Conceiving of Exceptions to the First Principles

1. In my immediately previous post, the “First Thoughts on the First Principles” of January 19, 2018, I offered statements of the principles, of non-contradiction and excluded middle, recognized as “first principles” by classical philosophical thought. I further pointed to a passage in Plato’s Apology and a couple of passages in Peter Kreeft’s Socrates Meets Jesus* where at least the principle of non-contradiction makes an appearance. In the present post I will first restate the two principles. I will next take note of the passage in Socrates Meets Jesus, also noted in the preceding post, where Kreeft has Socrates claim that one cannot conceive of an exception to the principle of non-contradiction. I will then proceed to the point of the present post and to the conceiving of exceptions, not to just the one, but to both of the principles, in a most direct way, that of simply negating them.

2. First, then, the principle of non-contradiction is the principle that, quite simply:

No beings can both be and not be (in the same respect and at the same time).

The principle of excluded middle is the principle that, equally as simply:

All beings must either be or not be (in the same respect and at the same time).

Two notes should perhaps be added here. First, the qualification, “(in the same respect and at the same time),” is inserted simply to ward off possible equivocation. A person can be, in different respects, but at one and the same time, both off, because not working, and not off, because his mind is functioning well; the word “off” needs to have the same meaning in its two occurrences. And a person can be, in the same respect, but at different times, both off, because not working, and not off, because working.

Second, I offered some illustrations of the application of the two principles in the aforementioned “First Thoughts on the First Principles.”

3. On now to the passage in Kreeft’s Socrates Meets Jesus where he has his Socrates claim that one cannot conceive of an exception to the principle of non-contradiction. Closely repeating what I said in “First Thoughts on the First Principles,” the background to the story has Socrates, finding himself, much to his astonishment, alive and well and a student at Have It University in Camp Rich, Massachusetts. In the passage at hand, he is defending the possibility of miracles in a conversation with a Professor Flatland. One part of the conversation reads as follows:

Socrates: Let’s try it another way. You can’t even conceive of an exception of the laws of logic or math, but you can conceive of exceptions to the laws of nature.
Flatland: How’s that? Give an example.
Socrates: All right. You can’t conceive of a man both walking through a wall and not walking through a wall at the same time, can you?
Flatland: No.
Socrates: But you can conceive of a man walking through a wall, can’t you?

4. To make sure that my most direct way of conceiving of exceptions to both of the principles, that of simply negating them, is well understood, I will now illustrate that act of simple negation with a pair of propositions less imposing than our two principles. First, reversing the order in which they usually are presented, let us note that the principle of excluded middle is both a universal proposition, bearing on all beings, and, let us be careful to notice, an affirmative proposition, affirming that they must either be or not be. So too the less imposing proposition:

All humans must be animals.

is both a universal proposition, bearing on all humans, and an affirmative proposition, affirming that all humans must be animals.

Similarly, let us note that the principle of non-contradiction is both a universal proposition, bearing on all beings, and, let us be careful to notice, a negative proposition, denying that they can both be or not be. So too the less imposing proposition, the obverse, as logicians would identify it, of the proposition just reviewed and logically equivalent to it:

No humans can be non-animals.

is both a universal proposition, bearing on all humans, and a negative proposition, denying that they can be non-animals.

5. Now let me go on to deny first the less imposing universal affirmative proposition and then the less imposing universal negative proposition. The denial of the former is:

It is not the case that all humans must be animals.

This, a few moments’ thought will tell you, is equivalent to:

At least one human can not be an animal.

(Note that this is very different from “At least one human cannot be an animal.).

The denial of the less imposing universal negative proposition, of course, is:

It is not the case that no humans can be non-animals.

This, a few moments’ thought will tell you, is equivalent to:

At least one human can be a non-animal.

6. The negations of the more imposing universal affirmative proposition, the principle of excluded middle, and of the more imposing universal negative proposition, the principle of non-contradiction, now beckon. The negation of the principle of excluded middle has to be:

It is not the case that all beings must either be or not be (in the same respect and at the same time).

This is equivalent to:

At least one being can not either be or not be (in the same respect and at the same time).

The negation of the principle of non-contradiction has to be:

It is not the case that no beings can both be and not be (in the same respect and at the same time).

This is equivalent to:

At least one being can both be and not be (in the same respect and at the same time).

7. That’s how easy it is for one, even one who is sure, as I am, that they are without exception, to conceive of exceptions to the principles of non-contradiction and of excluded middle. Actually, it seems to be even easier than that, for I cannot recall an introductory philosophy course that I have taught in which no student advanced the thesis that God, at least, was not bound by the two principles; at least two of my students in the introductory course I am teaching this semester have thought that this might be so.

And, returning to the thesis put forward by Kreeft’s Socrates, that “You can’t conceive of a man both walking through a wall and not walking through a wall at the same time,” I can conceive both that:

There is at least one man who can both be walking through a wall and not be walking through a wall (in the same respect and at the same time).

and even that:

There is at least one man who both is walking through a wall and not walking through a wall (in the same respect and at the same time).

In brief, I can very easily conceive that which I do not believe.

