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1. Although not included here, Billy Wheeler has made an appeal forcomputational models in metaphysics (Wheeler 2019). Since 1994 MagnaniLorenzo has directed aComputational Philosophy Lab at the University of Pavia, emphasizing abduction and model-basedcognition.

2. Argument undoubtedly has a history as old as human communication, andthe self-conscious consideration of what makes an argument validcannot have been far behind. The latter is clearly evident in theSophists and Plato (see Bobzien 2019). The first structured andsystematized formalization of valid argument, however, is generallycredited to Aristotle. The vision of formalization embodied inAristotle is breathtaking: that properties crucial to the rationalityof something as richly human and context-dependent as argument, tiedto content and intended for social persuasion, can be captured in askeleton of icy symbolism that has neither human content nor socialcontext. It is that vision of formalization as capturing the validityof argument—of various forms and regardless ofapplication—that continues through the 2500 years of thedevelopment of logic since Aristotle.

3. The combined work of Gödel, Church and Turing in the 1930sdemonstrated the close connection between formal systems, generalrecursive functions, and Turing’s abstract vision ofsymbol-processing machines (Gödel 1931, Church 1936, Turing1936–1937). That abstract vision lay the groundwork for fullyconcrete symbol-processing machines: our contemporary computers. Incomputational philosophy, that contemporary computer power is appliedto a range of philosophical questions, including complex questions inlogic.

4. Leibniz appears to have been inspired in part by the work of RamonLlull, whoseArs Magna orArs generalis ultima of1308 outlines what is intended as a combinatorial tool of argument andanalysis in ethics and religion (Lull 1308 [1986]). Differentpermutations of principles regarding goodness, eternity, will, truth,concordance, and the like are intended to generate and answerquestions such as “is eternal goodness concordant?”Lull’s vision traces in turn to the medieval Arabiczairja, a combinatoric algorithm intended to generate truthsfrom a finite number of elements (Gray 2016, Khaldūn 1377[1958]). In fiction, the image of combinatoric machines continues inHerman Hesse’sThe Glass Bead Game, a version set farin the future. The game is described as “a kind of synthesis ofhuman learning” in which elements or themes are combined, withdeeper and more varied associations developing as the game progresses(Hesse 1943).

5. Many of the features of the Hegselmann-Krause model are anticipatedin Lehrer and Wagner (1981), though there the emphasis is on beliefconvergence rather than polarization.

6. In a series of linked articles, Alexander Riegler and Igor Douvenextend the Hegselmann Krause model in several ways (Riegler &Douven 2009, 2010, Douven & Riegler 2010). They introduceparameters regarding the degree to which an agent’s evidence maybe inaccurate, a different weighting for the influence of differentagents, and a “space” of interaction in the cellularautomata tradition. In a further extension, their agents hold“theories” composed of sets of logically linked beliefsrather than simply single beliefs, and interaction is guided by an“epistemic space” of theory proximity as well. Riegler andDouven find a consistent set of results in these extensions,indicating that increased interaction with other agents helps agentsbetter track the truth in the long run, but that stronger emphasis onindividual evidence is faster.

7. The attempt to track the impact of argumentative strategies andcognitive limitations with regard to the exchange of argumentscontinues. For example, see Singer et al. (2021).

8. Technically, Weisberg and Muldoon’s agents occupy square cellson a grid. Interaction is with their “Moore neighborhood”:the 8 cells touching theirs on each side and corner.

9. In her critique, Thoma (2015) in fact outlines an alternativelandscape model which supports claims regarding the epistemicadvantage of division of labor. A crucial difference from the Weisbergand Muldoon model is that agents are not limited to information andmovement in their immediate theoretical neighborhood.

10. Zollman (2005) also merges the work on communication with the work ongame-theoretic cooperation above. Agents on a spatialized grid developa signaling a system as outlined, but also play Stag Hunt withneighbors, where play in Stag Hunt can be conditional on the signalreceived. Play in Stag Hunt co-evolves with signaling systems, withthe result that all agents end up playing Stag (Skyrms 2010).

11. We leave discussion of computation in the context of epistemic logicto other contexts (Fagin, Halbern, Moses, & Vardi 1995; vanBenthem 2006; Rendsvig & Symons 2006 [2019]). In classical form,epistemic logic is an attempt to model belief and knowledge with focuson the individual and at a particular time. The classic source forextension to dynamic logics—in which one considers how anindividual’s body of knowledge changes with the addition(expansion) or removal (contraction) of particular beliefs, or thereplacement of one belief by another (revision)—is the AGMmodel, named after developers Carlos Alchourrón, PeterGärdenfors, and David Makinson (Alchourrón,Gärdenfors, & Makinson 1985; see also van Ditmarsch, van derHoek, & Kooi 2008; Baltag & Renne 2016 [2019]). Work has alsobeen done on expanding epistemic logic to a form appropriate to groupsrather than individuals (Halpern & Moses 1984; Baltag, Boddy andSmetts 2018). A link between that work and the agent-based approachhighlighted above would be fascinating, but has not yet beendeveloped.

12. Herbert Simon, interviewed by A. Dale, Pittsburgh, April 21, 1994.Quoted in MacKenzie (1995: 11).

13. Also of note is Paradox, developed by Koen Lindström Claessen andNiklas Sörensson.

14. For a very different computational approach to logic see Mar and Grim(1991) and St. Denis and Grim (1997), both further developed in Grim,Mar, and St. Denis (1998).

15. For a very different computational approach to philosophy ofreligion, more akin to agent-based modeling, see Shults (2019).