Conceptual Puzzles

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, 319 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 sH ?main stress M-PARSE
• Numerical/HG typology sH sH ? sH iff sHs gt n
  ?n,
• OT typology sH sH ? sH iff sHs gt n for n ?
  1, ?
• Variation through Losers
• Relative Harmony predicts relative frequency
• Harmony Theory/MaxEnt and HG also Paters
  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