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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
G.E.M.Anscombe
Anselm
Louise Antony
Thomas Aquinas
Aristotle
David Armstrong
Harald Atmanspacher
Robert Audi
Augustine
J.L.Austin
A.J.Ayer
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Belsham
Henri Bergson
Isaiah Berlin
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
F.H.Bradley
C.D.Broad
Michael Burke
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
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
Democritus
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Epictetus
Epicurus
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
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
R.E.Hobart
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
Leucippus
Michael Levin
George Henry Lewes
C.I.Lewis
David Lewis
Peter Lipton
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Lucretius
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
G.E.Moore
C. Lloyd Morgan
Thomas Nagel
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
C.W.Rietdijk
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
T.M.Scanlon
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
J.J.C.Smart
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
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
Voltaire
G.H. von Wright
David Foster Wallace
R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

Michael Arbib
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
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
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
A.O.Gomes
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Martin Heisenberg
John Herschel
Werner Heisenberg
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Simon Kochen
Stephen Kosslyn
Ladislav Kovàč
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
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
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
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
William Thomson (Kelvin)
Peter Tse
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

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Philosophers

Mortimer Adler
Rogers Albritton
G.E.M.Anscombe
Anselm
Thomas Aquinas
Aristotle
Augustine
J.L.Austin
A.J.Ayer
Alexander Bain
Mark Balaguer
William Belsham
Henri Bergson
Isaiah Berlin
Bernard Berofsky
Susanne Bobzien
George Boole
Émile Boutroux
F.H.Bradley
C.D.Broad
C.A.Campbell
Joseph Keim Campbell
Carneades
Ernst Cassirer
David Chalmers
Roderick Chisholm
Chrysippus
Cicero
Randolph Clarke
Samuel Clarke
Anthony Collins
Diodorus Cronus
Donald Davidson
Mario De Caro
Democritus
Daniel Dennett
René Descartes
Richard Double
Emil du Bois-Reymond
Fred Dretske
John Earman
Laura Waddell Ekstrom
Epictetus
Epicurus
John Martin Fischer
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouillée
Harry Frankfurt
Richard L. Franklin
Michael Frede
Carl Ginet
H.Paul Grice
Nicholas St. John Green
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
W.F.R.Hardie
R.M.Hare
Georg W.F. Hegel
Martin Heidegger
R.E.Hobart
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Ted Honderich
Pamela Huby
David Hume
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Jaegwon Kim
William King
Christine Korsgaard
Keith Lehrer
Gottfried Leibniz
Leucippus
Michael Levin
C.I.Lewis
David Lewis
Peter Lipton
John Locke
Michael Lockwood
John R. Lucas
Lucretius
James Martineau
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Paul E. Meehl
Alfred Mele
John Stuart Mill
Dickinson Miller
G.E.Moore
Thomas Nagel
Friedrich Nietzsche
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Karl Popper
H.A.Prichard
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Thomas Reid
Charles Renouvier
Nicholas Rescher
C.W.Rietdijk
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
T.M.Scanlon
Moritz Schlick
Arthur Schopenhauer
John Searle
Henry Sidgwick
Walter Sinnott-Armstrong
J.J.C.Smart
Saul Smilansky
Michael Smith
L. Susan Stebbing
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Richard Taylor
Kevin Timpe
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
Voltaire
G.H. von Wright
David Foster Wallace
R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Ludwig Wittgenstein
Susan Wolf

Scientists
Steven Pinker

Steven Pinker is a psychologist and prolific writer who occasionally comments on free will. In his 1997 How the Mind Works, he condensed the standard argument against free will into a single sentence,

"a random event does not fit the concept of free will any more than a lawful one does, and could not serve as the long-sought locus of moral responsibility." (p.54)

Pinker is a strong supporter of the "computational theory of mind," his "recurring metaphor of the mind as machine." This is the idea in cognitive science that we can learn a great deal from computing machines about intelligence and the reasoning processes in our minds.

He examines alternative explanations for intelligence.

