Aquinas’s Argument That Wisdom Is the Ruler of the Other Sciences. A Critical Assessment

0. This post is the fifth in a series dedicated to a sustained reading of and commentary upon Aquinas’s Commentary on the Metaphysics of Aristotle. In my post of July 16, 2017, “Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment,” the second such post, I presented a critique of one of the several arguments present in the opening paragraph of Aquinas’s “Prologue” to his commentary, the one of which he gave the most explicit and easily understood statement. The paragraph in question reads:

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.

The argument critiqued in the July 16 post, so “regimented,” i.e., so simplified and rephrased as to make more fully evident its logical essentials, reads as follows:

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 took it to be sufficiently evident for the purposes at hand that the 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. But I did not take it to be as 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 thought it evident that it is false and offered argumentation in “Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment” to that effect, to which argumentation I refer you. I also noted, on the other hand, that the fact of the argument’s not being sound does not by any means entail that its conclusion is false.

1. In today’s post I propose to offer a similarly critical examination of the paragraph’s main argument, an argument discernible in the paragraph’s last sentence.

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.

Now, it seems to me that the argument that can therein be discerned is:

The ruler of the other sciences is wisdom.
One of the sciences is the ruler of the other sciences.
Therefore, one of the sciences is wisdom.

2. My revision of Aquinas’s statement of the minor premise of the argument,

[O]ne of these sciences and arts must be the mistress of all of the others.

as

One of the sciences is the ruler of the other sciences.

is done simply in order to remain consistent with the choice I have made of “ruler,” rather than the paragraph’s alternatives of “governor,” “director,” and “mistress,” as the means of expressing the relationship of authority at hand.

At any rate, that minor premise follows from the conclusion of the argument examined in “Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment” and reproduced early on in this post:

The set of the sciences is a set of things one of which must rule the others.

The argument having that proposition as its premise and the minor premise at hand as its conclusion is:

The set of the sciences is a set of things one of which must rule the others.
Therefore, one of the sciences is the ruler of the other sciences and arts.

Fully expressed, this argument too is somewhat complex. But I will assume it to be evident that the argument is valid.

3. Let us turn now to the major premise of the paragraph’s main argument. In Aquinas’s own words, the premise reads as:

[O]ne of these sciences and arts must be the mistress of all the others, and this one rightly lays claim to the name of wisdom….

As somewhat regimented, it reads:

The mistress of all of these sciences rightly lays claim to the name of wisdom.

or, as further regimented:

The mistress of all of these sciences is wisdom.

With one more step in its regimentation, we have:

The ruler of the other sciences is wisdom.

4. This premise too requires that an argument be made on its behalf; there needs to be a middle or mediating term between the subject and the predicate of the conclusion. Inspection of the paragraph reveals, however, but one candidate for the role of the needed premise for the argument:

[I]t is the office of the wise man to direct others.

But the argument that we then have

[I]t is the office of the wise man to direct others.
Therefore, the ruler of the other sciences is wisdom.

is far from complete; it is lacking the additional premises that any valid argument for the given conclusion must include.

This is not to claim, clearly, that a valid, and indeed sound, argument involving the premise and the conclusion we have cannot be elaborated. Nor is it by any means to claim that the conclusion is false. But it is to claim that it is not evident that the main argument of the first paragraph of Aquinas’s “Prologue” to his Commentary on the Metaphysics of Aristotle is one justifying its conclusion.

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])

This edition of Aquinas’s text is serving 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:

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Aquinas on the First Principles 1

Do I contradict myself?
Very well, then, I contradict myself,
(I am large, I contain multitudes.)
Walt Whitman, “Song of Myself”

0. This post is the fourth in a series dedicated to a sustained reading of and commentary upon Thomas Aquinas’s Commentary on the Metaphysics of Aristotle (as its subtitle indicates, I think of my immediately preceding “postlette,” “Metaphysical Pluralism. An Appendix to ‘The Principle of Metaphysical Realism’,” as but an appendix to the full post immediately preceding it, and not itself a full post.). In the post that I identify as the third in this series, “The Principle of Metaphysical Realism,” I presented the principle in question, that

There is at least something.

or that

At least something exists.

as “the utterly basic, and thus absolutely first, principle of metaphysics,” prior even to the principles of non-contradiction and excluded middle most often, if not always, identified by the Aristotelian tradition in philosophy as the “first principles.” I further presented it as one basis for identifying the philosophical perspective motivating After Aristotle as Aristotelian or, at least, neo-Aristotelian in nature. In the postlette immediately following that post, I went on to point out that the philosophical perspective motivating After Aristotle accepts not only the principle of metaphysical realism but also the thesis of metaphysical pluralism, that

At least one being is an existent and it is not the case that at most one being is an existent.

or, more briefly

There are at least two beings.

or, yet again, though I there neglected to offer this version

There are many beings.