8. Let me go a bit further and enter an area that may be somewhat, shall I say, controversial by affirming that I, along with at least some others, can conceive both that:

There is at least one person who can both be identical with his father and not be identical with his father (in the same respect and at the same time).

and even that:

There is at least one person who both is identical with his father and not identical with his father (in the same respect and at the same time).

(I deal more definitely with the matter here brought up in a post published some time ago (April 4, 2014), “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism.”)

9. A final observation: Let us, at least for present purposes, adopt the name, “rationalism,” as that of the theory for which both the principle of non-contradiction and that of excluded middle are true. Let us then adopt the name, “irrationalism,” as that of the theory which negates them. Next let us note that the negations in question are both particular propositions, i.e., not universal propositions. Finally, let us adopt the phrase, “universalist irrationalism,” as the name of the theory that asserts the universal propositions corresponding to the two particular propositions. The one thesis of the theory, then, is:

All beings can not either be or not be (in the same respect and at the same time).

The other is:

All beings can both be and not be (in the same respect and at the same time).

We have here two more theses contrary to the first principles that you and I can easily conceive, even if we cannot believe them.

Until next time.

Richard

*Peter Kreeft, Socrates Meets Jesus. History’s Greatest Questioner Confronts the Claims of Christ (2nd edition; Downers Grove, Illinois: Intervarsity Press, 2002 [1987])

Should you wish to purchase a copy of Socrates Meets Jesus, you may do so quite easily by clicking on the following image.

Posted in First Principles | Tagged , , , , , , , , , , , , , , , , , , , | Leave a comment

First Thoughts on the First Principles

1. As I noted in the immediately previous post, (1) the coming semester will seem me teaching an “Introduction to Philosophy” course and (2) at least some, if not most, of the posts to come as the semester unfolds will focus on the matters suggested by or explicitly coming up in the conduct of the course.

One reason for doing this is that I would like to introduce the students in my classroom to at least some of the philosophical thinking that goes on online. Another is that I would like to offer to those not in my classroom, or even in any classroom who would like to engage in at least some of the philosophical thinking that goes on in a college-level introduction to philosophy course the opportunity to do so. A third is that I would like to engage with other philosophy instructors in some reflection on just how we can best go about introducing college students or their equivalents to philosophy.

2. Central, of course, to the course are its primary texts. The most primary of the three primary texts in the course at hand is:

Plato, Five Dialogues, translated by G. M. Grube and revised by John M. Cooper (2nd edition; Indianapolis, Indiana, 2002)

The course schedule has the reading of the five dialogues in question (the Euthyphro, the Apology, the Crito, the Meno, and the Phaedo, in that order) taking place over the course of the entire semester.

The other two texts are more or less contemporary, that of Peter Kreeft being the more contemporary, and yet the more traditional, and that of Bertrand Russell being the less contemporary, and yet the less traditional.

Peter Kreeft, Socrates Meets Jesus. History’s Greatest Questioner Confronts the Claims of Christ (2nd edition; Downers Grove, Illinois: Intervarsity Press, 2002 [1987])

Bertrand Russell, Religion and Philosophy, with an introduction by Michael Ruse (Oxford and New York: Oxford University Press, 1997 [1935])

Should you wish to purchase one, two, or all of the texts, you may do so quite easily by clicking on the images of them to be found at the end of this post.

3. A beginning course in philosophy should, it seems, begin at the beginning. It seems apt then that the first topic that I will be introducing in the current set of reflections is that of the “first principles” of non-contradiction and excluded middle recognized as such by classical philosophical thought, and also, though I’m open to some quibbling about whether they are absolutely first, by yours truly. I will first offer statements and, for those not familiar with them, some illustrations of them, and then point to a passage in Plato’s Apology and a couple of passages in Kreeft’s Socrates Meets Jesus where they make an appearance.

4. First, then, the principle of noncontradiction, the principle that:

No being can both be and not be (in the same respect and at the same time).

That which no being can both be and not be can be anything whatsoever. This will be clear as one thinks one’s way through the following illustrations:

a. I cannot both be in a room and not be in that room, at least in the same respect and at the same time. I can, however, both be in the room and not be in the room, in distinct respects, even though at the same time; for example, my left side can be in the room while my right side is not in the room. And I can both be in the room and not be in the room, in the same respect, but at different times.

b. Donald Trump cannot both be guilty of impeachable offenses and not be guilty of impeachable offenses, in the same respect and at the same time. (The same has been true or will be true, I hasten to add, of any other president of the United States of America.)

c. No being can both be a being of some sort or other and not be a being of that sort. Thus, no being can both be a living organism and not be a living organism. Indeed, no being can both be a being (an existent) and not be a being. For example, no divine being can both be a being (an existent) and not be a being.

5. Next, the principle of excluded middle, the principle that:

All beings must either be or not be (in the same respect and at the same time).

