Two puzzles in experimental syntax and semantics

1 Two puzzles Relating standard linguistic data to theory is hard; making experimental data bear on the theory is even harder. Two difficult problems are central, one relating to experimental design, and the other, to the interpretation of results. In this short note, I discuss these problems in the context of specific studies in experimental syntax and semantics. I begin with an experimental design issue – THE DIMENSIONALITY-REDUCTION PROBLEM, arising in the midst of complex stimuli: theoretical linguists typically investigate the grammatical properties of complex linguistic objects through contrasts. As minimal pairs are hard to come by, multiple controls are introduced. This is done at no additional cost. Experiments, however, are usually subject to severe logistical, technological and analytic constraints that preclude the proliferation of controls. When we work with multi-dimensional contrasts, our task is to design compact tests that reduce dimensionality to a bare minimum, but still ascertain that the property that interests us is isolated. But when complex stimuli are compared along some dimension, and given a limited room for controls, how can other dimensions of the stimuli be made orthogonal to the test, namely, precluded from affecting the dependent variable? This problem is pronounced in the context of functional Magnetic Resonance Imaging (fMRI) language experiments, although it also arises when Reaction Time (RT) is the dependent measure. I describe the puzzle, sketch a solution – parametric designs – and illustrate it with 2 experiments, where syntactic or semantic properties of stimuli modulate brain responses. I then move on to data analysis, and discuss THE MAPPING PROBLEM: most formal linguistic theories are designed to handle categorical variables, placed on a nominal scale, and carrying labels (e.g., ±well-formed, ±Grammatical) rather than numerical values. How can such variables be related to ordinal ones – numerical values on a scale, e.g., the time it takes to parse a sentence, or to changes in the intensity of some brain signal that their processing modulates? Experimental results presumably give us a special angle on linguistic knowledge and its implementation. But how do we incorporate these results into the theory? This problem was considered early on in the history of generative grammar (Miller & Chomsky, 1963), and in much subsequent work, mostly in the context of Reaction Time data. Interest in it has been recently renewed, as quantitative analyses of judgment behavior raised new questions (Bard, Robertson & Sorace, 1996, passim). Below, I consider how this problem arises for other types of experimental data (mostly errors by linguistically deficient individuals, whether aphasic patients suffering from focal brain-damage, or normally or pathologically developing children). Here, too, I illustrate with several concrete syntactic and semantic examples, and reflect on possible solutions, and on how they impact the way one should bring experimental results to bear on the theory.