Midterm 3 study guide

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Department
Cognitive Science
Course
COG SCI 190
Professor
Terry Regier
Semester
Fall

Description
Lecture: Intro Classic Questions 1. Where does knowledge come from? 2. What is the nature of thought? 3. Are there uniquely human aspects of cognition? Lecture 1 Innate • Rationalist: Knowledge comes partly from reason, some aspects of which may be innate o Plato o Leibniz o Boole, Frege o Turing o Chomsky • Empiricist: Neither principles nor ideas are innate. Knowledge comes from experience. o Aristotle o Locke o Skinner • Plato (Rationalist) teacher of Aristotle (Empiricist) • Aristotle (Empiricist) o Blank Slate/ Tabula Rasa • Plato (rationalist) o Innate knowledge o We know things we could not have learned. SO the soul must have “understood them for all time.” (Meno-Play we read for hw with the squares) o Like the stingray we have made him numb o Learning is remembering o Plato’s Problem: Poverty of stimulus= limited experience  How comes it that human beings whose contacts with the world are brief and personal and limited, are able to know as much as they know?  Solution: • The only way we could know is if we knew it already • We don’t learn about the world… we remember facts from before our birth • Objects in our world are mere shadows of their ideal forms, but similar enough to remind us of those ideal forms, but similar enough to remind us of those ideal forms • Locke (Empiricist) o Says NO to innate knowledge o “Neither principles nor ideas are innate.” o Blank Slate similar to Aristotle- same idea, updated technology o Two sorts of experience  Sensation  Reflection (the operations of our mind) o Children acquire their knowledge gradually by degrees • Leibniz (Rationalist) o Locke is just wrong o Experience is necessary but not sufficient to account for our knowledge o Triangle angles = 180 degrees example o “Our minds must contain seeds of eternity, flashes of light hidden inside us, that reveal something divine and eternal and allow us to go beyond the merely empiricial” o Humans v. Beasts  Beasts are solely empirical o Block of marble with veins • Induction o Acquiring knowledge from instances is a problem of induction o Generalizing beyond the data given o Guided by biases (veins in the marble)? o Conclusions could always be wrong o Cylinder on checkerboard example • Deduction o Goes from known truths to derive new truths o Conclusions are absolutely certain • Lecture Summary o Where does knowledge come from?  Aristotle: “the blank slate”  Plato: learning as remembering  Locke: building knowledge from experience  Leibniz: veins in the marble o Two strong positions with different answers  Rationalism/nativism (innate ideas)  Empiricism (experience) o The big questions is what can be learned  a questions for modern cog sci Lecture 2 – Logic • Modern Cog Sci takes a scientific approach o Develop theories that aim to predict and explain phenomena o Use experimental methods to gather new info and to test theories • Induction o Argument from particular experiences to universal truths – not certain • Deduction o Argument from known truths to other truths – absolutely certain • Syllogisms o Speech in which certain things have been supposed, something different from those supposed results of necessity because of their being so o Premises + conclusion o All philosophers are people, all people are mortal thus all philosophers are mortal o Artistotle’s project: catalogue the valid syllogisms  Systematically enumerated the syllogisms & identified which are valid  Assumed some were valid and reduced others to those by proofs o Universal All As are Bs or All As are not Bs o Particular Some As are Bs or Some As are not Bs • Leibniz (Rationalist) o Veins in the marble o Fundamentally optimisitic:  World is neither accidental nor undetermined  It has been planned by a benevolent God: we live in the best of possible worlds o Wonderful Idea  Leibnize believed that people were largely benevolent and cooperative, but were hampered in cooperation by language which is an imperfect mirror of intelligible thoughts, and often makes reasoning obscure  What is needed is an ideal language that perfectly represents the relationships between our thoughts o 3 points Leibniz is arguing  People are fundamentally well-meaning  Human discord results from imperfect communication through language  An ideal language would solve many