Abstract
We advance a theory of inductive reasoning based on similarity, and test it on arguments involving mammal categories. To measure similarity, we quantified the overlap of neural activation in left Brodmann area 19 and the left ventral temporal cortex in response to pictures of different categories; the choice of of these regions is motivated by previous literature. The theory was tested against probability judgments for 40 arguments generated from 9 mammal categories and a common predicate. The results are interpreted in the context of Hume’s thesis relating similarity to inductive inference.
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Notes
The model presented here is an alternative to “QPf,” described in Blok et al. (2007). It relies on some of the same concepts.
Participants were interviewed singly. Questions were posed in individualized random order via computer interface. Responses were made with a slider that controlled a field displaying numbers in the unit interval. The concept of conditional probability was reviewed prior to testing.
The same categoricity, however, was observed when the monkeys were trained on concepts involving cat/dog mixtures. Note that the LPFC is directly interconnected with inferior temporal cortex (Webster et al. 1994).
The results reported below are virtually identical if the activations for each mammal in a given region are “mean-centered.” To mean-center mammal M in region R, the average activation (β) in the map for M in R is subtracted from all the activations in the map prior to computing the sum of squared deviations between M and any other mammal.
A natural generalization of our model replaces (binary) similarity with the homogeneity of sets of n ≥ 2 objects. To illustrate, such a measure might assign greater homogeneity to { camels, horses, giraffes } compared to { camels, bears, lions }. All distributions over Qb 1, Qb 2 ⋯ Qb n can be generated by a model like ours that relies on n-ary homogeneity.
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Acknowledgements
We thank Sergey Blok, James Haxby, Douglas Medin, and Lawrence Parsons for discussion and assistance in various stages of this work.
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Appendix: fMRI Details
Appendix: fMRI Details
1.1 Image Acquisition
Scanning was performed with a 3-Tesla Siemens Allegra fMRI scanner. Participants’ anatomical data were acquired with an MPRAGE pulse sequence (176 sagittal slices) before functional scanning. Functional images were acquired using a T2-weighted echo-planar pulse sequence with 33 64 ×64-voxel slices, rotated back by 5 degrees on the left-right axis (axial-coronal − 5°). Voxel size was 3 ×3 ×3 mm, with a 1-mm gap between slices. The phase encoding direction was anterior-to-posterior. TR was 2000 ms; time to echo was 30 ms; flip angle was 90°. Field of view was 192 × 192 cm.
1.2 fMRI Task
During scanning, participants performed several trials of an experimental task on intact stimuli and a visual baseline task on phase-scrambled stimuli. During a trial of the experimental task, participants saw the name of one of our nine mammals (bear, camel, cougar, dolphin, elephant, giraffe, hippo, horse, lion) for 2 s, then a series of 8 intact mammal images presented for 1.5 s each (totaling 12 s of images), then a question mark. Participants were instructed to press a key at the question mark just in case any of the presented images did not match the presented name. Thus, if the word “bear” was followed by 8 bear images, a key-press was not required at the end of the trial; in contrast, a key-press was expected if (e.g.) a zebra intruded in the sequence of bears. The form of the visual baseline task was identical, except that no word was presented before the images, and participants searched for a low-contrast crosshatch (#) in the sequence instead of a category mismatch. The images in each baseline trial were phase-scrambled versions of one of the mammals; thus there was a baseline trial consisting only of scrambled bears, one consisting only of scrambled camels, etc.
The study was organized into 7 runs of the experimental task, with 9 trials each (one for each mammal). There was also 1 run of the baseline task, with 11 trials (one trial without # for each mammal plus two with #). Each run contained 0, 1, or 2 trials requiring a response; these trials were discarded, and only trials in which participants verified an unbroken stream of intact or scrambled images were analyzed. (Discarded trials thus served to verify the subject’s attention; performance on them was in fact perfect.)
1.3 Image Analysis
Functional data were registered to the participant’s anatomical MRI, despiked, and normalized to percent signal change. For each participant, multiple regression was used to generate β values representing each voxel’s activity in each mammal condition and each visual baseline condition. To calculate the β’s, all variables were convolved with a canonical, double gamma hemodynamic response function and entered into a general linear model. Motion estimates were included as regressors of no interest; trials requiring a key-press were discarded. In a given voxel, the activation level for mammal m was then defined as the β for m’s mammal condition minus the β for m’s visual baseline. We relied on the statistical package AFNI (Cox 1996) for preprocessing.
The 12 resulting β maps for a given mammal (one for each subject) were projected into Talairach space and averaged, leaving us with nine such maps, one for each mammal. Only voxels present in the intersection of all participants’ intracranial masks were considered. These average activation maps were the input to all subsequent analyses.
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Weber, M., Osherson, D. Similarity and Induction. Rev.Phil.Psych. 1, 245–264 (2010). https://doi.org/10.1007/s13164-009-0017-0
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DOI: https://doi.org/10.1007/s13164-009-0017-0