Finally, in the same postlette, I went on to offer a statement of the thesis I identify as that of philosophical dynamism, that

At least one being is a changing being.

as another thesis which the philosophical perspective of this blog shares with the Aristotelianism, or Aristotelianisms, of Aristotle and Aquinas. I could have, and probably should have, gone on to take the obvious step of affirming the thesis of pluralistic dynamism, that

There are many changing beings.

But I did not.

1. In the present post I want to move on to offer a part of the discussion of the principles of non-contradiction and excluded middle which I promised in “The Principle of Metaphysical Realism” would be forthcoming; in the next post I’ll offer its continuation, relating the principles as formulated here to their formulations in a mode reflective of a more contemporary conception of logic.

I’ll begin with statements of the two principles as metaphysical principles, i.e., as principles bearing upon beings. The metaphysical principle of non-contradiction is the principle that:

No being can both be and not be, in any one respect and at any one time.

The metaphysical principle of excluded middle is the principle that:

Any being must either be or not be, in any one respect and at any one time.

Understand that the “be” of “be and not be” and “be or not be” is taking the place either of “be a being” or “be an existent” or of “be a being of a certain kind,” as in, for example

Venus exists.

and

Venus is the Morning Star.

2. The statements that Aquinas, like Aristotle before him, offers of these principles are not always similar in expression to those I have just offered. In some cases, of course, their expressions, though dissimilar, are perfectly equivalent. Thus, for example, in his Comment 600, in Lesson 6 of his commentary on Book IV of the Metaphysics, speaking of Aristotle’s notion that (Comment 599) “the most certain or firmest principle should be such that there can be no error regarding it; that it is not hypothetical; and that it comes naturally to the one having it,” Aquinas says*

Then he indicates the principle to which the above definition applies. He says that it applies to this principle, as the one which is firmest: it is impossible for the same attribute both to belong and not belong to the same subject at the same time. And it is necessary to add “in the same respect”; and any other qualifications that have to be given regarding this principle “to meet dialectical difficulties” must be laid down, since without these qualifications there would seem to be a contradiction when there is none.

I’ll take it to be sufficiently evident for our purposes that Aquinas’s formulation of the principle of non-contradiction, as

[I]t is impossible for the same attribute both to belong and not belong to the same subject at the same time [and…] in the same respect….

is equivalent to the formulation I offered above, in that the one is true if and only if the other is.

3. But not all statements of a principle identified as that first principle are equivalent to that formulation. There is, for example the statement of “the most certain of all opinions” that we can read in Comment 718, in Lesson 15 of his commentary on Book IV of the Metaphysics.

He accordingly says, first (381), that it is clear from the above statement that the most certain of all opinions or views is the one which states that opposite statements or propositions, i.e., contradictory ones, are not true at the same time.

The doctrine, however, that contradictory propositions cannot both be true, at the same time, etc., is not a metaphysical doctrine, one bearing upon extra-mental and extra-linguistic reality. Rather, it is a logical doctrine, bearing upon, first, propositions and then statements, mental realities and linguistic realities respectively. We have to distinguish, that is, between the metaphysical principle of non-contradiction and the logical principle of non-contradiction. The one is prior to the other: it is because, in reality, no being can both be and not be, in any one respect and at any one time, that no two propositions, one of which affirms something and the other of which denies it, can be both true.

We find Aquinas similarly offering a statement of the logical principle of excluded middle, rather than one of the metaphysical principle of excluded middle, in Comment 720, in Lesson 16 of his commentary on Book IV of the Metaphysics.

He [Aristotle] says … that, just as contradictories cannot be true at the same time, neither can there be an intermediate between contradictories, but it is necessary either to affirm or deny one or the other.

