What is Cognitive Science? Part 1

What is Cognitive Science? Part 1
Zenon Pylyshyn, Rutgers Center for Cognitive Science
What’s in the mind? How do we know?
What is special about cognition?
• Cognition (from Latin “cogito”) refers to the capacity to
know, and by extension to reason, perceive, plan, decide,
solve problems, infer the beliefs of others, communicate
by language as well as by other ways, and all the other
capabilities we associated with intelligent activity.
• What is central to all such activity is that it relies on
representations of the (actual or imagined) world.
 Cognitive science is the study of systems that represent and that
use their representations rationally, e.g.,draw inferences.
 A computer is another such system, so computing has become
the basic paradigm of cognitive science.
• In the last 40 years, The Representational Theory of Mind
has become The Computational Theory of Mind
Cognitive science is a delicate mixture
of the obvious and the incredible
Granny was almost right:
Behavior really is governed by what we know and
what we want (together with the mechanisms for
representing and for drawing inferences from these)
It’s emic, not etic properties that matter
Kenneth Pike
What determines our behavior is not how the
world is, but how we represent it as being
 As Chomsky pointed out in his review of Skinner, if
we describe behavior in relation to the objective
properties of the world, we would have to conclude
that behavior is essentially stimulus-independent
 Every behavioral regularity (other than physical ones
like falling) is cognitively penetrable
It’s emic
states that
matter!
The central role of representation creates
some serious problems for a natural science
 What matters is what representations are about
 But how can the fact that a belief is about some
particular thing have an observable consequence?
• How can beliefs about ‘Santa Claus’ or the ‘Holy
Grail’ determine behavior when they don’t exist?
 In a natural science if “X causes Y” then X must
exist and be causally (lawfully) connected to Y!
• Even when X exists, it is not X’s physical properties
that are relevant, it’s what they are perceived as!
 e.g., the North Star & navigation
Is it hopeless to think we can have
a natural science of cognition?
Along comes The computational theory of mind
“the only straw afloat”
The major historical milestones
•
Brentano’s recognition of the problem of
intentionality: Mental States are about something,
but aboutness is not a physical relation. Therefore,
psychology cannot be a natural science.
• The formalist movement in the foundations of
mathematics: Hilbert, Kurt Gödel, Bertrand Russell
& Alfred Whitehead, Alan Turing, Alonzo Church,
… provided a technique by which logical reasoning
could be automated.
• Representational/Computational theory of mind: The
modern era: Newell & Simon, Chomsky, Fodor
So…intelligent systems behave the way
they do because of what the represent
• But in order to function under causal laws,
the representations must be instantiated in
physical properties
• To encode knowledge in physical properties
one first encode it in symbolic form (Proof
Theory tells us how) and then instantiates
those symbolic codes physically (computer
science tells us how)
How to make a purely mechanical system reason about things
it does not ‘understand’ or ‘know about’? Symbolic logic.
(1) Married (John, Mary) or Married (John, Susan)
and the equation or “statement”,
(2) not[Married (John, Susan) ].
from these two statements you can conclude,
(3) Married (John, Mary)
But notice that (3) follows from (1) and (2) regardless of what is in the
parts of the equation not occupied by the terms or or not so that you could
write down the equations without mentioning marriage or John or Mary
or, for that matter, anything having to do with the world. Try replacing
these expressions with the meaningless letters P and Q. The inference still
holds:
(1') P or Q
(2') not Q
therefore,
(3') P
Cognitive Science and the Tri-Level Hypothesis
Intelligent systems are organized at three
(or more) distinct levels:
1. The physical or biological level
2. The symbolic or syntactic level
3. The knowledge or semantic level
This means that different regularities may
require appeal to different levels
The essential role of representation creates
some serious problems for a natural science
 We are not aware of our thoughts …
 What we are usually aware of is what our thoughts are
about, not properties of the representation itself
 Need to distinguish properties of our thoughts and
properties of what they are about (e.g. mental images)
 We are not even aware of deciding, choosing or willing
an action [Wegner, D. M. (2002). The illusion of conscious will.
Cambridge, MA: MIT Press.]
 Introspective evidence is just one type of
evidence and it has turned out to be unreliable
 We are not directly aware of our representations
If that is so, how can we find out
what goes on in our mind…?
 Given these serious problems in
understanding cognition, is it even possible
in principal to find out how the mind works?
 Is there even a fact of the matter about what
process is responsible for certain behaviors?
 Is the only road to understanding cognition
through neuroscience?
 How can we discover the details of our
mental processes and how they work?
Weak vs Strong Equivalence
● Is cognitive science concerned only with developing
models that generate the same Input-Output behavior
as people do?
● A theory that correctly predicts (i.e., mimics) I-O
behavior is said to be weakly equivalent to the
psychological process.
● Everyone in Cognitive Science is interested in strong
equivalence – we want not only to predict the observed
behavior, but also to understand how it is generated.
● The how will usually take the form of an algorithm.
Simulating the Input-Output function
Input
Black Box
Output
Can we do any better than I-O simulation
without looking inside the black box?
 If all you have is observed behavior, how
can you go beyond I-O simulation?
Simulating the Input-Output function
Think about this for a few minutes:

