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Cognitive Science
Terry Regier

Review sheet for Midterm 1 Cognitive Science 1 Fall 2013 1. Rationalist vs. empiricist: Where does knowledge come from? Arationalist would say that some of it is innate while and empiricist would say that all knowledge comes from experience. What is the nature of thought?Arationalist would say that it is language-like, propositional, and logical. An empiricist would argue that it is experience-like, imagistic, and associative.Are there uniquely human aspects of cognition? Arationalist would say yes; an empiricist would say not fundamentally. Rationalists believe that knowledge comes partly from reason, however there are some aspects that are innate.An empiricist would argue that neither principles nor ideas are innate. Knowledge comes only from experience. Rationalists include Plato, Leibniz, Boole, Frege, Turing, and Chomsky. Empiricists includeAristotle, Locke, and Skinner. 2. CRUM = computational-representational understanding of mind Cognition = information processing. Information processing can be formalized. Information processing operates on representations (symbols that have meaning). The study of information processing can be divorced from physiology and biology Innateness : 1. Aristotle: blank slate; a writing tablet on which as yet nothing actually stands. 2. Plato: Innate knowledge; We could not have learned everything we know. The soul must have understood them for all time. Meno’s memo. ; Plato’s problem; how can human beings, who are limited with brief knowledge know as much as they know; argument from poverty of stimulus - limited knowledge. The solution to this is that the only way we know this much is if we remembered it from our birth; learning is remembering. We have some piece of knowledge K; our experience is too limited for us to have learned K from experience. Therefore we always knew K. It is innate, stamped in our souls from birth. 3. Locke: Neither principles nor ideas are innate, and agrees withAristotle. He says there is a blank slate.Also experience is key to knowledge - sensation and reflection - our senses convey to the mind perceptions of things; reflection is understanding with another set of ideas - it is internal experience; white paper; experience and reflection. 4. Leibniz: Experience is necessary but not sufficient to account for knowledge; disagrees with Locke. All of the instances confirming a general truth are not sufficient to establish the universal necessary truths; Our minds must contain the seeds of eternity; beasts are purely empirical; veins in the marble. Induction is acquiring knowledge from instances; we generalize beyond the given data and are guided by biases; the conclusions could be wrong. There is a lot of induction in cognitive science: learning rules and concepts, detective work, perception, learning language, making scientific discoveries (all veins in the marble). Deduction goes from the truths we derive to knew truths; completely certain of the conclusions. Alphabet of human thought : Syllogisms are speech where there are premises and then something that is different results of the necessity because of their being; no valid syllogism has two negative premises. 1. Aristotle: Catalog the valid syllogisms; in order to do this, we must define a space of possible syllogisms and determine which syllogisms in that space are valid, as special case of deductive reasoning. IfA= B and B = C thenA= C. Logic:A=AB, B=BC, A=AC. 2. Leibniz: He was fundamentally optimistic; the world is neither accidental nor undetermined. It has been planned by a good god and we live in the best of possible worlds. His optimism is central to his wonderful idea. The dream or “wonderful idea”, language as imperfect mirror of human thought, need an ideal language that “perfectly represents the relationships between our thoughts”. People mean well, but language gets in the way; human discord results from imperfect communication, an ideal language would solve many human problems, and an ideal language would solve many human problems. Let us calculate. The notation will do the work, by analogy withArabic numerals. The Universal Characteristic - we need to create a compendium of all human knowledge; describe knowledge in a key underlying notions and provide a symbol for each notion; reduce the rules of deduction to manipulations of these symbols. It would aid clarity of thought - resolve miscommunication and we can just calculate to see who is right. 3. Boole: propositional logic, classes or sets, xy = x and y. xx = x is the foundational rule of Boole’s system: in ordinary algebra it is true only for x=0 and x=1. Can castAristotle’s “principle of contradiction” (nothing can both belong to and not belong to class x) in these terms: x(1-x)=0. “All plants are alive”: P = PL. Can verify validity ofAristotelian syllogisms using Boole’s logic. 0 has no objects; 1 contains all objects. Boole’s logic works for statements…x = 1 means statement x is true; x = 0 means statement x is false (“not x” is true); xy = 1 means x and y are true; x(1-y) = 0 means if x is true, then y is true; x + y = 1 means that either x or y is true. Logic : 1. Frege: Begriffsschrift = concept script; propositional vs. predicate logic; Instead of propositions, Frege used predicates to denote properties of objects. quantification, universal and existential. Truth tables. Aristotle in predicate logic. Possible worlds consist of assignments of truth values to all predicates applied to all objects, models of a formula is still an assignment of truth values that make the formula true. Modus ponens (affirming the antecedent), modus tollens (denying the consequent). There are limitations in that we can’t say things like “For every property P, there is some object that possesses that property.” The syntax in logic refers to properties of formulas while semantics refers to statements that those formulas make about possible worlds. Inference rules are operations that depend only on syntax, but have semantic implications. In modus ponens: syntax is used to draw a conclusion based on having formulas of just the right kinds, which semantics are conclusions that are guaranteed to be true in the possible worlds described by the formulas. Russell’s letter to Frege. Frege did not provide a procedure that will tell you whether or not a conclusion C follows from premises P. This showed that Leibniz wanted a language that could be an efficient instrument of calculation; however Frege’s logic was complicated and time-consuming. 