Convergence strategies for theory assessment

This paper addresses the issue of the import of convergence arguments in theory assessment. A first part is devoted to making the point of the different types of strategies based on convergence, providing new distinctions with respect to the existing literature. Specific attention is devoted to robustness vs consilience arguments and one representative example for each category is then discussed in some detail. These are: (a) Perrin's famous robustness argument on behalf of the atomic hypothesis on the grounds of the concordance of thirteen different procedures to the same result for the Avogadro number; (b) the consilience argument motivating the trust in the viability of the extra-dimension conjecture in the context of early string theory. These two cases are expressly chosen in order to highlight possible differences, also including whether the convergence obtains in terms of empirical or theoretical procedures. Notwithstanding these various differences, in both cases the evaluation of the assessment strategy similarly depends, in a significant way, on how the convergence argument is interpreted, as shown in the final part of the paper.