Is there any way to find out HOW a
person does a simple problem such as
adding two 4 digit numbers?

What are possible sources of evidence
that may be relevant to this question?
Modeling the Actual Process
(the algorithm used)
Input
Black Box
Output
Index of
process
If all you have is observed behavior, how can you go
beyond I-O simulation (mimicry)?
 Answer: Not all observations are Inputs or Outputs:
some are meta-behavior or indexes of processes.
Example of the Sternberg
memory search task
● The initial input consists of the instructions and
the presentation of the memory set (n items).
● On each trial the particular input to the black box
consists of the presentation of a target letter.
● The output consists of a binary response (present
or absent). The time taken to respond is also
recorded. That is called the “Reaction Time”.
● The reaction time is not part of the output but is
interpreted as an index of the process (e.g., an
indication of how many steps were performed).
Example of the input-output of a
computational model of the Sternberg task
● Inputs: Memory set is (e.g.) C, D, H, N
● Inputs: Probe (e.g., C or F)
● Output: Pairs of Responses and Reaction Times
(e.g. output is something like “Yes, 460 msecs”)
● Does it matter how the Output is derived?
 It doesn’t if all you care about is predicting behavior
 It does if you care about how it works
 It does if you want your prediction to be robust and
scalable – i.e., to be based on general principles
Example of the input-output of a
computational model of the Sternberg task
• Inputs are: (1) Memory set = C,D,H,N
(2) Target probe = C (or R)
• Input-Output prediction using a table:
Input to model
C
N
R
H
M
Yes
Yes
No
Yes
No
Model prints out
460 ms
530 ms
600 ms
520 ms
620 ms
Is this model weakly- or strongly-equivalent to a person?
Example of a weakly equivalent
model of the Sternberg task
1.
2.
3.
4.
5.
6.
7.
8.
Store memory set as a list L. Call the list size = n
Read target item, call it  (If there is no , then quit)
Check if  is one of the letters in the list L
If found in list, assign =“yes” otherwise  =“no”
(That provides the answer, but what about the time ?)
If  =“yes”, set  = 500 + K * n  Rand(20  x  50)
If  =“no”, set  = 800 + K * n  Rand(20  x  50)
Print , Print 
Go to 2
Is this the way people do it? How do you know?
What reasons do you have for
doubting that people do it this way?
 Because in this case time should not be one of the
computed outputs, but a measure of how many steps
it took.
 The same is true of intermediate states (e.g.,
evidence includes what subjects say, error rates, eye
tracking, judgments about the output, and so on.)
 Reaction time is one of the main sources of
evidence in cog sci.
 Question: Is time always a valid index of processing
complexity?
Results of the Sternberg memory search task
What do they tell us about how people do it? Is this Input-Output
equivalent or is it strongly equivalent to human performance?
Exhaustive search
Self-terminating search
More examples – arithmetic
 How can we tell what algorithm is being used
when children do arithmetic?
 Consider these examples of students doing
addition and subtraction. What can you tell
from these few examples?
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 How else could we try to find out what
method they were using?
Studying human arithmetic
algorithms
• Arithmetic (VanLehn & Brown. “Buggy”)
Buggy – a model of children’s arithmetic – has about
350 “rules” which help uncover “deep bugs”
• Newell & Simon’s study of problem solving
Problem behavior graph and production systems
Use of protocols, eye tracking
• Information-Processing style of theory.
Computational but not always a computer model.