Boundaries, Conventions, and Realism
Achille C. Varzi
Department of Philosophy, Columbia University[Final version published in J. K. Campbell, M. O’Rourke, and M. H. Slater (eds.), Carving
Nature at Its Joints: Natural Kinds in Metaphysics and Science, Cambridge MA: MIT Press,
2011, pp. 129–153]

1. Natural vs. Artificial Boundaries
If you have been driving in Europe recently, you must have had that strange
feeling. You see a sign that says ‘Deutschland’, or ‘France’, or ‘España’, andjust drive through. No customs barrier, no passport control—just a sign. You
say ‘Ah!’ and carry on; the sign could be a hundred yards further out and it
would make no difference. Yet by crossing that line you enter a different
world-district, magically separated from its surroundings—you enter a region
where people suddenly speak another language, rely on their own authorities,
share a different heritage, and struggle to solve their problems and to improve the quality of their common life. The line is there, even if you don’t
see it. That sign conceals a long history, perhaps even a thread of blood,
though all you see today is a spread of asphalt, souvenir shops, motels, gas
stations, abandoned customs houses. It is more difficult to get that feeling as
you drive across the United States of America. Most drivers feel nothing at
all as they pass the border between Wyoming and Idaho, a line whose embarrassing geometric straightness says very little about its history (or says it all).
Yet even here there are differences, and Idahoans are proud of their license
plates just as Wyomingites are proud of theirs. Such is the magic of boundary lines: they are thin, yet powerful; they separate, and thereby unite; they
are invisible, yet a lot depends on them, including one’s sense of belongingness to a country, a people, a place; they are abstract, in a way, yet people
take them seriously and some states expend huge sums of money and sacrifice soldiers’ lives to protect them, or to re-draw them properly. (Kashmir is
one example where the drawing of boundaries—even the precise drawing of
the Line of Control—is still central to the conflict.)
Not all boundaries are so magic, though—are they? As I was flying overYellowstone Park, I did not, in fact, see the Idaho-Wyoming boundary, as
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you don’t see the boundary between Germany and France when you fly over
Europe. Nor did I see the boundaries of the Park itself, or those of the Missouri Plateau earlier on. But I did have the clear and distinct impression ofseeing other boundaries: the shoreline of Lake Erie, for instance, or the edgesof the Missouri River. I saw the boundaries of Long Island when my flight
took off. And I think at some point I saw the crater of a volcano, probably
Bear Butte, though I am not positive about that. (It might have just been asmall lake.) In his celebrated Romanes Lecture of 19071, the British Viceroyof India, Lord Curzon of Kedleston, introduced an important distinction inthis regard, a distinction that is so intuitive as to be part of common sense,
and that geographers officially embraced ever since. And it fits the bill. It’s
the distinction between artificial boundaries, or frontiers, on the one hand,and natural boundaries, or frontiers, on the other.
The boundaries I didn’t see would be of the first sort. National and stateborders are artificial insofar as they are our own making, the product of human decisions and stipulations, an expression of collective intentionality thattranslates into political, social, and legal agreements whereby it is determined
where a certain territory begins and where it ends. So, too, are the boundaries
of many other geographic entities, such as plateaus or wetlands or areas of agiven soil type, though these may be induced by cognitive or cultural processes, or by scientific stipulation, rather than by legal or political practices.
Such artificial boundaries may be drawn with great accuracy (a national border) or left somewhat vague, fuzzy, underspecified (the boundaries of a plateau); it depends on the importance we attribute to the relevant demarcations,on the role they play in our lives. But whether sharp or vague, they all qualify
as “artificial” precisely because the demarcations are human-induced; theyneed not correspond to any genuine, physical or otherwise objective differentiations in the underlying territory. They are de dicto, so to speak, not de reboundaries.
Geographic boundaries of the second sort—the natural, or de re boundaries—would by contrast be characterized precisely by their apparent independence from our organizing activity. We can stipulate that one half of Lake
Erie belongs to Canada and the rest to the US, and the dividing line will be
an artifact. But the shoreline—the border of the whole lake—does not seemto depend on us. It’s there regardless, it exists “on its own”. Ditto for theboundaries of certain political or administrative entities, such as the Regionof Sicily, whose limits are for the most part identified with the limits of the2

Sicilian island; or such as Spain, which although connected to the continent,
is separated from it by the admirably fashioned Pyrenean wall (“the most obvious of features—wrote Joseph Calmette—the plainest of lines, designed bynature in her boldest manner”2). Artificial boundaries may be subject to controversy. They can be ignored or deleted, and thereby go out of existence;
they can be drawn anew, and thereby come into being. Not so with natural
boundaries. We are free to ignore them for certain purposes, but we cannot
ask a cartographer to omit them from a map of the world. In a physical map
we may omit all political boundaries; but a political map will perforce include all physical boundaries—at least, physical boundaries that are visible atthe relevant scale.
Now, it is, of course, an open question whether Lord Curzon’s intuitive
distinction is well grounded. That is precisely the question I want to address.
First, however, let me emphasize that the question does not only arise in relation to the large-scale geographic world that we find depicted in ordinary
maps and atlases. It also arises, for instance, in the smaller-scale world featured in a cadastre. Here, too, the parceling of land into real estate is not simply a geometrical affair. In some cases it would seem to rely on natural, preexisting physical discontinuities, such as creeks, rocks, cliffs, or ditches; inother cases, it is crucial that people believe that whoever fenced off a plot of
land is the person who actually owns it, so collective intentionality appears tobe necessary to explain the difference between landed property and raw land.
And what goes for the cadastre goes for everything. Boundaries play a central role at any level of representation or organization of the world around us,
and so does the relevant artificial/natural distinction. We think of a boundary
every time we think of an object as of something separated from or distinct
within its surroundings. There is a boundary (artificial) separating my part ofthe desk from my colleague’s, my head from the rest of my body, or the sirloin from the ramp on a butcher’s beef chart; there is a boundary (natural)
demarcating the interior of this apple from its exterior, the hole from the donut, or shadow from light. Events, too, have boundaries, including temporal
ones, and the distinction appears to apply equally well: the end of the war or
my turning 21 years old would be examples of artificial boundaries; my birthand death or the point in the cooling process when water begins to solidify
would be obvious candidates for natural boundaries. Even abstract entities,
such as concepts or properties, may be said to have boundaries of their own.
Those expressed by disjunctive predicates such as ‘emerose’ and ‘grue’, or3