2. Infinity : Infinity: a rationalist challenge to empiricism, going beyond (necessarily finite) experience; seeds of eternity; it goes beyond the data given. Mathematical “business as usual” does not apply at infinity. Countably vs. uncountably infinite. Assume that there are only countably infinitely many subsets of N. Use the diagonal method to create a new subset of N, beyond the countable ones. The existence of that new subset means our assumption was false. “Uncountably infinite” Cantor, diagonal method. Thought as computation : 1. Hilbert: decision problem (Entscheidungsproblem). Want a procedure that accepts premises P and a conclusion C, and determines whether C follows from P. This would fulfill Leibniz’s dream. Turing used the diagonal method to show that this doesn’t exist. 2. Turing: Turing machine (a machine for a specific purpose). ATuring Machine is a formal model of computation. They are hypothetical computational devices that read input and spit out new output. Universal Turing machines as general-purpose computers, distinction between program and data. These can simulate any Turing Machines on an arbitrary input; they read the description of the machine as well as the input from their own tape. Undecidable problems, a negative answer to Hilbert, and a proof that Leibniz’s dream is not fully attainable. Upside: a formal model of computation, making possible the view of mind as a symbolic system, a processor of symbolically expressed information. The mind and the computer: different hardware, same software. Thought, computation, and the world : 1. Thinking as computation. Every TM can be specified as a number.Any TM is discrete & finite (input tape aside). Thus a number can specify its finite components. See Davis for details. TMs take numbers as input. Some input numbers will cause the TM to eventually halt; others will cause it to loop. The “halting set” of a TM is the set of input numbers that cause it to halt, rather than loop. The main point is there exists claims that cannot be computationally decided. 2. Symbol grounding problem – need to know when our symbolic representations are true of the world. Our senses provide us with information about which facts are true of the world. We use inference to derive new facts from this knowledge. Our inferences lead us to take actions that provide us with more information. What if our senses are wrong, considering they are the foundation? We can be misled, therefore what can we know with certainty? 3. Descartes: what can we know with certainty? Skepticism. Evil genius, deceives me by changing the information I receive through my senses. I can doubt the existence of my body and of the senses generally. But I cannot doubt the existence of my mind: by doubting, I establish the existence of my mind. I am a thing that thinks. Therefore mind and body are of different sorts: dualism - the mind and the body are different kinds of entities and they cannot be reduced to one another; there is no explanation of minds in physical terms. Contrast: materialism - belief that the mind can be reduced to physical manner. The relationship of dualism to the computational view of mind. Levels of analysis. To understand minds, we can ask questions at different levels.At the physical level, questions that can be answered using tools of physical science.At a more abstract level, questions that can be answered in computational terms. Behavior and the mind : 1. Boole: the laws of nature are inductive inferences from a large body of facts. In contrast, laws of mind do not require a large collection of observations: the general truth is seen in a single particular instance. The mind is special: dualist. Focus on deduction, not induction. 2. Wundt: introspection, reaction times, complication apparatus, pendulum; Pendulum position is perceived late; we have to add a delta to every x. Wundt came up with the concept of apperception which is the process of making an experience clear in the conscious; takes time and effort; inferring an unobserved mental process from observed behavioral data. “Brass instrument psychology”. Subjective element in introspection: unusual in science, uncomfortable. 3. Ebbinghaus: not introspection, measured memory retention: do you or do you not remember a given experience? Exponential forgetting curve. Spacing effect; a list of items is better remembered when studied at spaced intervals, rather than all at once. 4. Behaviorism: John Watson, analysis of behavior, not mind or mental states. Deliberate rejection of introspection. Emphasize role of environment – blank slate empiricism. Psychology as the behaviorist views it is purely objective natural science. Its theoretical gain is the prediction and control of behavior. Introspection forms no essential part of its method. No dividing line between man and brute – contrast with Leibniz. 5. Classical conditioning, e.g. Pavlov. Passive: associate stimuli that are paired in your experience, but are not directly under your control. LittleAlbert experiment as attempt to extend these ideas to humans (Watson). 6. Operant conditioning. Thorndike.Active: associate your actions with resulting reward or punishment. Cats in puzzle boxes. 7. Skinner: radical behaviorist, sought to dispense with talk of mental states entirely. Our behavior can change, but we have no evidence of acquired knowledge. An inversion of Cartesian skepticism: privilege the senses, not the mind. Skinner box. The cognitive revolution : 1. Tolman: challenge to behaviorism, originally from within the camp. Insight in rats: latent learning, not driven by reinforcement. Cognitive maps, a mental representation of the maze. Mental representations as central to cognitive science, a key feature that distinguishes cogsci from behaviorism. 1. Study: three groups of rats were run through a maze 1. The first group was rewarded each time they succeeded 2. Second group was never rewarded 3. Third group was unrewarded for the first 10 days, then was rewarded upon success. This group learned more quickly than the other two. 2. The conclusion was that learning is driven by more than reinforcement. 2. Birth of cogsci at 1956 MIT symposium. The mind as a symbolic system. 1. Newell and Simon: Logic Theorist, a realization of Leibniz’s dream, the firstAI program, found proofs of mathematical facts, used heuristics (e.g. work backwards) to explore an extremely large search space. The Logic Theorist was a computer program to mimic problem solving in humans. Computers can solve problems that are characteristic of human thought. Human thought can guide us in how these computer programs should work. 2. Miller: magical number 7, plus or minus 2. People can hold about seven “chunks” of information in memory. Aconstraint on human mental representation. Opens the possibility of hierarchical embedding of chunks inside one another. Not only are there mental representations, but they have structure. Some thought is hierarchically structured; this is true in various mental domains. 3. Lashley: hierarchical structure of plans. Hypothesis of subconscious information processing; hypothesis of task analysis 4. Chomsky: hierarchical structure of language. Language : 1. Chomsky: Language as hierarchically structured – not just a string of words. Link to Miller, Lashley. There are hierarchical structure and chunks in language, as there are in plans and task analysis, and in memory. 2. Language as uniquely human. Each of us has a large amount of linguistic knowledge and we are unaware of most of it 3. Language as rule-driven. Infinite generative capacity from finite means, Humboldt. Link to Frege, but now we have rules of language, not rules of thought. 4. Skinner and Whitehead, Skinner’s Verbal Behavior , Chomsky’s review of Skinner. Dinner conversation between Skinner and Whitehead in which Whitehead told Skinner to deny mental representations through the use of language -AH language is innate. Claim: Language is special - it is a human ability that differs from others. Language is infinite - always can string together new words to make a new sentence. 5. Skinner as classic empiricist; Chomsky as classic rationalist. Skinner published a book in response to Whitehead’s challenge, however it failed due to Chomsky's negative review in 1959. “Language reflects knowledge and cannot be accounted for without references to mental representations. Some of this knowledge is innate.” 6. Plato’s problem, argument from poverty of stimulus, as applied to grammar. The logical problem of language acquisition. Language is not just a stream of words, rather it is hierarchically structured. That structure could not have been learned from the linguistic input that children receive - therefore, at least some linguistic knowledge must be innate. 7. Universal grammar; UG as proposed answer to 3 questions: Plato’s problem, why is language uniquely human, why are there language universals - patterns found amongst all or many languages? Alternative perspectives on universal grammar. 8. Link to Turing: Turing machines as part of the Chomsky hierarchy. Review sheet for Midterm 2 Cognitive Science 1 Fall 2013 The discipline matures: 1. Symbolic vs. imagistic (or more generally experiential) representations: Imagistic representation is a contrast to the rationalist language-like nature of thought. We have seen how linguistic knowledge is represented but not how it is processed. Language understanding is necessarily at least partly symbolic. ELIZAwas a chatterbot used to mimic human understanding, however there was no representation of the meaning of the statements. This is symbolic, yet shallow. SHRDLU focused on natural language understanding in a microworld; language was linked to action. There are three components: syntactic analysis (grammatical analysis of input sentences), semantic analysis (determining what the sentence means), and perception and inference (consult the world for answers to questions posed). Symbolic representation is a procedure for action and inference. SHRDLU was narrow and limited in domain, however it linked language “understanding,” symbolically represented, with observable action in the world. Language understanding is dependent on multiple interacting processes. However mental representations don’t always have to be language like. 1. Imagistic/Experiential representations: Shepard and Metzler worked with mental rotations by displaying 3D images and asking if they were the same image, just rotated at a different angle; the bigger the angle of rotation, the more difficult it is to tell. There is a linear model to represent this; this is also proof of imagistic mental representations. Kosslyn did a study with images and told the participants to focus on one part, while the next image, there was a change; found that the farther the change from the focal point, the longer it takes to identify the different feature; interpretation is that there is a scanning of a mental image. 2. Marr’s 3-level framework: Question: how do we think about cognitive systems?Answer: Marr. His three levels: computational theory (the functional goal of the visual system; what the system is up to and what the goal of its information processing is); Representational andAlgorithmic; Hardware implementation 3. Marr’s model of vision: it is a continuum from imagistic to symbolic; there is a hierarchical structure in perception. This shows the representations and processes the visual system uses, but doesn’t say the functional goal or the physical implementation. The Turing test and its critics: 1. Many theories assume that the human mind is a machine. If the assumption is wrong, we’re all in trouble. There is a possibility of non-human understanders if machines actually understand. 2. Two extreme positions: solipsism is the view that no mind exists except your own; anthropomorphism attributes human abilities to anything - we need an intermediate position. 3. Theories of the mind often driven by current technology; they come and go, however they can be useful as basis for theories and hypothe
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