David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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British Journal for the Philosophy of Science 45 (2):679-691 (1994)
The axiom of extensionality of set theory states that any two classes that have identical members are identical. Yet the class of persons age i at time t and the class of persons age i + 1 at t + l, both including same persons, possess different demographic attributes, and thus appear to be two different classes. The contradiction could be resolved by making a clear distinction between age groups and cohorts. Cohort is a multitude of individuals, which is constituted within a time interval, and endures throughout part of the time continuum. Age group, on the other hand, is only a reference term to which empirical measurement relates, as in birth or death rates. Accordingly, the two concepts, age group i at t, and age group i + 1 at t + 1, are different. The standard population growth model of Leslie and Lotka, however, does not support such a distinction in age groups. An alternative model, proposed recently, implies precisely such a distinction
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