And I respond similarly: The doctrine that one of two contradictory propositions must be true, at the same time, etc., is not a metaphysical doctrine, one bearing upon extra-mental and extra-linguistic reality. Rather, it is a logical doctrine, bearing upon, first, propositions and then statements, mental realities and linguistic realities respectively. We have to distinguish, that is, between the metaphysical principle of excluded middle and the logical principle of excluded middle. The one is prior to the other: it is because, in reality, any being must either be or not be, in any one respect and at any one time, that of two contradictory propositions, one affirming something and the other denying it, one or the other, but not both, must be true.

In brief, a logical doctrine, bearing upon propositions, and a metaphysical doctrine, bearing upon real beings, have to be distinct, because propositions and real beings are distinct.

4. Now, like the principle of metaphysical realism, the principles of non-contradiction and of excluded middle are not principles that can simply go without saying, for there are those who deny them. There is, of course, the statement of Walt Whitman that serves above as a preface to this post. And there are philosophers of the highest stature who deny them. Thus the striking statements of the pre-Socratic philosopher, Heraclitus of Ephesus (who “flourished,” as they say, circa 500 BCE)**:

110. Into the same rivers we step and do not step. We exist and we do not exist.

113. It is one and the same thing to be living and dead, awake or asleep, young or old. The former aspect in each case becomes the latter, and the latter becomes the former, by sudden unexpected reversal.

And in contemporary philosophy, there is the thesis of “dialetheism.” In their article, “Dialetheism,” in The Stanford Encyclopedia of Philosophy,*** Graham Priest, perhaps the foremost of its proponents, and Francesco Berto describe it as follows:

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as one’s favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

Dialetheism is the view that there are dialetheias. One can define a contradiction as a couple of sentences, one of which is the negation of the other, or as a conjunction of such sentences. Therefore, dialetheism amounts to the claim that there are true contradictions. As such, dialetheism opposes the so-called Law of Non-Contradiction (LNC) (sometimes also called the Law of Contradiction). The Law can, and has been, expressed in various ways, but the simplest and most perspicuous for our purposes is probably the following: for any A, it is impossible for both A and ¬A to be true.

If, of course, there are true contradictions, then there have to be things which, in an Aristotelian formulation, both be and not be, in the same respect and at the same time. And similarly, if there are true denials of the principle of excluded middle, then there have to be things which, in an Aristotelian formulation, need neither be nor not be, in the same respect and at the same time.

5. One of the primary aims of this series of posts on Aquinas’s commentary on Aristotle’s Metaphysics has to be that of replying to the vision of thinkers like Heraclitus and Graham Priest. I plan to do this as the opportunities for doing so arise as I work my way through the commentary. For now, let me close the present post by observing that this blogger’s philosophical perspective is in complete accord with that, or those, of Aristotle and Aquinas in its recognition of the principles of non-contradiction and excluded middle as essential philosophical truths.

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])

This edition of Aquinas’s text is serving 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:

** William Harris, “Heraclitus. The Complete Fragments.”
http://community.middlebury.edu/~harris/Philosophy/heraclitus.pdf. Accessed August 7, 2017.

*** Graham Priest and Francesco Berto, “Dialetheism”, The Stanford Encyclopedia of Philosophy (Spring 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/spr2017/entries/dialetheism/. Accessed August 7, 2017.

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Metaphysical Pluralism. An Appendix to “The Principle of Metaphysical Realism”

0. In my immediately previous post, “The Principle of Metaphysical Realism,” I presented said principle, that

There is at least something.

or that

At least something exists.

as “the utterly basic, and thus absolutely first, principle of metaphysics,” prior even to the principles of non-contradiction and excluded middle standardly identified by the Aristotelian tradition in philosophy as the “first principles.” I further presented it as one basis for identifying the philosophical perspective motivating After Aristotle as Aristotelian or, at least, neo-Aristotelian in nature. In today’s postlette, I’d like to offer a bit of a precision of that identification before moving on, in the next post, to the discussion of the principles of non-contradiction and excluded middle I had promised to put forward.

1. An Aristotelian philosophical perspective, then, be it that of Aristotle, Aquinas, or a quibbler like yours truly, nipping at their heels, is not only to be classified as a metaphysical realism, in the very minimalist sense pointed to by the principle of metaphysical realism, but also, more specifically, as a pluralistic realism. That is, the principle of metaphysical realism, contrasting though it does with the thesis of metaphysical nihilism, that

Nothing exists.

is consistent with both of two very different metaphysical perspectives, that of metaphysical monism and that of metaphysical pluralism.

