Before one can reasonably investigate the question of whether two things are identical, it stands to reason that one must have a clear understanding not only of what counts as a thing but, even more importantly, of what it means for two things to be identical. The question of the nature of identity is indeed a perplexing one, and has served as a starting point for much recent philosophical investigations. It drove Frege to make the distinction between sense and reference,1 has been a central factor in much of Quine's ontological analysis, and recently has played a central role in Butchvarov protometaphysical Being Qua Being.2
The initial difficulty becomes apparent from the very way in which the problem has been stated. If there really are two things, then how could we correctly claim that they are identical, in the sense of numerical identity? If there is only one thing, then why bother saying that it is identical? As Wittgenstein says: "Roughly speaking, to say of two things that they are identical is non-sense, and to say of one thing that it is identical with itself is to say nothing at all."3 The question can be phrased as exactly what is it being claimed to be identical in a true identity statement?
The other problems emerge when one investigates more general usages of the concept of identity. We speak of two dresses as being identical, two houses as being identical, two battle plans as being identical. In these cases, do we have the central usages of the identity concept, leaving the concept of numerical identity a limiting, perhaps even degenerate, case? Or, is the concept of numerical identity the primary one with the others being instances of identity in a certain respect or with reference to a common property or set of properties? Would this later view commit us to a thoery of numerical identity of properties, that is to say, a realist theory of the universals?
A complete understanding of the problem of identity is ultimately going to deal with all these questions. In this paper we will attempt to explicate why some identity statements are tautologies, or even mere tautologies, and others are nontautological and important. In doing this, we will first of all present the distinction between formal and material identity and then apply it to a famous philosophically perplexing issue--in particular, the question of whether "tat tvam asi"4 is a tautology or a true and factual statement about Brahman.
I
One more point needs to be investigated before we can consider whether statements of formal identities are tautologies, or even 'mere tautologies'. In one sense, an earlier sense, a tautology involves the unnecessary repetition of the same idea in different words; it is sometimes called a "pleonasm." In the more modern sense in which the word is used by most contemporary philosophers, a
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 Philosophy East and West 34, no. 1 ( January, 1984 ). © by University of Hawaii Press. All rights reserved.
 Bina Gupta is Associate Professor of Philosophy and Director of the South Asia Language and Area Center at the University of Missouri.
 William C. Wilcox is Associate Professor of Philosophy at the Universty of Missouri.

