by Lyle Burkhead
After I graduated from the University of Texas, I knocked around for a while and ended up in Palo Alto, California. I decided to go back to school. I enrolled in the summer session at Stanford and took a course in Wittgenstein's philosophy. I met a Stanford student who was interested in some of the same things I'm interested in. We met regularly and wrote long letters about philosophy (this was before e-mail, so we wrote letters). He was an Objectivist, i.e. a follower of Ayn Rand, and I was still more or less Objectivist at that time, although I didn't really take it that seriously anymore. (Incidentally, he was Steve Jolivette, and apparently he is still Objectivist; he is mentioned at the bottom of this page.) At one point the law of identity came up in our discussions, and it occurred to me that I had never looked up what Aristotle actually said.
First I turned to my own bookcase. I had several of Aristotle's books, and at least three books about him, including two recommended by Ayn Rand (Randall and Ross). None of them said anything about the law of identity. It wasn't even listed in the index. This was quite a puzzle to me. It was as if I opened an atlas (no, three atlases) and tried to find a map of Australia, and found that there was no mention of Australia, even in the index. I have never been to Australia, but it never occurred to me that it might not exist. Of course, Australia exists! But then why isn't it in the atlases????
The Wittgenstein course was over, but my student ID was still valid until about the middle of September, so I had access to the main library at Stanford (which wasn't open to the public). I went to the philosophy section. They had shelf after shelf of books about Aristotle. I started looking through them. They didn't say anything about the law of identity. Finally I found one that did. It was about a hundred years old. The author was George Grote, a professor at Cambridge. In the chapter on Posterior Analytics, he listed the three "laws of thought," starting with the Maxim of Identity, as he called it.
So I read Posterior Analytics again, and it's just not there. The Law of Non-contradiction and the Law of the Excluded Middle are there, but not the Law of Identity.
I tried the logic section of the library. Again, I looked at book after book, and found nothing. Finally I found something in a book by Susan Stebbing, published in the 1920's. She said, in passing, that apparently Aristotle didn't say that A is A after all. That's all she said. She didn't elaborate on what she meant by "after all." Reading between the lines, there must have been some controversy about this in the early 20th century, which concluded that Aristotle didn't say that A is A. In other words, somebody else had done the same thing I was doing, and discovered that Aristotle's famous law is not to be found in his writings. But then the controversy was forgotten. I looked in back issues of philosophy journals from around the turn of the century, but found nothing.
I tried to trace A is A back to its source. I discovered that there is no Greek expression for "law of identity." There is a Latin expression, principium identitatis. I drove up to the University of San Fransisco. It's a Catholic school, and their library has a lot of books about Thomas Aquinas. His collected works have been thoroughly indexed in both Latin and English. There was no mention of the law of identity. So it must have had its origin sometime after the 13th century, or at least after 1274, when Aquinas died.
In modern times, from the 17th century through the 19th, the law of identity was well known. Many philosophers referred to it. So it must have originated in the late middle ages.
I never succeeded in tracing it to its source. The relevant materials would be in Latin, and they didn't have a Latin collection at the main library at Stanford. I tried going to the classics library, but they wouldn't let me in. It's not open to anybody, not even Stanford students, unless you are in the classics department. (I minored in classics at the University of Texas, but that didn't make any difference.) I guess I could have gone farther afield, to other libraries, but I gave up at that point.
My conjecture is that it must have happened like this: In the late 13th century, Aristotle became part of the philosophy curriculum. But not many students (or professors) knew enough Greek to read Aristotle in the original. There was a Latin translation, but not many people wanted to read that, either. To save them the trouble, somebody wrote a textbook, and that's when the bogus law of identity was introduced. Everybody read the textbook instead of reading Aristotle. Then other textbooks were written based on the first one, and they kept repeating the myth of Aristotle's law for several hundred years. It became part of the folklore of philosophy. Finally somebody tried to look it up, and found that there is no such thing (this is what Susan Stebbing was referring to). But most people never heard about that, and the myth lives on. There are still philosophy professors who teach their students about "Aristotle's Law of Identity".
I spent three solid weeks on this investigation. It was quite an event in my young life.
