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Meeting on Cognitive Design

School of Advanced Studies IUSS Pavia - NEtS Center & Institut Jean Nicod, CNRS Paris
Joint IUSS-Nicod Meeting on Cognitive Design
Friday, May 5th, 2017


Roberto Casati (Institut Jean Nicod, Paris), Redesigning Formalism

Open Discussion on Cognitive Design

Roberto Casati (Institut Jean Nicod, Paris)
Michele Di Francesco (IUSS Pavia)
Marco Fasoli (University of Milano Bicocca)
Giulia Piredda (IUSS Pavia)
Andrea Sereni (IUSS Pavia)
Alfredo Tomasetta (IUSS Pavia)

IUSS Pavia
Palazzo del Broletto
Room 1.17
Piazza della Vittoria 15
27100 Pavia
Everyone is invited

Abstract: We teach logic by using different notations: tableaux, axiomatic systems, Polish notation, Fitch's derivation trees, boxes. We even quarrel on which notation is the most perspicuous or pedagogically valid. Surprising! Given that artificial languages for logic were supposed to solve once and for all the communication and reasoning problems arising from the imprecision and ambiguities of natural language. We teach children the entire multiplication table: seven by eight, and then eight by seven. Surprising! Once you have learned seven by eight, there is no need to memorize eight by seven, so why load semantic memory? French has countless ways to write the sound [o]: 'o', 'ot', 'os', 'au', 'aux', 'eau', 'eaux', 'oh'... Surprising! Given that this causes a delay in learning to read that can be measured in months relative to the use of more perspicuous orthographies (in Italian, there is only one way to write [o]: 'o'. Statisticians use the same symbol 'p' in a number of different ways, for proportion, probability value, then have '^' and '¯' mean the same thing, and make no concession when it comes to guess the symbol for the sample statistics given knowledge of the symbol for the corresponding population parameter (you can project from the proportion parameter p to the sample parameter p̂, but then you cannot project from the proportion mean μ to the sample mean x̅). And so on and so forth.
The reason for the notational mess are largely historical: different schools, different traditions, contingencies, what your teacher taught you, all played a role in shaping the symbolic systems we use. How did we get here? Where can we go from here, and what are the cognitive constraints? And what can be done? As an example, if you plan to teach sentential logic, prefer the use of propositional letters 'A' and 'B' to the use of 'p' and 'q'. 'A' and 'B' are different on many dimensions (shape, symmetry, topology), and this contributes to an easier identification of the visual patterns used in demonstrations. What are the tradeoffs between effectiveness and implementability? We may be not expecting an act of super-duper design, a radical orthographic reform any soon (although there are examples to learn from), but we may begin to change some of our more peripheral teaching habits.