18 April 2008, Logic Tea, Michael Morreau, University of Maryland

A comparative conception of similarity lies at the foundation of much philosophy. Which of several future persons is you? According to closest-continuer theory, whichever resembles you more closely, overall. Would the match have lit, if struck? Possible-worlds theorists say this depends on what happened in those worlds in which the match was struck, but which are otherwise, overall, most like the actual world.

I take up the question of how a relation of overall comparative similarity might emerge from a multitude of similarities and differences in various respects. The surprising answer is that, basically, it cannot. Kenneth Arrow's celebrated theorem of social choice shows that the only way to combine several dimensions of comparative similarity into a single overall comparison is for one of the dimensions to be a dictator. This plays havoc with philosophy founded on comparative similarity.

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