Ruth Barcan Marcus published her original proof of the necessity of identity in 1947 and repeated her argument at a 1961 Boston University colloquium.

Whether Wiggins knew of Marcus 1961 is not clear. He should have known of her 1947, and there is similarity to her 1961 derivation (which uses Leibniz's Law). Wiggins gives no credit to Marcus, a pattern in the literature for the next few decades and still seen today.

Saul Kripke clearly modeled much of his derivation after Wiggins, especially his criticism of the derivation as "paradoxical". Kripke gives no credit to either Marcus or Wiggins for the steps in the argument, but his quote from Wiggins, that such a claim makes contingent identity statements impossible, when they clearly are possible, at least tells us he has read Wiggins. And we know Kripke heard Marcus present her work at the 1961 colloquium.

Here is Wiggins (1965),

I WANT to try to show (i) that there are insuperable difficulties any term + relation + term or subject + predicate analysis of statements of identity, (ii) that, however important and helpful the sense-reference distinction is,¹ this distinction does not make it possible to retain the relational or predicative analysis of identity statements, and (iii) that a realistic and radically new account is needed both of ' = ' and of the manner in which noun-phrases occur in identity-statements.

Till we have such an account many questions about identity and individuation will be partly unclear, and modal logics will continue without the single compelling interpretation one might wish.

The connexion of what I am going to say with modal calculi can be indicated in the following way. It would seem to be a necessary truth that if a = b then whatever is truly ascribable to a is truly ascribable to b and vice versa (Leibniz's Law). This amounts to the principle

(1) (x)(y) ((x = y) ⊃ (φ)(φx ≡ φy))

Suppose that identity-statements are ascriptions or predications. Then the predicate variable in (1) will apparently range over properties like that expressed by ' ( =a) ' ² and we shall get as consequence of (1)

Note that Wiggins predicates the property "= x" of y. Kripke writes this as "x = y," logically equivalent, but intensionally predicating "= y" of x!

(2) (x)(y) ((x = y) ⊃ (x = x. ⊃ . y = x))

There is nothing puzzling about this. But if (as many modal logicians believe), there exist de re modalities of the form

◻ (φa) (i.e., necessarily (φa)),

then something less innocent follows. If '( = a) ' expresses a property, then '◻ (a = a)', if this too is about the object a, also ascribes something to a, namely the property ◻ ( = a). For on a naive and pre-theoretical view of properties, you will reach an expression for a property whenever you subtract a noun-expression with material occurrence (something like ' a ' in this case) from a simple declarative sentence. The property ◻ ( = a) then falls within the range of the predicate variable in Leibniz's Law (understood in this intuitive way) and we get

Note (3) is almost Kripke's (3), but with intensional "y = x." Wiggins needs one more step. His (4) is Kripke's (3)

(3) (x) (y) (x = y ⊃ (◻ (x = x). ⊃ .◻ (y = x)))

Hence, reversing the antecedents,

(4) (x) (y) (◻(x = x ). ⊃ (x = y) ⊃ ◻ (x = y)))

But '(◻ (x = x)) ' is a necessary truth, so we can drop this antecedent and reach

(5) (x) (y) ((x = y). ⊃ .◻ (x = y)))

Now there undoubtedly exist contingent identity-statements. Let 'a = b' be one of them. From its simple truth and (5) we can derive '◻ (a = b)'. But how then can there be any contingent identity-statements?...

4. The derivation of (2) itself, via x's predicate ' ( = x)', might be blocked by insisting that when expressions for properties are formed by subtraction of a constant or free variable, then every occurrence of that constant or free variable must be subtracted. '( a = a )' would then yield ' ( = )', and (2) could not be derived by using ' ( = x ) ' . One would only get the impotent

(2') (x = y) ⊃ (x = x. ⊃ . y = y)

The paradox could still be derived however. Suppose that a is contingently b. Then <> ~{a=b); i.e., it is possible that not a=^H This gives the predicate '◇ ~ (a = ) ' . This is true of b. Then by (1), if a = b, this predicate is true also of a. This yields '◇ ~ (a = a) '. But ' (x) ◻(x = x)' is a logical truth and implies ' ~ ◇ ~ (a = a)'.

1 G. Frege, 'On Sense and Reference ', Translations from the Philosophic Writings of Gottlob Frege, ed. P. T . Geach and M. Black (Oxford, 1952), pp. 56-4]
2 Quotation marks are used under the convention that they serve to form a designation of whatever expression would result in a particular case from rewriting the expression within the quotation-marks with genuine constants in the place of free variables and dummy-expressions.

