Summary I work on different aspects of social epistemology; mostly using formal methods to study questions around opinion pooling, consensus, disagreement, altruism, and some further issues in the social dimensions of science.
Probabilistic Opinion Pooling with Imprecise Probabilities (with Rush Stewart) [Preprint] [Journal of Philosophical Logic, 2017] The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution (Madansky ; Lehrer and Wagner ; McConway Journal of the American Statistical Association, 76(374), 410–414, ; Bordley Management Science, 28(10), 1137–1148, ; Genest et al. The Annals of Statistics, 487–501, ; Genest and Zidek Statistical Science, 114–135, ; Mongin Journal of Economic Theory, 66(2), 313–351, ; Clemen and Winkler Risk Analysis, 19(2), 187–203, ; Dietrich and List ; Herzberg Theory and Decision, 1–19, ). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities (IP) by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi (Synthese, 62(1), 3–11, ), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.
Learning and Pooling, Pooling and Learning (with Rush Stewart) [Preprint] [Erkenntnis, 2018] We explore which types of probabilistic updating commute with convex IP pooling (Stewart and Ojea Quintana 2017). Positive results are stated for Bayesian conditionalization (and a mild generalization of it), imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of (precise) externally Bayesian pooling operators due to Wagner (2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.
Radical Pooling and Imprecise Probabilities (Submitted for Review) This paper focuses on radical pooling, or the question of how to aggregate credences when there is a fundamental disagreement among agents about which is the relevant sample or event space. The solution advanced is based on the notion of consensus as common ground at the outset of inquiry first introduced by Isaac Levi (1985). If this notion is accepted, then using imprecise probabilities is grounded on the principles of marginalization, rigidity, and minimum divergence. This account builds on previous work (Stewart and Ojea Quintana 2017, 2018) showing the advantages of imprecision when it comes to pooling.
Formal Representations of Moral Sentimentalism
Altruistic and Spiteful Utilities (Submitted for Review) This essay bridges Harsanyi's Aggregation Theorem (1955, 1977) with Adam Smith moral sentiments, and makes use of the formalism to characterize altruism, spite and self-interest in line with contemporary work by Kitcher (2010). This is a departure from the traditional understanding of Harsanyi's results as defining a utilitarian social welfare function. Instead, they here provide a formalization of Smith's tripartite distinction of other-directed attitudes. Furthermore, I will emphasize the importance of the recognition of unsocial passions like spite, and how this aspect of Smith's account makes Das Adam Smith Problem even harder to solve.
Emotional Contagion on Networks (In Progress) The sixth essay provides a representation of David Hume's contagion account of moral passions by making use of epidemiological diffusion models on networks. The question guiding the investigation is how does the social structure, represented as a network, affects the spread of emotions and opinions. For example, more hierarchical structures like trees and stars make it harder for emotions to spread than more "democratic" ones like random networks. More precisely, using epidemiological models of contagion I show the effect that networks variables like centrality, clustering, homophily, and others have on the contagion of moral sentiments.
Networks and Social Epistemology
Political Polarization on Networks (In Progress) The final chapter is concerned with polarization. I extend Thomas Schelling's model for segregation to networks of individuals with an different political stances and show that even minor disagreements leads to clustering and polarization. This is done by considering strategic network formations and network dynamics based on political homophily.
Game Theory and Logic
On Semantic Gamification [Lecture Notes in Computer Science - 7th Indian Conference, ICLA 2017, Proceedings] [Preprint] The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Łukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation logic). This lead to the presentation of the work at LOFT 2016 and ICLA 2017, and the latter lead to a proceedings publication.
Logic and Paradoxes During my time in Buenos Aires, I was focused in Logic and I worked on issues about circularity in paradoxes. This led to two publications.
The structural collapse approach reconsidered [Preprint] Análisis Filosófico, 2012] (a response to Roy T. Cook), In this paper I argue that Roy Cook’s reformulation of Yablo’s Paradox in the infinitary system D is a genuinely non-circular paradox, but for different reasons than the ones he sustained. In fact, the first part of the job will be to show that his argument regarding the absence of fixed points in the construction is insufficient to prove the non-circularity of it; at much it proves its non-self referentiality. The second is to reconsider the structural collapse approach Cook rejects, and argue that a correct understanding of it leads us to the claim that the infinitary paradox is actually non-circular.
Non-standard models and Yablo's Paradox [Preprint] [Cuadernos de Filosofía, 2008]. This is an undergraduate essay (in Spanish, and quite rough) about the structure of the non-standard models that Yablo's Paradox has.