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15 - Mental Models and Algorithms of Deduction
- from Part III - Computational Modeling of Basic Cognitive Functionalities
- Edited by Ron Sun, Rensselaer Polytechnic Institute, New York
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- The Cambridge Handbook of Computational Cognitive Sciences
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- 21 April 2023
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- 11 May 2023, pp 474-498
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Summary
This chapter begins with an outline of logic and of the attempts to use it as a theory of human deduction. The fatal impediments to this approach led to the model theory in which models based on the meanings of premises yield deductive conclusions. And the chapter describes in detail the implementation of this theory’s account of deductions based on sentential connectives such as “if,” and how this simulation led to the discovery of systematic but compelling fallacies.The chapter outlines how algorithms based on models simulate deductions of the spatial relations among objects. And it points out the problems that need to be solved to extend accounts of elementary inferences from quantified assertions to deal with multiply-quantified relations. One alternative to the model theory is the idea that human deduction relies on probabilities. This approach concerns only which inferences people make, not the underlying mental processes by which they are made. The model theory fills the gap, because it applies to the deductions of probabilities, both those based on frequencies or proportions, and those based on evidence pertinent to unique events. The chapter ends with an account of why theories of human deduction need to be simulated in computer programs.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- Book:
- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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Mental Models in Deductive Reasoning
- Juan A. García-Madruga, Francisco Gutiérrez, Nuria Carriedo, Sergio Moreno, Philip N. Johnson-Laird
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- The Spanish Journal of Psychology / Volume 5 / Issue 2 / November 2002
- Published online by Cambridge University Press:
- 10 April 2014, pp. 125-140
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We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.
Précis of Deduction
- Philip N. Johnson-Laird, Ruth M. J. Byrne
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- Journal:
- Behavioral and Brain Sciences / Volume 16 / Issue 2 / June 1993
- Published online by Cambridge University Press:
- 04 February 2010, pp. 323-333
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How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system. Deduction argues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises.
Mental models or formal rules?
- Philip N. Johnson-Laird, Ruth M. J. Byrne
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- Behavioral and Brain Sciences / Volume 16 / Issue 2 / June 1993
- Published online by Cambridge University Press:
- 04 February 2010, pp. 368-380
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10 - Mental Models and Deductive Reasoning
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- By Philip N. Johnson-Laird, Princeton University
- Edited by Jonathan E. Adler, Brooklyn College, City University of New York, Lance J. Rips, Northwestern University, Illinois
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- Reasoning
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- 05 June 2012
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- 05 May 2008, pp 206-222
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Summary
How do people reason? The view that I learned at my mother's knee was that they rely on logic. During the 1960s and 1970s when the study of thinking had become respectable again after the Dark Ages of Behaviorism, psychologists – including the present author – took this view for granted. The idea that logic provided the norms of reasoning can be traced back to the rise of modern logic, and was defended in the nineteenth century by both Boole (1854) and Mill (1874). In the twentieth century, the Swiss psychologist, Jean Piaget, and his colleagues argued that the construction of a formal logic in the mind was the last great step in children's intellectual development, and that it occurred at about the age of twelve (see, e.g., Inhelder and Piaget, 1958). And so thirty years ago the task for psychologists appeared to be to determine which particular formal logic was laid down in the mind and which particular rules of inference were used in its mental formulation. That, at least, was how several like-minded authors conceived their research (see, e.g., Osherson 1974–1976; Johnson-Laird 1975; Braine 1978; Rips 1983). In the parallel “universe” of artificial intelligence, researchers were similarly developing computer programs that proved theorems relying on formal rules of inference (e.g., Bledsoe 1977). The main skeptics were those engaged in trying to analyze everyday arguments. They discovered that it was extraordinarily difficult to translate such arguments into formal logic.
12 - Mental Logic, Mental Models, and Simulations of Human Deductive Reasoning
- from Part III - Computational Modeling of Various Cognitive Functionalities and Domains
- Edited by Ron Sun
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- The Cambridge Handbook of Computational Psychology
- Published online:
- 05 June 2012
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- 28 April 2008, pp 339-358
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Summary
The term episodic memory refers to the ability to recall previously experienced events and to recognize things as having been encountered previously. Research on the neural basis of episodic memory has increasingly come to focus on three structures: The hippocampus, Perirhinal cortex and Prefrontal cortex. This chapter reviews the Complementary Learning Systems (CLS) model and how it has been applied to understanding hippocampal and neocortical contributions to episodic memory. In addition to the biologically based models, there is a rich tradition of researchers building more abstract computational models of episodic memory. The chapter describes an abstract modeling framework, the Temporal Context Model (TCM) that has proved to be very useful in understanding how to selectively retrieve memories from a particular temporal context in free recall experiments. Episodic memory modeling has a long tradition of trying to build comprehensive models that can simultaneously account for multiple recall and recognition findings.
