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? 32795 21826 + + ?? 54621 53511 10969 11179 11875  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.