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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Anaximander
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Anselm
Louise Antony
Thomas Aquinas
Aristotle
David Armstrong
Harald Atmanspacher
Robert Audi
Augustine
J.L.Austin
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Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Barrett
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Henri Bergson
George Berkeley
Isaiah Berlin
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Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
Daniel Boyd
F.H.Bradley
C.D.Broad
Michael Burke
Lawrence Cahoone
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Nancy Cartwright
Gregg Caruso
Ernst Cassirer
David Chalmers
Roderick Chisholm
Chrysippus
Cicero
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
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Jacques Derrida
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Fred Dretske
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John Earman
Laura Waddell Ekstrom
Epictetus
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Austin Farrer
Herbert Feigl
Arthur Fine
John Martin Fischer
Frederic Fitch
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Bas van Fraassen
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Gorgias
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
W.F.R.Hardie
Sam Harris
William Hasker
R.M.Hare
Georg W.F. Hegel
Martin Heidegger
Heraclitus
R.E.Hobart
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
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David Hume
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Jaegwon Kim
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Thomas Kuhn
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Keith Lehrer
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Jules Lequyer
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Joseph Levine
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David Lewis
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Ruth Barcan Marcus
Tim Maudlin
James Martineau
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Storrs McCall
Hugh McCann
Colin McGinn
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Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
G.E.Moore
Thomas Nagel
Otto Neurath
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
Parmenides
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
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Frank Ramsey
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Michael Rea
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Charles Renouvier
Nicholas Rescher
C.W.Rietdijk
Richard Rorty
Josiah Royce
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Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
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Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
J.J.C.Smart
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
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Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
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John Venn
Kadri Vihvelin
Voltaire
G.H. von Wright
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R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
C.F. von Weizsäcker
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

David Albert
Michael Arbib
Walter Baade
Bernard Baars
Jeffrey Bada
Leslie Ballentine
Marcello Barbieri
Gregory Bateson
Horace Barlow
John S. Bell
Mara Beller
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Jean Bricmont
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Melvin Calvin
Donald Campbell
Sadi Carnot
Anthony Cashmore
Eric Chaisson
Gregory Chaitin
Jean-Pierre Changeux
Rudolf Clausius
Arthur Holly Compton
John Conway
Jerry Coyne
John Cramer
Francis Crick
E. P. Culverwell
Antonio Damasio
Olivier Darrigol
Charles Darwin
Richard Dawkins
Terrence Deacon
Lüder Deecke
Richard Dedekind
Louis de Broglie
Stanislas Dehaene
Max Delbrück
Abraham de Moivre
Bernard d'Espagnat
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Gerald Edelman
Paul Ehrenfest
Manfred Eigen
Albert Einstein
George F. R. Ellis
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
David Foster
Joseph Fourier
Philipp Frank
Steven Frautschi
Edward Fredkin
Benjamin Gal-Or
Howard Gardner
Lila Gatlin
Michael Gazzaniga
Nicholas Georgescu-Roegen
GianCarlo Ghirardi
J. Willard Gibbs
James J. Gibson
Nicolas Gisin
Paul Glimcher
Thomas Gold
A. O. Gomes
Brian Goodwin
Joshua Greene
Dirk ter Haar
Jacques Hadamard
Mark Hadley
Patrick Haggard
J. B. S. Haldane
Stuart Hameroff
Augustin Hamon
Sam Harris
Ralph Hartley
Hyman Hartman
Jeff Hawkins
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Basil Hiley
Art Hobson
Jesper Hoffmeyer
Don Howard
John H. Jackson
William Stanley Jevons
Roman Jakobson
E. T. Jaynes
Pascual Jordan
Eric Kandel
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
William R. Klemm
Christof Koch
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Daniel Koshland
Ladislav Kovàč
Leopold Kronecker
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
Karl Lashley
David Layzer
Joseph LeDoux
Gerald Lettvin
Gilbert Lewis
Benjamin Libet
David Lindley
Seth Lloyd
Hendrik Lorentz
Werner Loewenstein
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
Owen Maroney
David Marr
Humberto Maturana
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Ernst Mayr
John McCarthy
Warren McCulloch
N. David Mermin
George Miller
Stanley Miller
Ulrich Mohrhoff
Jacques Monod
Vernon Mountcastle
Emmy Noether
Donald Norman
Alexander Oparin
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
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Roger Penrose
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Colin Pittendrigh
Walter Pitts
Max Planck
Susan Pockett
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Daniel Pollen
Ilya Prigogine
Hans Primas
Zenon Pylyshyn
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Adolphe Quételet
Pasco Rakic
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Frederick Reif
Jürgen Renn
Giacomo Rizzolati
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Juan Roederer
Jerome Rothstein
David Ruelle
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Aaron Schurger
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Thomas Sebeok
Franco Selleri
Claude Shannon
Charles Sherrington
David Shiang
Abner Shimony
Herbert Simon
Dean Keith Simonton
Edmund Sinnott
B. F. Skinner
Lee Smolin
Ray Solomonoff
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John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
Max Tegmark
Teilhard de Chardin
Libb Thims
William Thomson (Kelvin)
Richard Tolman
Giulio Tononi
Peter Tse
Alan Turing
Francisco Varela
Vlatko Vedral
Mikhail Volkenstein
Heinz von Foerster
Richard von Mises
John von Neumann
Jakob von Uexküll
C. S. Unnikrishnan
C. H. Waddington
John B. Watson
Daniel Wegner
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Paul A. Weiss
Herman Weyl
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
Günther Witzany
Stephen Wolfram
H. Dieter Zeh
Semir Zeki
Ernst Zermelo
Wojciech Zurek
Konrad Zuse
Fritz Zwicky