As a first step in towards the further precision I have in mind, let me restate the
principle of metaphysical realism as the principle that

At least one being is an existent.

A statement of the thesis of metaphysical monism is the conjunction according to which

At least one being is an existent and it is not the case that there is a being which is distinct from, or not identical with, that being.

or

At least one being is an existent and any being whatsoever is identical with that being.

or, again

At least one being is an existent and at most one being is an existent.

2. A statement of the thesis of metaphysical pluralism, on the other hand, will conjoin an affirmation of the first conjunct of the thesis of metaphysical monism with a denial of metaphysical monism’s second conjunct, thus

At least one being is an existent and it is not the case that at most one being is an existent.

or

At least one being is an existent and it is not the case that any being whatsoever is identical with that being.

3. That is

At least one being is an existent and at least one other being too is existent.

or, more briefly

There are at least two beings.

or, yet again, making use of a bit more of the apparatus of modern logic in its expression

There is a being x and there is a being y, and being x is not identical with being y.

Again, it is at least in principle possible for there to be the metaphysical theory that

There are at least two beings and there are at most two beings.

or

There is a being x, there is a being y, such that being x is not identical with being y and, for any being z, either z is identical with x or z is identical with y.

So, too, for three existents, the “at least” variety

There is a being x, there is a being y, and there is a being z such that being x is not identical with being y, being x is not identical with being z, and being y is not identical with being z.

and the “at most” variety

There is a being x, there is a being y, and there is a being z such that being x is not identical with being y, being x is not identical with being z, being y is not identical with being z, and, for any being w, w is identical with x, w is identical with y, or w is identical with z.

Etc. The answer to the question, central and difficult, of whether, for an Aristotelian philosophical perspective, there is not just a finite number but an infinite number of beings, is one that I am not yet prepared to claim that I know the answer to, though I am inclined in the direction of infinitism.

4. The foregoing is sufficient to demonstrate that the philosophical perspective animating this blog is, in that it is metaphysically pluralist as well as metaphysically realist, at least to that extent consistent with the philosophical perspectives of Aristotle and Aquinas. Not all philosophical perspectives are.

A yet more complete demonstration of the coincidence of the philosophical perspective animating this blog with that or those of Aristotle and Aquinas is ready to hand. That is, I need only point out that it, like they, is a philosophical dynamism, affirming the thesis that

At least one being is a changing being.

You will almost certainly have immediately seen where that thesis fits in the array of possibilities, contradicting as it does the thesis of philosophical staticism, according to which all beings are static and unchanging, or

No being is a changing being.

Etc. The answer to the question, central and difficult, of whether, for an Aristotelian philosophical perspective, it is the case that

All beings are changing beings.

or it is the case that

At least one being, i.e., God, is not a changing being.

is one that I am not yet prepared to claim that I know the answer to.

Until next time.

Richard

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The Principle of Metaphysical Realism

0. This post is the third in a series dedicated to a sustained reading of and commentary upon Aquinas’s Commentary on the Metaphysics of Aristotle. In the immediately previous post, I spelled out and then criticized one of the very first arguments Aquinas put forward in his “Prologue” to the work; in fact, he set forth a statement of one of the argument’s two premises in the prologue’s very first sentence. To here make the long story short, I there declared it evident that the argument is valid, on the one hand, but not evident that the argument is sound; I even went so far as to declare it to be evident that the argument is unsound. I further noted, however, however, that that, by itself, does not entail that its conclusion is false. For the long story, I refer you to the previous post.

Now, the initial impression one might have from a reading of the immediately previous post is that I am writing from a non-Thomistic and non-Aristotelian point of view, or even from an anti-Thomistic and anti-Aristotelian standpoint. In this post and the two immediately following it, then, I want to offer an at least partial response to that impression, before returning to the primary purpose of the series.

The response will first, in this post and the next one, point to some of the fundamental ways in which the philosophical perspective motivating this blog is in agreement with the Aristotelianism of Aristotle and Aquinas. These points of agreement are such, I believe, that the “Aristotelian” of the “neo-Aristotelian” of the tag, “Analyses and Essays from a Neo-Aristotelian Point of View,” at the top of this page is fully justified.

