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Topological variability of collectives and its import for social epistemology

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Abstract

Social epistemology studies knowledge and justified belief acquisition through organized group cooperation. To do this, the way such group cooperation is structured has to be modeled. The obvious way of modeling a group structure is with a directed graph; unfortunately, most types of social cooperation directed at epistemological aims are variably implementable, including in their structural expression. Furthermore, the frequency with which a practice is implemented in a certain way can vary with topology. This entails that the topology of social practices directed toward epistemological ends has to be modeled by a set of directed graphs, or their equivalent, together with a probability distribution over that set. In theory, this is eminently possible; however, there are considerable practical obstacles to the specification of a practice’s topology in this way. This paper examines these practical difficulties and concludes that todays sampling protocols are either far too slow to handle pratices with 10 or more participants, or else prone to produce misleading evaluations.

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Notes

  1. See Robins et al. (2007) for an introduction and for references to further reading including Frank and Strauss (1986) where Markov Random Graphs are introduced and further developments in Pattison and Wasserman (1999), Robins et al. (1999) and Skvoretz and Faust (1999).

  2. See Robins et al. (2007), Strauss (1986) and Snijders (2002) for an introduction.

  3. The fastest known algorithm by Luks and Brooksbank (2008) can establish whether two graphs are isomorphic in \(2^{O(\sqrt{n log n})}\).

  4. This is a very generous assumption considering that Nauty—the best extant computer program for detecting isomorphisms that works using a cannonical labelling algorithm and not Luks’ (1982) algorithm—takes, on average, between tenths of a millisecond (for graphs of order less than 10) and a tenths of a second (for graphs of order circa 1000) to establish whether two graphs are isomorphic on a standard desktop (Foggia et al. 2001).

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  1. Lund University, Lund, Sweden

    George Masterton

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  1. George Masterton
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Correspondence to George Masterton.

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Masterton, G. Topological variability of collectives and its import for social epistemology. Synthese 191, 2433–2443 (2014). https://doi.org/10.1007/s11229-014-0433-2

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