Citation for this page in APA citation style.           Close


Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Louise Antony
Thomas Aquinas
David Armstrong
Harald Atmanspacher
Robert Audi
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Belsham
Henri Bergson
George Berkeley
Isaiah Berlin
Richard J. Bernstein
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
émile Boutroux
Michael Burke
Joseph Keim Campbell
Rudolf Carnap
Ernst Cassirer
David Chalmers
Roderick Chisholm
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Herbert Feigl
John Martin Fischer
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
Sam Harris
William Hasker
Georg W.F. Hegel
Martin Heidegger
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
Pamela Huby
David Hume
Ferenc Huoranszki
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Andrea Lavazza
Keith Lehrer
Gottfried Leibniz
Michael Levin
George Henry Lewes
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Alasdair MacIntyre
Ruth Barcan Marcus
James Martineau
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
Thomas Nagel
Otto Neurath
Friedrich Nietzsche
John Norton
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Karl Popper
Huw Price
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
Peter Unger
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
G.H. von Wright
David Foster Wallace
R. Jay Wallace
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf


Michael Arbib
Walter Baade
Bernard Baars
Gregory Bateson
John S. Bell
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Donald Campbell
Anthony Cashmore
Eric Chaisson
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Lüder Deecke
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Philipp Frank
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Art Hobson
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Ladislav Kovà?
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Benjamin Libet
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
James Clerk Maxwell
Ernst Mayr
John McCarthy
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Roger Penrose
Steven Pinker
Colin Pittendrigh
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Adolphe Quételet
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
Max Tegmark
William Thomson (Kelvin)
Peter Tse
Vlatko Vedral
Heinz von Foerster
John von Neumann
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek
Fritz Zwicky


Free Will
Mental Causation
James Symposium
The Problem of the Many
Modern metaphysicians make the problem of vagueness the central issue in the Problem of the Many. Vagueness may also be involved in the Sorites paradox.

The Problem of the Many may also be a consequence of the significant use of set theory in analytic philosophy along with the view that inanimate "composite objects" are nothing but "simples arranged object-wise," as Peter van Inwagen has maintained.

Van Inwagen criticized the tendency of metaphysicians to pick out selected "parts" or even just some properties of an object and claim to see another individual, as the Stoic Chrysippus did in his so-called "Growing Argument."

Recall that the Skeptics accused the Stoics of putting two entities at the same place and the same time, making us all double. Now this was only because the Stoics distinguished the substance (ο?σ?α?) or substrate (?ποκε?μενον) from the "peculiarly qualified individual" (?δ?ο? ποι?ν), much as Aristotle saw a man as a combination of matter and form, body and mind.

Plutarch says if the Stoics add two individual qualifications to one and the same substance, there could also be three or four or more...

(1) One can hear them [the Stoics], and find them in many works, disagreeing with the Academics and crying that they confuse everything by their 'indiscernibilities' and force a single qualified individual to occupy two substances. (2) And yet there is nobody who does not think this and consider that on the contrary it is extraordinary and paradoxical if one dove has not, in the whole of time, been indiscernible from another dove, and bee from bee, wheat-grain from wheat-grain, or fig from proverbial fig.
Adding a second individual to the same substance may refer to the puzzle of Dion and Theon?
And here Plutarch anticipates the modern problem of the many
(3) What really is contrary to our conception is these people's assertions and pretences to the effect that two peculiarly qualified individuals occupy one substance, and that the same substance which houses one peculiarly qualified individual, on the arrival of a second, receives and keeps both alike.
For, if two, there will be three, four, five, and untold numbers, belonging to a single substance; and I do not mean in different parts, but all the infinite number of them belonging alike to the whole.

The Problem of the Many is mostly associated with the modern metaphysician Peter Unger. who named it in 1980, and Peter Geach, who the same year showed how his metaphysical cat Tibbles could be reimagined as 1,001 numerically distinct cats by plucking each of 1,000 cat hairs.

Losing hairs reminds us of a variation of the Sorites puzzle of the heap of grains of wheat. It asks for the exact moment that a man becomes bald as his last few hairs fall out.

David Wiggins tells us that Geach's first version of Tibbles was as a cat that loses just one part, his tail, in an update of the " body-minus" problem of Dion and Theon,

If we remove something inessential (say one water molecule from a cloud, one hair from the second Tibbles, a foot from Dion, a tail from the first Tibbles, a leg from Descartes, or replace one plank in the Ship of Theseus), do we have a new entity, as the Academic Skeptics first argued?

Can we discover a criterion of parthood that makes some "proper parts" mereologically essential to the identity of the whole?

If we could, that would stop merely dialectical claims about different sets of the simplest components of a material object that are picked out by a metaphysician to start an argument. Van Inwagen attacks this as the "Doctrine of Arbitrary Undetached Parts."