That which all beings must either be or not be can be anything whatsoever. This will be clear as one thinks one’s way through the following illustrations:

a. I must either be in a room or not be in that room, at least in the same respect and at the same time.

b. Donald Trump must either be guilty of impeachable offenses or not be guilty of impeachable offenses, in the same respect and at the same time. (The same has been true or will be true, I hasten to add, of any other president of the United States of America.)

c. Any being must either be a being of some sort or other or not be a being of that sort. Thus, any being must either be a living organism or not be a living organism. And, any being must either be a being (an existent) or not be a being. For example, any divine being must either be a being (an existent) or not be a being.

6. The principle of non-contradiction makes an implicit appearance in Plato’s Apology (p. 31 of the Grube and Cooper text) in the course of Socrates’s defense against the charge of atheism that has been brought against him by one Meletus. Plato has Socrates say:

He [Meletus] is like one who composed a riddle and is trying it out: “Will the wise Socrates realize that I am jesting and contradicting myself, or shall I deceive him and others?” I think he contradicts himself in the avadavat, as if he said, “Socrates is guilty of not believing in gods but believing in gods,” and surely that is the part of a jester!

It is evident that Socrates expects his listeners to understand that:

No person can both be a believer in gods and not be a believer in gods (in the same respect and at the same time).

7. The principle of non-contradiction also, as noted above, appears in some passages in Kreeft’s Socrates Meets Jesus. The background to one of them has Socrates finding himself, much to his astonishment, alive and well and a student at Have It University in Camp Rich, Massachusetts (yes, I know). The following exchange with a student, one Bertha Broadmind, takes place (pp. 17-18).

Bertha: Socrates! Is that really you?
Socrates (surprised and pleased): Why, yes. How do you know me? Were you sent here to meet me? I expected a messenger of the gods, but forgive me, you don’t look the part.
Bertha: Oh, Socrates! You’re so—so Socratic! It is you, isn’t it?
Socrates: Of course I am I, unless the law of noncontradiction has been abolished here.

8. In another, more philosophically loaded passage (p. 70), we find Socrates defending the possibility of miracles in a conversation with a Professor Flatland:

Socrates: Let’s try it another way. You can’t even conceive of an exception of the laws of logic or math, but you can conceive of exceptions to the laws of nature.
Flatland: How’s that? Give an example.
Socrates: All right. You can’t conceive of a man both walking through a wall and not walking through a wall at the same time, can you?
Flatland: No.
Socrates: But you can conceive of a man walking through a wall, can’t you?

In a post to appear in the not too distant future, I will have to take exception to the view that one cannot conceive of an exception to the laws of logic, even as I defend those laws, for there are those who reject the thesis of the universal applicability of the one, the other, or both of the first principles.

9. I think, then, that I know how to reply to the thesis that Kreeft has Socrates express in the texts we are just now leaving. But I don’t know quite what to make of the things he has to say about logic and logical principles in a passage in his “Introduction” to Socrates Meets Jesus (pp. 7-8). The first half of the passage reads:

Socrates had no prophets to guide him except the universal prophet of reason. But Christians know that this is not merely a human power but a beam of light from the Son of God, “the true light that enlightens every man (John 1:9), the Logos, the logic of God. In the beginning was the logic, and the logic was with God, and the logic was God. Socrates has only logic, but logic is not a batch of man-made rules for playing a game with concepts as though they are poker chips; logic is the science of the divine nature.

There is more going on here, of course, than just an identification of logic with a part of theology, for that is possible, if it is at all possible, only with a particular conception of logic. I hope one day to be able to turn my attention to his understanding of logic, which may perhaps be discernible in the logic text that he has written and that I have purchased, but not yet read:

Peter Kreeft, Socratic Logic. A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles (Edition 3.1; South Bend, Indiana: St. Augustine’s Press, 2014 [2004])

That is “one day,” not “now.”

Kreeft continues with the second half (p. 8) of the passage:

The law of identity is founded on the real divine identity and immutability. The law of noncontradiction is founded on the unity of the divine nature, the fact that God never contradicts himself. The law of excluded middle is founded on the fact that all either-ors are based on the one God: either God or not God, truth or falsehood, light or darkness, reality or unreality

Here, I must confess, he has left me behind; evidently I am not being enlightened by the requisite beam of light, because I do not quite get the arguments at work here. The argument that, say,

God never contradicts himself.
Therefore, no being can both be and not be (in the same respect and at the same time).

is at the very least missing one or more premises.

I have sent Dr. Kreeft a note asking that he shed some light on the two chunks of text or point to some place where the argumentation has been set out more fully. I will, if and when I receive any help from him (or anyone else), let you know.

Until then.

Richard

As said above, should you wish to purchase one or more of the texts mentioned in this post, you may do so quite easily by clicking on the appropriate of the following images.

Posted in First Principles | Tagged , , , , , , , , , , , | Leave a comment

Postings During the Spring 2018 Semester

The primary reason why I have for some time not published any posts to this blog is that that my teaching responsibilities took over my professional life. There is also a secondary reason, that I have begun seeing a diminishing of the intellectual returns on my efforts at extracting the arguments at work in Aquinas’s “Prologue” to his Commentary on Aristotle’s Metaphysics. But the primary reason is the primary reason and the secondary the secondary.