("Identity Statements," in Analytical Philosophy, Second Series, Oxford: Blackwell. pp.40-41
)

It gradually became evident to me in constructing this work that for the future of metaphysics no single part of the philosophy of science was in more urgent need of development than the philosophy of biology. It is well known that Aristotle believed something like this but it seems to be the misfortune of that particular philosopher that few of the things he said can be understood or believed until they are laboriously rediscovered. And it is a misfortune of present-day analytical philosophy that it has not inspired the production of any writings in the philosophy of biology which are both worthy to succeed the seminal writing of J. H. Woodger and capable of illuminating present day philosophical discussions of classification and individuation in the way Aristotle would have argued that they require. To this important task I incite those better qualified than I am to undertake it.

(Identity and Spatio-Temporal Continuity, p.vii)

The chief aim of this book is to elaborate a theory of the individuation of continuants, including living substances and other substances. Such a theory ought to comprise at least three things: an elucidation first of the primitive concept of identity or sameness; second, some account of what it is for something to be a substance or continuant that persists through change; third, an account of what it amounts to, practically and cognitively for a thinker, to single a thing out at a time. Here, with this last task, there is the supplementary question of what it amounts to for the same thinker, having once singled something out, later to single out that same thing as the same thing.

From a philosopher's attitude towards the logical and methodological ordering of these tasks one can tell something about his or her attitude towards the idea that the meaning of a word is a function of its use. In this work, it is everywhere accepted that the meanings of such words as 'same', 'substance', 'change', 'persist' and 'recognize' depend upon their use. The life and semantic identity of such terms is only sustained by the activity of singling out or individuating. But the thesis of meaning as use is consistent with two converse or complementary theses (A)(B), which have an equal relevance to what is to be attempted and an equal claim upon rational acceptance.

(A) The relation between the meaning and the use of such words as 'same', 'substance', 'change', 'persist' is in fact reciprocal or two-way Everything that concerns meaning registers upon use; but, unless we redefine use, that does not imply that meaning can be reduced to use. Among the concerns I began by enumerating, there is no question of collapsing the first two into the third, for instance.

(B) An interpretation of a set of linguistic uses or conceptual practices must speak of the subject matter to which they relate. For that reason, it must refer to the various things themselves towards which the uses or practices themselves are directed, together with the properties and relations of these things. The child who is learning to find for himself the persisting substances in the world, to think the thoughts that involve them and recognize the same ones again, grasps a skill and a subject matter at one and the same time. A philosopher who seeks properly to understand those thoughts must proceed accordingly. Let the philosopher elucidate same, identical, substance, change, persist, etc., directly and from within the same practices as those that an ordinary untheoretical human being is initiated into. At the same time, let the philosopher show by example what good elucidations can be made of such ideas as these. To this end, let him shadow the practical commerce between things singled out and thinkers who find their way around the world by singling out places and objects — and singling out one another. If the meaning of the terms 'same', 'substance', 'change', 'persist', etc., is a function of use and use is a function of the said commerce, then one by-product of this mode of elucidation will be that the task I began by calling the third task is undertaken in concert with the first and the second. The first and second tasks acknowledge the importance of the third; but, by their constant appropriate acknowledgment of this importance, they will in fact absorb the third.

(Sameness and Substance, p.1)

(Sameness and Substance, p.1)

Like the statue and clay, both the tree and the wood, and the sweater/socks and the wool, have different persistence conditions, setting up the classic problem of coinciding objects. All of them seem to be Aristotle's ancient problem of matter and (immaterial) form in the clay and the statue.

Wiggins comments:

If it is a materialistic thesis that T = W, then my denial that T = W is a form of denial of materialism. It is interesting how very uninteresting an obstacle these Leibnizian difficulties – real though they are – put in the way of the reduction of botany and all its primitive terms to organic chemistry or to physics. (If it does not follow from T ≠ W that trees are something over and above their matter, how much the less can it follow that they are immanent or transcendent or supervenient or immaterial beings. This is obviously absurd for trees. A Leibnizian disproof of strict identity could never be enough to show something so intriguing or obscure.)

Wiggins is unabashedly materialist and reductionist. Form over and above matter does not exist

I should expect there to be equally valid, and from the point of view of ontology almost equally unexciting, difficulties in the reduction of persons to flesh and bones, in psychophysical event-materialism, and in the materialisms which one might formulate in other categories (such as the Aristotelian categories property and state or the categories situation and fact). Over and above is one question, identity is another. But of course the only stuff there is is stuff.

("Being in the same place at the same time,"The Philosophical Review, p.92)

As to identity, just like the clay that remains when the statue is crushed, the wood and the wool remain, but their information, organization, or arrangement, what Aristotle called τὸ σχῆμα τῆς ἰδέας, has largely disappeared. This is the ancient terminology of the Stoics (and Aristotle).