tautology is a sentence that is true solely by virtue of its formal structure. Some people reserve the word tautology simply for logical truths or, possibly, for the subset of logical truths of propositional logic. Others use the word in a broader sense, such that not only logical truth but analytic propositions, that is to say, propositions which are reducible to logical truths by the use of definition, would be considered tautologies. One must be very careful to understand the sense in which the word is being used. A tautology in the first sense given above, one which involves the unnecessary repetition of words, need not, as in our example, even be true, let alone necessarily true. "He is writing his own autobiography" could very well be false because he is not writing an autobiography, not because the autobiography that he is "is not writing" is not his. Or, perhaps, after years of writing autobiographies for other people he may finally get around to writing his own, in which case the repetition may be necessary and quite informative. The second sense of tautology also does not appear to be one under consideration here, since "tat tvam asi" is not an instance of a structurally redundant sentence. It may be, however, that the sense of tautology which we have indicated above means the same thing as "analytic." "Thou art thou" would be a tautology in the first sense, but "thou art that" would be a tautology only if "thou" and "that" were interdefinable, or if the concept of one of these was contained in the other. This may very well be the case, but it is not obviously so, and the claim that the proposition in question is a tautology ought not to be accepted lightly.
Nevertheless, let's assume that in what follows (1) we have some usable criteria for acceptable definitions, (2) that it is analytic propositions and not tautologies that we are concerned with, and (3) that the necessity of logical truths is not in question. Furthermore, nothing we will say assumes that in order to be a necessary truth a proposition must be either logically true or analytic.
In what follows we shall distinguish between formal identity statements and material identity statements.5 A formal identity statement is a logical truth, such as a = a; a material identity statement, a = b, may or may not be a necessary proposition, or at least whether it can be or cannot be ought to remain an open question. But if such a statement is necessary must it be an analytic proposition, or could it be necessary in some other sense? The meaningfulness, the importance, of material identity statements is basically what is at issue.
In Being Qua Being, Butchvarov considers Frege's distinction between sense and reference and concludes that in some ways it is important but in other ways deficient. Butchvarov agrees that an expression has a sense and a reference but concludes that the reference of such a referring expression need not exist. He distinguishes between entities and objects, object being the broader term, both entities and nonentities being objects. An existent object is an entity. He states:
I shall refer to the domain of the logically first applications of our conceptual apparatus, that is, the application of the concepts of identity and existence, as the domain of objects, and to the domain that emerges from it by virtue of these applications as the domain of entities.6
A statement of formal identity, that is to say, a = a, may be about either entities or objects. A material identity statement, that is to say, a = b, may be about either entities or objects, and it will be true if the objects a and b are the same entity, that is to say, if the object a exists and the object b exists and they are the same entity. It will be false if the objects a and b both exist and are different entities. It will also be false if one or both of the objects a and b are not entities.
Thus, we have what initially looks like Frege's distinction between sense and reference with its application to the problem of identity but with another layer inserted between the sense and the reference. Actually, the argument is slightly more complicated than this, since the term in question denotes or refers not to the entity, which may or may not exist, but to the object which may exist whether the entity does or not. The reference of a term is not to an entity but to an object. Frege is still not free of Wittgenstein's dilemma. His analysis of identity statements still requires the relata, if the identity statements are to be true, to be the same thing. What Butchvarov's analysis adds is a further layer of things in terms of which a true identity statement can be about two different things, and yet in another sense of thing about a single thing. Thus, the basic problem of determining whether a material identity statement is true is that of determining whether each of two objects is possibly existent, whether they do exist or not, and whether if they do exist they are the same entity. There will be senses for which there are no corresponding objects, for instance, objects whose existence would involve self-contradiction, and since Butchvarov considers existence not to be a predicate, it will be possible to completely identify an object without determining whether it exists or not. The truth of a material identity statement, one which is nonanalytic, will always be a factual question. In fact, it will be the question whether something exists.
This helps solve the problem of how we are to understand material identity statements. They appear to be about two different things. Not just about two different things, following Frege, under two different modes of presentation, but about two different things. And yet, if they are true they cannot be about two different things. Butchvarov's solution is that a material identity statement is about two different things, if we understand thing in the sense of object, and yet, when we understand thing in the sense of entity, they are about a single thing. Many objects can be the same entity and the same entity can be many objects.
All of this, of course, depends upon the material identity statements which we are discussing being nontautological or, better yet, being nonanalytic in the sense that we have discussed above. If two terms are related to each other in such a way that they must refer to the same object, whether or not that object is an entity, then the statement is reducible, via definitional substitution, to a formal identity, and as we have seen, a formal identity is true whether the objects involved are entities or not. Thus, the problem is, with respect to a material identity, firstly to determine whether the terms in question are analytically or definitionally related
