Michael Burke is Professor Emeritus of Philosophy at Indiana University.

He worked on problems of material constitution and critically examined Chrysippus's ancient problem of Dion and Theon and its modern version Tibbles, the Cat .

Burke wrote in 1994:

The Stoic philosopher Chrysippus is said to have posed the following puzzle. Yesterday, there was a whole-bodied man called 'Dion' who had a proper part called 'Theon'. Theon was that part of Dion which consisted of all of Dion except his left foot. Today, Dion's left foot was successfully amputated.

The Academic Skeptics said no individual can survive a material loss. Chrysippus argued that Dion could. Theon was just a name for a part of Dion, not a distinct individual, hypothesized for dialectical purposes

So, if Dion and Theon both still exist, they are numerically different objects now occupying just the same place and wholly composed of just the same matter. Presuming this to be impossible, the question is which of the two, Dion or Theon, has ceased to exist.

At first thought, of course, it seems that neither has ceased to exist. It would seem absurd to deny that Dion is still with us. Surely, a man can retain his identity despite the loss of a foot. But it also seems undeniable that Theon still exists. Theon, it seems, has emerged from the surgery intact.

Might it be that Dion and Theon, who initially were two, have both survived, but now are one? Assuming the indiscernibility of identicals, a principle invoked even in Hellenistic philosophy, the answer is "no." For even now there is something true of Dion which is not true of Theon: that he once had two feet.

As will be obvious to those familiar with contemporary identity theory, the puzzle of Dion and Theon is of more than antiquarian interest. The same type of puzzle commands much attention today. (The example discussed most often is that of Tibbles the cat.) Interestingly, none of today's theorists would agree with Chrysippus that Theon has perished.

(Dion and Theon: An essentialist solution to an ancient puzzle, p.129 )

About the same time, Peter van Inwagen (1981) imagined a Descartes who had lost a leg ("Doctrine of Arbitrary Undetached Parts," reprinted in Michael Rea's 1997 book, Material Constitution). Van Inwagen denied the legitimacy of a second individual occupying the same space and time as even a part of Dion.

Wiggins described his Tibbles, beginning 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.

Arbitrarily "picking out" a subset of some whole set creates another set, but not another individual

A cat called Tibbles loses his tail at time t₂. But before t₂ somebody 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)

Wiggins sees that "one cannot define into existence a cat" or a cat-part at the same place and time as part of another cat. But the Tibbles version has left out what Chrysippus wanted to achieve with his explanation of growing, that an individual can survive material loss. This was his whole point in cutting off a foot, generally not appreciated by modern accounts.

In their great 1987 compilation of Hellenic thought, A. A. Long and D. N. Sedley described Tibbles as an example of "two peculiarly qualified individuals coming to occupy one substance," something the Stoics explicitly denied is possible. Long and Sedley clearly are following Wiggins' 1968 version of Tibbles. They suggest that Chrysippus has given us an example of Dion surviving a diminution in his material without losing his identity, as the Academic Skeptics claimed.

The key is to recognize this as the ancestor of a puzzle which has featured in recent discussions of place and identity. Take a cat, Tibbies, and assign the name Tib to that portion of her which excludes her tail. Tibbies is a cat with a tail, Tib is a cat without a tail. Then amputate the tail. The result is that Tibbies, now tailless, occupies precisely the same space as Tib. Yet they are two distinct cats, because their histories are different. The conclusion is unacceptable, and the philosophical interest lies in pin-pointing the false step.

That Chrysippus' puzzle works along similar lines is made clear by Philo's later comments, in which he takes Theon to be related to Dion as part to whole. Dion corresponds to Tibbies, Theon to Tib, and Dion's foot to Tibbies' tail. The differences are twofold. First, the problem is about occupying the_same substance, not the same place. Second, Chrysippus assumes both the validity of the opening steps of the argument and the truth of the principle that two peculiarly qualified individuals cannot occupy the same substance at the same time. He therefore concludes that one of the two must have perished, and his problem is to see why it should be one rather than the other. Philo's elliptical summary leaves unclear Chrissippus' reason for selecting Theon for this honour, but it is probably that if we are asked whose foot has been amputated we can only answer 'Dion's'. Theon cannot have lost a foot which he never had.

