Hegel and the Law of Identity

Reynold L Siemens. The Review of Metaphysics. Volume 42, Issue 1. Philosophy Education Society, Inc. The Catholic University of America, 1988.

It would be a mistake to assume that Hegel’s comments about the law of identity form a consistent package. On the one hand, Hegel admits that the law of identity, which he expresses in words as
everything is identical with itself,

and in symbols as
A = A,

and as
A is A,

is a trivial and necessary truth. He classifies the law itself as a “formal truth” and as “nothing more than the expression of an empty tautology.” Its instances he describes as “correct but ab­surd,” “boring and tedious.” In one place, Hegel says that the law of identity and its instances are self-evident truths.

Now as regards other confirmation of the absolute truth of the law of identity, this is based on the experience of every consciousness; for anyone to whom this proposition ‘A is A’, ‘A tree is a tree’ is made, immediately admits it and is satisfied that the proposition as imme­diately self-evident [unmittelbar klar durch sich selbst] requires no further confirmation or proof.

On the other hand, Hegel denies that the law of identity is a law of thought, as it has been assumed traditionally to be: it “is not a law of thought,” he writes in the Science of Logic, “but rather the opposite of one.” And it is the opposite of a law of thought, he explains, because it has “no truth,” and because experience “refutes” it. In the Encyclopaedia, Hegel proclaims

that no mind thinks or forms conceptions or speaks in accordance with this law, and that no existence of any kind whatever conforms to it. Utterances after the fashion of this pretended law (‘A planet is—a planet’, ‘Magnetism is—magnetism’, ‘Mind is—mind’) are, as they deserve to be, reputed silly. That is certainly a matter of general experience. The logic which seriously propounds such laws and the scholastic world in which alone they are valid have long been dis­credited with sound common sense as well as with reason.

Either stance, the sympathetic one or the critical one, is consonant with Hegel’s assumptions that the propositions of logic purport to describe general features of our experience, and that they are susceptible of disconfirmation.

Everybody knows that Hegel’s arguments are dialectical, so his ambivalence about the law of identity should come as no surprise. In the second preface to his Science of Logic, Hegel tells us that there is one sense of the word ‘true’ in which the traditional laws of thought are true, and in which forms of syllogistic inference may be valid (i.e., productive of true conclusions from true premises), and another sense of the word ‘true’ (which he describes as a “higher” sense) in which the laws of thought are not true, and all the forms of syllogistic inference invalid.

Sound common sense has so much lost its respect for the school which is in possession of such laws of truth and carries on adhering to them, that it ... regards anyone as insufferable who can utter truths in accordance with them: such as ‘The plant is—a plant’, ‘Science is—science’, and so on, ad infinitum. It has formed an equally just estimate of the formulas that are the rules of syllogizing (which is in fact a cardinal employment of the understanding, so that it is a mistake not to recognize that these have their place in cognition, wherein they must be valid) ... It knows that ... however truth may be defined, they cannot serve higher, e.g. religious truth; that generally speaking they concern only the correctness [Richtigkeit] of cognition, not the truth [Wahrheit].

It is clear that Hegel’s equivocation over the meaning of ‘true’ saves him from outright inconsistency. It is less clear that it saves him from inconsistency simpliciter. The question of whether it does is one I choose not to address. It is begged, however, by all those of Hegel’s apologists who assure us that Hegelian logic embraces the tautologies of Aristotle and Russell.

I


Hegel sometimes presents the law of identity as a statement form: ‘A = A' or ‘A is A’. These formulations differ from the modern logician’s ‘x = x’. Our familiar variable V is used for re­placing unquantified singular terms only, whereas Hegel’s variable ‘A’ does duty for quantified general terms too. Among the examples of “A is A” statements given by Hegel we find
God is God,
Air is air,
Magnetism is magnetism,
Science is science,
Mind is mind,
Identity is identity,

which all appear to be of the familiar “x = x” kind, and
The plant is the plant,
The moon is the moon,
The sea is the sea,

which are, arguably, “x = x” statements too. We also find
The plant is a plant,

which certainly is not, and

A plant is a plant,
A planet is a planet,A tree is a tree,A lion is a lion,

which are not either.