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Peter Geach

Peter Geach and Elizabeth Anscombe were younger colleagues of Ludwig Wittgenstein. Geach tried to synthesize analytic philosophy and Thomism. He was an expert on Gottlob Frege. With Max Black, in 1952 he translated Frege's works.

Relative Identity
Geach worked on problems of identity and debated for years with David Wiggins about relative identity.

For Geach and Wiggins, relative identity means "x is the same F as y," but "x may not be the same G as y." Wiggins argued against this idea of relative identity, but accepted what he called a sortal-dependent identity, "x is the same F as y." Geach called this a "criterion of identity."

I had here best interject a note on how I mean this term "criterion of identity". I maintain that it makes no sense to judge whether x and y are 'the same', or whether x remains 'the same', unless we add or understand some general term—"the same F". That in accordance with which we thus judge as to the identity, I call a criterion of identity; this agrees with the etymology of "criterion". Frege sees clearly that "one" cannot significantly stand as a predicate of objects unless it is (at least understood as) attached to a general term; I am surprised he did not see that the like holds for the closely allied expression "the same".
In his 1967 article "Identity," in the Review of Metaphysics, Geach wrote
I am arguing for the thesis that identity is relative. When one says "x is identical with y", this, I hold, is an incomplete expression; it is short for "x is the same A as y", where "A" represents some count noun understood from the context of utterance—or else, it is just a vague expression of a half-formed thought. Frege emphasized that "x is one" is an incomplete way of saying "x is one A, a single A", or else has no clear sense; since the connection of the concepts one and identity comes out just as much in the German "ein und dasselbe" as in the English "one and the same", it has always surprised me that Frege did not similarly maintain the parallel doctrine of relativized identity, which I have just briefly stated. On the contrary, Frege actually enunciated with all vigour a doctrine that identity cannot be relativized: "Identity is a relation given to us in such a specific form that it is inconceivable that various forms of it should occur" (Grundgesetze, Vol. II, p. 254).

Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory (for bound name-variables):

⊢Fa ↔ Vx(Fx ∧ x=a).         (1)

Quine in his Set Theory and its Logic attributes to Hao Wang (p. 13) the recognition that (1) will serve as a single axiom schema for identity theory. In the vernacular we may intuitively express the content of (1) by saying: Whatever is true of something identical with an object a is true of a, and conversely. We readily derive from schema (1) the Law of Self-Identity, "⊢(a = a)". For if we take "Fξ" to be "ξ ≠ a", then schema (1) gives us:

⊢(a ≠ a) ↔ Vx(x ≠ a) ∧ x = a),        (2)

It was Ruth Barcan Marcus who introduced the identity of indiscernibles
which of course yields "⊢a = a". And there are equally easy proofs of what has been called (I believe by Quine) the Indiscernibility of Identicals:

⊢Fb ∧ b = a → Fa           (3)

and of theorems asserting the symmetry and transitiveness of identity as a relation. The logical system got by adjoining schema (1) to classical quantification theory is a system with a complete proof procedure; moreover, its interpretation is categorical, in the following sense: If we try to introduce two two-place predicables, each separately conforming to schema (1), they turn out to coincide in application. (In this paper, as in my book Reference and Generality, I use "predicables" as a term for the verbal expressions called "predicates" by other logicians; I reserve the term "predicate" for a predicable actually being used as the main functor in a given proposition.)

Tibbles, the Cat
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.

Wiggins begins his argument with an assertion S*

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

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

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

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

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

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

In Geach's second account of Tibbles as an exemplar of a metaphysical problem, published some years later (1980), Tibbles is a cat with 1,000 hairs that can be interpreted as 1,001 cats, by "picking out" and then pulling out one of those cat hairs at a time and each time identifying a new cat..

Geach's second version of Tibbles is widely cited as a discussion of the problem of vagueness or what Peter Unger called the Problem of the Many, also published in 1980. It is not the "body-minus" problem of the original Tibbles.

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

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

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

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.

References
Burke, M. B. (1994). Dion and Theon: An essentialist solution to an ancient puzzle. The Journal of Philosophy, 91(3), 129-139.
Burke, M. B. (2004). Dion, Theon, and the many-thinkers problem. Analysis, 64(3), 242-250.
Geach, Peter, (1980) Reference and Generality, 3rd edition.
Lowe, E. J. (1995). Coinciding objects: in defence of the'standard account'. Analysis, 55(3), 171-178.
Rea, M. C. (1995). The problem of material constitution. The Philosophical Review, 104(4), 525-552.
Wiggins, David.1968. "On Being in the Same Place at the Same Time." Philosophical Review 77:90-5
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