The title of Chrysippus' work shows that this puzzle was developed in connexion with the Growing Argument. But to what purpose? The following is a guess. According to the Growing Argument, matter is the sole principle of individuation, so that a change of matter constitutes a change of identity. Hence Socrates is a different person from the same individual with one extra particle of matter added. Now these two individuals are related as part to whole —just as Theon and Dion in the amputation paradox are related. Thus the paradox's presupposition that Dion and Theon start out as distinct individuals is not one that Chrysippus need endorse; it is a premise attributed for dialectical purposes to the Academic opponents, who cannot deny it without giving up the Growing Argument. But once they have accepted it, the Growing Argument is doomed anyhow. For whereas the Growing Argument holds that any material diminution constitutes a loss of identity. Chrysippus has presented them with a case, based on their own premises, where material diminution is the necessary condition of enduring identity: it is the diminished Dion who survives, the undiminished Theon who perishes.

(Stoic Ontology, The Hellenistic Philosophers, A. A. Long and D. N. Sedley, p.175)

In his 1996 article "Tibbles the cat: A Modern 'Sophisma'," Burke claimed Tibbles was "scholastic in origin," which is puzzling as he knows the story of the Greek Dion and Theon very well (Burke 1994b). He describes Tibbles, clearly following Wiggins or Long and Sedley?,

Before us stands a 10-pound cat named 'Tibbles'. Before us also is that 9-pound part of Tibbles which consists of all of Tibbles except his tail. Following philosophical custom, call that bodily part, for which English has no common name, a 'puss'; and give Tibbles' puss the proper name 'Tib'. Further, assume that cats are wholly physical. (Or else let 'Tibbles' name the body of the cat, or even a toy cat.) Suppose now that Tibbles loses his tail. We are left with a tailless cat - and a puzzle. If Tib and Tibbles both still exist, they are numerically different physical objects, one a former 10-pounder, one not, which now consist of just the same matter and occupy just the same place. That, presumably, is impossible. Either Tib or Tibbles, therefore, has ceased to exist. But which one? The identity of a cat surely is not tied to its tail. So Tibbles still exists. But surely Tib has not ceased to exist: Tib lost none of its parts. Something has to give. But what?

Tibbles-type puzzles are a mainstay of revisionist metaphysics. They figure in arguments for mereological esssentialism, the doctrine that every part of an object, no matter how small, is essential to its identity. They persuade some philosophers to deny the dictum that different objects cannot occupy the same place at the same time. They are part of what persuades other philosophers to relativize numerical identity, whether to time or to sort. They are used to motivate rejection of our ordinary conception of (physical) objects as three-dimensional in favor of a conception on which objects are assimilated to events and have temporal as well as spatial parts. And they convince Peter van Inwagen that there are no such things as undetached tails and pusses...

(Tibbles the cat: A Modern "Sophisma". Philosophical Studies, 84(1), 63)

Here is what I propose to say about Tib and Tibbies: Initially we had a 10-pound cat, Tibbies, which contained a 9-pound puss, Tib. Before us now, following the loss of the tail, is a single 9-pound object, one which is both a cat and a puss. That object is Tibbies, which earlier had a tail but now is tailless. Tib has ceased to exist.

What is novel in this account, and what will surely seem counterintuitive, is the claim that Tib has ceased to exist. After all, I allow that there was such a thing as the puss Tib. And I allow that there is a puss before us now. The latter is spatiotemporally continuous with Tib. And it is both qualitatively and compositionally identical to Tib. So how could it fail to be Tib? My answer, very simply, is that Tib was merely a puss, whereas the puss now before us is also a cat...

I assume that cats are essentially cats, from which it follows that noncats are essentially noncats. In doing so, I presuppose Aristotelian essentialism, the doctrine that some of the properties of an object are (non-trivially) essential to it, that others are accidental to it, and that the essentiality or accidentality of those properties is independent of how the object is described. More specifically, I presuppose sortal essentialism, the doctrine that an object's sort is essential to it. Second, I assume that Tib was a noncat. More generally, I assume the maximality of (the concept) cat. That is, I make the commonsensical assumption that proper parts of cats are not themselves cats. Third, I assume that if Tib still exists, now that Tibbles' tail is no longer connected to it, then Tib is now a cat. This, too, is a thoroughly commonsensical assumption. If Tib still exists, why wouldn't it be a cat? What qualification would it lack?

From the first two assumptions it follows that Tib was a noncat essentially, meaning that Tib could not have survived a change that would have made it, if it survived, a cat. In effect, the third assumption is that Tib's disconnection from Tibbles' tail was just such a change. Taken together, the three assumptions yield the surprising conclusion that Tib has ceased to exist.

( Tibbles the cat: A Modern "Sophisma". Philosophical Studies, 84(1), 64-65)

The essence of an object, the "kind" or "sort" of object that it "is", its "constitution," its "identity," includes those "proper" parts of the object without which it would cease to be that sort or kind. It would lose its identity.