The response will then, in the succeeding post, point to some of the fundamental ways in which this blog’s philosophical perspective is in disagreement with that of Aristotle and Aquinas. These points of disagreement are such that the “neo” in “neo-Aristotelian” is justified. (I’ll note in passing that I adopted the “neo” for lack of a better prefix; “amended Aristotelianism” would have been a more fully descriptive tag, but I find it somehow lacking. I’m open to suggestions.)

1. In the Aristotelian tradition, much is made of the so-called “first principles,” specifically the principle of non-contradiction and the principle of excluded middle, sometimes identified as the principle of excluded third. I’ll take them up in the next post.

It turns out, however, that the principles the tradition has identified as the first principles are not absolutely first, for there is at least one prior to them. That is, the utterly basic, and thus absolutely first, principle of metaphysics is one that I like to identify as the “Principle of Metaphysical Realism.” It is the principle that:

There is at least something.

or that:

At least something exists.

2. There are those who deny it. Take, for one example from twentieth-century popular culture, the Beatles’ song, “Strawberry Fields Forever,” wherein we can hear:

Nothing is real.**

On a somewhat more serious note, there is the thought of the Greek sophist, one Gorgias of Leontini (ca. 483-376 B.C.E.). As reported by Sextus Empiricus (160-210 C. E.) in his Against the Schoolmasters, Gorgias squarely rejected the principle of metaphysical realism in the first of the three headings found in the following:

In what is entitled On the Nonexistent or On Nature he [Gorgias] proposes three successive headings: first and foremost, that nothing exists; second, that even if it exists, it is inapprehensible to man; third, that even if it is apprehensible; still it is without a doubt incapable of being expressed or expressed to the next man.**

Let us agree to call the Gorgias’s denial of the principle of metaphysical realism the thesis of metaphysical nihilism.

3. The falsity of the thesis of ontological nihilism will most likely seem as utterly obvious to you as the truth of the principle of ontological realism did. And you will have guessed, from the use of the words “principle” and “thesis,” which one I hold to be true and which one false. But we should not be quick to simply dismiss the thesis, for there are prominent thinkers today who hold to a doctrine closely akin to that of ontological nihilism. When, for example, we reflect upon the first four words in the title of physicist Lawrence Krauss’s bestselling A Universe from Nothing: Why There Is Something Rather Than Nothing***, we can see that they announce or entail the following theses.

At one time, there was nothing.

At that time, therefore, there was no cause in existence which could bring things into existence.

At the present time, there are some things in existence and which have come into existence.

At or prior to the present time, therefore, there are or have been some things in existence which have come or came into existence both from nothing and caused by nothing.

4. More than seven centuries ago, however, Aquinas had already offered a reply to Krauss’s thesis. This he does in his statement of the famous third way, i.e., argument for, or (at least attempted) proof of, the existence of God. In the course of the argument, he takes up the supposition that “at some time nothing existed in the world” and its implication.

But if this [that “at some time nothing existed in the world”] were true, then nothing would exist even now. For what does not exist begins to exist only through something that does exist; therefore, if there were no beings, then it was impossible that anything should have begun to exist, and so nothing would exist now—which is obviously false.#

The argument is complex and difficult. Because, however, I am bringing it up simply to document Aquinas’s upholding of the principle of metaphysical realism, I will defer any substantive discussion of the doctrines of causality and of time at work in it to subsequent posts.

5. I trust, then, that any impression that one might have from a reading of the post immediately previous to this one that I am writing from a non-Thomistic and non-Aristotelian point of view, or even from an anti-Thomistic and anti-Aristotelian standpoint, has been at least partially allayed, if only partially; I share with them the affirmation of the principle of metaphysical realism.

Until next time.

Richard

* http://www.azlyrics.com/lyrics/beatles/strawberryfieldsforever.html.

** Sextus Empiricus, Against the Schoolmasters, vii, 65-87. https://users.wfu.edu/zulick/300/gorgias/negative.html. Accessed July 22, 2017.