to each other, in which case it is not really a material identity, and then factually to determine whether the distinct objects are really entities.
Let us consider several examples. In a Victorian society, the expression "my son's mother" has a certain sense and refers to an object and, possibly, if I have a son, to an entity. The expression "my wife" has a sense and refers to an object and, if I am married, to an entity. Given that this is a Victorian society, however, the meaning of the phrase "my wife" being identical to that of "my son's mother," "my son's mother is my wife" is not really a material identity. It reduces, given the way those words would function in such a society, to a formal identity whether or not I have a son or a wife: The mother of my son and my wife would have to be the same object. In a non-Victorian society, however, the phrase "my son's mother"' has a sense and a reference, an object, and the phrase "my wife" has a sense and a reference, another object, and nothing in the meaning of either expression would require that they be the same object. I might have a wife--and the object which is my wife may be an entity--but no son. I may have a son--who, of course, would have a mother who would be an entity-but no wife. It may be the case both that I have a wife and that my son has a mother but that those two objects be different objects. The actual determinations whether two objects are the same entity is based upon determining that both objects exist and that they are the same entity.
Keeping this distinction between formal and material identity statements in mind, we will now proceed to examine the famous identity statement "tat tvam asi" in order to explicate its status as a claim. Is it an important truth, or is it simply a mere tautology?
II
"Tat tvam asi" (that thou art) is one of the most important Upani?adic statements, which occurs in the Ch?ndogya Upani?ad.7 Advaitins regard it as the edifice on which their entire philosophy is based. Advaitins regard it as the very foundation of their school because, in their opinion, this statement clearly and undoubtedly points to the oneness of ultimate reality. On the other hand, nonAdvaitins in the Ved?ntic tradition believe that such oneness is neither intended nor implied by this statement. As a matter of fact, the interpretation given to this statement to a large extent determines the ontological and epistemological perspectives of the various schools of Ved?nta. In fact, different schools of Ved?nta have given significantly different interpretations of this famous mah?v?kya. The main purpose of this section is (1) to give an Advaitin analysis of the statement in question, and (2) to investigate what sense of identity is implied by it.
?a.kara claims that "tat tvam asi" should be understood as an assertion of absolute identity between Brahman and the individual self (j?va). He also claims that Brahman is different from the embodied self because the Upani?ads repeatedly emphasize that Brahman is other than the embodied self. How can that be possible? In his commentary on the Brahman S?tras, ?a.kara states:
But (says the opponent) there is a mention also of the non-distinction between the two, such as--"That thou art". How can a distinction and non-distinction which are contrary to each other be both possible? (We reply)--this is no fault, because we have already established in several places, that according to the maxim of "The Akasha and the Akasha of the pot", both are possible. Besides, when the non-distinction (between the two) comes to be realized, by means of such reference to non-distinction, as "That thou art", then the nature of the transmigratory existence of the Jiva-Self, and the creative activity of Brahma, both vanish, on account of the removal of the entire set of transactions, depending upon the notion of distinction which is but only a display of false ignorance, by true knowledge.8
Similarly, although there is only one self, the embodied self is taken to be different from Brahman because of the limitations of mind and body. Thus, we can see that ?a.kara clearly believes that individual self is not different from Brahman.
To fully understand the significance of "tat tvam asi," one must obtain an accurate knowledge of the constituents that make up the statement under consideration. Therefore, before proceeding further let us examine briefly what is meant by "tat"' and "tvam." According to the Advaitins, in "tat tvam asi" if "tat" (that) is taken to refer to Brahman (pure consciousness) and "tvam" (thou) is taken to refer j?va (embodied self), then one cannot talk of identity between the two in any sense of the term. However, if "tat" is understood as pure consciousness, direct and immediate, and "tvam" is understood as pure consciousness, which underlies embodied being, it is possible to talk of absolute identity between the two. In order to comprehend the true meaning of the statement, constituent words must be taken in their secondary meanings (the second sense) rather than their primary meanings (the first sense). In the case of both "that" and "thou," part of the usual meaning is left out and part is retained. In the case of "thou," egoism, immediacy, and so forth are left out, and, in the case of "that," remoteness and so forth are left out to arrive at the underlying unity. In Sanskrit rhetorics, this method of finding out the secondary meaning by eliminating differentiating elements is called jahal-ajahal-lak?a??. It differs from ajahal-lak?a??, where the original meaning is preserved in its entirety, and jahallak?a??, where the original meaning is entirely given up and a quite new meaning is acquired. Thus, ?a.kara, following the method of jahal-ajahal-lak?a??, maintains that "tat tvam asi" points to identity between Brahman and the individual self. Pure consciousness is the reality underlying individual mind/body complexes: the products of avidy? (ignorance). The self viewed apart from n?ma-r?pa (name-form), apart from the psychophysical organism, is identical with Brahman. As long as the individual self is under the influence of ignorance, he is taken to be identical with the body, ego, and so forth and therefore different from Brahman. And "tat tvam asi" points to the reality in us as ultimate.
When ?a.kara maintains that "tat tvam asi" asserts the identity between Brahman and the individual self, he is not talking of identity, meaning tautology, in either of the senses explained in the first part of our paper: It does not involve the unnecessary repetition of the same idea in different words nor is it a tautology