For many of Hegel’s predecessors, statements in the last cat­egory were “A is A” statements paradigmatically. Leibniz and Wollf would have called them “identical propositions” and Kant would have called them “analytic.” Hegel borrows both labels but uses them differently: he describes the law of identity itself as an­alytic, and any substitution instance of it as a proposition of identity (Satz der Identitat).

Hegel ignores a kind of identity statement that philosophers since Frege have emphasized: namely, statements like
The morning star is the evening star,
Scott is the author of Waverly,
Mount Everest is Chomolungma.

Arguably, these are all to be represented by x = y. None of them instantiates the law of identity. The mistaken assumption to the contrary is commonly made by Hegel's commentators.

II


Hegel criticizes the law of identity. I will approach his criti­cisms obliquely, by way of some comments of Bertrand Russell’s and of G. E. Moore’s.

First, Russell:

Identity is a rather puzzling thing at first sight. When you say ‘Scott is the author of Waverly’, you are half-tempted to think that there are two people, one of whom is Scott and the other the author of Waverly, and they happen to be the same. This is obviously absurd, but that is the sort of way one is always tempted to deal with identity.

There is half a temptation, Russell says, to assume that anybody who makes an assertion of identity, such as,
Scott is the author of Waverly,

says that two things are one. The assumption, Russell points out, is absurd. For, many identity statements are true, among them:
Scott is the author of Waverly,

is among them. But if every such statement were a statement that two things are one, none could be true. Therefore, Russell concludes, one must resist “the sort of way one is always tempted to deal with identity.”

Russell’s comment echoes one of G. E. Moore’s, in which pre­cisely the assumption that Russell declares absurd gets attributed to Hegel. Moore agrees with the claim, with which he credits Hegel, that every proposition must have a predicate distinct from its subject.

It is true, as Hegel himself remarks, that the propositional form always “promises a distinction between subject and predicate.”

It is not obvious what someone agrees with who agrees with this. Hegel sometimes points to the relata of an identity statement as its subject and predicate. Yet this idea, taken together with the prem­ise that subjects must be distinct from their predicates, makes for absurdity. For surely, a statement of identity like
Mind is mind

cannot be an assertion that different things are identical. Is it less ridiculous to suppose that statements like
Mind is identical with itself

and
This is identical with itself,

like the statement

This is identical with that,

do admit of the promised distinction? It can be inferred at least, Moore maintains,

from the fact that we are ever tempted to express it by [propositions like] “Mind is mind,” that it is a distinction which is somewhat difficult to catch. When we say, “This is identical with itself,” the truth of which we are thinking seems to belong to the class of truths of which the general form is, “This is identical with that,” and it seems as if in all cases “this” and “that” must have some difference from one another, and therefore that, in this case, the thing must be different from itself in order to be identical.

Here absurdity resurfaces. For, Moore writes, it is not clear how either
Mind is mind

or
Mind is identical with itself

can identify different things except on pain of contradiction; for, Moore suggests, two things cannot be one. That statements of iden­tity identify different things, Moore contends, “is the conclusion to which Hegel wishes to drive us.” Yet, he objects,

It is undoubtedly this which the Law of Identity wishes to deny. We must, therefore, find a point of difference between what we mean by “This is identical with itself,” and what we mean by “This is identical with that,” if we are to hold that any instance of our Law does not imply its own contradictory.

Moore, of course, does conclude safely that “Identity is not here a relation between two things, nor does it imply any difference [between them].”

III


In the Science of Logic, Hegel describes the statement form ‘A is A’ as “the form of the proposition in which identity is expressed.” Hegel makes the following claims about it. First, he claims that

In the form of the proposition in which identity is expressed ... there lies more than simple abstract identity;

such that

‘A is—’, is a beginning that hints at something different to which an advance is to be made.

Second, he claims that in ‘A is A’ statements this difference never actually materializes; or rather, that it “appears only as an illusion, as an immediate vanishing.”

In the form of the proposition in which identity is expressed ... there lies more than simple abstract identity; in it, there lies this pure movement of reflection in which the other appears only as an illusion, as an immediate vanishing. ‘A is—’, is a beginning that hints at something different to which an advance is to be made. But this different something does not materialize: A is—A. The difference is only a vanishing; the movement returns to itself.

