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Conceptual Puzzles & Theoretical Elegance (principledness? naturalness?)

Conceptual Puzzles & Theoretical Elegance (principledness? naturalness?). Need to add cognition — not just numbers, experiments, and algorithms Multiple representations are tapped differentially by different tasks/conditions (Boersma, 3:19 pm) Especially important in study of gradience

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Conceptual Puzzles & Theoretical Elegance (principledness? naturalness?)

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  1. Conceptual Puzzles & Theoretical Elegance (principledness? naturalness?)

  2. Need to add cognition — not just numbers, experiments, and algorithms • Multiple representations are tapped differentially by different tasks/conditions (Boersma, 3:19 pm) • Especially important in study of gradience • Probability distribution family* • *but see distribution-free methods (PAC learning) • Rankings: Natural for (partial) orders? (MaxEnt: 1) • Outputs: Natural for induction/generalization? (MaxEnt maximizes entropy) • Bias:Bayesian inference

  3. Constraint interaction through numbers • The Counting Catastrophe • WSP [σH main stress]; M-PARSE • Numerical/HG typology: *σH σH ⋯σH iff #σH’s > n∀n, • OT typology: *σH σH ⋯ σH iff #σH’s > n for n {1,  } • Variation through Losers • Relative Harmony predicts relative frequency • Harmony Theory/MaxEnt and HG; also Pater’s relativized H in HG (yesterday) • The Epenthesis Catastrophe • MAX≫ DEP/batak/  bataka  but /batak/  batakatatata ≻ /batak/ bata  • Fate of harmonically bounded forms?

  4. Variation through winners of multiple rankings • Number of rankings producing an output predicts relative frequency • All other approaches (?) • Bogus Rankings Catastrophe • A, B conflict: Proportion of A-obeying output (A ≫ B) • {A; B}: 1/2 • X bogus; no (relevant) violations • {X ≫ A; B}: 1/3; {A ≫ X; B} : 2/3; {A ≫ X, X ≫ B}: 1 • Ordinal, not just quantitative, effects

  5. Analogical Combinatorial Catastrophe • Theorem.Lexical Similarity Theory cannot explain Basic Combinatorial Generalization. • Lex = {ta, ki}  ti/ka ≻ pa/tu • Smolensky, P. 2006. On theoretical facts and empirical abstractions. In Wondering at the natural fecundity of things: Essays in honor of Alan Prince, eds. E. Bakovic, J. Ito, and J. McCarthy. Linguistics Research Center [http://repositories.cdlib.org/lrc/prince/13] & ROA. • Role of puzzles, thought experiments & generality of proposed solutions

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