by phase sortals such as ‘student’ and ‘jobless’, would have de dicto boundaries. Those expressed by substance sortals and so-called natural kind terms,
such as ‘cow’ or ‘water’, would have genuine, de re boundaries.
It is not an exaggeration to say that boundaries are at work in articulating
every aspect of the reality with which we have to deal. They stand out inevery map we draw of the world—not only the world of geography, but theworld of nature at large, as well as the secular world that emerges through the
weaves of our social and individual practices. And this ubiquity of boundaries goes hand in hand with that of the artificial/natural distinction, the apparent contrast between merely de dicto and genuinely de re demarcations, theopposition—in Barry Smith’s more recent terminology—between fiat articulations and bona fide joints of reality.3 It is not, therefore, an exaggeration to
say that our question bites deeply: How tenable is the distinction? And how
does the answer affect our overall metaphysical picture of the world? How
does it affect our understanding of the identity and survival conditions of thevery things that boundaries demarcate?
2. Boundaries and Things
To begin with, the relationship between a boundary and the entity it bounds
demands clarification. Brentano, following a tradition that goes back to
Abelard if not to Aristotle,4 held that the distinguishing feature of boundaries
lies in their being ontologically dependent on the entities they bound: aboundary “can never exist except … as belonging to a continuum which possesses a larger number of dimensions”5. And it is true: there are, in reality, no
isolated points, lines, or surfaces. We cannot eat all the interior parts of anapple and just keep the surface—not the skin (which is a bulky part) but theperfectly two-dimensional entity that circumscribes the skin from the outside.
We cannot display the boundary of our country in a museum, or steal the
point of intersection between the equator and the Greenwich meridian. Not
even God could do such marvels, pace Suarez.6 However, this relation of dependency is symmetrical: it is equally impossible to have an apple without asurface, or a nation without a border (with few exceptions, such as Poland
during the Era of Partition). Indeed, when it comes to de dicto boundaries, itwould seem that the latter sort of dependency is especially strong, precisely
insofar as those boundaries emerge from our social or cognitive fiats. Someentities begin to exist only when we draw their boundaries. Think of the4states of the so-called Northwest Ordinance, as they were literally brought
into being by Thomas Jefferson’s pencil (and ruler). Or think of when thecolonial powers relied on cartography to subdivide the “heaten lands”: thedrawing of a few lines of ink was all it took to legitimize—and simplify—
their territorial conquest in spite of any existing social and political structures. As Mark Monmonier put it, sometimes the pen really is mightier than
the sword.7 But even when the sword prevails, the outcome is a boundary
which, though conforming with Brentano’s thesis, bears witness to the double-barreled nature of the relevant dependency: were it not for those boundaries, those states would never have existed.
In fact, it is not even correct to speak of the relation between a boundary
and the extended entity to which it must belong: every time we have aboundary, we have two entities, one on each side. Boundaries separate, butthey separate two entities (or two parts of the same entity) which are continuous with each other. The Idaho-Wyoming boundary is thus a boundary of
Idaho, but also a boundary of Wyoming. Who gets to claim ownership?
Surely the boundary does not belong to both, for the two States do not overlap. And we cannot simply say that it belongs to neither: the two States useup the whole territory by definition—no boundary can be left as a thin, unowned slice between them. So? This is an old problem, and it goes without
saying that it is not peculiar to geography. Euclid defined a boundary as “thatwhich is an extremity of anything”8, and Aristotle made this more precise
by defining the extremity of a thing x as “the first thing outside of which nopart [of x] is to be found, and the first thing inside of which every part [of x]
is to be found.”.9 It is a definition that today we may also find in a dictionary.
But what about the extremity itself—does it belong to x or to the complementof x? Consider the dilemma raised by Leonardo in his Notebooks: What is itthat divides the atmosphere from the water? Is it air or is it water?10 Or thinkof the boundary of a black spot on a white surface, as Peirce wrote in his
Logic of Quantity.11 What color is it—black or white? Also in relation totemporal boundaries, the puzzle arises. As Aristotle himself asked in the
Physics, at the instant when an object begins to move, is it in motion or is it
at rest?12
Here one cannot just dispose of the puzzle by treating it as a mere artefact of the modelling process. As Antony Galton points out, properties likecolor or material constitution only apply to extended bodies, so in a way it
makes no sense to ask whether a lower-dimensional entity is air, water, or5colored.13 Yet, at bottom the problem is one of ownership, not of physicalcharacterization. The puzzle is purely topological and originates in the factthat space and time, hence the entities that according to common sense occupy space and endure through time, have the dense geometry of the continuum. There are no adjacent points, lines, or surfaces. Either they coincide,or they are separated by an infinity of further points, lines, surfaces. In termsof the classic doctrine that goes back to Bolzano, this means that when two
regions or bodies are adjacent, one must be “closed”, i.e., include the boundary among its parts, and the other “open”.14 It’s no help to stigmatize the doctrine as “monstrous”, as Brentano did.15 What happens when we cut an apple
in half?—he asked. Which half will come out “closed” leaving the other“open” and bleeding? Alas, this is the very problem at issue, and one cannot
solve it merely by jeering at the apparent counterintuitiveness of the continuum.
Now, I like to think that precisely the distinction between de dicto and dere boundaries may help us solve the puzzle.16 On the one hand, with regard
to artificial boundaries of the first sort, it is true that the question of theirownership can hardly be settled without contravening to the principle of sufficient reason. To assign the Idaho-Wyoming border to Idaho, or to Wyoming, would amount to a peculiar privileging of one State over the other. But
precisely insofar as such boundaries are our own making, it is also true that
their actual ownership is no real issue. Simply, we have not decided which
State gets to own the border, as we have not decided which hemisphere getsto own the Equator, or who gets to own the line separating my part of thedesk from my colleague’s. We have not decided because the decision would
be of no practical consequence whatsoever. And this sort of indeterminacy isof no metaphysical consequence, either. To say that there is no fact of thematter, here, is not to endorse worldly indeterminacy, precisely because weare not dealing with bona fide facts; the indeterminacy pertains exclusively to
our fiat practices. In this regard, the picture is no different from the one we
get as we consider the vagueness of certain boundaries, such as the boundaryof the Missouri Plateau. There is no clear-cut line separating the interior of
the plateau from its exterior, but that doesn’t mean that the plateau is a vague
entity. It means that it is vague what we mean by ‘the Missouri Plateau’: nobody has been “fool enough”, in David Lewis’s phrase17, to draw a precise
line around its intended referent. It means that it is indeterminate (widescope) whether certain parcels of land belong to the Missouri Plateau, not6that the Missouri Plateau is indeterminate (narrow scope) with regard to theinclusion of those parcels of land.
On the other hand, when it comes to de re boundaries—such as the margin of a black spot on a white panel, or the line separating water from the atmosphere—one might think that their ownership need not be up for grabs.
After all, in such cases we are confronted with two entities, one of which isfigure while the other is ground, and it would not be implausible to resolve
the asymmetry in favor of the former. This “ecological” intuition may befound, for instance, in Ray Jackendoff.18 The black spot wins the status of“figure” over its white exterior, hence the relevant boundary belongs to thespot, not the exterior. Water wins over air, which is only “ground”, hence therelevant boundary belongs to the ocean, not the atmosphere. And the same
could be said of the surface of an apple. We never have two closed bodies incontact with each other, only one body embedded in its surroundings, and itis the body—one could say—that gets to own the boundary. Only the apple istopologically closed; the background is open, and that is why the two can be
genuinely in touch. As for Brentano’s problem of explaining what goes onwhen we cut the apple in half, one could say that the dilemma betrays an incorrect model of the cutting process. Surely it would be arbitrary to elect one
half as figure and the other as ground: after the cutting, each half is equally
figure with respect to their common background, hence each will be enveloped by a complete surface. But that is not to say that such surfaces were already hidden inside the apple before the cutting. By dissecting an object we
do not “bring to light new surfaces,” as Ernest Adams has it19, nor do weconvert a de dicto boundary into two de re boundaries. Rather, topologically,
when the cutting takes place the extant outer surface of the object is progressively deformed. A long, continuous process suddenly results in an abrupt
topological change: there was one thing; now there are two. (Think of a splitting soap bubble.) There is indeed something deeply problematic about theabruptness of such a change, but never mind: whatever the explanation, thefigure/ground account would go through.20
Still, I don’t think this can be the whole story. Figure wins, ground loses.
But what happens when two figures come into contact? Think of the Dovercliffs. Hard to construe them as an “open” background for the waters of the
Channel. Even harder if we consider that the cliffs themselves stand out on
the horizon: Should we say that they are open against the water, but closed
against the sky? And what about the line along which they all meet—water,
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rock, air? Whichever item gets the honor of figure, the other two should beground, hence open. But how could they meet, then? The topology of thecontinuum forbids contact between two closed bodies, but also between two
open bodies. Clearly something is going astray. Brentano would say that thisis yet another proof of the inadequacy of classical topology, and would begin
to speak of plerosis and other complicated things that supposedly yield a better fit with intuition and common sense. I would rather say that here intuitionand common sense begin to show their limits, and there is a serious possibility that we embarked on a wrong path.
Indeed, to me it seems obvious that for certain de re boundaries, especially those that mark the limits of material bodies, the ownership problem
does not even arise, for on closer look such boundaries are not what we
think. On closer look, as we know, an apple is not a solid, continuous object.
On closer look, material objects are just swarms of subatomic particles franctically dancing in an otherwise empty space (the “material” volume of an apple is really only one billionth of what we commonly measure), and speakingof their surfaces is like speaking of the “flat top” of a fakir’s bed of nails, asPeter Simons’ put it.21 On closer look, therefore, it makes little sense to speakof continuous objects separated by a common de re boundary. It makes nosense to ask who gets to own that boundary. All there is are smudgy bunchesof hadrons and leptons, and if we really wish to insist, we can say that eachsuch thing is figure against an empty background. But the background isempty: there is nothing else that could claim ownership. To put it differently,
on closer look the spatial boundaries of common material bodies involve thesame degree of arbitrariness as those of any mathematical graph smoothed
out of scattered and inexact data, the same degree of idealization of a drawing obtained by “connecting the dots”, the same degree of abstraction as thefigures’ contours in a Seurat painting. It makes no sense to inquire about theowners of those boundaries, or rather, it only makes sense insofar as we recognize their ephimeral status as fiat demarcations that exist in virtue of ourcognitive acts but that are not genuinely present in the autonomous (which is
to say mind-independent) physical world—hence as de dicto boundaries.
And we have seen that the ownership of such boundaries can be left indeterminate. Ditto when we move from objects to events. On closer look, as weknow, a body’s being at rest amounts to the fact that the vector sum of the
motions of the trillions of restless atoms of which the body is composed, averaged over time, equals zero, hence it makes no sense to speak of the instant8