human problems o Basically Leibniz wants something that “perfectly represents the relationships between our thoughts” o To create this (UNIVERSAL CHARACTERISTIC) language , we must:  Create a compendium of all human knowledge  Describe that knowledge in terms of a set of key underlying notions and provide a symbol for each such notion  Reduce rules of deduction to manipulations of these symbols  (AI ahead of its time!) o Think of the Universal characteristic as the difference between adding 50 +200 and the roman numeral version of the same thing  Aids clarity of thought and the notation does much of its work • Boole (Propositional logic) o “all Plants are alive” o Can be represented in terms of classes or sets of objects o Foundational rule of Boole’s system xx= x o X+Y is all things in either x or y (union) o X-Y is all things in x but not y (difference) o o X=1 means x is true o X= 0 means x is false o XY=1 means x and y are true o X(1-Y)= 0 means if x is true, then y is true o Limitations  Boolean algebra is a basic component of computer programming and the operation of circuits and silicon chips  But there are thoughts it cannot express cleanly – “everybody loves somebody” • Summary o A mathematical theory of thought should predict and explain how we reason o Logic attempts to do this  Aristotle: cataloguing the syllogisms  Leibniz: the vision  Boole: an algebra of thought o Modern logic can express more complex thoughts Lecture 3- More Logic • Truth Tables o Truth of a formula depends on the truth of its parts o An assignment of truth values to propositions (a possible world) that results in a formula being true is a model of that formula • Limitations of Boole’s Logic: Multiple generality (every v. some) – An affirmation that is both universal and particular • Frege o Begriffsschrift -> Concept Script  A formal language that aims to capture the relationships between our thoughts o Modern logic o First-order predicate logic (instead of propositions use predicates to denote properties of objects)  P(a) like Hairy (Rex) – rex= name of dog o Two new symbols:  Universal Quantifier: Upside down A (for all)  Existential Quantifier: Backwards E (for some, there exists)  Quantifiers: concern variables • All objects or at least one object o Fixes the problem of Multiple generality (“Everybody loves somebody”) o CAN’T say “For every property P, there is some object that possesses that property” (that is second-order logic) • Inference Rule o X  Y o X o ____ o Y o Modus Ponens (always works no matter what X and Y mean  Syntax: draw a conclusion based just on having formulas of the right kinds (x  Y, X)  Semantics: conclusion is guaranteed to be true in the possible worlds described by those formulas • Syntax and Semantics o Syntax: how things are written o Semantics: what things mean o In logic:  Syntax – properties of formulas  Semantics – the statements that those formulas make about possible worlds • Other Inference rules o X ^ Y o ____ o X o Y o o X o _____ o X (or) Y o o X  Y o Not Y o _____ o Not X o Modus Tollens • Power of logic o Take a world and describe it with formulas o Using purely syntactic operations on those formulas, you can discover new things that are true about that world o The satisfaction of Leibniz’s dream: an algebra that yields valid inferences • 2 Sobering notes o Russell’s letter to Frege  Call set S extraordinary if it contains itself; otherwise call it ordinary  O – being the set of all ordinary sets- ordinary or extraordinary?! • THE BIG FLAW o Leibniz wanted a language that was simple and efficient for calculation but Frege’s logic made deductions very complicated and time-consuming Lecture 4 • Guest Lecture Summary o Levels of explanation ex. For schizophrenia. Why can’t you tickle yourself? o Chinese room: is computation enough? o Consciousness – a challenge! o Eliminativism – doing away with the mental altogether o Recurring theme: critiques and limitations of cognitive science • Why Infinity o Relevant  A rationalist challenge to the empiricist view that all things come from experience  Our experience = finite, yet we can conceive of the infinite  God = infinite and all-powerful o Pleasant  Infinity is connected to large, important, positive concepts (like God)  Rules break down in interesting ways when it comes to infinity  Countably infinite and the idea of more than 1 size to infinity (Cant
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