One source of Hegel’s illusion may be this: his assumption that when the two variable letters (i.e., the two occurrences of the letter ‘A’) in the formula ‘A is A’ replace two token singular terms, they replace singular terms for two things. The puzzling upshot is that, in just this sense, it lies in the very form of a statement like
(1) The plant is the plant

that it identifies different things. From this, it is easily inferred that statements like (1) are self-contradictory, at least in the extended sense that they identify things that they require to be non-identical.

Hegel draws precisely this conclusion about (1):

we see that the beginning, ‘The plant is—’, sets out to say something, to bring forward a further determination. But since only the same thing is repeated, the opposite has happened, nothing has emerged. Such identical talk therefore contradicts itself.

Hegel concludes also that the statement form ‘A is A’ contradicts itself. This is easily inferred from the apparent incompatibility of the assertion for some A, that A is A, with the assumption that the two token singular terms replaced by the different occurrences of the letter ‘A’ must be singular terms for two different things. That, at any rate, is all the sense I can give to Hegel’s celebrated claim, concerning the formula ‘A is A’, that

The propositional form itself contradicts it: for a proposition always promises a distinction between subject and predicate, while the present one does not fulfil what its form requires.

Hegel intends this criticism to apply to the general statement “Everything is identical with itself” too. He follows Hume in doing so.

For in that proposition, an object is the same with itself, if the idea express’d by the word, object, were no ways distinguished from that meant by itself; we really should mean nothing, nor would the prop­osition contain a predicate and a subject, which however are imply’d in this affirmation.

IV


In the Science of Logic, Hegel comments on the vacuousness of ‘A is A’ statements. He comments first on statements like
(2) A plant is a plant,

in which the two “A” expressions contain general terms but no sin­gular terms.

If, for example, to the question “What is a plant?” the answer is given: “A plant is—a plant”, the truth of such a statement is at once admitted by the entire company on whom it is tried, and at the same time it is equally unanimously declared that therewith nothing is said.

The statement (2) says nothing not merely because nobody would deny its truth, but because (2) and all other statements with the same quantificational structure are, in virtue of that structure, true. Hegel comments next on statements like
(1) The plant is the plant

and
(3) God is God,

in which the “A" expressions are singular terms.

If anyone opens his mouth and promises to state what God is, namely “God is—God”, expectation is cheated, for what was expected was a different determination. And if this statement is absolute truth, such absolute verbiage is very lightly esteemed. Nothing will be held to be more boring and tedious than conversation which merely reiterates the same thing, or than such talk which is yet supposed to be truth.

Looking more closely at the tedious effect produced by such truth, we see that the beginning, “The plant is—”, sets out to say something, to bring forward a further characteristic. But since only the same thing is repeated [i.e., by “The plant is—the plant”! the opposite has happened, nothing has emerged.

Statements like (1) and (3) say nothing in the following sense. If, in the statement ‘N is N’, ‘N’ is a non-empty singular term, then the statement is necessarily true: 'N' may have a referent without anything satisfying the predicates ‘is a brother of N' or 'is a sister of N', but 'N' cannot have a referent without something satisfying the predicate 'is (identical with) N'.

Obviously, if it were the case that the expressions flanking the word ‘is’ in the statement
(1) The plant is the plant

were singular terms for different things, or that the expressions flanking the word ‘is’ in the statement
(2) A plant is a plant

contained general terms for different classes of things, it would not be the case that (1) and (2) say nothing in the senses I have indicated. Hence, Hegel’s claim that the law of identity promises a distinction between “subject” and “predicate” must be wrong if statements like (1), (2) and (3) say nothing. As J. M. E. McTaggart, Hegel’s most perspicacious commentator, argued, the law which

asserts A to be A ... is a complete tautology. Its truth rests, not on identity in difference, but on the absence of all difference. If any difference existed between the A of the subject and the A of the pred­icate, the assertion of their identity would be a proposition which might be true, and which, true or false, would have some interest. But it would not be the Law of Identity of formal logic. And it is this Law of Identity of which Hegel speaks here.

V


I have suggested that when Hegel says that statements like
(1) The plant is the plant

contradict themselves, he means that what they assert (namely, for some A, that A is identical with A) is incompatible with the supposed requirement that their two singular terms pick out different things.

