0. This post is the second in a series dedicated to a sustained reading of and commentary upon Aquinas’s Commentary on the Metaphysics of Aristotle. In my immediately previous post, I stated that this post would be focused upon the one of the several arguments present in the opening paragraph of Aquinas’s “Prologue” to his Commentary that I find to be the most explicitly expressed and easily understood. In this post, then, I will set out and assess the argument, offering my treatment of it as an at least partial illustration of the approach that I will be taking in the course of the series.
So, the first paragraph of Aquinas’s “Prologue” to the Commentary reads as follows:
When several things are ordained to a single thing, one of them must rule or govern and the rest be ruled or governed, as the Philosopher [i.e., Aristotle] teaches in the Politics. This is evident in the union of soul and body, for the soul naturally commands and the body obeys. The same thing is also true of the soul’s powers, for the concupiscible and irascible appetites are ruled in the natural order by reason. Now all the sciences and arts are ordained to a single thing, namely, to man’s perfection, which is happiness. Hence one of these sciences and arts must be the mistress of all the others, and this one rightly lays claim to the name of wisdom; for it is the office of the wise man to direct others.*
1. One premise of the argument at hand, the major premise, finds its expression in the paragraph’s first sentence:
When several things are ordained to a single thing, one of them must rule or govern and the rest be ruled or governed, as the Philosopher [i.e., Aristotle] teaches in the Politics.
As “regimented,” i.e., so rephrased as to make more fully evident its logical essentials, this premise reads as follows:
All sets of several things ordained to some one thing are sets of things one of which must rule the others.
2. His statement of this argument’s minor premise appears in the paragraph’s fourth sentence:
Now all the sciences and arts are ordained to a single thing, namely, to man’s perfection, which is happiness.
Now, the perfection of man [sic] and the happiness which Aquinas points to are both of the utmost importance in his philosophy taken as a whole. But they are beside the immediate point of the present argument and paragraph. Setting them aside, then, the premise, as regimented, reads as follows:
The set of the sciences and arts is a set of several things ordained to a single thing.
One more step in the regimentation of this premise: because, as it will turn out in the course of our reading of the commentary, Aquinas and Aristotle understand the wisdom which our paragraph mentions to be a science, the “and arts” of the “sciences and arts” is superfluous, the premise can be a bit more more simply expressed as:
The set of the sciences is a set of several things ordained to a single thing.
3. Given, then, those two premises, what the argument and its conclusion have to be is immediately evident.
All sets of several things ordained to some one thing are sets of things one of which must rule the others.
The set of the sciences is a set of several things ordained to a single thing.
Therefore, the set of the sciences is a set of things one of which must rule the others.
I will take it to be sufficiently evident for our purposes that this argument is valid, that is, it is such that, if the two premises are true, the conclusion too has to be true; were it necessary, one could easily set the argument forth in full set-theoretical dress.
4. It is not, however, quite so evident that the argument is also sound. That is, though it is evident that the argument is valid, it is not evident that, in addition, both of its premises, and therefore also its conclusion, are true. In particular, it is not evident that the first premise is true; in fact, I think it evident that it is false.
Let us first dispose of what one might take to be an argument on behalf of the first premise, as represented by the paragraph’s second and third sentences,
This is evident in the union of soul and body, for the soul naturally commands and the body obeys. The same thing is also true of the soul’s powers, for the concupiscible and irascible appetites are ruled in the natural order by reason.
I do not here question the truth of either of the two sentences; in fact, I am inclined to think that, properly understood, they are true. But let us assume, for the sake of argument, that they are true. We are then licensed to assume the truth of the following particular affirmative proposition:
At least some sets of several things ordained to some one thing are sets of things one of which must rule the others.
But clearly this does not license an assumption that the corresponding universal affirmative proposition, our
All sets of several things ordained to some one thing are sets of things one of which must rule the others.
is also true, for while it is consistent with the universal affirmative proposition, it is also consistent with the particular negative proposition that
At least some sets of several things ordained to some one thing are not sets of things one of which must rule the others.
Aquinas’s observations present us, not with compelling evidence of the truth of the universal affirmative proposition, but with instantiations of the particular affirmative proposition.
5. I am claiming, however, not just that Aquinas has not made his major premise evident, but that it is false. So let us observe first that if
All sets of several things ordained to some one thing are sets of things one of which must rule the others.
is true, then
All sets of two things ordained to some one thing are sets of things one of which must rule the others.
has to be true.
6. One such set would be:
The set of two parents, William and Ruth, both of whom are, in their very being, committed to, ordered to, and, in other words, ordained to the health and happiness of some one child, their favorite child, Richard.
Aristotle’s principle would have it, then, that, pruning and regimenting things a bit,
The set of two parents, William and Ruth, ordained to the health and happiness of Richard, is a set of parents one of which must rule the other.
or
The set of two parents, William and Ruth, ordained to the health and happiness of Richard, is a set of parents for whom it must be the case that either William rules Ruth or Ruth rules William.
But, given the two propositions “William rules Ruth” and “Ruth rules William,” there are in fact four logical possibilities at hand here.
