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.
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 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.
* Thomas Aquinas, Commentary on the Metaphysics of Aristotle. Translated and introduced by John P. Rowan (Revised edition; Notre Dame, Indiana: Dumb Ox Books, 1995 )
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:
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.