Unger and van Inwagen independently came up with the extreme opposite position from the Problem of the Many, which became known as "mereological universalism," the belief in the existence of arbitrary "mereological sums." Give a set with a large number N of simple members, the Problem of the Many suggests that the N! different combinations of those members composes a new object.

Peter Unger

In 1980 Peter Unger formulated what he called "The Problem of the Many." It led Unger to propose that nothing exists and that even he did not exist, a position known as nihilism.

Today this is the metaphysical problem of material composition and of vagueness.

The Problem of the Many
In 1999 Unger redescribed the problem in Oxford Studies in Metaphysics
let us start by considering certain cases of ordinary clouds, clouds like those we sometimes seem to see in the sky.

As often viewed by us from here on the ground, sometimes puffy ‘‘picture-postcard’’ clouds give the appearance of having a nice enough boundary, each white entity sharply surrounded by blue sky. (In marked contrast, there are other times when it’s a wonder that we don’t simply speak singularly of ‘‘the cloud in the sky’’, where each visible cloudy region runs so messily together with many other cloudy ‘‘parts of the sky’’.) But upon closer scrutiny, as may happen sometimes when you’re in an airplane, even the puffiest, cleanest clouds don’t seem to be so nicely bounded. And this closer look seems a more revealing one. For, as science seems clearly to say, our clouds are almost wholly composed of tiny water droplets, and the dispersion of these droplets, in the sky or the atmosphere, is always, in fact, a gradual matter. With pretty much any route out of even a comparatively clean cloud’s center, there is no stark stopping place to be encountered. Rather, anywhere near anything presumed a boundary, there’s only a gradual decrease in the density of droplets fit, more or less, to be constituents of a cloud that’s there.

With that being so, we might see that there are enormously many complexes of droplets, each as fit as any other for being a constituted cloud. Each of the many will be a cloud, we must suppose, if there are even as many as just one constituted cloud where, at first, it surely seemed there was exactly one. For example, consider the two candidates I’ll now describe. Except for two ‘‘widely opposing’’ droplets, one on one side of two overlapping cloudy complexes, way over on the left, say, and another way over on the right, two candidate clouds may wholly overlap each other, so far as droplets goes. The cited droplet that’s on the left is a constituent of just one of the two candidates, not a component of the other; and the one on the right is a component of the other candidate, not the one first mentioned. So each of these two candidate clouds has exactly the same number of constituent droplets. And each might have exactly the same mass, and volume, as the other.

In his 1990 book Material Beings, Peter van Inwagen said Unger's original insight that there are many ways to compose a cloud from innumerable water droplets should be called"mereological universalism.

Van Inwagen denies there is any way for simples to compose anything other than themselves, which van Inwagen calls "mereological nihilism.

Peter Geach

Geach worked on problems of identity and some time in the early 1960's reformulated Chrysippus's ancient problem of Dion and Theon as "Tibbles, the Cat."

In 1968, David Wiggins described Geach's first version of Tibbles. Where Theon is identical to Dion except he is missing a foot, we now have a cat named Tibbles and a second cat named Tib who lacks a tail.

In 1980, Geach repurposed his metaphysical cat Tibbles. Geach's second version of Tibbles is widely cited as a discussion of the problem of vagueness or what Peter Unger in the same year called the Problem of the Many.

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. He writes:

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 h1,000.

Now let c be the largest continuous mass of feline tissue on the mat. Then for any of our 1,000 cat-hairs, say hn, there is a proper part cn of c which contains precisely all of c except the hair hn; and every such part cn differs in a describable way both from any other such part, say cm, 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 cn is a cat: cn would clearly be a cat were the hair hn plucked out, and we cannot reasonably suppose that plucking out a hair generates a cat, so cn 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, . . . c1.000 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.

Burke, M. B. (2004). Dion, Theon, and the many-thinkers problem. Analysis, 64(3), 242-250.
Geach, P. T. 1980b. Reference and Generality. 3d ed. Ithaca, NY: Cornell University Press.
Long, A. A. and D. N. Sedley, (1987) The Hellenistic Philosophers, Cambridge University Press
Unger, Peter. 1979a. "There Are No Ordinary Things." Synthese 41: 117-54.
Unger, Peter. 1979b. "Why There Are No People." In Midwest Studies in Philosophy. Vol 4. pp. 177-222 Minneapolis: University of Minnesota Press.
Unger, Peter.1980a. "Skepticism and Nihilism." Nous 14: 517-45.
Unger, Peter.1980b. "The Problem of the Many." In Midwest Studies in Philosophy. Vol. 5 Studies in Epistemology (pp. 411-68), ed. P. French, T. Uehling, and H. Wettstein Minneapolis: University of Minnesota Press.
Van Inwagen, P. (1981). "The Doctrine of Arbitrary Undetached Parts," Pacific Philosophical Quarterly, 62, 123-137.

The Problem of the Many, Stanford Encyclopedia of Philosophy

Normal | Teacher | Scholar