Mereology is the study of parts and is historically the decomposition of an entity into its components, the parts which "compose" the whole. Some of these may be "proper parts," but in what sense can we say that? Others may be merely parts that we have picked out to focus on and have given names. They may in no way be "natural" parts, kinds, or sorts.

Aristotle knew that most living things can survive the loss of various parts (limbs, for example), but not others (the head, say). By analogy, he thought that other objects (and even concepts) could have parts (or properties) that are essential to its definition and other properties or qualities that are merely accidental. Mereological essentialism should ba the study of those essential parts.

At his presidential address to the twenty-fourth annual meeting of the Metaphysical Society of America in 1973, Roderick Chisholm defined "mereological essentialism," the idea that if some object has parts, then those parts are essential, metaphysically necessary, to the particular object..

The puzzle pertains to what I shall call the principle of mereological essentialism. The principle may be formulated by saying that, for any whole x, if x has y as one of its parts then y is part of x in every possible world in which x exists. The principle may also be put by saying that every whole has the parts that it has necessarily, or by saying that if y is part of x then the property of having y as one of its parts is essential to x. If the principle is true, then if y is ever part of x, y will be part of x as long as x exists.

("Parts as essential to their wholes. The Review of Metaphysics, 1973, 26: p.582.)

No doubt some parts are essential, in the sense that the brain or heart is essential to a human being. But surely not every part of any whole is a necessary part in all possible worlds? As Aristotle said, some parts may be accidental. And some parts may not persist as criteria of the object's "identity through time."

An information analysis shows that much of the verbal quibbling in metaphysical disputes is about objects or "parts" of objects that are arbitrarily named, defined by language conventions, as opposed to objects that are "natural kinds."

Theon and Tib are what Peter van Inwagen called "arbitrary undetached parts." They have been "picked out" a separate objects to pose puzzles about the different persistence properties of different objects.

An information-based metaphysics can show that for two "coinciding objects" can often be shown to be distinguishing between the matter and form of a single object, for example the statue and the lump of clay. But the immaterial form (abstract information) and the concrete material are not "parts" in the same sense. This seems to be a "category mistake."

In his 1992 article "Copper Statues and Pieces of Copper: A Challenge to the Standard Account," describes this "standard account."

We have before us a copper statue. In the same place,presumably, there is a piece of copper. Let's call the statue 'Statue' and the piece of copper 'Piece'. Now what is the relationship between Statue and Piece?

Information philosophy denies these two "consist" of the same matter. The Piece is wholly matter. The Statue is merely form. They have been picked out and named for their dialectical value as having different persistence conditions

Among philosophers who reject the view that objects have temporal parts, by far the most popular account of such cases is one on which Statue and Piece are numerically different objects even though they consist of just the same matter and are wholly present in just the same place. What shows them to be different objects, according to this account, is that they have different persistence conditions: Piece could survive a drastic change in shape; Statue could not. Let's call this 'the standard account.'

("A Challenge to the Standard Account." Analysis 52: 12-17)

In his 1994 article "Preserving the principle of one object to a place," Burke begins by arguing that the standard account for many metaphysical identity theorists is:

It is common for the whole of one object and the whole of another object to occupy just the same place at the same time. So say many identity theorists...

(Philosophy and Phenomenological Research, 54(3), p.591)

Among the "identity theorists" cited by Burke are David Wiggins (1967), Saul Kripke (1971), Roderick Chisholm (1973), and E. Jonathan Lowe (1983).

Exceptions include Peter van Inwagen (1981), who Burke says calls it a "desperate expedient," David Lewis (1986), who wrote, "This multiplication of entities is absurd on its face," and Harold Noonan (1988), who says it "manifests a bad case of double vision" (as the Ancient Skeptics complained about the Stoic categories of material substate or body and the 'peculiarly qualified individual' or person in their discussions of the Growing Argument )."

In his extensive article, Burke cites several examples of coinciding objects, the statue and clay, a tree and its molecules, cats and pusses, and persons and bodies.

Information philosophy, and an information-based metaphysics, analyzes all these problems as distinctions between the immaterial form (the information) and the material substance. As such, information philosophy is a dualist theory. Burke recognizes the importance of this distinction, potentially solving problems that are intractable for a modern materialist or naturalist philosopher, who denies anything immaterial, notably the mind.

Perhaps the most frequently cited example of coincidence is that of persons and their bodies. Let's briefly consider the example from both dualist and materialist points of view.