I have thought, then, that I had to choose between writing for my blog and taking care of my courses and, so thinking, I had to choose the latter. Having, however, reflected over the past couple of weeks on what had happened in the course of the past semester and on what I would like to see happen over the course of the coming semester, I have come to see that my options are not quite so limited. That is, I have come to see that it is quite possible for me to combine my blogging and my teaching activities by writing about matters suggested by or explicitly coming up in my teaching.

It turns out, on the one hand, that I am not teaching a course tightly related to the review I have undertaken of Aquinas’s commentary. I therefore do not foresee my advancing that review any further during the course of the coming semester, though I do envision returning to it once the semester is over. It also turns out, on the other hand, that the coming semester will seem me teaching an “Introduction to Philosophy” course. It is upon matters suggested by or explicitly coming up in my teaching of this course that I have decided to focus the coming posts.

Thus the next post.

Until then.

Richard

Posted in About this Blog | Leave a comment

Aquinas and the Theory of Comparative Intelligence

0. (This post is the tenth in a series dedicated to a sustained reading of and commentary upon Thomas Aquinas’s Commentary on Aristotle’s Metaphysics.*)

I devoted my post of September 19, 2017, “Aquinas’s Arguments for the Thesis That the Science of the Most Intelligible Objects Is Wisdom,” to a review of the primary argument of the second paragraph of the prologue to his commentary. That paragraph reads:

We can discover which science this is and the sort of things with which it is concerned by carefully examining the qualities of a good ruler; for just as men of superior intelligence are naturally the rulers and masters of others, whereas those of great physical strength and little intelligence are naturally slaves, as the Philosopher says in the aforementioned book, in a similar way that science which is intellectual in the highest degree should be naturally the ruler of the others. This science is the one which treats of the most intelligible objects.

I took note of two things in the passage that “immediately command our attention,” the one Aquinas’s seeming acceptance of slavery and the other “the comparatively straightforward statement of the paragraph’s argument” in its closing lines. First, then, those lines again, and that argument:

[T]hat science which is intellectual in the highest degree should be naturally the ruler of the others. This science is the one which treats of the most intelligible objects.

I went on to review the argument, first offering the following formulation of it

The science which is intellectual in the highest degree is the science which is by nature the ruler of the other sciences.
The science which treats of the most intelligible objects is the science which is intellectual in the highest degree.
Therefore, the science which treats of the most intelligible objects is the science which is by nature the ruler of the other sciences.

and then offering an assessment of it as, on the one hand, obviously valid but, on the other, not evidently sound. (Judging that it is not evidently sound is, of course, not the same thing as judging that it is evidently not sound.)

1. The matter of slavery I left for the succeeding post in the series. That post, however, is this post, and I am not yet ready to spell out even a relatively complete argument, let alone a sound or a demonstrative argument, on behalf of the thesis that “those of great physical strength and little intelligence are naturally slaves,” that I would think myself justified in attributing to Aquinas.

One difficulty, of course, in spelling out such an argument, is that so little is presented in the paragraph that could serve as a basis for it. One would, for example, need to know which, if any, of the following propositions express, for Aquinas, the or a necessary condition for a person being by nature a slave:

All persons who are by nature slaves are persons both having great physical strength and having little intelligence.

All persons who are by nature slaves are persons having great physical strength but not having little intelligence.

All persons who are by nature slaves are persons not having great physical strength but having little intelligence.

All persons who are by nature slaves are persons not having great physical strength and not having little intelligence.

Etc.

I don’t have confidence that Aquinas would say, after due reflection, that the first of the options, the one he most nearly gives expression to, really identifies the or a necessary condition for a person being by nature a slave. Having or not having inferior physical strength is not, after all, identified as a necessary condition of being a ruler.

2. But there is at least that context provided in the passage, one in which “men [sic] of superior intelligence are naturally the rulers and masters of others.” Whatever else pertains specifically to the relationship of slave-master, I presume, and slave, the slave-master stands to the slave as ruler to ruled. And the person who is by nature the ruler of another stands to the ruled as the person who is the more intelligent to the person who is the less intelligent.

That, of course, suggests convincingly that, in parallel with the argument spelled out above, concluding that “the science which treats of the most intelligible objects is the science which is by nature the ruler of the other sciences,” Aquinas is committed to the following argument:

The person who is intelligent in the highest degree is the person who is by nature the ruler of the other persons.
The person who is capable of understanding the most intelligible objects is the person who is intelligent in the highest degree.
Therefore, the person who is capable of understanding the most intelligible objects is the person who is by nature the ruler of the other persons.

With his introduction of the notion of superior intelligence and inferior intelligence, etc., Aquinas is committed to a theory of comparative intelligence. It is the task of the present post to spell out some of the basics of that theory of comparative intelligence. Then, in the next post, I intend to weigh the argument just spelled out and concluding that “the person who is capable of understanding the most intelligible objects is the person which is by nature the ruler of the other persons.” And, just perhaps, I may be ready to offer a pronouncement on Aquinas’s apparent acceptance of slavery.

3. To begin, I will assume the following theses to be evident:

It is the case, for any intelligent being, x, and any intelligent being, y, that x is equal in intelligence to y or x is not equal in intelligence to y.