1. William rules Ruth and Ruth rules William.
2. William rules Ruth and Ruth does not rule William.
3. William does not rule Ruth and Ruth rules William.
4. William does not rule Ruth and Ruth does not rule William.
Now the propositions “William rules Ruth” and “Ruth rules William” are logical contraries. That is, they cannot both be true. This eliminates the first of the four logical possibilities. Here, I assume, Aristotle, Aquinas, and I are, and have to be, in agreement. It has further to be granted that the second and third possibilities are real possibilities; we all know marriages similar to the one and others similar to the other. And the second and third possibilities are the possibilities that Aristotle’s principle admits. Here again Aristotle, Aquinas, and I are, and have to be, in agreement.
But, though the two contrary propositions cannot both be true, they can both be false. It is at least logically possible, then, for it to be false that William rules Ruth and false that Ruth rules William. In other words, it is at least logically possible that William does not rule Ruth and Ruth does not rule William, that theirs is a marriage of equals, if only in their devotion to Richard. This Aristotle’s principle implies the opposite of. And so Aristotle’s principle must be false.
7. What, other than that the argument at hand is unsound, can we conclude from the foregoing? One thing we cannot conclude is that the fact that the argument is not sound means that its conclusion, that
The set of the sciences is a set of things one of which must rule the others.
is not true. It is perfectly possible for an argument that is not sound to yet have a conclusion that is perfectly true; indeed, an argument that is not even valid may yet have a conclusion that is perfectly true. The conclusion at hand, then, may well be true. And in fact I am inclined to believe that, properly understood, it is.
7. But we can conclude that Aquinas is capable of imperfection in his argumentation and that therefore, when we find ourselves reading any of his arguments, we should subject it to as rigorous an examination as possible.
Until next time.
Richard
* Thomas Aquinas, Commentary on the Metaphysics of Aristotle. Translated and introduced by John P. Rowan (Revised edition; Notre Dame, Indiana: Dumb Ox Books, 1995 [1961]), p. xxix. The text of Aristotle to which Aquinas makes reference is the Politics, I, 5 (1254a20).
This edition of Aquinas’s text will serve as the text at hand in the present series of readings and comments. It is available online, at:
http://dhspriory.org/thomas/Metaphysics.htm
If you prefer to do your reading in hard copy, you may easily purchase a copy of the work through Amazon.com., by simply clicking on the following:
After Aristotle 
Hello Richard (if I may), this is great. I agree that we have to hold Aq’s feet to the fire as well as we’re able!
Just a quickie. I think you need to go into more depth on “ordo” and “ordinare,” i.e. “order” and “put things in an order.”
My understanding so far is that among the kinds of groups that we find in Ari and Aq, one is an ordo, and one is a series. In an order/ordo, the members are ranked relatively to each other by a priority among them, according to their distance from the head item. In a series, the things are in a numerical order but not necessarily an order of priority. As I understand it, an ordo is like the standings of teams in a league, while a series is like the games in what we call a series. By definition, there is some first place and last place team (doesn’t matter if there’s a tie). In a series, there are up to seven games, say, but victory in one game is not worth more than victory in another game in the series.
So your example of husband and wife in a position of subordination to the end of child rearing doesn’t seem to me to be an ordo. I’m not sure it’s a series, either. Aristotle wouldn’t say that all the free male Athenian citizens are ordered among themselves qua citizens, though they are ordered qua magistracies or property classifications and so on.
Sometimes we find the Greek “taxis” used where Aquinas would use the Latin “ordo,” and sometimes Aristotle uses verbs like “stand at an interval,” as he does at Pol. 1254a20, the passage Aq quotes at the beginning of his Prologue.
This is Ari on ordering:
“things in an ordo (κατὰ τάξιν) are things that stand at intervals in relation to some defined thing according to some description, logon, e.g. the second in the chorus is prior to the third in the chorus, and the next-to-bottom string is prior to the bottom one, for in one case the chorus leader is the arche, and in the other, the middle string,” Meta. Δ.11, 1018b26-29
To refute Aquinas as you undertake to do, you need counterexamples where the text establishes that a given “ordo” consists of members that are not ranked among themselves by intervals up to a highest, supreme member.
Tell me if I’m running off the rails here.
On the other hand, just a quickie: I think Aquinas’ argument about soul/body ordering omits the obvious point that faculties of soul that serve vegetative functions are not under the control of reason. We don’t exercise “prohairesis” about our digestive processes, etc. And yet the vegetative functions are ordered below the rational ones because they contribute much less to the fulfillment of our nature. So that example of Aqu’s is not really apposite, as I see it.
And anyway, your post goes straight to the heart of one of the issues I’m grappling with, which concerns exactly what is true of the different kinds of groupings we find in these guys, esp. genus, species, order/ordo, and some other sorts of groupings. **
Um, wow! If you offer your “quickie” re “ordo” and “ordinare” as indeed a “quickie,” I quake at the thought of what I might encounter if you were to offer a “slowie.” So let me ponder your comment a bit before replying.
Well, I had a good typing teacher in 8th grade.