The material substrate (ὑποκείμενον) is transformed when matter is lost or gained, but the Stoics said it is wrong to call such material changes "growth (αὐξήσεις) and decay (φθίσεις)." They suggested these changes should be called "generation (γενέσεις) and destruction (φθορὰς)." These terms were already present in Aristotle, who said that the form, as essence, is not generated. He said that generation and destruction are material changes that do not persist (as does the Stoic peculiarly qualified individual with an Aristotelian mind).

Wiggins begins with an assertion S*

S*: No two things of the same kind (that is, no two things which satisfy the same sortal or substance concept) can occupy exactly the same volume at exactly the same time.

This, I think, is a sort of necessary truth...

A final test for the soundness of S* or, if you wish, for Leibniz' Law, is provided by a puzzle contrived by Geach out of a discussion in William of Sherwood. A cat called Tibbles loses his tail at time t₂. But before t₂somebody had picked out, identified, and distinguished from Tibbles a different and rather peculiar animate entity-namely, Tibbles minus Tibbles' tail. Let us suppose that he decided to call this entity "Tib." Suppose Tibbles was on the mat at time t₁. Then both Tib and Tibbles were on the mat at t₁. This does not violate S*.

But consider the position from t₃ onward when, something the worse for wear, the cat is sitting on the mat without a tail. Is there one cat or are there two cats there? Tib is certainly sitting there. In a way nothing happened to him at all. But so is Tibbles. For Tibbles lost his tail, survived this experience, and then at t₃ was sitting on the mat. And we agreed that Tib ≠ Tibbles. We can uphold the transitivity of identity, it seems, only if we stick by that decision at t₃ and allow that at t₃ there are two cats on the mat in exactly the same place at exactly the same time. But my adherence to S* obliges me to reject this. So I am obliged to find something independently wrong with the way in which the puzzle was set up.

This is a clear case of Peter van Inwagen's Doctrine of Arbitrary Undetached Parts

It was set up in such a way that before t₂ Tibbles had a tail as a part and Tib allegedly did not have a tail as a part. If one dislikes this feature (as I do), then one has to ask, "Can one identify and name a part of a cat, insist one is naming just that, and insist that what one is naming is a cat"? This is my argument against the supposition that one can: Does Tib have a tail or not? I mean the question in the ordinary sense of "have," not in any peculiar sense "have as a part." For in a way it is precisely the propriety of some other concept of having as a part which is in question.

As an arbitrary undetached part, Tib has been picked out and defined as coinciding with Tibbles, except for the tail Tibbles is about to lose. This violates S*

Surely Tib adjoins and is connected to a tail in the standard way in which cats who have tails are connected with their tails. There is no peculiarity in this case. Otherwise Tibbles himself might not have a tail. Surely any animal which has a tail loses a member or part of itself if its tail is cut off. But then there was no such cat as the cat who at t₁ has no tail as a part of himself. Certainly there was a cat-part which anybody could call "Tib" if they wished. But one cannot define into existence a cat called Tib who had no tail as part of himself at t, if there was no such cat at t₁. If someone thought he could, then one might ask him (before the cutting at t₂), "Is this Tib of yours the same cat as Tibbles or is he a different cat?"

("Being in the same place at the same time,"The Philosophical Review, p.94)

His second version of Tibbles is widely cited as a discussion of the problem of vagueness.

If a few of Tibbles' hairs are pulled out, do we still have Tibbles, the Cat? Obviously we do. Have we created other cats, now multiple things in the same place at the same time? Obviously not.

Geach argues that removing one of a thousand hairs from Tibbles shows that there are actually 1,001 cats on the mat.

The fat cat sat on the mat. There was just one cat on the mat. The cat's name was "Tibbles": "Tibbles" is moreover a name for a cat.—This simple story leads us into difficulties if we assume that Tibbles is a normal cat. For a normal cat has at least 1,000 hairs. Like many empirical concepts, the concept (single) hair is fuzzy at the edges; but it is reasonable to assume that we can identify in Tibbles at least 1,000 of his parts each of which definitely is a single hair. I shall refer to these hairs as h₁, h₂, h₃, . . . up to h_1,000.

Now let c be the largest continuous mass of feline tissue on the mat. Then for any of our 1,000 cat-hairs, say h_n, there is a proper part c_n of c which contains precisely all of c except the hair h_n; and every such part cn differs in a describable way both from any other such part, say c_m, and from c as a whole. Moreover, fuzzy as the concept cat may be, it is clear that not only is c a cat, but also any part c_n is a cat: c_n would clearly be a cat were the hair h_n plucked out, and we cannot reasonably suppose that plucking out a hair generates a cat, so c_n must already have been a cat. So, contrary to our story, there was not just one cat called 'Tibbles' sitting on the mat; there were at least 1,001 sitting there!