The traditional explanation of intelligence is that human flesh is suffused with a non-material entity, the soul, usually envisioned as some kind of ghost or spirit. But the theory faces an insurmountable problem: How does the spook interact with solid matter? (p.64)

Another explanation is that mind comes from some extraordinary form of matter. Darwin wrote that the brain "secretes" the mind, and recently the philosopher John Searle has argued that the physico-chemical properties of brain tissue somehow produce the mind just as breast tissue produces milk and plant tissue produces sugar...

Intelligence has often been attributed to some kind of energy flow or force field. Orbs, luminous vapors, auras, vibrations, magnetic fields, and lines of force figure prominently in spiritualism, pseudoscience, and science-fiction kitsch. The school of Gestalt psychology tried to explain visual illusions in terms of electromagnetic force fields on the surface of the brain, but the fields were never found. Occasionally the brain surface has been described as a continuous vibrating medium that supports holograms or other wave interference patterns, but that idea, too, has not panned out. The hydraulic model, with its psychic pressure building up, bursting out, or being diverted through alternative channels, lay at the center of Freud's theory and can be found in dozens of everyday metaphors: anger welling up, letting off steam, exploding under the pressure, blowing one's stack, venting one's feelings, bottling up rage. But even the hottest emotions do not literally correspond to a buildup and discharge of energy (in the physicist's sense) somewhere in the brain. (p.65)

Pinker concludes that none of these is a successful explanation, then offers one that focuses on the abrstract idea of information, which leads him to his metaphor of the mind as an information-processing machine, a biological Turing machine (or virtual mental computer).
No, intelligence does not come from a special kind of spirit or matter or energy but from a different commodity, information. (p.65)

Does this mean that the human brain is a Turing machine? Certainly not...other kinds of symbol-processors have been proposed as models of the human mind. These models are often simulated on commercial computers, but that is just a convenience. The commercial computer is first programmed to emulate the hypothetical mental computer (creating what computer scientists call a virtual machine), in much the same way that a Macintosh can be programmed to emulate a PC. Only the virtual mental computer is taken seriously, not the silicon chips that emulate it. Then a program that is meant to model some sort of thinking (solving a problem, understanding a sentence) is run on the virtual mental computer. A new way of understanding human intelligence has been born. (p.68-9)

Abstract information is neither matter nor energy, yet it needs matter for its concrete embodiment and energy for its communication. Information is the modern spirit, the ghost in Pinker's machine.

For Teachers
For Scholars
Excerpts fom How The Mind Works
As science advances and explanations of behavior become less fanciful, the Specter of Creeping Exculpation, as Dennett calls it, will loom larger. Without a clearer moral philosophy, any cause of behavior could be taken to undermine free will and hence moral responsibility. Science is guaranteed to appear to eat away at the will, regardless of what it finds, because the scientific mode of explanation cannot accommodate the mysterious notion of uncaused causation that underlies the will. If scientists wanted to show that people had free will, what would they look for? Some random neural event that the rest of the brain amplifies into a signal triggering behavior?

Pinker puts the standard argument against free will in one sentence
But a random event does not fit the concept of free will any more than a lawful one does, and could not serve as the long-sought locus of moral responsibility. We would not find someone guilty if his finger pulled the trigger when it was mechanically connected to a roulette wheel, why should it be any different if the roulette wheel is inside his skull? The same problem arises for another unpredictable cause that has been suggested as the source of free will, chaos theory, in which, according to the cliche, a butterfly's flutter can set off a cascade of events culminating in a hurricane. A fluttering in the brain that causes a hurricane of behavior, if it were ever found, would still be a cause of behavior and would not fit the concept of uncaused free will that underlies moral responsibility.

Either we dispense with all morality as an unscientific superstition, or we find a way to reconcile causation (genetic or otherwise) with responsibility and free will. I doubt that our puzzlement will ever be completely assuaged, but we can surely reconcile them in part. Like many philosophers, I believe that science and ethics are two self-contained systems played out among the same entities in the world, just as poker and bridge are different games played with the same fifty-two-card deck. The science game treats people as material objects, and its rules are the physical processes that cause behavior through natural selection and neurophysiology. The ethics game treats people as equivalent, sentient, rational, free-willed agents, and its rules are the calculus that assigns moral value to behavior through the behavior's inherent nature or its consequences.