at which an object begins to move.22 Either we are dealing with a de dicto
boundary, in which case we know how to handle the problem, or rather leave
it unresolved; or we are dealing with particles that are restlessly in motion, in
which case the problem does not even arise.
3. From Boundaries to Things
At this point, however, the very distinction between de dicto (artificial) andde re (natural) boundaries demands reexamination, and it is here that thequestion of its tenability bites deeply. Were it just a matter of boundaries, theexact extension of these two concepts might leave us unmoved; it is their intension that takes care of the problems. But once the de dicto / de re distinction has been recognized, it can be drawn across the board: not merely in relation to boundaries but also in relation to all those entities that may be said
to have boundaries. If a certain entity enjoys natural boundaries, it is reasonable to suppose that its identity and survival conditions do not depend on us;
it is a bona fide entity of its own. By contrast, if (some of) its boundaries are
artificial—if they reflect the articulation of reality that is effected throughhuman cognition and social practices—then the entity itself is to some degree
a fiat entity, a product of our worldmaking. This is not to say that fiat entitiesof the second sort are imaginary or otherwise irreal entities. As Frege put it,
the objectivity of the North Sea “is not affected by the fact that it is a matterof our arbitrary choice which part of all the water on the earth’s surface wemark off and elect to call the ‘North Sea’”.23 It does, however, mean thatsuch entities would only enjoy an individuality as a result of our cognitive
and/or social practices, like the cookies carved out of the dough: their objectivity is independent, but their individuality—their being what they are, including their having the identity and survival conditions they have—depends
on the baker’s action. (In the terminology of John Searle, they are “social objects”: from a God’s eye point of view you don’t see a cookie just as you
don’t see a nation or the North Sea; you only see us treating certain chunks ofreality as cookies, nations, or the North Sea.24)
Now, the existence of de dicto boundaries, hence of fiat entities, is uncontroversial. We can even be more fine-grained, if we wish. We can, forinstance, draw a further distinction between fiat entities that owe their existence to collective intentionality, or to the beliefs and habits of a community,
as with geopolitical or social entites at large, and fiat entities that emerge in9

stead from the cognitive acts of single individuals, beginning with perception, which as we know from our experience of Seurat paintings has the function of articulating reality in terms of continuous boundaries even when suchboundaries are not genuinely present. Individual fiats are more ephemeralthan social fiats because they are rigidly dependent (on these acts, taking
place now) rather than generically dependent (on the existence of relevant
acts of a certain kind). We can also distinguish between those cases where afiat entity is delineated or carved out as a proper part of a larger entity, aswith our initial examples, and those cases where a fiat entity is obtained bycircumcluding a number of smaller entities within larger wholes, as with
Polynesia, the constellation Orion, or ordinary material bodies such as apples
upon recognition of their microscopic structure, or as when we describe theworld as consisting of forests, physaliae, schools of fish, swams of bees,
fleets of ships, pairs of shoes.25 (Natural language contributes to the generation of fiat entities also through the opposition between mass nouns, such as‘cattle’, and count nouns, such as ‘cow’. A hungry carnivore points towards
the cattlefield and pronounces ‘There is cattle over there’. How does thispronouncement differ, in its object, from ‘There are cows over there’? Not,
certainly, in the underlying real bovine material.) Regardless of all such refinements, it is clear that in each case de dicto boundaries are at work in articulating the reality with which we have to deal, and the entities obtained
thereby are themselves of the fiat sort. Nor will such entities acquire a bonafide status upon further work on our side. As we have seen, no pre-existent
inner surface is brought to light by a process of cutting. Indeed, administrative or political borders may in course of time come to involve boundarymarkers (barriers, walls, barbed-wire fences, or electronic devices) that willtend in cumulation to replace what is initially a pure de dicto boundary withsomething more substantial. Yet, again, this is not a process of ontic transformation. Such markers can be very robust, but not so robust as to turn theartificial into the natural. The Chinese Great Wall has survived for centuries,
but the Berlin Wall lasted a mere fifty years and Israel’s “Separation Wall” inthe West Bank has not been recognized by the International Court of Justice.
On Sept. 22, 2005, the US Secretary of Homeland Security used his power to“waive in their entirety” the Endangered Species Act, the Migratory Bird
Treaty Act, the National Environmental Policy Act, the Coastal Zone Management Act, the Clean Water Act, the Clean Air Act, and the National Historic Preservation Act to extend triple fencing along the US/Mexico border10

