Modest deontologism in epistemology

Deontologism in epistemology holds that epistemic justification may be understood in terms of “deontological” sentences about what one ought to believe or is permitted to believe, or what one deserves praise for believing, or in some similar way. If deonotologism is true, and people have justified beliefs, then the deontological sentences can be true. However, some say, these deontological sentences can be true only if people have a kind of freedom or control over their beliefs that they do not in fact have. Thus, deontologism in epistemology, combined with anti-skepticism, has implausible implications. I first describe one sort of control that people typically have over ordinary actions but do not have over typical beliefs. I then argue that there is a paradigmatic type of epistemic evaluation that does properly apply to beliefs even though we lack this sort of control over them. Finally, I argue that these paradigmatic epistemic evaluations are sufficient to make true some of the deontological sentences.     

Horgan on Sleeping Beauty

With the notable exception of David Lewis, most of those writing on the Sleeping Beauty problem have argued that 1/3 is the correct answer. Terence Horgan has provided the clearest account of why, contrary to Lewis, Beauty has evidence against the proposition that the coin comes up heads when she awakens on Monday. In this paper, I argue that Horgan’s proposal fails because it neglects important facts about epistemic probability.     

Haack’s foundherentism is a foundationalism

Susan Haack has always maintained that her unquestionably important foundherentist theory of epistemic justification is not a foundationalism. In a 1997 Synthese exchange, Laurence BonJour questioned her right to this claim, and she dug in and defended it. What was at stake is of timeless importance to epistemology: it goes directly to the question, “What is foundationalism?” I inquire with greater care than either Haack or BonJour took in 1997, and I find decisively in favor of the view that foundherentism is a foundationalism. In the process, I explore the outer limits of foundationalism: I examine just how far a foundationalism can go in allowing the relevance of coherence to epistemic justification.     

Synchronic Bayesian updating and the Sleeping Beauty problem: reply to Pust

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4.     

Responsibility for believing

Many assume that we can be responsible only what is voluntary. This leads to puzzlement about our responsibility for our beliefs, since beliefs seem not to be voluntary. I argue against the initial assumption, presenting an account of responsibility and of voluntariness according to which, not only is voluntariness not required for responsibility, but the feature which renders an attitude a fundamental object of responsibility (that the attitude embodies one’s take on the world and one’s place in it) also guarantees that it could not be voluntary. It turns out, then, that, for failing to be voluntary, beliefs are a central example of the sort of thing for which we are most fundamentally responsible.     

Interpolation in non-classical logics

We discuss the interpolation property on some important families of non classical logics, such as intuitionistic, modal, fuzzy, and linear logics. A special paragraph is devoted to a generalization of the interpolation property, uniform interpolation. Supported by PRIN project 2006/2007 ‘Large-scale development of certified mathematical proofs’.     

Evidence for the role of self-priming in epistemic action: expertise and the effective use of memory

Epistemic actions are physical actions people take to simplify internal problem solving rather than to move closer to an external goal. When playing the video game Tetris, for instance, experts routinely rotate falling shapes more than is strictly needed to place the shapes. Maglio and Kirsh [Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18, 513-549; Maglio, P. P. (1995). The computational basis of interactive skill. PhD thesis, University of California, San Diego] proposed that such actions might serve the purpose of priming memory by external means, reducing the need for internal computation (e.g., mental rotation), and resulting in performance improvements that exceed the cost of taking additional actions. The present study tests this priming hypothesis in a set of four experiments. The first three explored precisely the conditions under which priming produces benefits. Results showed that presentation of multiple orientations of a shape led to faster responses than did presentation of a single orientation, and that this effect depended on the interval between preview and test. The fourth explored whether the benefit of seeing shapes in multiple orientations outweighs the cost of taking the extra actions to rotate shapes physically. Benefits were measured using a novel statistical method for mapping reaction-time data onto an estimate of the increase in processing capacity afforded by seeing multiple orientations. Cost was measured using an empirical estimate of time needed to take action in Tetris. Results showed that indeed the increase in internal processing capacity obtained from seeing shapes in multiple orientations outweighed the time to take extra actions.     

Permission from an Input/Output Perspective

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission.     

Routes to Triviality

It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension – the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.     

Light Affine Set Theory: A Naive Set Theory of Polynomial Time

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST.