Download Lecture Notes 12: Cognition and Computation

Philosophy 024: Big Ideas
Prof. Robert DiSalle ([email protected])
Talbot College 408, 519-661-2111 x85763
Office Hours: Monday and Wednesday 11:30-12:30
Course Website:
http://instruct.uwo.ca/philosophy/024/
Philosophical questions about the computer:
What is “intelligence”? What is “thought”?
Are these functions that a machine can have?
If machines can display “thought” or “intelligence,” does this
imply that human cognition is a kind of computational ability?
If human cognition is computation, does that imply that the
human mind in general is a kind of machine?
Some philosophical background to the computer
René Descartes, 1596-1650: “Mathesis universalis”
G.W. Leibniz (1646-1716): “Universal characteristic,”
calculating machine
Charles Babbage (1791-1871): Calculating machines
George Boole (1815-1864): “The Laws of Thought”
Gottlob Frege (1848-1925): “Conceptual Notation”
Kurt Gödel (1906-1978): “Formally Undecidable Propositions”
Alan Turing (1912-1954): The “Turing Machine”
Descartes on how to tell the difference between a human
being and a mechanical imitation:
“They could never use speech or other signs as we do when
placing our thoughts on record for the benefit of others. For we
can easily understand a machine’s being constituted so that it can
utter words, and even emit some responses to actions on it of a
corporeal kind, which brings about a change in its organs…But it
never happens that it arranges its speech in various ways, in order
to reply appropriately to everything that may be said in its
presence, as even the lowest type of man can do…”
Descartes:
“And the second difference is, that although machines can
perform certain things as well as or perhaps better than any
of us can do, they infallibly fall short in others, by the which
means we may discover that they did not act from
knowledge, but only from the disposition of their organs. For
while reason is a universal instrument which can serve for all
contingencies, these organs have need of some special
adaptation for every particular action. …It is morally
impossible that there should be sufficient diversity in any
machine to allow it to act in all the events of life in the same
way as our reason causes us to act.”
1956: Howard Aiken, Harvard University, on the idea of
a “universal machine” :
“If it should turn out that the basic logics of a machine
designed for the numerical solution of differential equations
coincide with the logics of a machine intended to make bills
for a department store, I would regard this as the most
amazing coincidence that I have ever encountered.”
Leibniz
“When, several years ago, I saw for the first
time an instrument which, when carried,
automatically records the number of steps
taken by a pedestrian, it occurred to me at
once that the entire arithmetic could be
subjected to a similar kind of machinery so
that not only counting, but also addition and
subtraction, multiplication and division
could be accomplished by, a suitably
arranged machine easily, promptly, and
with sure results.”
Leibniz on the “Universal Characteristic:
Although many persons of great ability, especially in our century,
may have claimed to offer us demonstrations in questions of
physics, metaphysics, ethics, and even in politics, jurisprudence,
and medicine, nevertheless they have either been mistaken
(because every step is on slippery ground and it is difficult not to
fall unless guided by some tangible directions), or even when
they succeed, they have been unable to convince everyone with
their reasoning (because there has not yet been a way to examine
arguments by means of some easy tests available to everyone).
Whence it is manifest that if we could find characters or signs
appropriate for expressing all our thoughts as definitely and as
exactly as arithmetic expresses numbers or geometric analysis
expresses lines, we could in all subjects in so far as they are
amenable to reasoning accomplish what is done in Arithmetic
and Geometry.
For all inquiries which depend on reasoning would be performed
by the transposition of characters and by a kind of calculus,
which would immediately facilitate the discovery of beautiful
results. For we should not have to break our heads as much as is
necessary today, and yet we should be sure of accomplishing
everything the given facts allow.
Indeed for a long time excellent men have brought to light a kind
of "universal language" or "characteristic" in which diverse
concepts and things were to be brought together in an appropriate
order, with its help, it was to become for people of different
nations to communicate their thoughts to one and to translate into
their own language the written signs of a foreign language.
However, nobody, so far, has gotten hold of a language which
would embrace both the technique of discovering propositions and
their critical examination -- a language whose signs or characters
would play the same rôle as the signs of arithmetic for numbers
and those of algebra for quantities in general. And yet it is as if
God, when he bestowed these two sciences on mankind, wanted us
to realize that our understanding conceals a far deeper secret
foreshadowed by these two sciences.
Leibniz’s Calculating Machine:
George Boole on “The Laws of Thought” (1854):
The design of the following treatise is to investigate the
fundamental laws of those operations of the mind by which
reasoning is performed; to give expression to them in the
symbolic language of a Calculus, and upon this foundation to
establish the science of Logic and construct its method.
They who are acquainted with the present state of the theory
of Symbolic Algebra, are aware that the validity of the
processes of analysis does not depend upon the interpretation
of the symbols which are employed, but solely upon the laws
of their combination. Every system of interpretation which
does not affect the truth of the relations supposed, is equally
admissible, and it is thus that the same processes may, under
one scheme of interpretation, represent the solution of a
question on the properties of number, under another, that of a
geometrical problem, and under a third, that of a problem of
dynamics or optics. ... It is upon the foundation of this general
principle, that I purpose to establish the Calculus of Logic ...
