and Pesch hold the former and the later to be possible (followed by the Lutherans). St. Albert, St. Thomas, St. Bonaventure, St. Anselm, Henry of Ghent, Capreolus, Vasquez, Ferrara, John of St. Thomas, Sylvester Maurus, de San, de Maria, Lorenzelli, teach the former to be impossible, but admit the latter (followed by the Reformed).
Thesis Presented and Confirmed
The Thomists generally conclude two theses from their premises, first, that mixed bilocation is not repugnant, and, second, that circumscriptive bilocation is. The first is agreed upon and therefore can be assumed. The second is where there is disagreement, in the words of the Angelic Doctor “To say that a body is in two places circumscriptively is to posit two contradictories together.” (Quodlibet III, q. 1, a. 2.)
There are four arguments wherein the Theses is proved.
(Major) It is contradictory for a certain thing with one dimension to have two dimensions; (minor) but, if one body is in two bodies circumscriptively it would have two dimensions; ERGO…
The major is self-evident.
The minor is proved: (Antecedent) To be in a place properly is to have the dimensions of the thing contained in the dimensions of the containing place. (consequent) ERGO, the thing properly in two places will have the dimensions of those two places.
Confirmation: “That which is fully and totally exhausted in one does not retain anything that can be conferred to another. But the quantity of a located body is fully and totally exhausted in one place, such that the whole quantity corresponds to the one place and each of its parts to each of the parts of the place. Therefore, nothing whatsoever remains by reason of which the body can be in another place.” 
(Antecedent) A which which is properly in two places would have two positions; (Consequent) ERGO, a certain thing would be both above and below, left and right, etc., itself, which is impossible.
The antecedent is self evident, for position follows upon place.
(Major) It is contradictory for one body to be contained and not contained by the same place at the same time; (minor) but, a body which is properly contained by two places would be contained and not contained by the first place (and the second place) at the same time, ERGO…
The major is self evident
The minor is confirmed: “It would be contained by the first place, for to be circumscribed is the same as to be contained; it would not be contained by it, for at the same time it would be circumscribed by another place.” 
(Major) It is contradictory for a single body to have two numerically distinct quantities; (minor) but, a body which is properly in two places has two numerically distinct quantities; ERGO…
The Major is confirmed: “Two quantities are numerically distinct from each other only by their reception into two distinct bodies.” 
The minor is confirmed: “It would have one quantity by which it would be circumscribed by one place, and another quantity by which it would be circumscribed by the other place.” 
 Cursus Philosophiae, 289.
 Hugon, Cosmology, Second Treatise, Third Question, Art. 3, 15
 Cursus, 290.