I turn now to a pair of obvious questions: first, what reason is there for saying that the two singular terms in an ‘A is A’ statement must pick out different things? and second, what reason is there for saying that the difference of one thing from another is incompatible with their being identical?

Some of Hegel’s apologists argue that the singular terms in statements like (1) must pick out different things because all ‘A is A’ statements like (1) are relational statements. What is it about (1)’s being a relational statement that is supposed to compel its singular terms to pick out different things? It is, we are told, first, that if (1) is true, then for some relation R something, A, stands in the relation R to something, A; second, that a relation can obtain only between different things; and third, that statements like (1) are trivially true.

The second premise is objectionable. It is stated by W. T. Stace as follows: “A relation implies at least two terms between which the relation subsists.” It is used by Stace in Hegel's defense.

In the present case the term relates itself to itself. The first “itself” which is related is different from the second “itself” to which it is related. If there were not this inner distinction then there could be no relation. If we express identity in the form A is A, then the A which is subject is different from the A which is predicate. Hence identity necessarily involves difference.

Recently, E. E. Harris has resurrected the argument. “A relation, to be a relation, must have at least two terms.” From this it can be inferred, Harris contends, that

a relation with only one is a self-contradiction, like the Buddhist’s attempt to imagine the sound of one hand clapping.

In particular, it can be inferred, Harris says, that statements like (1) are self-contradictory.

A is A. But then the first A must be distinguished from the second; and if it is, the second is not the first. ... So it contradicts itself, and the traditional statement of the Law of Identity violates the Law of Non-contradiction.

Harris's idea is that an 'A is A' statement like
(1) The plant is the plant,

because it is a relational statement, entails a statement like
(4) The plant is different from the plant.

And his idea is that a statement like (4), in turn, entails a statement like
(5)   Not-(The plant is the plant).

So that, by (1) and (5), for example, we end up with a contradiction: namely, that both (1) and not-(1).

I said that one premise on which Harris’s argument rests, namely, the premise that a relation can obtain only between different things, is objectionable. It is venerable nonetheless. It was chiefly responsible for Hume’s bewilderment over what is relational about identity.

First, As to the principle of individuation; we may observe, that the view of one object is not sufficient to convey the idea of identity ... One single object conveys the idea of unity [or continuity through time], not that of [numerical] identity.

On the one hand, a multiplicity of objects can never convey this idea, however resembling they may be supposed. The mind always pronounces the one not to be the other, and considers them as forming two, three, or any determinate number of objects, whose existences are entirely distinct and independent.

Since then both number and unity are incompatible with the relation of identity, it must lie in something that is neither of them.

If a relation can obtain only between two or more objects, and if identical objects are one, then it should be concluded not that nu­merical identity is a contradictory relation (as Harris concludes), but that it is not a relation at all (as Hume concludes). The ap­pearances must then be saved by showing how statements like (1) can be reconstrued otherwise than as assertions of numerical iden­tity. This is what Hume does when he proposes that we take ‘iden­tity’ as a synonym for ‘temporal continuity’.

Here then is an idea, which is a medium betwixt unity and number; or more properly speaking, is either of them, according to the view, in which we take it: And this idea we call that of identity. We cannot, in any propriety of speech, say, that an object is the same with itself, unless we mean, that the object existent at one time is the same with itself at another.

The same objectionable premise, that a relation can obtain only between different things, has led Peter Geach to conclude that

Frege is wrong in treating identity as a relation between objects. The predicate “is the A” must not be analyzed as meaning “has identity with the A”, where “the A” is used to name an object.

Given that it is necessary for the truth of a statement of identity that the statement’s singular terms be intersubstitutable salve veritate in other contexts, is it necessary also that the object for which those singular terms stand should bear to itself the relation of being identical? Geach argues that it is not. For, he continues,

a thing cannot be significantly said to be substitutable for the same thing; what are interchangeable are the names of a thing. To regard “is identical with Cicero” as standing for a property of Tully is the same sort of mistake as to think donkeys have the property of begin­ning with D.