Free will is an idealization of human beings that makes the ethics game playable. Euclidean geometry requires idealizations like infinite straight lines and perfect circles, and its deductions are sound and useful even though the world does not really have infinite straight lines or perfect circles. The world is close enough to the idealization that the theorems can usefully be applied. Similarly, ethical theory requires idealizations like free, sentient, rational, equivalent agents whose behavior is uncaused, and its conclusions can be sound and useful even though the world, as seen by science, does not really have uncaused events. As long as there is no outright coercion or gross malfunction of reasoning, the world is close enough to the idealization of free will that moral theory can meaningfully be applied to it. Science and morality are separate spheres of reasoning. Only by recognizing them as separate can we have them both. If discrimination is wrong only if group averages are the same, if war and rape and greed are wrong only if people are never inclined toward them, if people are responsible for their actions only if' the actions are mysterious, then either scientists mist be prepared to fudge their data or all of us must be prepared to give up our values.

Scientific arguments would turn into the National Lampoon cover showing a puppy with a gun at its head and the caption "Buy This Magazine or We'll Shoot the Dog." The knife that separates causal explanations of behavior from moral responsibility for behavior cuts both ways. In the latest twist in the human-nature morality play, a chromosomal marker for homosexuality in some men, the so-called gay gene, was identified by the geneticist Dean Hamer. To the bemusement of Science for the People, this time it is the genetic explanation that is politically correct. Supposedly it refutes right-wingers like Dan Quayle, who had said that homosexuality "is more of a choice than a biological situation. It is a wrong choice." The gay gene has been used to argue that homosexuality is not a choice for which gay people can be held responsible but an involuntary orientation they just can't help. But the reasoning is dangerous. The gay gene could just as easily be said to influence some people to choose homosexuality. And like all good science, Hamer's result might be falsified someday, and then where would we be? Conceding that bigotry against gay people is OK after all? The argument against persecuting gay people must be made not in terms of the gay gene or the gay brain but in terms of people's right to engage in private consensual acts without discrimination or harassment.

The cloistering of scientific and moral reasoning in separate arenas also lies behind my recurring metaphor of the mind as a machine, of people as robots. Does this not dehumanize and objectify people and lead us to treat them as inanimate objects? As one humanistic scholar lucidly put it in an Internet posting, does it not render human experience invalid, reifying a model of relating based on an I-It relationship, and delegitimating all other forms of discourse with fundamentally destructive consequences to society? Only if one is so literal-minded that one cannot shift among different stances in conceptualizing people for different purposes. A human being is simultaneously a machine and a sentient free agent, depending on the purpose of the discussion, just as he is also a taxpayer, an insurance salesman, a dental patient, and two hundred pounds of ballast on a commuter airplane, depending on the purpose of the discussion. The mechanistic stance allows us to understand what makes us tick and how we fit into the physical universe. When those discussions wind down for the day, we go back to talking about each other as free and dignified human beings.
(pp.54-56)

The traditional explanation of intelligence is that human flesh is suffused with a non-material entity, the soul, usually envisioned as some kind of ghost or spirit. But the theory faces an insurmountable problem: How does the spook interact with solid matter? How does an ethereal nothing respond to flashes, pokes, and beeps and get arms and legs to move? Another problem is the overwhelming evidence that the mind is the activity of the brain. The supposedly immaterial soul, we now know, can be bisected with a knife, altered by chemicals, started or stopped by electricity, and extinguished by a sharp blow or by insufficient oxygen. Under a microscope, the brain has a breathtaking complexity of physical structure fully commensurate with the richness of the mind.

Another explanation is that mind comes from some extraordinary form of matter. Pinocchio was animated by a magical kind of wood found by Geppetto that talked, laughed, and moved on its own. Alas, no one has ever discovered such a wonder substance. At first one might think that the wonder substance is brain tissue. Darwin wrote that the brain "secretes" the mind, and recently the philosopher John Searle has argued that the physico-chemical properties of brain tissue somehow produce the mind just as breast tissue produces milk and plant tissue produces sugar. But recall that the same kinds of membranes, pores, and chemicals are found in brain tissue throughout the animal kingdom, not to mention in brain tumors and cultures in dishes, All of these globs of neural tissue have the same physico-chemical properties. but not aII of them accomplish humanlike intelligence. Of course, something about the tissue in the human brain is necessary for our intelligence, but the physical properties are not sufficient, just as the physical properties of bricks are not sufficient to explain architecture and the physical properties of oxide particles are not sufficient to explain music. Something in the patterning of neural tissue is crucial.

