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 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

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?    

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

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