Degree supervaluational logic

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There???s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical???all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail

Confidence Reports

We advocate and develop a states-based semantics for both nominal and adjectival confidence reports, as in "Ann is confident/has confidence that it's raining", and their comparatives "Ann is more confident/has more confidence that it's raining than that it's snowing". Other examples of adjectives that can report confidence include "sure" and "certain". Our account adapts Wellwood's account of adjectival comparatives in which the adjectives denote properties of states, and measure functions are introduced compositionally. We further explore the prospects of applying these tools to the semantics of probability operators. We emphasize three desirable and novel features of our semantics: (i) probability claims only exploit qualitative resources unless there is explicit compositional pressure for quantitative resources; (ii) the semantics applies to both probabilistic adjectives (e.g., "likely") and probabilistic nouns (e.g., "probability"); (iii) the semantics can be combined with an account of belief reports that allows thinkers to have incoherent probabilistic beliefs (e.g. thinking that A & B is more likely than A) even while validating the relevant purely probabilistic claims (e.g. validating the claim that A & B is never more likely than A). Finally, we explore the interaction between confidence-reporting discourse (e.g., "I am confident that...") and belief-reports about probabilistic discourse (e.g.,"I think it's likely that..")

Dilating and contracting arbitrarily

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a precise state arbitrarily

A Probabilistic Defense of Proper De Jure Objections to Theism

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections

Axiomatic Bayesian Utilitarianism

L'article examine les relations qu'entretiennent les conditions suivantes, formulées dans la théorie axiomatique de la décision de Jeffrey-Bolker. (1) La condition utilitariste voulant que l'utilité espérée de la société se représente comme une somme pondérée des utilités espérées individuelles. (2) Des conditions d'uniformité imposées aux fonctions d'utilité et de probabilité des individus. On montre en particulier que l'identité des probabilités individuelles est nécessaire et suffisante pour que l'on obtienne l'utilitarisme, et qu'elle dérive d'une condition antérieure de type parétien reliant les préférences individuelles et sociales, pour autant que ces préférences soient séparables en un sens convenable.Principe de Pareto;Utilitarisme;Bayésianisme collectif;Bolker-Jeffrey;Savage;Théorèmes d'identité

There are no universal rules for induction

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to universal schemas. An inductive inference problem concerning indeterministic, nonprobabilistic systems in physics is posed, and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction. Copyright 2010 by the Philosophy of Science Association.All right reserved

Comparing Probabilistic Models for Melodic Sequences

Modelling the real world complexity of music is a challenge for machine learning. We address the task of modeling melodic sequences from the same music genre. We perform a comparative analysis of two probabilistic models; a Dirichlet Variable Length Markov Model (Dirichlet-VMM) and a Time Convolutional Restricted Boltzmann Machine (TC-RBM). We show that the TC-RBM learns descriptive music features, such as underlying chords and typical melody transitions and dynamics. We assess the models for future prediction and compare their performance to a VMM, which is the current state of the art in melody generation. We show that both models perform significantly better than the VMM, with the Dirichlet-VMM marginally outperforming the TC-RBM. Finally, we evaluate the short order statistics of the models, using the Kullback-Leibler divergence between test sequences and model samples, and show that our proposed methods match the statistics of the music genre significantly better than the VMM.Comment: in Proceedings of the ECML-PKDD 2011. Lecture Notes in Computer Science, vol. 6913, pp. 289-304. Springer (2011