through the Tijuana River estuary; a few months later, the San Diegans wereplaying volleyball with the Tijuanans using the fence at the beach border as anet. Even Romulus’s plowshare could not make natural what natural is not;the blade cuts the soil, tears the grass, uproots all that lies on its fiat path.
Let us rather ask whether, and to what extent, it is appropriate to countenance the existence of natural, de re boundaries, hence of natural, bona fide
entities that do not depend on our deeds. By itself, the concept is perfectly
intelligible, and we should be thankful to Lord Curzon for emphasizing its
political significance. As Lucien Febvre famously argued, the very notion ofa natural frontier began to emerge in the nineteenth century precisely as an
expression of the idea that in some cases the limits within which we are allowed to act are set by Nature itself: natural boundaries are “fixed by destiny”, they represent “ideals to conquer and realize”26. It is one thing to takeup arms on the crest line of the Pyrenees, quite another to sacrifice your life
for a Jeffersonian line. It is not surprising that the Irish Republican Armywants the whole island of Ireland, but who would fight for the Wyoming Independentist Party? Still, even in relation to the geopolitical world, the natural/artificial distinction is all but robust. It is true that I had the impression ofseeing the shoreline of Long Island from my plane. But it is also true thatwhen you actually go there, ground-level, things look very different. Whatlooked from the air like a sharp line turns out to be an intricate disarray ofstones, sand, algae, piers, boardwalks, cement blocks, musk sediments,
marshy spots, putrid waters, decayed fish. Ditto for the much celebrated Irish
coast. And it’s not just a matter of our disrespect for Nature; the worry would
not change significantly if we took a close look at the coast of a virgin islandin the middle of the ocean. Suppose we locate the boundary of the island at
the water/sand interface. That boundary is constantly in flux, and it is only byfiltering it through our cognitive apparatus—it is only by interpolating objects and concepts—that a clear-cut line may emerge. Even if both water andsoil were perfectly still and each were materially homogeneous, it would be
hard to locate the boundary with precision. One is reminded here of a question familiar from the early literature on fractals: Just where, and how long, isthe coastline of Britain? When measured with increased precision, the coastline would furnish lengths ten, a hundred, a thousand times greater than thelength read off a schoolroom map. As ever-finer features are taken accountof, the measured total length increases, and Benoît Mandelbrot concluded
that “there is usually no clear-cut gap between the realm of geography and11details with which geography need not be concerned”.27 Cartographers know
this well: one works with calipers, but their opening is not fixed by Nature.
And if there is no fact of the matter answering the question, “How long is thecoastline?”, one wonders whether it is even meaningful to think of the coast
as of a natural, objectively determined boundary. One begins to wonder
whether the island itself might not in some sense be the product of our subjective and approximate worldmaking. And what goes for islands goes for all
prima facie natural geographical or celestial entities: lakes, rivers, craters,
glaciers, mountain chains, whole planets. “Even stars?”, asked Israel Sheffler. Yes, even stars, answered Nelson Goodman: “As we make constellations by picking and putting together certain stars rather than others, so wemake stars by drawing certain boundaries rather than others”28.
It is a short step, now, to extend such doubts to all those boundaries that
intuitively belong to the de re category, hence all those entities that would
seem to enjoy a bona fide, mind-independent reality. We have already seenthat ordinary material objects tend to dissolve as soon as we acknowledge
their microscopic structure: this apple is just a smudgy bunch of hadrons andleptons whose exact shape and properties are no more settled than those of aschool of fish. Or perhaps they are more settled, for the causal connectednessof the apple appears to be stronger than that of a school of fish; yet thisseems to be a matter of degree, not the sort of categorial difference involvedin the de re/de dicto opposition. But never mind that line of reasoning; oneneed not resort to microscopes to realize that the notion of a natural object is
far from being clear and distinct. Take this cat, Tibbles—a paradigm example
of a living creature, hence a perfect candidate to the status of a bona fide individual. Regardless of its subatomic structure, the question of what counts
as it has no clear answer. Tibbles is eating a chunk of tuna. When it was in
the plate, that chunk was definetly not part of Tibbles. But now it is in Tibbles’s mouth: Is it part of Tibbles? Will it be part of Tibbles only after somechewing? Only when Tibbles swallows it? Only at the end of the digestive
process? Surely, whatever mewing-and-purring portion of reality we markoff and elect to call ‘Tibbles’ is something that exists in its own right; as with
the North Sea, its objectivity is not affected by the fact that our stipulation isa matter of arbitrary choice. Yet surely the stipulation adds a fiat element to
its individuality. Tibbles is not entirely a product of our own making; yet its
identity and survival conditions will obtain only relative to us. And thiswould remain true even if our stipulation were not quite “arbitrary”—even if
12

it fully returned what Jack Wilson calls the “biological individuality” of ourcat.29 Alas, biology is a science, and as such it involves its own stipulations.
A workshop being held at the University of Utah at this very moment, on the
topic “Edges and Boundaries of Biological Objects”, focuses precisely on thethesis that “delimiting biological objects cannot be determined by empiricalfacts alone; which facts are salient, and what counts as evidence, often depend on theoretical and conceptual context”.30
What goes for objects goes for events, including biological processes.
Earlier I mentioned a person’s birth and death as obvious examples of de retemporal boundaries, yet the controversies on abortion and euthanasia seemto push for a different treatment. Sometimes it is a matter of our deciding
whether a person is still alive. We decide whether her “vital” functions arestill in force, and the criteria for such decisions give expression to our beliefs,
our principles, our theories. Similarly, on closer look the initial boundary of aperson’s life is hardly fixed by Nature alone. Surely that boundary does notcoincide with the person’s birth—itself a rather intricate, messy, often protracted process (later cleaned up by the registry office)—but neither is there
an earlier moment that fits the bill comfortably. Would it be: the moment of
fertilization, when the membrane of the sperm cell fuses with that of the egg?
Or upon formation of the zygote? When the zygote begins to undergo a process of genetic replication and cell division? Upon formation of the morula?
The beginning of the implantation process? The beginning of the gastrulation process, which gives structure to the embryo? The candidates are many.
We can base our decision on as many factors we like, including up-to-theminute scientific findings—but a decision it is. And if it is a matter of our(arbitrary or informed) decision, then the boundary is not genuinely de re after all and even a person’s life becomes, to some extent at least, a fiat process.
What about natural properties? Natural kinds? Natural taxa? Here things
get more complicated, of course, since the relevant notion of a boundary—especially the notion of a de re boundary—is less clear. In fact, when it
comes to such entities, the natural/artificial distinction intertwines with thewhole realism/nominalism controversy, and our geographic metaphor isbound to sound naïve and dismissive. Still, even here it’s obvious and wellknown that, on closer look, our parochial concerns—historical and cultural
circumstances, practical interests and limitations, theoretical priorities—tend
to play a major role in the maps we draw of the world. Surely quadrupeds do
not form a “natural” kind. But it would be quite remarkable, to use Catherine
13Elgin’s example, if a taxonomy that draws the distinction between horses andzebras where we do aligned with categories fitting the cosmos as a whole,
but indifferent to our human faculties and ends (including our interest in domesticating animals).31 Surely emeroses do not form a natural kind—but neither do roses. Why settle on Rosa chinensis? Even in physics, our microscopic categories seem to suffer from a variety of human contingencies. If weconstrue different isotopes as variants of the same type of atom, it is becauseof certain reasonable interests that predominated in the development of ourbest theories. One could as well construe oxygen-17 and oxygen-18 as different types of atom altogether, hence as “natural” kinds of their own. Herethe problem is not that there are no differences in the physical world; theproblem is that there are too many differences, and to privilege some over theothers is to draw a fiat line—like the dotted line demarcating this apple fromits exterior, or Tibbles from the rest of the world. Besides, it is a fact thateven within specific domains of inquiry, our scientific practices are not uniform. The thought that the taxa countenanced by biology (for instance) are
fiat entities seems to clash with “the certainty of biologists on the objective
reality of evolution”, as David Stamos puts it.32 Yet even today many taxonomists base their classifications more on phenetic than on phylogenetic
criteria, regardless of the avowed principles under which they operate, and inphenetics a natural classification is simply one in which the members of eachtaxon are on the average more similar to each other than they are to membersof other taxa “at the same level” (by itself a problematic notion). Maybe suchtaxonomists are being sloppy. Maybe the phylogenetic criterion is better. (Iteven fits the creationists paradigm, as the God of Genesis supposedly created
all living things to reproduce “according to their kinds”33). But that’s enoughto cast the doubt: a criterion is a criterion. We should not shudder if, in theend, we read in the Annual Review of Ecology and Systematics that “taxa arehuman constructs” and “natural taxa are those that are natural to humans”.34
And we should not complain if non-human animals have different taste. After all, there are horses and zebras, but also zorses and hebras. (Didn’t Lockeeven see “the issue of a cat and a rat”?35)
4. Conventionalism and Realism
It’s pretty clear where all this is going. In the Phaedrus, Socrates famously
recommends that we should carve the world along its natural joints, trying
14