All the same, this result is absurd. We simply do not speak of cats, or use names of cats, in this way; nor is our ordinary practice open to logical censure. I am indeed far from thinking that ordinary practice never is open to logical censure; but I do not believe our ordinary use of proper names and count nouns is so radically at fault as this conclusion would imply.

Everything falls into place if we realize that the number of cats on the mat is the number of different cats on the mat; and c₁₃, c₂₇₉, and c are not three different cats, they are one and the same cat. Though none of these 1,001 lumps of feline tissue is the same lump of feline tissue as another, each is the same cat as any other: each of them, then, is a cat, but there is only one cat on the mat, and our original story stands.

Thus each one of the names "c₁ ; c₂, . . . c_1.000 or again the name "c", is a name of a cat; but none of these 1,001 names is a name for a cat, as "Tibbles" is. By virtue of its sense "Tibbles" is a name, not for one and the same thing (in fact, to say that would really be to say nothing at all), but for one and the same cat. This name for a cat has reference, and it names the one and only cat on the mat; but just on that account "Tibbles" names, as a shared name, both c itself and any of the smaller masses of feline tissue like c₁₂ and c₂₇₉; for all of these are one and the same cat, though not one and the same mass of feline tissue. "Tibbles" is not a name for a mass of feline tissue.

As David Wiggins has argued, we only have relative identity between any two objects

So we recover the truth of the simple story we began with. The price to pay is that we must regard " is the same cat as " as expressing only a certain equivalence relation, not an absolute identity restricted to cats; but this price, I have elsewhere argued, must be paid anyhow, for there is no such absolute identity as logicians have assumed.

(Reference and Generality, 3rd edition, p.215.)

So we now have two metaphysical cats named Tibbles. Of course, it may have been Geach, not Wiggins, who repurposed his cat Tibbles between the 1960's and 1980's! In his 1997 republication of "Being in the same place" (in Michael Burke's book Material Constitution), Wiggins notes Geach had a different purpose for his Tibbles.

In their 1987 book The Hellenistic Philosophers (p.175), Long and Sedley use Wiggins' 1968 version of Tibbles to illustrate the "body-minus" problem, with no reference to Wiggins (or Geach). Just a few pages earlier, Long and Sedley had presented Philo's ancient version of Dion and Theon as part of Chrysippus's "growing argument." .

This paper caught the eye of Daniel Dennett, who expanded on Wiggins' theme of figuring out what libertarians say they want, and trying to give it to them. Wiggins described his goals:

One of the many reasons, I believe, why philosophy falls short of a satisfying solution to the problem of freedom is that we still cannot refer to an unflawed statement of libertarianism. Perhaps libertarianism is in the last analysis untenable. But if we are to salvage its insights, we certainly need to know what is the least unreasonable statement the position could be given. Compatibilist resolutions to the problem of freedom² must wear an appearance of superficiality, however serious or deep the reflections from which they originate, until what they offer by way of freedom can be compared with something else, whether actual or possible or only seemingly imaginable, which is known to be the best that any indeterminist or libertarian could describe.

A sympathetic and serviceable statement of libertarianism cannot be contrived overnight, nor can it be put into two or three sentences, which is all that some utilitarian and compatibilist writers have been willing to spare for the position. If they were more anxious to destroy or supersede libertarianism than to understand and improve it, this was natural enough; but time or human obstinacy have shown that the issue is too complex for such summary treatment. What follows is offered as a small step in the direction of a more reasonable exposition. It concentrates on two or three points, where many need attention. If the treatment of these two or three points has the final effect of making the position even less credible, or of making me sacrificial scapegoat for oddities which persist, I still hope to have shown that the libertarian perceived something which was missed by all extant compatibilist resolutions of the problem of freedom; and that the point the libertarian was making must bear upon any future reconstruction of our notions and practices.

(Towards a reasonable libertarianism, p.33)

2. By compatibilism (or dissolutionism) I mean the position which says that freedom (the freedom of being able to do otherwise) and physical determinism can coexist. By incompatibilism the position that they cannot coexist. Libertarianism is a species of incompatibilism, one which saves freedom by denying physical determinism. In refurbishing libertarianism I do not myself mean to subscribe to a priori or introspective or extra-scientific arguments against physical determinism (or to take any kind of stand about its truth or falsity) but to subscribe to an interest in what the libertarian wanted by way of freedom, whether or not the world will allow of this freedom. Whether libertarianism is true or false, it is the only good source for the position which it entails (without being entailed by it), viz. incompatibilism. It is true that some classical determinists were incompatibilists of a sort, but for the most part libertarian writings are a better guide for the understanding of incompatibilism.