in virtue of its formal structure. Because what is asserted is that the underlying self of the individual is Brahman or ultimate reality. Each individual qua individual is locked into subject/object distinctions. Through scriptures, proper discipline, an individual comes to realize that there is something changeless, permanent, behind all that appears in the world, and that is Brahman.9 "Tat tvam asi" asserts that ?tman is Brahman which must not be expressed as x = x because what is meant by ?tman for the individual is different from what is meant by Brahman for the individual. Let us explain it further with an example. When I say, "This is that John Hinkley who shot the President," what am I really asserting? I am asserting that when I saw John Hinkley for the second time testifying in the court, I immediately recognized him to be the same person I talked with in the supermarket a few months ago. When I report my observation to my friend after seeing John the second time, I am not suggesting that the two places and times are identical. It is quite possible that when I saw John the first time a few months ago, he was fat and happy. When I say "This is that John ..." I am not expressing an identity between his mutable, accidental characteristics, that is, between fatness/slimness, happiness/sadness, and so forth, but rather implying the identity of his being or personality devoid of all accidental features. In the same fashion, when ?a.kara states that the self is Brahman, he is not stating that the individual self characterized by egoism and so forth is Brahman, but rather that the self apart from these accidental characteristics is identical with Brahman. Therefore, it is obvious we must conclude that ",?tman is Brahman" is not a tautology, nor is it a superfluous or trivial statement. Perhaps, that is what Eliot Deutsch is implying when he states: "Identity judgments such as ... 'Thou art that'--are not for the Advaitin, mere tautologies...."10 What Deutsch seems to be arguing is that all identity propositions are not tautologies, nor are they superfluous, as Bradley claims. The identity proposition in question is an important and significant statement in that it is "the concrete representation of a movement of thought from one ontological level (of particularity) through another (of universality) to yet another (of unity), wherein the attainment of the latter negates the distinctions between the former."11 We are in sympathy with Professor Deutsch's explication at this point; in the later part of the paper we will show how the movement of thought about which he talks might be clarified by the application of certain distinctions by Butchvarov. Butchvarov talks about different ontological categories, objects and entities, and argues that the truth of a material identity statement depends upon objects being the same entity. That the two objects are the same entity is a factual claim, yet underlying it, at another ontological level, is the formal identity, the strict identity, of an entity with itself. But we get ahead of ourselves.
Thus, it is not surprising that Advaita maintains that identity statements are indeed highly significant. In the statement under consideration, "art" is the "is" of identity, not of predication. It does not designate an action enjoined, as there is no expected result. As the statement does not speak of any relation between the
two, no further question is logically possible. An identity statement is strictly akandartha: It refers to the absolutely simple reality. All samsarg?vagrhi statements of the S-P form are relational propositions, and the number of questions that can be raised about the subject of their discourse is theoretically indeterminable. Therefore, it is not possible to express their complete meaning with the help of any completed system of propositions. In contrast, a proposition which only points to facts and does not attempt to describe them does not give rise to any ?ka.sha (expectation), and, consequently, there is no further need to explain the meaning to satisfy ?ka.sha. Only an identity statement keeps one exclusively confined to the present subject. ?a.kara states that:
Finally, here is this ultimate (decisive) argument to prove the oneness of the Atman: viz, there is nothing further beyond it of which an expectancy exists. While in an ordinary statement such as, 'one should make an offering,' there arises the expectancy as to 'unto whom','with what', and 'in what mode', no such expectancy is known to arise in connection with the declaration ... 'That thou art', or . . . 'I am Brahman', in as much as it intends to convey the knowledge of the absolute oneness of the true essence of everything. It is only when some other object exists as a remainder that there might arise the expectancy; but there does not exist any other object remaining apart from and beyond the Atman, which can give rise to the expectancy. 12
Sure?vara, a disciple of ?a.kara, though following the same line of reasoning as his teacher with regard to "tat tvam asi," devoted greater attention to this statement. In explaining its meaning in the third book of Nai?karmya Siddhi, he emphatically rejects any suggestion that it is relational in any sense of the term. He states:
In sentences like, "verily the ether in the jar is the ether in the sky", we point not to a subject qualified by its predicate but to a reality not directly expressed in the words of the sentence--to the ether unlimited by pot or sky. So in sentences like "That thou art", we immediately receive knowledge beyond the expressed meaning of the sentence.13
And if the meanings of the words are understood but the spiritual experience does not arise, it will not help to invoke purely imaginary injunctions to mediate. For there is no other meaning to be understood but that conveyed by the holy texts themselves.14
Thus, it is clear that Sure?vara, following ?a.kara, upholds the immediacy and finality of knowledge produced by the mah?v?kyas. The reality they signify is absolutely simple, although taken at their face value such statements do not appear to be any different from common relational statements.
We shall now examine the distinctions between material identity statements and formal identity statements and between objects and entities and see whether the application of these distinctions sheds any light upon our problem. If a formal identity is of the form a = a, where the "is" is the "is" of identity, then "tat tvam asi" is not a formal identity statement. It seems, then, that it must be a material identity statement or not an identity statement at all.
If the "is" is not the "is" of identity, then it would seem that it must be the "is"