“not to splinter any part, as a bad butcher might do”36, and we know that science and common sense alike have taken this advice very seriously. If all
boundaries were the product of some cognitive or social fiat, if the lines
along which we “splinter” the world depended entirely on our cognitive
joints and on the categories that we employ in drawing up our maps, then our
knowledge of the world would amount to neither more nor less than knowledge of those maps. The thesis according to which all boundaries—hence allentities—are of the fiat sort would take us straight to the brink of precipice,to that extreme form of conventionalism according to which “there are nofacts, just interpretations”. On the other hand, to posit the existence of genuine, bona fide boundaries—to think that the world comes pre-organized into
natural objects and properties—reflects a form of naïve realism that does notseem to stand close scrutiny.
We know how the compromise solution goes. Perhaps all boundaries are,on closer look, de dicto boundaries. It doesn’t follow that they must be utterly arbitrary, i.e., lack any foundation in reality. It is like beef or veal, says
Umberto Eco: “In different cultures the cuts vary, and so the names of certain
dishes are not always easy to translate from one language to another, yet it
would be very difficult to conceive of a cut that offered at the same moment
the tip of the nose and the tail”.37 In other words, perhaps there are no obligatory paths, no one-way streets in the realm of Being; it still does not meanthat anything goes. Some paths will still display a “no entry” sign, some constraints or “lines of resistance” may still be there, making it hard to cut thebeast as we like. Out of metaphor, there may still be objective limits to our
freedom to carve the world, and it is precisely in this spirit that the realism/conventionalism dichotomy is supposed to be handled. If it is presumptuous to think that the boundaries depicted on our physical maps are perfectly
accurate, it is also implausible to think that they are completely off the mark.
If it is implausible to think that biology can identify the exact moment at
which a person’s life begins, it is also implausible to suppose that life begins
before fertilization, or at kindergarten. The very notion of “natural kind” towhich scientists refer would not betray a commitment to naïve realism but,rather, a form of scientific realism whose cash value is first and foremost
pragmatic. Just as the maps in our atlases have become more and more accurate, so will the maps drawn by the sciences. And just as cartographers areoften forced to redraw their maps as a result of unexpected geo-politicalchanges (the artificial boundary of Israel, but also the prima facie natural
15

boundary of sand between Lybia and Egypt, which keeps drifting under thewind), so biologists and other scientists will not refrain, if necessary, fromupdating their maps of nature, in an effort to achieve greater accuracy andtruthfulness. (The taxonomic misadventures of the platypus would be a good
illustration of this fact. What sort of beast is that? Not a MAMMAL, for it layseggs. Not a REPTILE, for its blood is warm. Not a BIRD, for it’s got four legs.
For over eighty years, the naturalists were baffled: as René-Primevère Lesson
observed in 1839, that double-damned beast had set itself “athwart the pathof taxonomy to prove its fallaciousness”.38 Yet it was there, and eventually
the category MONOTREME was created ex novo.)
Now, I have no intention of denying the pragmatic reasonableness of thisstance. But I do not share its fundamental optimism, as I do not recognize thedistinction between metaphysical realism and scientific realism if not, indeed, on a deflated understanding of the term ‘realism’. That nobody cuts thebeef in funny ways does not mean that the laws of nature prevent it. It meansthat in spite of our cultural diversities, the culinary taste and aesthetic senseof human beings display surprisingly robust regularities, literally as well as
out of metaphor. Consider the debate on unrestricted composition. There isno question that we feel more at ease with certain mereological composites
than with others. We feel at ease, for instance, with regard to such things as
the fusion of Tibbles’s parts (whatever they are), or even a platypus’s parts;
but when it comes to such unlovely and gerrymandered mixtures as Lewisean
trout-turkeys, consisting of the front half of a trout and the back half of a turkey, we feel uncomfortable.39 Such feelings may exhibit surprising regularities across contexts and cultures. Yet, arguably they rest on psychologicalbiases and Gestalt factors that needn’t have any bearing on how the world isactually structured. As James van Cleve has pointed out, even if we came up
with a formula that jibed with all ordinary judgments about what counts as anatural fusion and what does not, it wouldn’t follow that there may exist innature only such objects as answer the formula.40 If anything, it would followthat the factors that guide our judgments of unity impose systematic constraints on our fiat articulations.
Besides, the controversies on biotechnology demonstrate that even suchfactors are less robust than one might think. We feel horror and disgust forsuch unlovely and gerrymandered mixtures as chimeras and genetically modified organisms, but we have long learned to feed on orange-mandarines, yogurth, peppermint, and seedless grapes, and we didn’t have many scruples
16