This AM came across pertinent stuff on “ordo” in Summa Contra Gentiles I.42. Aquinas talks a lot about how the items in an ordo are ranked with respect to each other, in position, according to a scheme imposed by or dependent on the supreme, head item. The text is available on the same Priory website that you linked for the text of Aq’s Arist in libr Meta Comm.
So, David, you have raised several important issues. I’d like to try to address them one at a time. You begin by pointing to a distinction, in Aristotle and Aquinas, between an order and a series. Let me begin by focusing on what you have to say about an order, deferring for the time being a discussion of what a series is.
You think of an “order,” first, as a set of things ordered, or “ranked relatively to each other by a priority among them,” “according to their distance from” a first member, “the head item.” I take it that the “head item” is the first member of the set of ranked things. Then, however, you state that, “by definition,” there is not only a first member of the ordered set (the one in first place) but also a last member of the ordered set (the one in last place). I assume, if somewhat hesitantly, that the “by definition” entails that in all cases an order has a first and a last member.
Whether you do or do not hold that all orders have first and last members, it seems to me that you have not pointed to all of the pertinent possibilities, for there are four, not just the one or two I think I see you pointing to. It is, that is, my “working” hypothesis the it is logically, or, more precisely, ontologically possible for an ordered set O to be such that:
1. Set O both has a first member and has a last member; the set of points on a finite straight line can serve as an illustration;
2. Set O has a first member but does not have a last member; the set of points on a straight line infinite in but one direction can serve as an illustration;
3. Set O does not have a first member but has a last member; the set of points on a straight line infinite in but the other direction can serve as an illustration; or
4. Set O does not have a first member and does not have a last member; the set of points on a straight line infinite in both direction can serve as an illustration.
If it is known, then, that there is some ordered set, it seems to me incumbent upon the one who would assert that it falls into, or does not fall into, one of the four kinds of ordered sets to provide a proof that that it does, or does not. Even more, then, is it incumbent upon those who would assert that no ordered set can be without a first member or without a first and a last member, to provide a proof that that is the case.
Hello Richard, your four possibilities are set forth very clearly.
I don’t know enough about “ordines” in Aristotle or Aquinas to know whether, in either man’s view, an “ordo” can lack either a first member or a last member or both. From what I’ve read so far, I should think they’d allow only your #1 to satisfy the requirements for being an ordo. It might be that some ordines would have a lower terminus consisting of many individuals, so that it becomes indistinct which individual would truly occupy the last slot, esp. if the number of them could be infinite (your #2). Aquinas might say that by reduction, many individuals can be treated as though one, as e.g. in his example of many men pulling a ship; their coordinated action by reduction can be treated so that the men count as one collective mover in the ordo of movers.
I haven’t found a discussion in either Ari or Aq of enough depth to know whether either man tried to prove that no ordered set can be without a first member or without a first and last member. I’ve only seen discussions where the definition of ordo seems simply to be posited.
As for your earlier example of father and mother ordered with respect to the end of raising the child but not with respect to each other, I guess one might say that the goal of child rearing is what I called the head item, and the two parents collectively are the last item. Again, I’m not sure that picture fits A’s or A’s conception of an order, but I don’t know enough right now to say.
I think it plausible that the four distinct possibilities in fact represent four different types of orders and that there may well be good reason to hold that the first is the order that causality in some strict sense exhibits. There may, in other words, be some good reason to hold that there is an uncausing caused only if there is an uncaused causing. But I have not grasped what that good reason might be. One of my hopes is that, in the course of reading and pondering the thought of Thomas and those of folks like you, I might see what it might be.
By the way, in one of your earlier responses, you briefly pointed to the possibility of an order of which the first member and the last member are identical. Now, in this response, you are briefly pointing to the various possibilities re the number of intervening members in orders in which the first member and the last member are not identical: there may be no intervening members, there may be one, two, or any finite number of intervening members, or there may be an infinity of them. I like to think that Aristotle would give his full blessing to such a setting out of the full range of pertinent possibilities as part of the dialectical process.
I should specify that I haven’t found a text in which Aquinas says that a group of men pulling a ship count as one member of an ordo of movers. But I suppose we could imagine a scenario in which they are such – ship owner or someone being the head item, and so on. Aquinas does explicitly give as an example of an ordo an army: general | tribune | soldiers, who exemplify an “ordinem agentium sive moventium,” ST 1a2ae Q. 109, art. 6.
It is fascinating to consider whether a group counts as an ordo if it does not have both a first and a last member. I presume this question is pertinent to cosmological arguments from motion or cause. Thanks for raising it.
I think it’s important to think of an ordo as a “ranking.” That English word fits the way I see the term used. You raised the question re Aquinas’ desire to rank knowledges so that there is one supreme one, which must rule the others.
Since “scientia” is not “of” individuals or accidents, I’m not sure that there is an infinite number of scientiae ranked beneath “first philosophy” or “wisdom.” Would Aristotle want an infinite number of universals to serve as their objects? But I can’t right now think of an argument by which the number of scientiae below 1st philosophy must be finite. If the types of musical instruments are infinite in number, let alone species of organisms, then perhaps we have to allow an infinite number of scientiae. ???