Intelligence has often been attributed to some kind of energy flow or force field. Orbs, luminous vapors, auras, vibrations, magnetic fields, and lines of force figure prominently in spiritualism, pseudoscience, and science-fiction kitsch. The school of Gestalt psychology tried to explain visual illusions in terms of electromagnetic force fields on the surface of the brain, but the fields were never found. Occasionally the brain surface has been described as a continuous vibrating medium that supports holograms or other wave interference patterns, but that idea, too, has not panned out. The hydraulic model, with its psychic pressure building up, bursting out, or being diverted through alternative channels, lay at the center of Freud's theory and can be found in dozens of everyday metaphors: anger welling up, letting off steam, exploding under the pressure, blowing one's stack, venting one's feelings, bottling up rage. But even the hottest emotions do not literally correspond to a buildup and discharge of energy (in the physicist's sense) somewhere in the brain. In Chapter 6 I will try to persuade you that the brain does not actually operate by internal pressures but contrives them as a negotiating tactic, like a terrorist with explosives strapped to his body.

A problem with all these ideas is that even if we did discover some gel or vortex or vibration or orb that spoke and plotted mischief like Geppetto's log, or that, more generally, made decisions based on rational rules and pursued a goal in the face of obstacles, we would still be faced with the mystery of how it accomplished those feats.

No, intelligence does not come from a special kind of spirit or matter or energy but from a different commodity, information. Information is a correlation between two things that is produced by a lawful process (as opposed to coming about by sheer chance). We say that the rings in a stump carry information about the age of the tree because their number correlates with the tree's age (the older the tree, the more rings it has), and the correlation is not a coincidence but is caused by the way trees grow. Correlation is a mathematical and logical concept; it is not defined in terms of the stuff that the correlated entities are made of. Information itself is nothing special; it is found wherever causes leave effects. What is special is information processing. We can regard a piece of matter that carries information about some state of affairs as a symbol; it can "stand for" that state of affairs. But as a piece of matter, it can do other things as well—physical things, whatever that kind of matter in that kind of state can do according to the laws of physics and chemistry. Tree rings carry information about age, but they also reflect light and absorb staining material. Footprints carry information about animal motions, but they also trap water and cause eddies in the wind. Now here is an idea. Suppose one were to build a machine with parts that are affected by the physical properties of some symbol. Some lever or electric eye or tripwire or magnet is set in motion by the pigment absorbed by a tree ring, or the water trapped by a footprint, or the light reflected by a chalk mark, or the magnetic charge in a bit of oxide. And suppose that the machine then causes something to happen in some other pile of matter. It burns new marks onto a piece of wood, or stamps impressions into nearby dirt, or charges some other bit of oxide. Nothing special has happened so far; all I have described is a chain of physical events accomplished by a pointless contraption.

Here is the special step. Imagine that we now try to interpret the newly arranged piece of matter using the scheme according to which the original piece carried information. Say we count the newly burned wood rings and interpret them as the age of some tree at some time, even though they were not caused by the growth of any tree. And let's say that the machine was carefully designed so that the interpretation of its new markings made sense—that is, so that they carried information about something in the world. For example, imagine a machine that scans the rings in a stump, burns one mark on a nearby plank for each ring, moves over to a smaller stump from a tree that was cut down at the same time, scans its rings, and sands off one mark in the plank for each ring. When we count the marks on the plank, we have the age of the first tree at the time that the second one was planted. We would have a kind of rational machine, a machine that produces true conclusions from true premises—not because of any special kind of matter or energy, or because of any part that was itself intelligent or rational. All we have is a carefully contrived chain of ordinary physical events, whose first link was a configuration of matter that carries information. Our rational machine owes its rationality to two properties glued together in the entity we call a symbol: a symbol carries information, and it causes things to happen, (Tree rings correlate with the age of the tree, and they can absorb the light beam of a scanner.) When the caused things themselves carry information, we call the whole system an information processor, or a computer.