when it came to forcing zoological categories to make room for mules andpoodles. According to the Royal Horticultural Society, in less than 150 years
we have managed to fill the world with over 110,000 orchid hybrids. Either
we are adamant that DNA is our model for an organism’s individuality—and
this is a metaphysical thesis that demands argument—or we must recognizethat even the “no entry” signs on the way of Being are on closer look an expression of our contingent biases, reasonable as they might be. Of course, we
are free to fight for or against such biases and to study their network in thespirit of honest descriptive metaphysics. After all, the world as we represent
it is the only world we really care about, for it is the world on which we bet
everything, including our happiness. That’s why Husserl called it the Lebenswelt.41 Nonetheless, that would not be a way of solving the dilemma between realism and conventionalism; it would be a reasonable way of getting
rid of it altogether.
For those who think that the dilemma ought to be addressed explicitly,
however, I am going to conclude with three remarks aimed at deflating, atleast partly, the sense of collapse that usually comes with the conventionalist
hypothesis, understood in the radical sense according to which there would
be no de re boundaries whatsoever, whether “one way” or “no entry”.
To begin with, one should not mistake the conventionalist hypothesis
with the ghost of Berkeleyan idealism. As I have described it here, the notionof a de dicto boundary is intelligible only to the extent that we acknowledge
an appropriate real basis for the sorts of demarcation that are effected by our
pencils, trenching tools, and cookie cutters. Even assuming that all boundaries are of this sort, and wholly arbitrary, it does not follow that everything is
the product of a percipemus. This is why I stressed that the cognitive dependence of a fiat entity affects its individuality but not its objectivity. This
may well be seen as a “last-ditch effort” to save realism, as Andrew Cortens
dubbed it,42 but so be it. That the factual material onto which we project ourcategories should itself be a cognitive construct is a different, stronger thesis,
which I do not even understand except in the figurative sense made popular
by the thought experiments of rational skepticism (Cartesian demons, brains
in a vat, the Matrix). From this perspective, conventionalism is not to be mistaken with Goodmanian irrealism, either. For Goodman—and for Richard
Rorty—all we learn about the world is contained in right versions of it; “andwhile the underlying world, bereft of these, need not be denied to those wholove it, it is perhaps on the whole a world well lost”.43 For a conventionalist,17the world is boneless, impoverished, almost bankrupt, but our love for it is
not at stake. For Goodman, a world-version need not be a version of theworld, just as a Pegasus-picture need not be a picture of Pegasus. For a conventionalist, all the maps we draw are indeed maps of one and the same reality. Putnamian relativism, then? Even less. For Hilary Putnam, the “cookie
cutter” metaphor founders on the question, “What are the ‘parts’ of thedough?”.44 No neutral description is available to compare a Leśniewskian
world (with x, y, and the fusion of x and y) and a Carnapian world (with only
x and y), and assigning a univocal meaning to ‘exists’ is already “wanderingin Cloud Cockoo Land”45. For the conventionalist, the metaphor holds and‘exists’ corresponds to the standard existential quantifier. The number of fiat
entities is up for grabs; but the parts of the dough, which provide the appropriate real basis for our fiat acts, are whatever they are and the relevant
mereology is a genuine piece of metaphysics. (As far as I am concerned,
composition is unrestricted, hence the mereology is Leśniewskian; so either
Carnapians are not speaking with their quantifiers wide open, as when we say‘There is no beer’ meaning ‘There is no beer in the refrigerator’, or else they
are objectively wrong. Others might favor a different account. For instance,
one may describe the conflict as stemming from the appeal to different“counting criteria”, as Searle suggested,46 or from a disagreement about
whether composition is “innocent”, in Lewis’s sense.47 But surely the world
could not care less about our criteria and our jury verdicts.)
Second, what’s so bad with conventions being arbitrary? We have justseen that, from a pragmatic perspective, it is not the putative de re structureof the world that drives our ways of carving it up, in our folklife as well as inscience, but the robustness and utility of certain ways against the ephemeralness and futility (if not the absurdity) of others. If we just replaced Socrates’snatural joints with Jefferson’s pen strokes, then it would be a disaster, andunfortunately that’s exactly what happens in some cases. The decision to annex Alaska to the US echoes the chef’s unlikely resolution to prepare a dishwith a veal’s tail and the tip of its nose, and the thought of classifying people
on the basis of their skin color or their intelligence quotient isn’t much better
than the idea of drawing the Dutch-Belgian border through the houses of
Baarle. Nonetheless, in most cases the arbitrariness of our conventions, thosethat govern our social interactions as well as those that are accorded scientificdignity, epitomizes a democratic reasonableness that treasures experienceand cooperation. Conventionalism, just like pre-Kantian empiricism, does18

obliterate any substantive differences between the laws of nature and train
timetables, as Maurizio Ferraris complains.48 But timetables are not drawn up
at random. They ensue from the necessity to solve, in an arbitrary but efficient way, coordination problems that can be extremely complex and that
could seriously impair our daily deeds. If we come up with a timetable thatworks poorly, we change it. If a convention fails to measure up to our expectations, we replace it with a new, hopefully better one. Ditto with the laws ofnature. For a conventionalist, not all biological taxonomies (for instance) areon a par. Some are better than others, because they better support the “laws”
that govern biology’s coordination game (laws of variation, selection, organic evolution, population growth, etc.). One may object that this sort ofpragmatic efficiency calls for more than arbitrary, fiat demarcations. But theburden of proof is on the objector, not on the friend of conventionalism. Linnaeus’s Systema Naturae, the bible of all classical taxonomies, was soakedwith essentialism—and the platypus didn’t fit in.49 Darwin, by contrast, wasadamant that the term ‘species’ is one “arbitrarily given for the sake of convenience to a set of individuals closely resembling each other”50—and his
theory is much better.
Indeed, the arbitrariness of conventions does not even rule out that insome cases there is a single best way to go, a single best theory. On David
Lewis’s classic account, conventions are arbitrary insofar as they always admit of “equally good alternatives”.51 If a problem has a unique solution, thenthe solution is not conventional. By contrast, as I understand the term here,
conventions are arbitrary insofar as they do not depend on the bona fidestructure of the world. This need not imply that there always be at least two
equally good choices that we could make; it simply implies that it is up to
us—in nostro arbitrio—to make the choice. Hence I agree with Mark Heller:
in some cases, “the adopted convention may be the single best choice, eventhe obvious best choice”.52 We may adopt a convention precisely because itis the best choice, but an arbitrary choice it is. It follows, therefore, that whenit comes to the monism/pluralism debate concerning the status of scientifictaxonomies (hence: theories), a conventionalist may even side with the monist, at least relative to a certain domain of inquiry. A conventionalist may be
a monist, not insofar as there is a unique correct way of carving up the world,
but insofar as there may be a unique best way of doing that.
Finally, for those who, like myself, believe in the significance of socalled prescriptive (or: revisionary, revolutionary, hard-core) metaphysics, it
19