On dualist theories of the human person, there is no threat of genuine coincidence. Dualist theories divide into those on which the body is a proper part of the person and those on which the body is something like a possession. On theories of the first type, it is true that a person occupies the place occupied by his body. But it's not the whole of the person that occupies that place; it's merely a part of him that does so. This is no more a case of coincidence than is the case of a pipe and its bowl... On theories of the second type, on which a person is a mind or soul that "possesses" a body, it is only in some non-literal sense that a person may be said to "occupy" the place occupied by her body. The sense is similar to that in which a general may be said to occupy the area occupied by his army, even if he commands the army from outside that area.

On materialist theories, the matter is more complicated. For materialists who identify persons with their bodies, there is no question of coincidence. But for supporters of (some version of) the brain criterion or the psychological criterion of personal identity, coincidence may seem unavoidable...

To conclude this subsection, I want to indicate, although I won't here develop, a line of reasoning that suggests that coincidence is especially worth resisting precisely in the case of persons and their bodies. Suppose that Pete, a person, coincides with his body, Bob. Then Pete, like Bob, is a physical object. (It is only on theories on which persons are purely physical objects that persons are literally coextensive with their bodies.) Indeed, Pete consists of just the same particles of matter as does Bob.

Now here is the problem. Suppose that Pete is thinking. On both type-type and token-token versions of materialism, Pete's thinking is identifiable with some physical event taking place within Pete. But any physical event taking place within Pete is taking place also within Bob. Does this mean that Bob, also, is thinking? If not, why not? If a person and his body are different physical objects composed of just the same particles of matter, the only differences between them, it would seem, lie in their persistence conditions and, perhaps, in their early histories. (No doubt it would be said that death without dismemberment would terminate the existence of Pete but not that of Bob. And perhaps it would be said that Bob came into existence some months or years earlier than Pete.) But there is no apparent way to explain, simply by reference to those differences, why thinking (or talking or walking) is something done by persons but not by their bodies. Unless an explanation can be provided, or unless materialists are willing to accept the multiplication and coincidence of agents, they had better find a way to avoid saying that persons and their bodies are different physical objects wholly present in just the same place. To materialists who favor the psychological criterion (or the brain criterion) of personal identity, I commend the sort of account presented above.

("Preserving the principle of one object to a place," in Rea, M. C., Material Constitution: A Reader p.261)

Dion is a whole-bodied, human person. Theon is that part of Dion which consists of all of Dion except his left foot. Now Dion's left foot has been successfully amputated. Presumably, Dion has survived the amputation. But so, presumably, has Theon, from which no part was removed. Dion and Theon still differ numerically, since there is something true of Dion but false of Theon: that he was diminished by the surgery. Evidently, then, Dion and Theon are now 'coinciding objects'. That is, they are different objects that now are composed of exactly the same matter and occupy exactly the same place, which seems absurd. And since Theon is now identical in its microphysical properties to the person Dion, it seems that Dion and Theon must now be coinciding persons, which seems even more absurd. Hence we have a problem.

There are many solutions on offer. Notoriously, all have features that at least initially seem counterintuitive. On my solution, Dion survives the surgery but Theon perishes. So there is no post-surgical coincidence. What raises eyebrows, of course, is my claim that Theon perishes. After all, Theon seems to undergo no intrinsic change (or none of significance). Theon seems to undergo merely a relational change, a 'Cambridge change'.

That Theon does indeed perish (if it exists in the first place) follows (given the assumptions I'll identify) from three premisses, each of which accords with ordinary ways of thinking. The first premiss - call it the maximality premiss - is that proper parts of men are not themselves men. Given the maximality premiss (and given the assumption that there is a man of whom Theon is a proper part), we can say that Theon is initially a non-man. The second premiss - call it the essentialist premiss - is that men (humans) are essentially men, from which it follows (in SS5) that non-men are essentially non-men. Given the essentialist premiss as well as the maximality premiss, we can say that Theon is a non-man essentially. This means, presumably, that Theon cannot change from being a non-man to being a man. (When I speak of something's changing from F to G, or of an F's becoming a G, I mean numerically the same thing's being first an F and then a G.) The third premiss - the no-coincidence premiss - is that no two objects coincide. (We would need to surrender this commonsensical assumption only if we could find no other, more congenial means of dealing with such problems as that of Dion and Theon.s) Given the nocoincidence premiss (and given an endurantist conception of persistence), we can say that if Theon survives its separation from Dion's left foot, Theon survives as a man. That's because there clearly is some man where a surviving Theon would be (whether he's Dion, Theon, or someone else). So if there can't be two objects there, a surviving Theon would have to be that man. Given all three plausible premisses (and the auxiliary assumptions), we can conclude that Theon does not survive. To survive, Theon would have to do what nothing can do: go from being a non-man to being a man.

("Dion, Theon, and the many-thinkers problem," . Analysis, 64(3), pp.243-244)