*** Lawrence Krauss, A Universe from Nothing: Why There Is Something Rather Than Nothing (New York: Free Press, 2012).

# I like the ongoing translation of the Summa Theologiae by Alfred J. Freddoso, subject to ongoing revision though it may be. It can be found at https://www3.nd.edu/~afreddos/summa-translation/TOC.htm. The passage quoted above is at https://www3.nd.edu/~afreddos/summa-translation/Part%201/st1-ques02.pdf.

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Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment.

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:

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Reading Aquinas’s Commentary on the Metaphysics of Aristotle. Introduction

One of the greatest works in the history of metaphysics is the Commentary on the Metaphysics of Aristotle of Thomas Aquinas. It is a work that I have longed for decades to read in the sustained and systematic way that a reading appropriate to such a work requires. Though, however, I have had a few false starts, I have never, for reasons compelling and others not so compelling, definitively set aside the time needed for that kind of reading. But I am now determined to set aside that time and undertake that reading. Not alone, however. I am establishing as one of the core threads of After Aristotle a series of posts setting forth some of the reflections that my readings of Aquinas’s commentary give rise to.

I say “my readings, in the plural,” of the commentary for two reasons. The first is that I of all people should understand that no one reading of a major work in philosophy, and perhaps more so this one than others, is enough for its full understanding. So the reading plan I have in mind includes, first, an initial reading and then one or more rereadings that will follow. Whatever will be the nature of any end result of any subsequent rereadings, the first reading will not be one in which I read and comment upon the text of Thomas in the way he does upon that of Aristotle, beginning at the beginning and proceeding line by line, passage by passage, and argument by argument, through the work until its end.

Rather, I foresee myself often understanding a line, a passage, or an argument but partially, if at all, and having to return to it later on. Thus, for example, the very first paragraph of Thomas’s “Prologue” contains several arguments; I count five. As of this writing, I on the one hand can understand and spell out and assess one of them quite to my satisfaction; this will serve as the focus of the next post. One of them, on the other hand, leaves me fairly baffled and incapable of any fully intelligible commentary on it; I think, and you might well say, “Of course you do,” that the problem lies in the argument and not in my understanding, but I do not claim to know that. And then there are the others, between the two hands. It is my hope that by the time I complete the first reading of Aquinas’s commentary, assuming that such a time ever arrives, I will be able to return to that first paragraph and offer something of a full commentary upon it. Before then, however, in this first reading, there will be much that I will have to pass over.

The second reason I spoke above of “my readings,” in the plural, of the commentary is that, even in, or especially in, my first reading, I will be reading and rereading the text and going back and forth between earlier passages, already subjected to one or more readings, and later passages that may shed light on them. I may well have to modify, add to, or delete from what I may have said in an earlier post.

One more note should be enough at this point. It is that I will also be reading and rereading the commentary in conjunction with other works, works by Aristotle, Aquinas and others, even others whose thinking is widely at variance with the Aristotelianisms of Aristotle and Aquinas; Ockham, Frege, Russell, and Quine come readily to mind. I will feel free to engage in occasional forays departing from immediate contact with the texts of Aristotle or Aquinas.

This is a project which will, should fortune smile upon me, keep me happily engaged for some years, certainly more years than it took Aquinas to write his original. It is my deepest hope that others will accept the invitation I hereby extend to enjoy it with me and to offer to me any comments, questions, suggestions, or critiques that they think what I have said might call for.

I will be using as my text St. Thomas Aquinas, Commentary on the Metaphysics of Aristotle, translated and introduced by John P. Rowan and with a preface by Ralph McInerny (Notre Dame, Indiana: Dumb Ox Books, 1995). It includes a translation of the version (or versions) of Aristotle’s text that Thomas commented upon, differing here and there and in varying degrees from the Metaphysics we know today.

The same Rowan translation of Thomas’s commentary is available online, along with and facing the original Latin, 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:

Until next time.

Richard

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Matthew Wright on Intelligent Aliens

One of my favorite blogs is Matthew Wright’s Matthew Wright. A post illustrating nicely why I enjoy what he writes is the “Are we so arrogant to suppose [intelligent] aliens will be like us?” appearing yesterday.

In the present post I respond (1) positively to what Wright says before answering the question his title poses and (2) negatively to his negative answer.