(Boole, 1845)
Boole on the “laws of thought”:
Logic is essentially mathematics with just two values, 0 and 1.
The basic logical connections are AND, OR, and NOT.
AND yields a 1
only if both
inputs are 1:
OR yields a 1 if
at least one input
is 1:
0x0=0
0+0+0
1x0=0
1+0=1
0x1=0
0+1=1
1x1=1
1+1=1
NOT yields the
negation of
whatever is put in:
1 0
0 1


These correspond to the “logic gates” of a computer.
Alan Turing (1912-1954)
“On Computable Numbers, with
an Application to the
Entscheidungsproblem” (1936)
“Proposed Electronic Calculator”
(1946)
“Intelligent Machinery” (1948)
“Computing Machines and
Intelligence” (1950)
I propose to consider the question, “Can machines think?”
This should begin with definitions of the meaning of the terms
“machine” and “think”. The definitions might be framed so as
to reflect so far as possible the normal use of the words, but
this attitude is dangerous. If the meaning of the words
“machine” and “think” are to be found by examining how they
are commonly used it is difficult to escape the conclusion that
the meaning and the answer to the question, “Can machines
think?” is to be sought in a statistical survey such as a Gallup
poll. Instead of attempting such a definition I shall replace the
question by another, which is closely related to it and is
expressed in relatively unambiguous words.
Turing, “Computing Machines and Intelligence” (1950)
(Available for download at www.jstor.org)
The “imitation game”:
A = a man
B = a woman
C = an interrogator, who knows A and B only as X and Y, and
who gets to ask questions of A and B..
C’s object is to determine which is which: either X is A and Y is
B, or vice-versa.
A’s object is to make C misidentify A and B.
B’s object is to make C identify A and B correctly.
Turing’s new question: “What will happen when a machine
takes the part of A in this game? Will the interrogator decide
wrongly as often when the game is played like this as he does
when the game is played between a man and a woman? These
questions replace our original, “Can machines think?”
“We are not asking whether all digital computers would do
well in the game nor whether the computers at present
available would do well, but whether there are imaginable
computers which would do well.”
Basic elements of a computer:
“Store”: a store of information, e.g. the human computer’s
memory or calculations on paper.
“Executive unit”: that which carries out the operations in a
calculation
“Control”: that which constrains the computer to carry out the
instructions exactly.
“Discrete state machine”: A machine that can be in a finite
number of definitely distinct states, eg. “On” or “Off,” “Open”
or “Closed”.
A simple Turing machine: A device capable of reading,
printing, and erasing symbols at defined places on a strip of
paper or tape.
This special property of digital computers, that they can mimic
any discrete state machine, is described by saying that they are
universal machines. The existence of machines with this
property has the important consequence that, considerations of
speed apart, it is unnecessary to design new machines to do
various computing processed. They can all be done with one
digital computer, suitably programmed for each case. It will be
seen that as a consequence of this all digital computers are in a
sense equivalent.
(Turing, 1950)
Objections to Turing’s account
The Theological Objection: Thinking is a function of man’s
immortal soul, so machines could never think.
Reply: If theological arguments are allowed, it must be argued
that God could not give a soul to an unthinking thing, or that
he could not give our soul the same machinery for thinking
that a computer uses. But there is no such argument. In any
case, theological arguments have generally hindered science.
The “Head in the Sand” Objection: “The consequences of
machines thinking would be too dreadful. Let us hope and
believe that they cannot do so.”
Reply: This is a feeling rather than a substantial argument
requiring refutation.
The Mathematical Objection: There are non-computable
functions, and therefore there are limits to the powers of
discrete-state machines.
Reply: It is not proven that humans are capable of computing
the non-computable functions, either.
The Consciousness Objection: A machine can never
have consciousness, which is a feature of human
thought.
Reply: We don’t know that other people think, since
we can’t feel what their consciousness is like. We only
think that they think because they pass the Turing test.
The Disability Argument: There are too many things
that human thought can do that machines can’t do (e.g.
self-reflection, appreciation of humor, etc.)
Reply: We are not fully aware of the capacities of
machines or people. It is not hard to foresee machines
that are aware of their own states.
The Originality Objection: Machines don’t have the
capacity to originate anything, or to do anything other than
what they are told.
Reply: It is foreseeable that there will be computers capable
of learning. Moreover, it is not clear how original humans
are, since human creativity is always manipulation of
available ideas or images
The Continuity Objection: The human nervous
system is continuous, unlike a digital computer.
Reply: Digital computers can closely match the
behaviour of continuous machines (e.g. in calculating
irrational numbers).
The Informality Objection: Human behavior is informal,
not subject to general rules like the behavior of a computer.
Reply: Human behaviour is more subject to laws than we
realize.