is worth emphasizing that even a radical conventionalist stance across theboard need not yield the nihilist apocalypse heralded by post-modern propaganda. The pervasiveness of de dicto boundaries does not coincide, for instance, with the death of the individual. On a Putnamian metaphysics, there
are no individuals except in a relative sense. On a Goodmanian metaphysics,
we make individuals by drawing boundaries as we like, and this goes “all theway down”.53 Not so for my conventionalist, or not necessarily. For a conventionalist, the identity of a cat, like the identiy of a cookie, a people, a nation, or a constellation, turns out to lack authonomous metaphysical thickness. But other individuals may present themselves. For instance, on a
Quinean metaphysics, there is an individual corresponding to “the material
content, however heterogeneous, of some portion of space-time, however
disconnected and gerrymandered”.54 (What then distinguishes a material“substance” from other individuals is a detail, namely, “that there are relatively few atoms that lie partly in it (temporally) and partly outside”.) Thatthe content of some such portions of space-time have de re boundaries is apossibility, but it is equally possible that the only boundaries are those warranted by geometry. Either way, the corresponding notion of an individual isperfectly intelligible. The relevant identity conditions are perfectly determinate, and one may suppose that it is perfectly determinate, for any property,
whether any given individual possesses it. Such individuals are perfectly
nonconventional, yet the overall picture is one that a conventionalist is free toendorse. The conventionalist stance simply entails that which of them cometo play a role in our life is up to us. From a God’s eye point of view, they are
all equally real. It’s just that only some are salient for us, only some make us“feel comfortable”, and only some are selected by us through the impositionof more or less precise and official de dicto boundaries. (Heller is one philosopher who explicitly endorses this view.55)
Evidently, a metaphysics of this sort presupposes the existence of a large,
all-embracing four-dimensional “dough”. But we have already seen that sucha presupposition is not incompatible with a conventionalist stance. Nor isreference to the boundaries warranted by geometry vetoed by that stance, as
though it surreptitiously reintroduced de re demarcations. As we have outlined it here, the de dicto / de re distinction does not apply to the geometricboundaries of space-time any more than it applies to the boundaries presupposed by set theory. They are bare boundaries, so to speak: they are not “artificial”, but neither are they “natural”. As for the overall plausibility of the20theory, this is not the place to embark on an articulated defense. Surely theintuitive plausibility is pretty low, and perhaps also its scientific tenability.
Yet, philosophically the deflationary purism of a theory of this sort would
have some advantages, including the extermination of the essentialist cancer
that besets those metaphysical theories that try to save common sense against
the paradoxes of persistence, vagueness, and material constitution.
But, as I said, this is not the place to embark on an articulated defense ofsuch metaphysics. (And it is but an example. A Sidellean metaphysics of“pure stuff” would do just as well.56) The relevant point is that, also in relation to the third worry, the conventionalist hypothesis need not result in adelegitimization of all philosophical inquiry; only a redistribution of the relative tasks and concerns of the different fields of inquiry, including metaphysics along with physics, psychology, or sociology. The costs are obvious, forepistemology and also for ethics. But so are the advantages. There are, on
this view, no obligatory or forbidden paths; conventionalism is as liberal as it
gets, and it is up to us to erect the “one way” or “no entry” signposts that we
find appropriate, just as it is up to us to remove them when things take a turnfor the worse. As Michael Dummett put it, the picture of reality as an amorphous lump, not yet articulated in discrete objects, is a good one “so long as
we make the right use of it”.57 Most importantly, given that even common
sense is far from being an all-or-nothing affair, except for certain surprising
regularities, it is up to us to acknowledge our parochial limits without camouflaging them as “natural”. At least then we would stop pretending thatboundary wars have a “just” solution. To conclude on a rhetorical note, if
there is a solution, let’s face it, it lies in the reciprocal and democratic agreement among all interested parties, hard as it might be to achieve it.58

Notes
1

Lord Curzon of Kedleston, Frontiers. The Romanes Lecture, Oxford, Clarendon Press, 1907.
2
J. Calmette, ‘La frontière pyrénéenne entre la France et l’Aragon’, Revue desPyrénées, 25 (1913), 1–19, at p. 1.
3
B. Smith, ‘On Drawing Lines on a Map’, in A. U. Frank e W. Kuhn (eds.),
Spatial Information Theory. A Thoretical Basis for GIS, Berlin, Springer, 1995, pp.
475–484; extended version as ‘Fiat Objects’, Topoi 20 (2001), 131–148.
4
See P. Abelard, Logica ingredientibus, commentary on Porphyry’s Isagoge
21

(partial Eng. trans. by P. V. Spade: ‘From the “Glosses on Porphyry”’, in P. V.
Spade, Five Texts on the Mediaeval Problem of Universals, Indianapolis: Hackett,
1994, pp. 26–56, at p. 26). Compare Aristotle, Metaphysics, K, 2, 1060b12ff.
5
F. Brentano, ‘Vom Kontinuierlichen’ (1914), in his Philosophische Untersuchungen zu Raum, Zeit und Kontinuum, ed. by S. Körner and R. M. Chisholm, Hamburg, Meiner, 1976, pp. 3–49, at p. 14 (Eng. trans. by B. Smith: ‘On What Is Continuous’, Philosophical Investigations on Space, Time and the Continuum, London,
Croom Helm, 1988, pp. 1–48, at p. 10).
6
See F. Suarez, Metaphysicae Disputationes, XL, 5, 41.
7
M. Monmonier, How to Lie with Maps, Chicago, University of Chicago Press,
1991, at p. 90.
8Euclid, Elements, Bk I, Df 13.
9
Aristotle, Metaphysics Δ, 17, 1022a.
10
Leonardo da Vinci, The Notebooks, selected Eng. trans. ed. by E. MacCurdy,
London, Reynal and Hitchock, 1938, at pp. 75–76.
11
C. S. Peirce, ‘The Logic of Quantity’ (1893), in C. Hartshorne and P. Weiss(eds.), Collected Papers of Charles Sanders Peirce, Vol. IV, Cambridge (MA),Harvard University Press, 1933, pp. 85–152, at p. 98.
12
Aristotele, Physics, VI, 234aff.
13
A. Galton, ‘On the Ontological Status of Geographical Boundaries’, in M.
Duckham et al. (eds.), Foundations of Geographic Information Science, London:
Taylor and Francis, 2003, pp. 151–71, at p. 167.
14
B. Bolzano, Paradoxien des Unendlichen (a cura di F. Přihonský), Leipzig,
Reclam, 1851 (Eng. trans. by D. A. Steele: Paradoxes of the Infinite, London, Routledge & Kegan Paul, 1950); see especially § 66.
15
F. Brentano, ‘Nativistische, empiristische und anoetistische Theorie unserer
Raumvorstellung’ (1906), in his Philosophische Untersuchungen zu Raum, Zeit und
Kontinuum, op. cit., pp. 164–177, at p. 174 (Eng. trans. by B. Smith: ‘Nativistic,
Empiricist and Anoetistic Theories of Our Presentation of Space’, PhilosophicalInvestigations on Space, Time and the Continuum, op. cit., 138–149, at p. 146).
16
Here I draw on B. Smith and A. C. Varzi, ‘Fiat and Bona Fide Boundaries’,
Philosophy and Phenomenological Research 60 (2000), pp. 401–420.
17
D. K. Lewis, On the Plurality of Worlds, Oxford, Blackwell, 1986, at p. 212.
18
See e.g. R. Jackendoff, Consciousness and the Computational Mind, Cambridge (MA), MIT Press, 1987, Appendix B.
19
E. W. Adams, ‘On the Superficial’, Pacific Philosophical Quarterly 65(1984): 386–407, at p. 400. In the same spirit, D. Zimmerman speaks of “a part ofthe object which was first imbedded in the [object] and then disclosed wearing a
new skin” (‘Could Extended Objects Be Made Out of Simple Parts?’, Philosophy
and Phenomenological Research 56 (1996): 1–29, at p. 25).
22