of predication or, possibly, of class membership. The latter can be ruled out, on the grounds that the sentence is not a sentence about class membership. Whatever "that" is, whatever Brahman is, it is not a collection of anything according to ?a.kara. The class of men is the collection of men, and while the class may be more than the mere assemblage of individuals, it does contain them as members. No one seems to understand Brahman simply as a collection of anything, even of all the individuals in the universe. Accordingly, the "is" is not the "is" of class membership. A similar argument should establish that it is not the "is" of predication either. That means it must be the "is" of identity. Accordingly, what we do have is an identity statement, and since it is not a formal identity statement it must be a material identity statement.
Material identity statements can be broken into two classes: those which are analytically true and those which are not analytically true. The classical examples of analytically true material identity statements come from mathematics. We are assured 3 + 1 is 4. Other examples would involve male siblings and brothers and the other usual terms. We have already seen that if "tat tvam asi" is, as some people have argued, a tautology, then it must be because it is analytic in the sense of that word which we have explained. If it is not analytic, then it must be synthetic, factual, since the distinction is complete. The conclusion that we draw from our brief discussion of ?a.kara seems to be that the statement is not analytic. It is possible to define words for technical purposes, but if the truth of the sentence in question is to have important consequences for us, then it is essential that the words must be used in their ordinary senses. If ?tman and Brahman are, in fact, words that people use and understand, then it should be as easy to determine that "?tman is Brahman," as it is to confirm that "all bachelors are unmarried." People could not disagree over whether bachelors are unmarried, and there is a great deal of disagreement over the truth of "?tman is Brahman." And the disagreement does not seem resolvable simply by going to the dictionary.
Hence, we conclude further that "tat tvam asi" is a material identity statement. It says of two different objects, in Butchvarov's sense, that they are, again in his sense, one entity. If, in fact, each object exists, and each existent object is the same entity, then the material identity statement is true. The movement between object and entity, or, better yet, the relation between object and entity, is described by Butchvarov as follows:
The distinction between objects and entities is not a real distinction, a distinction between classes of things, but a distinction of reason, a distinction due solely to the application of concepts. An object is anything that may be referred to, singled out for our attention, whether in perception, thought, or discourse; it is anything that may be classified, subjected to conceptualization. If the concepts of identity and existence are applicable to it, that is, if it exists and if it is identical with some other objects, then it is an entity.... This is why we can say, without paradox, that material identity statements are both about objects and about entities. If true, such a statement is about the entity that is each of the two objects
the statement is also about. And it is about objects because it asserts of two objects that they are one and the same entity. Unlike a formal identity statement, a material identity statement is about two objects. And, if true, it is about one entity.15
If we apply this quotation to ?ankara's understanding of "tat tvam asi," we can see that "thou" and "that" are different objects, again in Butchvarov's sense, but yet a single entity. Butchvarov's distinction of reason mirrors what is in ?a.kara a distinction in ontological levels. It is a movement from the way in which we conceptualize the world to an appreciation of the underlying reality that lies beyond that conceptualization. It is a movement from the way we think about the world to the level of ultimate reality: an ultimate reality which is independent of our thoughts and concepts.
Finally, the difference between material identity statement and formal identity statement is basically one which, although perhaps not always by those names, has a long philosophical history. Formal identity statements are those that are true formally. Material identity statements, narrowly so called, are those which are not analytically true and hence reducible to formal identity statements, and hence are true in virtue of some facts in or about the world. What is new in Butchvarov's approach is the distinction between objects and entities. Although both of these terms have a long philosophical history, Butchvarov treats them as technical terms, introduced to solve a particular problem. An object is the referent of a denoting expression. It need not be, although the word has sometimes been used in this way, a physical object. It need not be an object as opposed to a subject. It need only be something which, at least potentially, could exist. An entity is an object which has realized its potential for existence. It need not be a physical entity; the number 5 exists and is not a physical entity, and it need not be opposed to the subjective consciousness which is aware of it. If pure consciousness, pure subjectivity, can be identified, then it is an object, and if it exists, then it is an entity. ?a.kara's Brahman is pure subject; it is an object in Butchvarov's sense. Butchvarov's use of these words is clear enough, and it is obvious why he has chosen them, but what he says applies only to his stipulated sense of the word.
Applying Wittgenstein's dilemma here, it seems that to say that "tat tvam asi" is true is to say "nothing," and to say that they are different is "non-sense." It is easily seen how Butchvarov's distinction between objects and entities escapes Wittgenstein's criticism. A material identity statement is both about one thing and about two things. It is about one entity and two objects. In the sense that it is about one entity, it is not "non-sense," in the sense that it is about two objects; it does not say "nothing." Hence, it can be both true and informative.
We have indicated that the distinction between objects and entities also might help to clarify ?a.kara's doctrine of different ontological levels. We do not claim that this is an explication of ?a.kara's doctrine, but only that it might be useful as a tool for understanding. To the extent that it is such a useful tool it
enables one to describe what is basically indescribable (anirvacan?ya). To understand that which cannot be understood is, on the one hand, a futile goal, but on the other hand, it is a human being's highest achievement.
NOTES
1.  Gottleb Frege, "Sense and Reference," Contemporary Philosophic Logic, edited by I. M. Copi and J. A. Gould (New York: St. Martin's Press, 1978 ).
 