I'm making several points here:
1. You don't know what's in a book until you have read it. You cannot depend on hearsay. Ever. That applies to Aristotle's works, and to everything else. (Keynes is another example of an author nobody reads but everybody has an opinion about.) You have to check things out.
2. People who talk about "reason" and "critical thinking" don't mean what they say. Those are just code words. One afternoon in March of 1995 there was an Extropian meeting at Max More's apartment. He was just completing his dissertation and was about to receive a Ph.D. in philosophy from USC. He said he was going to teach courses in Critical Thinking, and write a book about it. Knowing he was an Objectivist, I asked him if he had ever looked up what Aristotle actually said about the Law of Identity. No, he hadn't.
"You've read Atlas Shrugged, though?"
"Yes."
"How long ago?"
"Fifteen years."
"But you never looked up what Aristotle said?"
"No."
But he and many others like him go on and on about "critical thinking."
Obviously Ayn Rand herself never looked up what Aristotle said. She believed what her professor told her about Aristotle and kept repeating it for the rest of her life. Her followers believed what she said, and they are still repeating it.
I recently discovered a web page which lists many criticisms of Objectivism - apparently all the criticisms the author could find. Looking through them, I don't see any mention of the Law of Identity. People have been arguing about Objectivism for more than 40 years, but how many have gone to the library and looked up what Aristotle said? (As of January 2005 the author of the Criticisms of Objectivism page has discovered this page and provided a link to it.)
3. The most important point is that the world we live in is an illusion. Aristotle's Law of Identity is just one example, a rather trivial example, of a general phenomenon. We live in a world of phantoms, on many levels, and that should be the starting point for epistemology. In other words epistemology shouldn't be concerned with questions such as "How do you know you are not dreaming?" or "How do you know that the external world exists?" It should start with the observation that we do in fact have false beliefs.
I read Atlas Shrugged when I was a senior in high school. It took me six years to look up "A is A." In the meantime, during my college years, I spent a lot of time in coffee houses where students talked about philosophy. Aristotle's Law of Identity was a subject that came up from time to time. Some of us said it was true and important, some said it was true but trivial, some said it was false, but it never crossed our minds that we might be arguing about something that doesn't exist. (I mean Aristotle's Law of Identity does not exist. Of course the law of identity itself exists, it just isn't due to Aristotle.)
Many other conversations are about nonexistent subjects. Going to college is supposed to be a journey from illusion to reality, but it seldom works that way. For many people it's a journey deeper into unreality.
Let's move on to a more important example of something "everybody knows."
My reply to Michael Shermer: This page is an analysis of Michael Shermer's attempt to prove that there were gas chambers at Auschwitz and the other Nazi concentration camps. I am not a historian. Neither is he. I am primarily concerned with the logical framework of the discussion. He says that is also his main concern. This page isn't about history per se, it's about epistemology.
Dr. Shermer says "I do not intend to prove the Holocaust so much as to demonstrate how the Holocaust is proven." So, what kind of proof does he use? - a "jumping together" argument.
The epistemological question is whether a jumping together argument can ever be a valid proof of anything. Is this logic, or is it something else?
When I wrote the first draft of my reply to Michael Shermer, I sent a copy to Max More, among others, and asked for his comments. Mr. Critical Thinking said he didn't have time to read it. Of course it's not just Max. Very few so-called 'critical thinkers', not to mention professors, are willing to look at this. Something is interfering with knowledge - something to which traditional epistemology is totally oblivious. You have to look to Orwell for a treatment of this problem.
One reason why philosophy has become irrelevant is that it is pre-Orwellian. It does not acknowledge the reality we live in. When it is illegal to say that 2 + 2 = 4, philosophers are supposed to (a) stand up and say that 2 + 2 = 4, and (b) figure how how this state of affairs came about.
As I said two pages back, on the Third Wave page, we are enmeshed in a web of lies, on many levels, and extricating ourselves is a nontrivial task. The Reply to Michael Shermer is part of my attempt to extricate myself. It is where I discuss the most important philosophical issue of our time.
I would be interested in hearing from anyone who can shed light on the origin of "A is A." Also, if someone is discussing this page in a forum, I would appreciate being notified.