Now, this whole scheme might seem like an unrealizable hope. What guarantee is there that any collection of thingamabobs can be arranged to fall or swing or shine in just the right pattern so that when their effects are interpreted, the interpretation will make sense? (More precisely, so that it will make sense according to some prior law or relationship we find interesting; any heap of stuff can be given a contrived interpretation after the fact.) How confident can we be that some machine will make marks that actually correspond to some meaningful state of the world, like the age of a tree when another tree was planted, or the average age of the tree's offspring, or anything else, as opposed to being a meaningless pattern corresponding to nothing at all?

The guarantee comes from the work of the mathematician Alan Turing. He designed a hypothetical machine whose input symbols and output symbols could correspond, depending on the details of the machine, to any one of a vast number of sensible interpretations. The machine consists of a tape divided into squares, a read-write head that can print or read a symbol on a square and move the tape in either direction, a pointer that can point to a fixed number of tickmarks on the machine, and a set of mechanical reflexes. Each reflex is triggered by the symbol being read and the current position of the pointer, and it prints a symbol on the tape, moves the tape, and/or shifts the pointer. The machine is allowed as much tape as it needs. This design is called a Turing machine.

What can this simple machine do? It can take in symbols standing for a number or a set of numbers, and print out symbols standing for new numbers that are the corresponding value for any mathematical function that can be solved by a step-by-step sequence of operations (addition, multiplication, exponentiation, factoring, and so on—I am being imprecise to convey the importance of Turing's discovery without the technicalities). It can apply the rules of any useful logical system to derive true statements from other true statements. It can apply the rules of any grammar to derive well-formed sentences. The equivalence among Turing machines, calculable mathematical functions, logics, and grammars, led the logician Alonzo Church to conjecture that any well-defined recipe or set of steps that is guaranteed to produce the solution to some problem in a finite amount of time (that is, any algorithm) can be implemented on a Turing Machine. ,p/> What does this mean? It means that to the extent that the work obeys mathematical equations that can be solved step by step, a machine can be built that simulates the world and makes predictions about it. To the extent that rational thought corresponds to the rules of logic, a machine can be built that carries out rational thought. To the extent that a language can be captured by a set of grammatical rules, a machine can be built that produces grammatical sentences. To the extent that thought consists of applying any set of well-specified rules, a machine can be built that, in some sense, thinks. Turing showed that rational machines—machines that use the physical properties of symbols to crank out new symbols that make some kind of sense—are buildable, indeed, easily buildable. The computer scientist Joseph Weizenbaum once showed how to build one out of a die, some rocks, and a roll of toilet paper. In fact, one doesn't even need a huge warehouse of these machines, one to do sums, another to do square roots, a third to print English sentences, and so on. One kind of Turing machine is called a universal Turing machine. It can take in a description of any other Turing machine printed on its tape and thereafter mimic that machine exactly. A single machine can be programmed to do anything that any set of rules can do.

Does this mean that the human brain is a Turing machine? Certainly not. There are no Turing machines in use anywhere, let alone in our heads. They are useless in practice: too clumsy, too hard to program, too big, and too slow. But it does not matter. Turing merely wanted to prove that some arrangement of gadgets could function as an intelligent symbol-processor. Not long after his discovery, more practical symbol-processors were designed, some of which became IBM and Univac mainframes and, later, Macintoshes and PCs. But all of them were equivalent to Turing's universal machine. If we ignore size and speed, and give them as much memory storage as they need, we can program them to produce the same outputs in response to the same inputs.

Still other kinds of symbol-processors have been proposed as models of the human mind. These models are often simulated on commercial computers, but that is just a convenience. The commercial computer is first programmed to emulate the hypothetical mental computer (creating what computer scientists call a virtual machine), in much the same way that a Macintosh can be programmed to emulate a PC. Only the virtual mental computer is taken seriously, not the silicon chips that emulate it. Then a program that is meant to model some sort of thinking (solving a problem, understanding a sentence) is run on the virtual mental computer. A new way of understanding human intelligence has been born. (pp.64-69)


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