It is the case, for any intelligent being, x, and any intelligent being, y, that, if x is not equal in intelligence to y, then x is greater in intelligence than y or y is greater in intelligence than x.

It is the case, for any intelligent being, x, and any intelligent being, y, that, if x is greater in intelligence than y, then y is lesser in intelligence than x. (Yes, I share your concern about “lesser.” I thought I needed “lesser in intelligence” to preserve parallelism of expression.)

4. Then, there are three fundamental theses bearing on equality of intelligence.

The Thesis of the Reflexivity of Equality in Intelligence: It is the case, for any intelligent being, x, that x is equal in intelligence to x.

The Thesis of the Symmetry of Equality in Intelligence: It is the case, for any intelligent being, x, and any intelligent being, y, that, if x is equal in intelligence to y, then y is equal in intelligence to x.

The Thesis of the Transitivity of Equality in Intelligence: It is the case, for any intelligent being, x, any intelligent being, y, and any intelligent being, z, that, if x is equal in intelligence to y and y is equal in intelligence to z, then x is equal in intelligence to z.

5. There are three fundamental theses bearing on superiority in intelligence:

The Thesis of the Irreflexivity of Superiority in Intelligence: It is not the case, for any intelligent being, x, that x is superior in intelligence to x.

The Thesis of the Asymmetry of Superiority in Intelligence: It is the case, for any intelligent being, x, and any intelligent being, y, that, if x is superior in intelligence to y, then y is not superior in intelligence to x.

The Thesis of the Transitivity of Equality in Intelligence: It is the case, for any intelligent being, x, any intelligent being, y, and any intelligent being, z, that, if x is superior in intelligence to y and y is superior in intelligence to z, then x is superior in intelligence to z.

6. There are two theses bearing on what I’ll dub “the utmost in intelligence”: the one is the Thesis of the De Facto Utmost in Intelligence and the other is the Thesis of the De Jure Utmost in Intelligence.

The Thesis of the De Facto Utmost in Intelligence: For any intelligent being, x, x is the most intelligent being if and only if, for any intelligent being, y, if y is not identical with x, then x is superior in intelligence to y.

The Thesis of the De Jure Utmost in Intelligence: For any intelligent being, x, x is the most intelligent being if and only if it is necessary that, for any intelligent being, y, if y is not identical with x, x is superior in intelligence to y.

7. There are, of course, the theses bearing on inferiority in intelligence analogous to those bearing on superiority in intelligence, including, with a plea for your understanding, those of the De Facto Leastmost in Intelligence and the De Jure Leastmost in Intelligence. I’ll leave the working out of their expression to you.

8. The theory of comparative intelligence is but one application of a broad theory of the comparative. Just to take note of the comparisons that Aquinas’s text has thus far called out for, there are the theories of comparative intellectuality, of comparative intelligibility, and of comparative wisdom. I’ll leave the working out of the expression of these theories too to you.

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, with occasional minor differences, 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:

Posted in Thomas Aquinas's Commentary on Aristotle's Metaphysics | Tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment

An Alternative to “Simultaneous” in the Logic of Priority and Posteriority

I am engaged in some thinking, surely elementary, about logical (or ontological) priority and posteriority and their analogy with temporal priority and posteriority. More specifically, I am thinking that, just as there is the one word, “simultaneous,” meaning “at the same time,” i.e., “neither temporally prior to nor temporally posterior to,” so there could or should be some one word, other than “simultaneous,” meaning “neither logically (or ontologically) prior to nor logically (or ontologically) posterior to.” The contrary thought is that I should just go ahead and use the one word, “simultaneous,” to express “neither logically (or ontologically) prior to nor logically (or ontologically) posterior to.” I will appreciate any suggestions or related thoughts.

The ruminations just noted came up as I thought about Aquinas’s understanding of superiority and inferiority, in the theory of which “equal” holds a place similar to that of “simultaneous” in the theory of time, and, more specifically, about his understanding of causal priority and posteriority.

Once again, I will appreciate any suggestions or related thoughts.

Until next time.

Richard

Posted in Uncategorized | Tagged , , , , , , , | 2 Comments

Aquinas’s Arguments for the Thesis That the Science of the Most Intelligible Objects Is Wisdom.

(This post is the ninth in a series dedicated to a sustained reading of and commentary upon Thomas Aquinas’s Commentary on Aristotle’s Metaphysics.*)

1. In the present post I will first offer, in an at least somewhat summary fashion, the results of the two posts in the present series that bear immediately on the arguments Aquinas has set in front of us in the first paragraph of his “Prologue” to the Commentary. I will next review the prologue’s second paragraph and the argument that it contains. I will then set forth in explicit form the argument which the first two paragraphs taken together present, an argument which Aquinas left implicit.

In, then, my post of July 16, 2017, “Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment,” I offered a “critical assessment” of the most explicitly stated of the several arguments that can be discerned in the first paragraph of Aquinas’s “Prologue” to the Commentary. As “regimented,” i.e., so rephrased as to make more fully evident its logical essentials, the argument 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 that the argument is valid, that is, it is such that, if the two premises are true, the conclusion also 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 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 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.