Geach is perfectly right that in identity statements like
Cicero is Tully

we have different singular terms which, if the statement is true, are interchangeable in other contexts. But is it the case, as Geach as­sumes it to be, that nothing is substitutable for the same thing? If this were so, then it would be a mystery, by Geach’s own lights, that identity statements like
(1) The plant is the plant

are ever true. For in statements like (1) we have only one singular term, not two different singular terms as we had in
Cicero is Tully.

If nothing is substitutable for itself, and if inter-substitutability salve veritate of an identity statement’s singular terms is the test of the statement’s truth, then statements like (1) cannot, on Geach’s view, be true.

Geach retracted his argument when Quine replied that doubts such as Hume’s and Geach’s about the relationality of identity are rooted in

confusion of sign and object. What makes identity a relation, and ’=’ a relative sign, is that ’=’ goes between distinct occurrences of singular terms, same or distinct, and not that it relates distinct objects

If statements of identity like
(1) The plant is the plant

as well as statements like
(6) Smith is the brother of Jones

are relational statements, then this cannot be because their singular terms pick out different things, or because their singular terms are themselves different. Instead, it must be because in inscriptions of sentences like (1) and (6) different occurrences of their singular terms flank relational expressions. For (1), unlike (6), contains only one singular term to be inscribed on both sides; and the truth of (1), unlike the truth of (6), depends on its singular terms picking out one and the same thing.

Confusion of sign and object is sometimes encouraged by sloppy talk about terms. W. T. Stace, we saw, says that “A relation implies at least two terms between which the relation subsists.” E. E. Ha­ris, we saw, agrees that “A relation, to be a relation, must have at least two terms.” Stace’s and Harris’s claim is a truism on one reading, but not on another. As we have seen, a relational statement must contain more than one token singular term; but it need not therefore be an assertion of a many-termed relation. Among He­gel’s commentators, J. M. E. McTaggart is clear on this point.

Relations can have more than two terms, as when A, B, and C are all equal. And, again, it is possible for a relation to have only one term, at any rate in the ordinary sense of the word. For a subject can have a relation to itself. Every substance has the relation of identity with itself. And some substances are equal to themselves, despise themselves, [and so on].

Thus we cannot say that every relation has more than one term. Yet that which stands in a relation, even if the relation has only one term, has a certain aspect of plurality. For a relation always connects something with something. Even when it only connects something with itself, the term so connected with itself is—to use a metaphor which is not, I think, misleading—at both ends of the relation, and this does involve a certain aspect of plurality, though not, of course, a plurality of substances. This may be more obvious if we notice that it is impossible to express any relation without either having two terms, or using one term twice. It may be the case that A loves nobody but himself, but this must be expressed by saying “A loves A,” or “A loves himself.” It cannot be expressed by saying simply “A loves,” which only means that A loves someone, without specifying whom.

From the truism that every relation requires at least two terms, contradictions arise only when one sense of the word ‘term’ is mis­taken for the other.

Is it obvious, as Harris assumes it to be, that any statement which does in fact identify different things “contradicts itself, and ... the Law of Non-contradiction”? Many philosophers would say not. It is often proposed that numerical identities depend upon, or are relative to, sortal descriptions, such that the assertion, for any A, that A is identical with A, either entails or is elliptical for some assertion that
A is the same F as A.

Clearly, this assertion may be perfectly compatible with
A is a different G from A,

depending on what gets substituted for F and G. For instance, the Thames may be the same river from one day to the next, despite being a different water. Tibbies may be the same cat from one year (and, perhaps, from one life) to the next, despite being a different mass of feline tissue. For that matter,
A is a different G from B

may be compatible with
A is the same F as B.

For instance, Kenny is a different man from Warnock, but he is the same official: namely, pro-vice-chancellor. Likewise, the vice-chan­cellor is a different official from the warden of All Souls, but he is the same man. What these examples suggest is that, contrary to Hegel's, Stace’s and Harris’s assumption, it is not self-evident that the numerical difference of one thing from another is incompatible with their being identical. Hence, it is not self-evident that we cannot assert of two things that they are one without a contradiction being entailed, or being generated otherwise.

The proposal that identities are relative to sortal descriptions does not sit well with the principle that things which are identical must be indiscernible. It may be both desirable and feasible, how­ever, to eliminate by translation the examples I adduced, or to defuse them by imposing restrictions on the use of the logical '=’ of iden­tity. Still, they provide at least a prima fade objection to the Hegelian, who would insist that two things can said to be one only on pain of contradiction.