I can be reached at the following address:
logic.to.lyle at the domain name, which is recursor.net
John Galt fans might be interested in a page in another part of the site - Coherent Energy from the Subatomic Domain.
Note added March 3, 2010 (several years after this page was originally written)
My conjecture about a textbook, dating back to the Middle Ages, which falsely attributed the Law of Identity to Aristotle, seems to be wrong. There may have been such a textbook - I would almost say there must have been - but it would have been written in the 18th century, not as far back as I thought. I don't know where I got the idea that "In modern times, from the 17th century through the 19th, the Law of Identity was well known." In fact it was Leibniz who introduced the expression "A is A" toward the end of the 17th century. He refers to it as "the axiom of identity," or, in another place, as "the principle of contradiction or of identity."
A correspondent told me that A is A appeared in a letter from Leibniz to Hermann Conring in 1678, but I have not tried to track that down. Here is what Leibniz wrote in 1686, in "Primary Truths":
Primary Truths are those which either state a term of itself or deny an opposite of its opposite. For example, 'A is A,' or 'A is not not-A'; 'If it is true that A is B, it is false that A is not B, or that A is not-B'; again, 'Each thing is what it is', 'Each thing is like itself, or is equal to itself', 'Nothing is greater or less than itself', - and others of this sort which, though they may have their own grades of priority, can all be included under the one name of 'identities'.
All other truths are reduced to primary truths by the aid of definitions - i.e. by the analysis of notions; and this constitutes a priori proof, independent of experience. I will give an example. A proposition accepted as an axiom by mathematicians and all others alike is 'The whole is greater than its part', or 'A part is less than the whole'. But this is very easily demonstrated from the definition of 'less' or 'greater', together with the primitive axiom, that of identity. The 'less' is that which is equal to a part of another ('greater') thing. (This definition is very easily understood, and agrees with the practice of the human race when men compare things with one another, and find the excess by taking away something equal to the smaller from the larger.) So we get the following reasoning: a part is equal to a part of the whole (namely to itself: for everything, by the axiom of identity, is equal to itself). But that which is equal to a part of the whole is less than the whole (by the definition of 'less'); therefore a part is less than the whole.
The predicate or consequent, therefore, is always in the subject or antecedent, and this constitutes the nature of truth in general, or, the connexion between the terms of a proposition, as Aristotle also has observed. In identities this connexion and inclusion of the predicate in the subject is express, whereas in all other truths it is implicit and must be shown through the analysis of notions, in which a priori demonstration consists.
But this is true in the case of every affirmative truth, universal or particular, necessary or contingent, and in the case of both an intrinsic and an extrinsic denomination. And here there lies hidden a wonderful secret in which is contained the nature of contingency, or, the essential distinction between necessary and contingent truths; and by this also there is removed the difficulty about the fatal necessity of even those things which are free.
From these facts, which have not yet been sufficiently considered because of their excessive easiness, there follow many things of great importance. For from this there at once arises the accepted axiom, 'There is nothing without a reason', or, 'There is no effect without a cause'. For otherwise there would be a truth which could not be proved a priori, i.e. which is not analysed into identities; and this is contrary to the nature of truth, which is always, either expressly or implicitly, identical.
