It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-how .

This is a supplementary document to my "Why I am not an Absolutist (Or a First-Orderist)", which is forthcoming in a volume on higher-order logic edited by Peter Fritz and Nick Jones.

In his important book The Construction of Logical Space, Agustín Rayo lays out a distinctive metametaphysical view and applies it fruitfully to disputes concerning ontology and concerning modality. In this article, I present a number of criticisms of the view developed, mostly focusing on the underlying metametaphysics and Rayo’s claims on its behalf.

Review of "The Construction of Logical Space", by Augustin Rayo. Oxford: OxfordUniversity Press, 2013. Pp. xix+220. H/b$35.00.

This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian strategy. But (...) in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (shrink)

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions (...) imposed by STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Recent metaphysics has turned its focus to two notions that are—as well as having a common Aristotelian pedigree—widely thought to be intimately related: grounding and essence. Yet how, exactly, the two are related remains opaque. We develop a unified and uniform account of grounding and essence, one which understands them both in terms of a generalized notion of identity examined in recent work by Fabrice Correia, Cian Dorr, Agustín Rayo, and others. We argue that the account comports with antecedently (...) plausible principles governing grounding, essence, and identity taken individually, and illuminates how the three interact. We also argue that the account compares favorably to an alternative unification of grounding and essence recently proposed by Kit Fine. (shrink)

The term ‘continuous’ in real analysis wasn’t given an adequate formal definition until 1817. However, important theorems about continuity were proven long before that. How was this possible? In this paper, I introduce and refine a proposed answer to this question, derived from the work of Frank Jackson, David Lewis and other proponents of the ‘Canberra plan’. In brief, the proposal is that before 1817 the meaning of the term ‘continuous’ was determined by a number of ‘platitudes’ which had some (...) special epistemic status. (shrink)

En México y en otros países, eufemísticamente llama-dos "en desarrollo", los sistemas públicos de atención a la salud enfrentan continuos recortes presupuestales, lo que impacta negativamente a los recursos materiales y a la disminución de plazas para los egresados de las carreras de medicina, esto es, menos contratos de médicos de base en hospitales, clínicas y centros de salud. Bajo este panorama adverso, algunos administradores, desarrolladores de software y no pocos políticos preclaros, suponen que la salida a los problemas económicos (...) estará en el uso intensivo de la inteligencia artificial (en adelante IA) y la robótica. Una vez que los algoritmos sean adecuadamente entrenados, un ejército de robots doctores serán capaces de hacer valoraciones más precisas, diagnósticos 100% acertados, y prescripciones farmacológicas exactas; mucho mejor que los médicos humanos. Además, la IA no se cansa, no protesta, no se sindicaliza… ¿Realidad o ficción? En países como China y el Reino Unido ya se utilizan técnicas computacionales para la interpretación de imágenes de rayos X, detección de tumores, prótesis inteligentes e incluso IA para predecir los resultados de un ataque cerebrovascular isquémico. En México se incorporó a RoomieBot, un robot que sirve para el diagnóstico de pacientes con posible coronavirus. La cirugía robótica Da Vinci es buen ejemplo de cómo la IA puede trabajar colaborativamente con la o el cirujano en el quirófano. Sin embargo, aún quedan por resolver grandes desafíos antes de preocuparse por el llamado desempleo tecnológico de los egresados. Si bien la IA es una valiosa herramienta, en estricto sentido, en esta y en otras muchas áreas su autonomía total es todavía una quimera, por ejemplo: los vehículos autónomos pueden ser engañados y hackeados, y no existe aún un robot que pueda hacer un simple nudo a las correas de sus zapatos sin asistencia 2. Por otra parte, se requiere un marco normativo-todavía inexistente-para la aplicación universal de IA en los cuidados de la salud. Los principios de la bioética están claramente establecidos: la beneficencia, la no maleficencia, la autonomía y la justicia, así como el Juramento Hipocrático. No es así para IA, donde los países interesados no llegan al consenso de los principios morales básicos de la medicina que debería extrapolar 3. Hasta que no se solucionen los problemas técnicos, tecnológicos y, sobre todo, los dilemas éticos, la IA deberá continuar como la útil herramienta que es para la medicina; sin embargo, sustituir el valor intrínseco kantiano de la persona es algo que, seguramente, tendremos mucho tiempo para reflexionar y, acaso, algún día resolver de manera satisfactoria. (shrink)

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous (...) theory of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)