VI


In agreement with Hegel, Harris claims that statements like
(1) The plant is the plant

identify different things. Harris defends this claim by giving a pe­culiar account of what statements of identity are about. His account is wrong.

Harris makes the trivially true observation that when someone makes an an ‘A is A’ statement like (1), or like
(3) God is God,

“It is actually A that is being identified with A.” He glosses his remark, however, as follows.

When the formal logician asserts that A is A, what A represents is said to be a proper name, and is supposed to be the same token at each occurrence ... Yet if they were indistinguishable there could be but one occurrence and the statements could not be made.

According to Harris, when, in doing logic, we produce a statement of identity like (3), we are producing an assertion about two token singular terms. What we assert is that one token or inscription is numerically identical with another. On Harris’s account, what is asserted in example (3) is that the first three letter inscriptions in the sentence are identical with the last three: that is, that the token or occurrence of the name ‘God’ on the left is identical with the token or occurrence on the right. I take it that Harris’s account is meant to cover examples like
(1) The plant is the plant

too, where the two ‘A’ expressions are not proper names but are singular terms nonetheless, just as they are in (3).

This, Harris tells us, is what “the formal logician [asserts when he] asserts that A is A.” Is it? The best way to find out is to look and see. Actually, modern logicians do not (unless they be Hege­lians) think that statements of identity, as a rule, are about words at all. Regarding the suggestion that someone who asserts that Scott is Sir Walter makes the contingently true assertion that the name ‘Scott’ stands in some relation to the name ‘Sir Walter’, Russell has this to say:

It is rather important to realize this about the two different uses of names or of any other symbols: the one when you are talking about the symbol and the other when you are using it as a symbol, as a means of talking about something else. Normally, if you talk about your dinner, you are not talking about the word ‘dinner’ but about what you are going to eat, and that is a different thing altogether. The ordinary use of words is as a means of getting through to things, and when you are using words in that way the statement ‘Scott is Sir Walter’ is a pure tautology, exactly on the same level as ‘Scott is Scott’.

Quine emphasizes that if a statement of identity is true, then

what are identical are the objects with themselves and not the names with one another; the names stand in the statement of identity, but it is the named objects that are identified. Moreover, no linguistic investigation of the names in a statement of identity will suffice, ordinarily, to determine whether the identity holds or fails. The identities:
Everest = Chomolungma,Evening Star = Morning Star,25th President of the U.S. = first President of the U.S. inaugurated at 42,Mean temperature at Tuxtla = 93°F

all depend for their substantiation upon inquiry into extra-linguistic matters of fact.

W. E. Johnson notes that a statement like (1) or (3) requires for its truth only that “identity applies to what is meant by the word, and otherness to its several occurrences.

There is nothing in Hegel's mature work to suggest that he would have agreed with Harris's account of what identity statements are about. However, in the Jena Metaphysics there is a passage which, though darkling, suggests something not unlike it.

A - A expresses a diversity (that is, two A’s), and this diversity, this other[ness], immediately is not. The two A's ought not to be equiv­alent ... But A = A; that is, it is the same A that is on both sides. They do not have an inequality in virtue of their place, as in judgment, merely through being left or right when written, or earlier or later when spoken. These are distinctions that fall away immediately in that one [can]not say which is right or left, etc.; it is not as [if] one were on the right and another on the left; each is the one and the other.

Several interpretations of this are possible. Hegel may be saying that the singular term that occurs on both sides of a statement like
(3) God is God

is identical with itself, or he may be saying that the two tokens or occurrences of it are identical with one another. Or, he may be saying that the letter inscribed on both sides of the formula ‘A is A’ is identical with itself, or that the two tokens or occurrences of it are identical with one another. I have already given reasons for thinking the second possibility perverse as a description of what someone asserts who makes a statement of identity. With respect to the first, we can do no better than listen to Quine again.

For truth of a statement of identity it is necessary only that ‘=’ [or ‘is’] appear between names of the same object; the names may, and in useful cases will, themselves be different. For it is not the names that are affirmed to be identical, it is the things named. Cicero is identical with Tully (same man), even though the name ‘Cicero’ is different from the name ‘Tully’. To say anything about given objects we apply the appropriate verb or predicate to names of the objects; but there is no reason to expect that what is thereby said of the objects will be true also of the names themselves. The Nile, e.g., is longer than the Tuscaloosahatchie, but the names are oppositely related.