2.  Panayot Butchvarov, Being Qua Being (Bloomington, Indiana: Indiana University Press, 1979 ).
 
3.  Ludwig J. Wittgenstein, Tractatus Logico-Philosophicus, translated by D. F. Peers and G. F. McGuninness (London: Routledge and Kegan Paul, 1965 ), p. 105.
 
4.  "Tat tvam asi" is one of the four mah?v?kyas, the four great teachings of the Upani?ads.
 
5.  Butchvarov, Being Qua Being, pp. 10-12.
 
6.  Ibid., pp. 44.
 
7.  Ch?ndogya Upani?ad, VI. viii. 3.
 
8.  V. M. Apte, Brahma-S?tra Sh?nkara-Bh?sya (Bombay: Popular Book Depot, 1960 ), II. i. 22, pp. 325-326.
 
9.  Bina Gupta and William C. Wilcox, "Are all names of the absolute synonymous?" Philosophy East and West 34, no. 3 ( July 1984 ).
 
10.  Eliot Deutsch, Advaita Ved?nta: A Philosophical Reconstruction (Honolulu, Hawaii: EastWest Center Press, 1969 ), p. 49.
 
11.  Ibid.
 
12.  S. K. Belvalkar, The Brahma-S?tras of B?dar?yana (Poona: Bilvakunja Publishing House, 1938 ), p. 34.
 
13.  A. J. Alston, trans., The Naiskarmya Siddhi of ?r? Sure?vara (London: Shantisadan, 1959 ), p. 127.
 
14.  Ibid., p. 195.
 
15.  Butchvarov, Being Qua Being, p. 45.