20

Here I refer to my ‘Boundaries, Continuity, and Contact’, Noûs 31 (1997),
pp. 26–58, esp. p. 42.
21
P. M. Simons, ‘Faces, Boundaries, and Thin Layers’, in A. P. Martinich and
M. J. White (eds.), Certainty and Surface in Epistemology and Philosophical
Method. Essays in Honor of Avrum Stroll, Lewiston, Edwin Mellen Press, 1991, pp.
87–99, at p. 91.
22
Here I concur with Galton. See his ‘Instantaneous Events’, in H. J. Ohlbach(ed.), Temporal Logic: Proceedings of the ICTL Workshop, Saarbrücken, MaxPlanck-Institut für Informatik, Technical Report MPI-I-94-230, 1994, pp. 4–11.
23
G. Frege, Die Grundlagen der Arithmetik, Breslau, Köbner, 1884 (Eng. trans.
by J. L. Austin: Foundations of Arithmetic, Oxford: Basil Blackwell, 1950), § 26.
24
See J. R. Searle, The Construction of Social Reality, New York, Free Press,
1995.
25
On all this, see B. Smith, op. cit., as also his ‘Agglomerations’, in C. Freksa,
and D. M. Mark (eds.), Spatial Information Theory. Cognitive and Computational
Foundations of Geographic Information Science, Berlin, Springer Verlag, 1999, pp.
267–282.
26
L. Febvre, La terre et l’évolution humaine. Introduction géographique àl’histoire, Paris, Alben Michel, 1922, at p. 354 (Eng. trans. by E. G. Mountford andJ. H. Paxton: A Geographical Introduction to History, New York, Knopf, 1925, at p.
297).
27
See B. B. Mandelbrot, ‘How Long Is the Coast of Britain? Statistical SelfSimilarity and Fractional Dimension’, Science 156 (1967): 636–638. Some philosophers take questions such as these, and the lack of a definite answer, to be a sign ofontological vagueness; see e.g. B. J. Copeland, ‘On Vague Objects, Fuzzy Logic,
and Fractal Boundaries’, Southern Journal of Philosophy 33 (Suppl.): 83–96.
28
Cfr. I. Scheffler, ‘The Wonderful Worlds of Goodman’, Synthese 45 (1980):
201–209, at p. 205, and N. Goodman, ‘Notes on the Well-Made World’, Erkenntnis
19 (1983): 99–108, at p. 104 (see also Goodman’s original reply in ‘On Starmaking’,
Synthese 45 (1980): 210–215, at p. 213).
29
J. Wilson, Biological Individuality. The Identity and Persistence of Living
Entities, Cambridge, Cambridge University Press, 1999.
30
Edges and Boundaries of Biological Objects, Annual Colloquium, Universityof Utah, Department of Philosophy, March 13–15, 2008. The quote is from the electronic flyer at http://www.phylosophy.org/eb.
31
See C. Z. Elgin, ‘Unnatural Science’, Journal of Philosophy 92 (1995): 289–
302, at p. 297.
32
D. N. Stamos, The Species Problem. Biological Species, Ontology, and theMetaphysics of Biology, Lanham (MD), Lexington Books, 2003, at p. 131 (n. 35).
33
Genesis 1:12, 21, 24–25.
23

34

R. R. Sokal, ‘Phenetic Taxonomy: Theory and Methods’, Annual Review of
Ecology and Systematics 17 (1986): 423–442, at p. 424.
35
J. Locke, Essay, § III.vi.23.
36
Plato, Phaedrus, 265d.
37
U. Eco, Kant e l’ornitorinco, Milano, Bompiani, 1997, at p. 39 (Eng. trans.
by A. McEwen: Kant and the Platypus. Essays on Language and Cognition, New
York, Harcourt Brace, 1999, at p. 53).
38
I got the quotation second-hand from Eco, op. cit., at p. 216 (Eng. trans. at p.
250), though I was not able to locate the source.
39
D. K. Lewis, Parts of Classes, Oxford, Blackwell, 1991, at p. 7.
40
See J. van Cleve, ‘Mereological Essentialism, Mereological Conjunctivism,
and Identity Through Time’, Midwest Studies in Philosophy 11 (1986): 141–156, at
p. 145.
41
E. Husserl, ‘Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie’, Philosophia 1 (1936): 77–176 (Eng. trans. by D. Carr:
The Crisis of European Sciences and Transcendental Phenomenology, Evanston(IL), Northwestern University Press, 1970), §9h.
42
A. Cortens, ‘Dividing the World into Objects’, in W. P. Alston (ed.), Realism
and Antirealism, Ithaca (NY), Cornell University Press, 2002, pp. 41–56, at p. 54.
43
N. Goodman, ‘Words, Works, Worlds’, Erkenntnis 9 (1975): 57–73, at p. 60.
Compare R. Rorty, ‘The World Well Lost’, Journal of Philosophy 69 (1972): 649–
665.
44
See H. Putnam, The Many Faces of Realism, LaSalle (IL), Open Court, 1987,
Lecture 1, esp. p. 19.
45
H. Putnam, Ethics without Ontology, Cambridge (MA), Harvard University
Press, 2004, at p. 85.
46
See J. R. Searle, op. cit., at p. 163.
47
See D. K. Lewis, Parts of Classes, op. cit., at p. 85.
48
M. Ferraris, Goodbye Kant!, Milano, Bompiani, 2004, at p. 17.
49
C. Linnaeus, Systema naturae, sive, Regna tria Naturae systematice proposita per classes, ordines, genera & species, Leiden, de Groot, 1735.
50
C. Darwin, The Origin of Species by Means of Natural Selection, London,
Murray, 1859, at p. 52 (repr. London, Penguin Classics, 1985, at p. 108).
51
See D. K. Lewis, Convention. A Philosophical Study, Cambridge, Cambridge
University Press, 1969.
52
M. Heller, The Ontology of Physical Objects. Four-Dimensional Hunks ofMatter, Cambridge, Cambridge University Press, 1990, at p. 44 (n. 44).
53
See N. Goodman, ‘Notes on the Well-Made World’, op. cit., at p. 107 (n. 6).
54
W. V. O. Quine, Word and Object, Cambridge (MA), MIT Press, 1960, at
p. 171.
24

55

See M. Heller, op. cit.
See A. Sidelle, Necessity, Essence, and Individuation. A Defense of Conventionalism, Ithaca (NY), Cornell University Press, 1989.
57
M. Dummett, Frege. Philosophy of Language, London, Duckworth, 1973, at
p. 577.
58
Many thanks to Sara Bernstein for her commentary at the INPC conference
and to Roberto Casati, Elena Casetta, Umberto Eco, Antony Galton, Allen Hazen,
Hud Hudson, David Mark, Barry Smith, Roy Sorensen, and Dean Zimmerman for
helpful discussion on various aspects of this work. I am also thankful to Luca Morena and Giuliano Torrengo for their comments and criticisms on an earlier version of
the paper, parts of which appeared in Italian as ‘Teoria e pratica dei confini’, Sistemi
intelligenti 17 (2005): 399–418.
5625