“Chaque vin a sa lie." versus “Toute nuit a un jour." --- does the difference in the human processing of " chaque" and " tout" match the difference between the proof rules for conjunction and quantification?
Résumé
This paper claims that the difference between the way French native speakers use the two universal quantifiers "tout" and "chaque" corresponds rather well to the proof theoretical difference between 1) proving P(a i) for each element a i in the domain and conjoining them and 2) proving P(x) for a generic element x. Experiments have been designed (but not yet realized) in order to support this claim.
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