Readers who are familiar with Objectivist epistemology should find some food for thought here. The quotation above is from Leibniz, Philosophical Writings, edited by G.H.R. Parkinson, Everyman paperback, pages 87-88. The principle of identity appears again on pages 206-7, in a letter to Clarke written in 1715 or 16:
It is rightly said in the Paper which was sent to the Princess of Wales, and which Her Royal Highness did me the honour of sending me, that next to vicious passions the principles of the Materialists do a great deal to support impiety. But I do not think the author was justified in adding that the Mathematical Principles of philosophy are opposed to those of the Materialists. On the contrary, they are the same except that Materialists follow the example of Democritus, Epicurus, and Hobbes, and restrict themselves to mathematical principles alone and admit nothing but bodies; while the Christian Mathematicians admit immaterial substances also. Thus it is not Mathematical Principles (in the ordinary sense of the term) but Metaphysical Principles which must be opposed to those of the Materialists. Pythagoras, Plato, and to some extent Aristotle had some knowledge of these, but it is my claim to have established them demonstratively in my Theodicy, although I have expounded them in a popular way. The great foundation of mathematics is the principle of contradiction or of identity, that is to say, that a statement cannot be true and false at the same time and that thus A is A, and cannot be not A. And this single principle is enough to prove the whole of arithmetic and the whole of geometry, that is to say all mathematical principles. But in order to proceed from mathematics to physics another principle is necessary, as I have observed in my Theodicy, that is, the principle of a sufficient reason, that nothing happens without there being a reason why it should be thus rather than otherwise. This is why Archimedes, wishing to proceed from mathematics to physics in his book On Equilibrium, was compelled to make use of a particular case of the great principle of sufficient reason; he takes it for granted that if there is a balance in which everything is the same on both sides, and if, further, two equal weights be hung on the two ends of the balance, the whole will remain at rest. This is because there is no reason why one side should go down rather than the other. Now by this principle alone, to wit, that there must be a sufficient reason why things are thus rather than otherwise, I prove the existence of the Divinity, and all the rest of metaphysics or natural theology, and even in some manner those physical principles which are independent of mathematics, that is to say, the principles of dynamics or of force.
So that is where the Law of Identity came from. I have quoted Leibniz at length, because I wanted to establish a context. These quotations indicate how the axiom of identity was originally understood and used. I would still like to know when and by whom it was first attributed to Aristotle.
March 10, 2010
Several people have asked me about Metaphysics VII.17, where the expression 'a thing is itself' occurs. It is claimed that this 'seems reasonably close to a statement of the law of identity', as one correspondent put it.
It is an anachronism to say that the words 'a thing is itself', in this context, were a statement of the law of identity. The expression 'a thing is itself' was not the law of identity until Leibniz called it that. A lot of people are unconscious Platonists, in the sense that they assume that concepts exist eternally, and words have meaning eternally. According to this view, the expression 'a thing is itself' has always been the law of identity; the law has always existed, and was just waiting for somebody to discover it and write it down; as soon as Aristotle wrote 'a thing is itself', he stated the law of identity.
No, he didn't.
Metaphysics VII.17 is one of the things my friend and I discussed in 1970. It is true that the expression 'a thing is itself' occurs here, but not as an assertion or statement of a law. On the contrary, 'a thing is itself' came up as a hypothetical answer to a question, and Aristotle said, dismissively, that it is a 'short and easy way with the question'.
Let's look at the context. I am going to give two translations. The first is the Ross translation, revised by J. Barnes, as it appears in A New Aristotle Reader, edited by J.L. Ackrill, page 311. The second is by Richard Hope, from his translation of Metaphysics, page 166.
Here is Ross:
We should say what, and what sort of thing, substance is, from another starting point; for perhaps from this we shall get a clear view also of that substance which exists apart from sensible things. Since, then, substance is a principle and a cause, let us attack it from this standpoint. The 'why' is always sought in this form - 'why does one thing attach to another?' For to inquire why the musical man is a musical man, is either to inquire - as we have said - why the man is musical, or it is something else. Now 'why a thing is itself' is doubtless a meaningless inquiry; for the fact or the existence of the thing must already be evident (e.g., that the moon is eclipsed), but the fact that a thing is itself is the single formula and the single cause to all such questions as why the man is man, or the musical musical, unless one were to say that each thing is inseparable from itself, and its being one just meant this. This, however, is common to all things and is a short and easy way with the question. But we can inquire why man is an animal of such and such a nature. Here, then, we are evidently not inquiring why he who is a man is a man. We are inquiring, then, why something is predicable of something; that it is predicable must be clear; for if not, the inquiry is an inquiry into nothing.
Richard Hope:
Now, taking another starting point, we ought to say what primary being is and what kind of being it is; for thus it may also become clear what to say about the primary being that is separate from those primary beings which are sensed. Since primary being involves a beginning and an explanatory factor, let us begin our explanation at this point.