1. First, what Wright says before answering the question his title poses: He observes, then, that at the time, decades ago, when Winston Churchill, Arthur C. Clarke, and the British Interplanetary Society were thinking about the question of intelligent alien life,

[T]he question was whether there were actually extra-solar planets at all. And if there were, did they host life? But it had a twist – one we don’t often realise. The questions were also posed around the unspoken assumption of ‘one planet, one intelligent alien species’.

A bit further on we find him observing and then ruminating as follows.

[W]e have a sample size of precisely one [that of evolution on the earth], so it’s risky to generalise. Who says that a planet will produce just one intelligent species? Maybe every species on a planet emerges with human-scale intelligence. Or maybe none evolve.

We can see therein that Wright knows how to use logic to free us from the limits of our unspoken and unexamined assumptions and bring all of the available theoretical possibilities out into the open. He has, for example, set before us, as one logical possibility deserving consideration, the universal affirmative proposition (lightly revised) that:

All species emerging on a particular planet are species having human-scale intelligence.

Now, elementary logic teaches us, let us take note, and Wright is evidently aware that alongside any universal affirmative proposition there are to be found universal negative, particular affirmative, and particular negative propositions having the same subjects and predicates. Thus he also sets before us, as another logical possibility deserving consideration, the universal negative proposition (also revised, albeit not so lightly) that:

No species emerging on a particular planet are species having human-scale intelligence.

Granted, he did not spell out the particular negative proposition contradicting his universal affirmative proposition, but we can do that for him quite easily.

At least one species emerging on a particular planet is not a species having human-scale intelligence.

Nor did he spell out the particular affirmative proposition contradicting his negative affirmative proposition, but we can, once again, do that for him quite easily.

At least one species emerging on a particular planet is a species having human-scale intelligence.

We can further advance his cause by taking note of the conjunction, in reverse order, of the last two propositions:

At least one species emerging on a particular planet is a species having human-scale intelligence and at least one species emerging on a particular planet is not a species having human-scale intelligence.

In asking, however, who it is who says that a planet will produce just one intelligent species, he himself is the one who brings to light yet another possibility, the conjunction

At least one species emerging on a particular planet is a species having human-scale intelligence and at most one species emerging on a particular planet is a species having human-scale intelligence.

So far, so good.

2. But only so far, for I think that, when he goes further and answers his question negatively, he goes too far. I part ways with him when he tells us that

I figure that once we do find alien life, it’ll be like nothing we imagined. And that includes the nature of any intelligence. Just as we’ve often imagined ‘aliens’ as being, in effect, mirror images of ourselves, we usually also suppose that ‘their’ intelligence will express itself like ours – inquisitive, actively seeking to expand the boundaries of knowledge and exploration – but will it? Who says ‘their’ intelligence will be like ‘ours’ at all? It might be so different we don’t even recognise it as such, or view the products of their intellect as a ‘civilisation’.

for, in setting forth what he takes to be the possibility that alien intelligence will be unlike human intelligence at all, he has actually set forth an impossibility. To make that evident, I will first ask that you recall the following, necessarily true principles of the theory of identity:

The Principle of Reflexivity: For any existent, x, x is identical to x.

The Principle of Symmetry: For any existent, x, and any existent, y, if x is identical to y, then y is identical to x.

The Principle of Transitivity: For any existent, x, any existent, y, and any existent, z, if x is identical to y and y is identical to z, then x is identical to z.

To instantiate:

The Principle of Reflexivity: Matthew Wright is identical to Matthew Wright.

The Principle of Symmetry: If Matthew Wright is identical to the blogger blogging at the Matthew Wright blog, then the blogger blogging at the Matthew Wright blog is identical to Matthew Wright.

The Principle of Transitivity: If Matthew Wright is identical to the blogger blogging at the Matthew Wright blog and the blogger blogging at the Matthew Wright blog is identical to the author of the sci-fi novella, Missionary, then Matthew Wright is identical to the author of the sci-fi novella, Missionary.

Now, I will declare without hesitation, that if a purportedly intelligent being, alien or indeed non-alien, is incapable in principle of grasping the truth of those three principles and of their instantiations, then it is impossible for that purportedly intelligent being to be a genuine intelligent being. (I say, “in principle,” because life presents many de facto circumstances, such as variously caused cases of unconsciousness, that may prevent an intelligent being from grasping such truths.) Any and all intelligent beings will be beings that will be capable in principle of recognizing the truth of our three principles and of untold many others.

Until next time.

Richard

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