2. Then, in my post of August 19, 2017, “Aquinas’s Argument That Wisdom Is the Ruler of the Other Sciences. A Critical Assessment,” I offered a “critical assessment” of the first paragraph’s primary argument. As duly regimented, the argument 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.

I took it to be sufficiently evident that this argument too is valid. But I did not take it to be as evident that the argument is also sound, for two reasons. The first is that the minor premise,

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

depends upon the argument examined in “Aquinas’s Argument That One Science Must “Rule” the Others. A Critical Assessment.” And, as I have indicated, though it is evident that that argument is valid, it is not evident that it is sound.

The second reason for my not taking it to be evident that the first paragraph’s primary argument is sound is that the argument for its major premise simply lacks the premise or premises that a valid argument for the given conclusion would require. As regimented, that argument given is:

It is the office of the wise man to direct others.
Therefore, the ruler of the other sciences is wisdom.

I am not saying, of course, that there is no valid or sound argument by which Aquinas, or anyone else, could arrive at that conclusion. Nor am I saying that the conclusion is false. I am simply saying that the complete argument that the valid argument would have to be has not been presented to us, at least not yet.

3. Now, on to the review of the prologue’s second paragraph and the argument that it contains. Remembering that Aquinas has, in the prologue’s first paragraph, concluded that

The ruler of the other sciences is wisdom.

the question now is that of which of the sciences is the ruler of the other sciences. Aquinas according says, in the prologue’s second paragraph:

We can discover which science this is and the sort of things with which it is concerned by carefully examining the qualities of a good ruler; for just as men of superior intelligence are naturally the rulers and masters of others, whereas those of great physical strength and little intelligence are naturally slaves, as the Philosopher says in the aforementioned book, in a similar way that science which is intellectual in the highest degree should be naturally the ruler of the others. This science is the one which treats of the most intelligible objects.

Two things immediately command our attention. The first, of course, is Aquinas’s argument related to ruler and slave. I will spell that argument out in the next post, something of an appendix to the present post, after I address in the present post the second thing that immediately commands our attention, the comparatively straightforward statement of the paragraph’s argument. I approach things in this order because my spelling out of Aquinas’s argument re slavery will depend upon my spelling out of his argument re the ruling science and the subordinate sciences.

I will render the major premise of the paragraph’s argument, which, in Aquinas’s words, is:

[T]hat science which is intellectual in the highest degree should be naturally the ruler of the others.

as:

The science which is intellectual in the highest degree is the science which is by nature the ruler of the other sciences.

This this rendition preserves, I believe, the meaning of the original while rendering it suitable for its role in the argument at hand.

I will similarly render the minor premise, which, in Aquinas’s words, is:

This science is the one which treats of the most intelligible objects.

as:

The science which treats of the most intelligible objects is the science which is intellectual in the highest degree.

The argument, accordingly, is:

The science which is intellectual in the highest degree is the science which is by nature the ruler of the other sciences.
The science which treats of the most intelligible objects is the science which is intellectual in the highest degree.
Therefore, the science which treats of the most intelligible objects is the science which is by nature the ruler of the other sciences.

The argument is, without question, valid. But is it sound? That is, are both of the premises true? It turns out that that has not been made evident in either case. That is, starting with the major premise, we can easily see that, if the science which is intellectual in the highest degree is, or is identical with, the science which is by nature the ruler of the other sciences, that identity, that being by the former of the latter, is not immediate. The major premise itself needs then to be demonstrated. And that demonstration will require, in the terminology of the logical tradition, a “middle term” the designee of which is both that which the science which is intellectual in the highest degree is and that which is the science which is by nature the ruler of the other sciences.

Likewise, turning to the minor premise, we can easily see that, if the science which treats of the most intelligible objects is, or is identical with, the science which is intellectual in the highest degree, that identity, that being by the former of the latter, is not immediate. The minor premise itself needs then to be demonstrated. And that demonstration will require a “middle term” the designee of which is both that which the science which treats of the most intelligible objects is and that which is the science which is intellectual in the highest degree.

It necessarily follows that, given what we have been given so far, it is not evident that that argument is sound. It remains to be seen whether Aquinas, in the prologue or later in his commentary, provides us with what is needed for the demonstrations of the two premises.

4. I turn now to the setting forth, in explicit form, of the argument which the first two paragraphs taken together present, an argument which Aquinas himself left implicit. First, then, we have the conclusion of the first paragraph, which will serve as the major premise of the argument being made explicit:

The ruler of the other sciences is wisdom.

and we have that of the second paragraph, which will serve as the minor premise of the argument being made explicit:

The science which treats of the most intelligible objects is the science which is by nature the ruler of the other sciences.

The subject of the major premise needs to be expanded so as to match the predicate of the minor premise, thus:

The science which is by nature the ruler of the other sciences is wisdom.

This rendition represents another instance of preserving the meaning of the original while rendering it suitable for its role in the argument at hand.

The argument of the first two paragraphs is then:

The science which is by nature the ruler of the other sciences is wisdom.
The science which treats of the most intelligible objects is the science which is by nature the ruler of the other sciences.
Therefore, the science which treats of the most intelligible objects is wisdom.