With respect to the third and fourth possibilities, it should be noted that the law of identity says neither that the first letter of the alphabet is identical with itself, nor that two inscriptions of it are identical with each other. The letter ‘A’ occurs in the logician’s formula “A is A” as a variable, not as a name of itself. To use Quine’s useful jargon, its occurrence in this context is not purely referential.

VII


The German word for “determination” is Bestimmung, which can be translated also as “characteristic.” Consider the following claims of Hegel’s.

If anyone opens his mouth and promises to state what God is, namely “God is God”, expectation is cheated, for what was expected was a different determination.

‘The plant is—’, sets out to say something, to bring forward a further determination.

When Hegel says that sentence frames like ‘The plant is—’ and ‘God is—’ set out to introduce different determinations, what he has in mind may be that they must be completable by general terms, or by terms that introduce general characteristics attributable to what their singular terms pick out.

Hegel may be suggesting, for example, that the sentence frame ‘The plant is—’ must be completable by expressions like “on your windowsill” and “blighted,” that the sentence frame ‘God is—’ must be completable by expressions like “omniscient” and “omnipotent.” Hence, that they must be completable not only into statements of identity like
(1) The plant is the plant

and
(3) God is God,

but also into statements like “The plant is on your windowsill” and “God is omniscient.”

What reason could Hegel have for suggesting this? In the Phe­nomenology, he claims that the meaningfulness of the singular terms in sentence frames like “God is—” depends upon those frames being completable in just the way I have indicated.

The need to represent the absolute as subject has found expression in propositions like: ‘God is eternal’, or ‘—is the moral world-order’, or ‘—is life’, and so on ... In a proposition of this kind one begins with the word ‘God’. This by itself is a senseless sound, an empty name; it is only the predicate that says what it is, gives it content and meaning. The empty beginning becomes actual knowledge only when we get to the end of the proposition.

So, in the Science of Logic, Hegel explains his claim that

‘A is—’, is a beginning that hints at something different to which an advance is to be made

by saying that

an A is introduced (or a plant or some other substrate too) which as a useless content has no meaning [bedeutung]; but it gives rise to the difference which seems accidentally associated with it.

Hegel’s suggestion is hardly more than tantalizing, but analytical philosophers will find it familiar. In one of its variations, the idea is that the successful referring use of singular terms depends upon speakers’ propositional knowledge about what they are referring to. So that for any competent speaker S, and for any singular term 'A,'

(i) there corresponds to ‘A’ a cluster of properties B such that S believes ‘B(A)’;

(ii) one of those properties, or some conjointly, are believed by S to pick out some individual uniquely;

(iii) if a reasonable number of the Bs are in fact satisfied by an object O, then O is the referent of ‘A’.

For instance, to the proper name ‘Hegel’ there might correspond, for some speaker S, a cluster of general properties b1 (living in Nu­remberg in 1812), b2 (being an author), b3 (writing the Phanomenologie des Geistes), b4 (being forty-one years old), ... , bn (writing the Wissenschafi der Logik), such that S believes that one of those properties, or several conjointly, pick out some one individual uniquely, and such that if any individual does uniquely satisfy a reasonable number of those properties, then the proper name ‘Hegel’ refers to him.

Hegel himself contends that this state of affairs is contradictory. His line of reasoning is that

(i)  for anything A, there are general properties B such that A has a some of the Bs;

(ii) therefore, for something B, A is B;

but,

(iii) because things are numerically different from their properties, A must be numerically different from any of the Bs;

(iv) therefore, A cannot be numerically identical with any of the Bs;

(v)  therefore, for any of the Bs, A is not B;

(vi) by (i)-(ii), and by (iii)-(v), we have a contradiction: for some B, A is B and A is not B.

As Russell urged upon us long ago, (vi) does not follow, since Hegel equivocates between (ii) and (v) in his use of the word ‘is’. Prem­ises (iii) and (iv) do indeed yield

(v) therefore, for any of the Bs, A is not B,

where 'is' is elliptical for “is identical with.” But premise (i) yields

(ii) therefore, for something B, A is B,

where 'is' is not elliptical for “is identical with.” If Russell is right, then (ii) and (v) are not genuine contradictories at all, so (vi) does not follow.