Ordinarily we try to explain why by telling why something belongs to something else. For to ask why the musical man is a musical man is either, as has been said, to ask why the man is musical or something else. It is pointless to ask why anything is itself. For *a* fact, such as that it is true that, let us say, a lunar eclipse is, must be clear at the start. But the fact that anything is itself is the one and only reason that can be given in answer to all such questions as why a man is a man or a musician is a musician; unless one were to add that this is so because everything is inseparable from itself and that just this is what is meant by "being one". But this fact is common to everything and is a short-cut explanation. We may properly ask, however, why man is an animal of a certain sort. This, then, is clear, that we are not asking why he who is a man is a man. We are asking why something belongs to something. But the fact that it belongs must be clear; for if it is not, the question why is futile.
Let's reformat the part where 'a thing is itself' occurs, to show the structure of the argument
(I am mixing translations here):
Now "why a thing is itself" is a meaningless/pointless inquiry for the fact or the existence of the thing must already be evident e.g., that the moon is eclipsed but the fact that a thing is itself is the one and only reason that can be given in answer to all such questions as why the man is man, or the musician musical, unless one were to add that each thing is inseparable from itself, and its being one just meant this. This, however, is common to all things and is a short and easy way with the question.
'This' applies to everything after 'but'. Since this is not entirely obvious - it does not have to be read that way, and in fact I did not read it that way at first - I need to justify my interpretation. Here is an alternate reading: the last sentence could be within the scope of 'unless', not the scope of 'but'. In other words, maybe in the phrase 'This, however, is common to all things' the word 'This' refers only to the second answer, not the first. If you read it that way, the dismissive 'short and easy way' comment does not apply to 'a thing is itself'. In that case the indentation should be changed so the last 'This' lines up under 'unless':
unless one were to add that each thing is inseparable from itself, and its being one just meant this. This, however, [i.e. the immediately preceding point and nothing else] is common to all things and is a short and easy way with the question.
But this reading is impossible, if you think about it. If you read it that way, it implies that the fact that each thing is inseparable from itself is common to all things, but the fact that a thing is itself is not common to all things. Aristotle did not intend to say that. He did not intend to make a distinction between 'a thing is itself' and 'each thing is inseparable from itself'. The two answers are both common to all things, because they are just different ways of saying the same thing. If 'short and easy way' only applied to 'each thing is inseparable from itself', Aristotle's argument would break down. Therefore this is the way to read it:
but the fact that a thing is itself is the one and only reason that can be given in answer to all such questions as why the man is man, or the musician musical; or, putting it another way, because each thing is inseparable from itself, and its being one just meant this. This, however, [i.e. the fact that a thing is itself, or, equivalently, a thing is inseparable from itself] is common to all things and is a short and easy way with the question.
Thus 'short and easy way' applies to 'a thing is itself'.
At first it may not be clear what 'short and easy way' or 'short-cut explanation' means. It brings the argument to a negative conclusion, but how exactly?
You have to look at how this passage fits into chapter 17. Aristotle asserts that it is meaningless to ask why a thing is itself. So what? Why did he bring this up? What role does this point play in the surrounding argument? - It is a borderline case that needs to be mentioned for completeness. Other questions do have meaning, in contrast to 'why a thing is itself', which does not have meaning. The question 'why' only makes sense if you are asking why one thing belongs or attaches to another, or why one thing is predicable of another. They have to be different things. First he gives examples of questions that make sense, and then he says 'why is a man a man' is an example of a question where you are not asking why one thing belongs to another. That kind of question is the limiting case, the null case.
So, finally, what role does 'a thing is itself' play in the argument? It's not exactly a starring role. Aristotle uses 'a thing is itself' as a kind of reductio ad absurdum. Here is the gist of Aristotle's argument:
The fact that 'a thing is itself' is the only answer that can be given implies that the question is meaningless.
My original claim (forty years ago!) was that Aristotle did not discuss the law of identity and did not say that A is A. That remains true. He mentioned the fact that a thing is itself, but he did not give this fact a name or point it out as having any significance. He did not hold up 'a thing is itself' as a shining Law of Thought which could be the foundation of philosophy. He just mentioned it in passing, as an example of a vacuous statement which is not a meaningful answer to a meaningful question. He did not call it the Law of Identity, he did not formally state it as A is A, and as far as I can tell it played no further role in his philosophy beyond its momentary appearance here.