List of Contributors
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- By John R. Anderson, Benjamin J. Balas, Margaret A. Boden, Todd S. Braver, Selmer Bringsjord, Jerome R. Busemeyer, Nick Chater, Morten H. Christiansen, Axel Cleeremans, Greg Detre, Zoltán Dienes, Wayne D. Gray, Thomas L. Griffiths, Evan Heit, Joseph G. Johnson, Philip N. Johnson-Laird, Charles Kemp, John K. Kruschke, Abninder Litt, Francisco J. López, James L. McClelland, Brian M. Monroe, Ferdinando A. Mussa, Kenneth A. Norman, Stellan Ohlsson, Nicola De, Sean M. Polyn, Stephen J. Read, Grega Repovš, Timothy T. Rogers, Gregor Schöner, David R. Shanks, Thomas R. Shultz, Pawan Sinha, Sylvain Sirois, Aaron Sloman, Sara A. Solla, Ron Sun, Niels A. Taatgen, Joshua B. Tenenbaum, Paul Thagard, Michael S. C. Thomas, Yingrui Yang
- Edited by Ron Sun
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- The Cambridge Handbook of Computational Psychology
- Published online:
- 05 June 2012
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- 28 April 2008, pp ix-xii
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7 - Mental Models and Reasoning
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- By Philip N. Johnson-Laird, Princeton University
- Edited by Jacqueline P. Leighton, University of Alberta, Robert J. Sternberg, Yale University, Connecticut
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- Book:
- The Nature of Reasoning
- Published online:
- 05 July 2011
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- 03 November 2003, pp 169-204
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Summary
Let us begin with three problems that call for you to reason:
Suppose that you are on the jury of a murder trial, and that two propositions are established beyond a reasonable doubt: The stabbing occurred on an Amtrak train to Washington, and the suspect was in a cinema at the time of the stabbing. What conclusion would you draw? You may want to take a pencil and paper, and record your answer to this problem and the two that follow.
Suppose that you have the following information: Either Omar is in Kandahar or at least he is in Afghanistan. In fact, he is not in Afghanistan. Is he in Kandahar: “yes,” “no,” or “don't know”?
You park your car in London on a double yellow line drawn at the side of the road. When you return, you car has been wheel-clamped, and a note on the windshield tells you where to pay the fine to get the wheel released. What offense have you committed?
Nearly everyone responds to problem (1): the suspect is innocent. They respond to problem (2): no, he is not in Kandahar. And they respond to problem (3): the offense was to park in a “no parking” zone. Our ability to reason is perhaps our preeminent cognitive skill. Without it, as these examples show, daily life would be impoverished, and there would be no science or mathematics, no legal systems or social conventions.
11 - Analogy and the exercise of creativity
- Edited by Stella Vosniadou, Andrew Ortony
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- Book:
- Similarity and Analogical Reasoning
- Published online:
- 22 October 2009
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- 28 July 1989, pp 313-331
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Summary
Introduction
Analogies are tools for thought and explanation. The realization that a problematical domain (the target) is analogous to another more familiar domain (the source) can enable a thinker to reach a better understanding of the target domain by transporting knowledge from the source domain. A scientific problem can be illuminated by the discovery of a profound analogy. A mundane problem can similarly be solved by the retrieval of the solution to an analogous problem. An analogy can also serve a helpful role in exposition: A speaker attempting to explain a difficult notion can appeal to the listener's existing knowledge by the use of an analogy. A psychological theory of analogies must accordingly account for three principal phenomena: (a) the discovery or retrieval of analogies of various sorts from the profound to the superficial, (b) the success or failure of analogies in the processes of thinking and learning, and (c) the interpretation of analogies that are used in explanations.
My main purpose in this chapter is to establish that psychological theories of analogy have so far failed to take the measure of the problem. The processes underlying the discovery of profound analogies are much harder to elucidate than is generally realized. Indeed, I shall argue that they cannot be guaranteed by any computationally tractable algorithm. But my goals are not entirely negative; I want to try to establish a taxonomy of analogies and to show that there are some forms of analogy that can be retrieved by tractable procedures. I shall begin with an area that has undergone considerable psychological investigation: the role of analogies in problem solving.
‘&’
- Philip N. Johnson-Laird
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- Journal:
- Journal of Linguistics / Volume 6 / Issue 1 / March 1970
- Published online by Cambridge University Press:
- 28 November 2008, pp. 111-114
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- March 1970
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Katz on analyticity
- Philip N. Johnson-Laird
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- Journal:
- Journal of Linguistics / Volume 3 / Issue 1 / April 1967
- Published online by Cambridge University Press:
- 28 November 2008, p. 82
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- April 1967
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Katz (1966) attempts to explicate the notion of analyticity on the basis of a theory of natural languages. This theory assumes that grammatical transformations do not affect semantic interpretations, which are performed on the underlying phrase markers. Hence, the interpretation of the conjunction of two co-ordinate clauses consists of the logical conjunction of their interpretations. The following two sentences have therefore identical interpretations:
1. The thief snatched the money and the clerk pressed the alarm.
2. The clerk pressed the alarm and the thief snatched the money.