Hegel tells us that the tautologousness of the assertion that A is A excludes the possibility of A being B.

The principle of identity affirms that A is only A, not B; and that A is only A, not B; and that B is only B, not A.

A = A, i.e. if anything is A it cannot be B.

This proposal has been made by philosophers more sober that Hegel. Unless several senses of 'is' are distinguished carefully, however, inferences such Hegel's, that

if it is assumed that no two things are the same, that is, everything is different from everything else, then A is not equal to A,

are bound to flow from commonplaces like (i) and (ii).

In Section V, we saw that there was some reason for being suspicious about transitions from
A is numerically different from B

to
A is not numerically identical with B.

The reason, it will be recalled, is that
A is the same F as B

may be perfectly compatible with
A is a different G from B.

Hegel’s inference from

(iii) because things are numerically different from their properties, A must be numerically different from any of the Bs

to

(iv) therefore, A cannot be numerically identical with any of the Bs

creates quite another kind of worry. For it is not clear that any sense can be given to (iii). Plainly, (iv) is true. But is (iv) true because, for example, Hegel is different from his property of writing the Wissenschaft der Logik? A different what? Not a different man, surely, since the property of writing the Wissenschaft der Logik is not a man. Not a different property, since Hegel is not a property. Not a different thing, either, for we cannot say that Hegel is a different thing from any of his properties without begging the question. ‘Thing’ by itself provides no criterion for deciding where one of its instances leaves off and another begins; it provides no principle for counting things. Here the question “A different what?” admits of no satisfactory answer. Either Hegel’s premise (iii) must be sense­less, or we must allow that statements of difference, perhaps unlike statements of identity, are not always dependent on or relative to sortal descriptions.

In the Science of Logic, Hegel makes the very curious assertion that if the law of identity were a law of thought,

then the declaration of its universality ... would be confirmed by every consciousness treating it as fundamental to all its utterances, or as implicit in them all.

This gives us one final explanation for Hegel's claim

that inherently everything is in its own self-equality unequal to itself and contradictory; and that in its difference, in its contradiction, it is identical with itself.

For, if the statement “Everything is identical with itself” is true, according to Hegel, then all the statements we can make about any thing must be statements of identity. But we have just seen that, and for what reasons, Hegel believes that contradictions would arise if all the statements that are true of a thing are statements of identity.

Of course, Hegel has misinterpreted the law. Someone who believes that the law of identity is true commits himself, not to saying that all statements are statements of identity (let alone that they instantiate the law of identity), but that all statements which instantiate the law of identity are true if not referentially empty.

Regarding the law of identity, Moore complains that

Hegel complains in one place that those who assert it also assert its “opposite,” and immediately afterwards, that utterances in accordance with it “deserve” to be “reputed silly.” I cannot take upon myself to decide whether or not he regards these charges as the same, and whether or not he means by opposite “contradictory.” The instances he gives (“A planet is—a planet; Magnetism is—magnetism; Mind is—mind”) seem to be justly accused of silliness. But are they untrue? I do not know that either he or any of his disciples have maintained that Mind is not mind, although they have maintained that Matter is not matter. It would seem, then, that some even of these silly in­stances have contradictories, which are false; and that when Hegel tells us that in asserting the Law of Identity we also assert its opposite, he only means that we must assert something else of Mind as well as the fact that it is Mind; not that we may assert that it is not Mind.

Accordingly, Moore concludes that Hegel’s

complaint would seem to amount to no more than a comment on the ambiguity of the copula, pointing out that many different things may in different senses be predicated of one and the same thing.

Hegel’s point, in claiming that those who assert the law of identity also assert its opposite, was not at all that “many different things may in different senses be predicated of one and the same thing.” If it had been, then he would not have claimed that those who assert the law of identity believe all statements to be statements of identity. No doubt cognizant of this, Moore ends by remarking that the fore­going observation about “the ambiguity of the copula”

is very true, and would be very useful if those who made it, or those who heard it, could be induced thereby to remember it in practice.