Once more, it is evident that the argument is valid. But it is not evident that it is sound, for it is not evident that the arguments which have been offered on behalf of its premises are themselves sound.

5. Setting aside the in fact more numerous posts attempting to specify to some initial degree the ways in which the philosophical perspective motivating this blog coincides, and does not coincide, with that or those of Aristotle and Thomas Aquinas, I have thus far in the present series of readings of and commentary upon the latter’s commentary on the former’s Metaphysics reviewed the arguments of the first two paragraphs of the “Prologue.” It is not evident that those arguments are sound, though, with one possible exception (see above), it is evident that they are valid. Sound or unsound, they have led Aquinas to the conclusion that:

The science which treats of the most intelligible objects is wisdom.

An understanding of that proposition depends necessarily upon one of just what the “most intelligible objects” in question are. In the initial sentence of the third paragraph, Aquinas tells us that:

Now the phrase “most intelligible objects” can be understood in three ways.

He accordingly, in the third paragraph and in the two succeeding paragraphs, will spell out those three understandings. In, then, the next post but one in the series, I will review the arguments that Aquinas sets forth in the third paragraph.

In, however, the next post, something of an appendix to the present one, I will turn my attention to the argument, noted above, related to ruler and slave.

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, with occasional minor differences, 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:

Posted in Thomas Aquinas's Commentary on Aristotle's Metaphysics | Tagged , , , , , , , , , , , , , | Leave a comment

Aquinas’s Thesis of the Identity of the Intellect Knowing and the Intellectual Object Known

This post is the eighth in a series dedicated to a sustained reading of and commentary upon Thomas Aquinas’s Commentary on Aristotle’s Metaphysics.*

0. In a previous post, the “Touching upon the Theory of Act and Potency,” of August 23, 2017, I drew attention to a central theory in the holding of which the philosophical perspective of After Aristotle stands in agreement with that or those of Aristotle and Aquinas, the theory of act and potency. I also promised that, in a later post (which I then thought, erroneously, would be the next), I would draw attention to a central thesis in the holding of which After Aristotle’s view differs from those of Aristotle and Aquinas. This is that later post.

1. I need, however, to be a bit more careful than I have been in how I put things. For one thing, the difference at hand consists in the fact, not that I affirm a thesis that Aquinas does not, but that Aquinas affirms a thesis that I do not. For another thing, as I have just signaled in excepting Aristotle, the precise thesis that I have had in mind, one that receives expression in the prologue to and in the first lesson of Aquinas’s commentary on Aristotle’s Metaphysics, is not one that, at least to my knowledge, is to be found in Aristotle, though others closely related are. That thesis of Aquinas is the thesis that, in my words:

The intellect knowing an object is a being identical with the intellectual object known.

Given the distinction between act and potency, and actually being and potential being, which I touched upon in “Touching upon the Theory of Act and Potency,” Aquinas is led to affirm both that, still in my words,

The intellect potentially knowing an object is a being potentially identical with the intellectual object potentially known.

and that

The intellect actually knowing an object is a being actually identical with the intellectual object actually known.

Accepting though I do the theory of act and potency, I do not accept the thesis that the intellect knowing an intellectual object is a being identical with the intellectual object known. In what follows, then, I propose to, first, present two passages of the commentary in which Aquinas affirms the identity in question. Second, I will “regiment” the expression of that affirmation, i.e., so rephrase it that its logical characteristics stand out unequivocally, in order to be able to better point out precisely how Aquinas’s thesis is wrong. Third, I will then point out how Aquinas’s thesis is wrong.

2. The text of Aquinas which I quoted in the previous post and in which Aquinas affirms, though in his own words, both that the intellect actually knowing an intellectual object and the intelligible object actually known are actually identical and that the intellect potentially knowing an intellectual object and the intellectual object potentially known are potentially identical, is that of Comment 2, in the first lesson of Aquinas’s Commentary on Aristotle’s Metaphysics. There, after having reported, in Comment 1, that Aristotle

says … that the desire to know belongs by nature to all men.

Aquinas goes on to say:

Three reasons can be given for this. The first is that each thing naturally desires its own perfection. Hence matter is said to desire form as any imperfect thing desires its perfection. Therefore, since the intellect, by which man is what he is, considered in itself is all things potentially, and becomes them actually only through knowledge, because the intellect is none of those things that exist before it understands them, as is stated in Book III of The Soul [429a23]; so each man naturally desires knowledge just as matter desires form.

The other text in which he offers an affirmation of the identity of the intellect knowing an intellectual object and the intellectual object known, though in this text more specifically of the identity of the intellect actually knowing an intellectual object and the intellectual object actually known, is that of the first half of the fifth paragraph of his prologue to the Commentary. There, speaking of the phrase, “most intelligible objects,” he says:

Third, this phrase can be understood from the viewpoint of the intellect’s own knowledge. For since each thing has intellective power by virtue of being free from matter, those things must be intelligible in the highest degree which are altogether separate, from matter. For the intellect and the intelligible object must be proportionate to each other and must belong to the same genus, since the intellect and the intelligible object are one in act.

In the present post I’ll refrain from dealing with the arguments of the two passages; I will take them up instead as I reach them in the course of the series of posts devoted to the Commentary (to which I pledge to return soon). Besides, the thesis of the identity of the intellect and the intellected object is introduced in the two passages as a premise, and not as a conclusion, of the arguments in them.

3. I’ll take it then as granted that Aquinas has affirmed in the passages quoted that, in my words,

The intellect knowing an intellectual object is a being identical with the intellectual object known.

Next, then, we have the regimentation of that affirmation. So, to begin, let us note that one can reword the thesis that, say,

The human intellect is an immaterial principle of the human person.

as the universal affirmative categorical proposition that

All human intellects are immaterial principles of human persons.

while yet preserving the equivalence of the one to the other; the one is true if and only if the other is true. So too one can reword the more complex thesis that

The intellect knowing an intellectual object is a being identical with the intellectual object known.

as the universal affirmative categorical proposition that

All intellects knowing intellectual objects are beings identical with the intellectual objects known.

4. Now, there are, as it well seems, instances in which it is true that intellects knowing intellectual objects are beings identical with the intellectual objects known, at least if there are intellects knowing themselves. If or as this is the case, then the particular affirmative categorical proposition that

At least some intellects knowing intellectual objects are beings identical with the intellectual objects known.

is true.

But there are also, as it equally well seems, instances in which it is not true that intellects knowing intellectual objects are beings identical with the intellectual objects known. Then the following two equivalent propositions are true, the one the proposition contradicting the above given universal affirmative categorical proposition, viz..”

It is not the case that all intellects knowing intellectual objects are beings identical with the intellectual objects known.

and the other the particular negative categorical proposition

At least some intellects knowing intellectual objects are not beings identical with the intellectual objects known.

5. You may have been looking for at least one example of an intellect knowing an intellectual object and yet not being identical with the intellectual object known. The matter is a bit complicated, but only a bit. So, let’s say that I understand, i.e., have an intellectual knowledge, that the intellectual object sitting in my back yard is a tiger. Then it is the case that

At least one intellect knowing an intellectual object is not a being identical with the intellectual object known.

for I am not, at least not literally, a tiger and neither is my intellect.

From my own Aristotelian philosophical perspective, that observation should be enough in the way of prima facie evidence that Aquinas’s identity thesis is false. But it may be objected that I am presupposing that the tiger sitting in my back yard is as such and simply the intellectual object known, as such and simply the object of the intellect. And some may not accept that presupposition, instead holding that it is not immediately the concrete tiger that is the intellectual object of my intellectual knowledge that the intellectual object sitting in my back yard is a tiger. Rather, that which is the intellectual object in that bit of intellectual knowledge is, not the tiger as such, but the tiger nature by which the tiger is a tiger.

With that precision, however, we still do not have not an exemplification of Aquinas’s thesis, for it would remain that the intellectual object, now the tiger nature, of my intellect’s knowledge is distinct from, not identical with, my intellect.

6. There is much more to be said that is intimately related to the topic of this post, for Aquinas’s identification of the intellect knowing an intellectual object and the intellectual object known, is but a middle position between two relative extremes. On the one hand, there is the thesis that the identity that knowledge is thought to be is not that of the intellect and the object of intellection, but rather that of the intelligent knower and the intellectual object known: the intelligent knower is the intellectual object known. On the other hand, there is the thesis that the identity that knowledge is thought to be is neither one of the intelligent knower nor one of the intellect with the intellectual object known. Rather it is one of the idea, thought, or concept, existing within the intellect and by means of which the intelligent knower and his, her, or its intellect knows and, it is held, is thereby identical with the intellectual known. These theses still require being addressed.

There is, moreover, my own understanding of what is involved in intellectual knowledge. I’ll just state now, and articulate and defend as coming occasions make appropriate, that I am relatively comfortable, at this stage in my philosophical development, in affirming that the real is intelligible and that we humans are capable of a genuine intellectual knowledge of that intelligible real, though we are hardly identical with the object of intellectual knowledge in all cases. I am further relatively comfortable with affirming that we humans are capable of a genuine intellectual knowledge of that which is intelligible only if and because there is within us an intellect by means of which we can have that knowledge, though that intellect is hardly identical with the object of intellectual knowledge in all cases.

Finally, I am yet further relatively comfortable with affirming that we humans are capable of a genuine intellectual knowledge of that which is intelligible only if and because there is within our intellect the conceptual means by which we can have that knowledge, though that conceptual means is hardly identical with the object of intellectual knowledge in all cases.

7. Once again, there is much more to be said. And much more will be said, fortune permitting, in the course of my reading of and reflection upon Aquinas’s commentary. But not here and now, for I have accomplished the primary aim of this post, that of drawing attention to a central difference between the Aristotelian perspective of After Aristotle, even as it remains Aristotelian, and the Aristotelian perspective of Aquinas.

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:

Posted in Thomas Aquinas's Commentary on the Metaphysics of Aristotle | Tagged , , , , , , , , , | 6 Comments