In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and belief on which (...) these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

In this paper, I develop an algorithmic impossible-worlds model of belief and knowledge that provides a middle ground between models that entail that everyone is logically omniscient and those that are compatible with even the most egregious kinds of logical incompetence. In outline, the model entails that an agent believes (knows) φ just in case she can easily (and correctly) compute that φ is true and thus has the capacity to make her actions depend on whether φ. The model thereby (...) captures the standard view that belief and knowledge ground are constitutively connected to dispositions to act. As I explain, the model improves upon standard algorithmic models developed by Parikh, Halpern, Moses, Vardi, and Duc, among other ways, by integrating them into an impossible-worlds framework. The model also avoids some important disadvantages of recent candidate middle-ground models based on dynamic epistemic logic or step logic, and it can subsume their most important advantages. (shrink)

The notion of “intentionality” is much invoked in various foundational theories of meaning, being very often equated with “meaning”, “content” and “reference”. In this paper, I propose and develop a basic distinction between two concepts and, more fundamentally, properties of intentionality: intentionality-T and intentionality-C. Representationalism is then defined as the position according to which intentionality-T can be reduced to intentionality-C, in the form of representational states. Nonrepresentationalism is rejecting this reduction, and argues that intentionality-T is more fundamental than intentionality-C. Non-representationalism (...) allows for a new layered view of the relations between cognitive intentionality and linguistic intentionality; this view is presented at the end of the paper. (shrink)

Robert Stalnaker argues that his causal-pragmatic account of the problem of intentionality commits him to a coarse-grained conception of the contents of mental states, where propositions are represented as sets of possible worlds. Stalnaker also accepts the "direct reference" theory of names, according to which co-referring names have the same content. Stalnaker's view of content is thus threatened by Frege's Puzzle. Stalnaker's classic paper "Assertion" is intended to provide a response to this threat. In this paper, I evaluate Stalnaker's claim (...) that the causal-pragmatic account of intentionality commits one to a coarse-grained conception of the contents of mental states, and argue that the apparatus laid out in "Assertion" is not sufficiently comprehensive to account for all versions of Frege's Puzzle. (shrink)

Causal theories of mental content (CTs) ground certain aspects of a concept's meaning in the causal relations a concept bears to what it represents. Section 1 explains the problems CTs are meant to solve and introduces terminology commonly used to discuss these problems. Section 2 specifies criteria that any acceptable CT must satisfy. Sections 3, 4, and 5 critically survey various CTs, including those proposed by Fred Dretske, Jerry Fodor, Ruth Garrett Millikan, David Papineau, Dennis Stampe, Dan Ryder, and the (...) author himself. The final section considers general objections to the causal approach. (shrink)

Intentional Mentalism is the view that mental intentionality is primary to non-mental intentionality and that the latter is derived from the former. In this article I examine three views which have been taken to motivate Intentional Mentalism: conventionalism as invoked by Searle, Gricean pragmatism, and the language of thought hypothesis. I argue that none of these views motivates Intentional Mentalism, and that, in fact, the former two imply its rejection.

The paper analyses theoretical presuppositions of the predominant form of semantic naturalism in contemporary analytic philosophy. The aim is to show that irrespective of the fact that the doctrine of semantic naturalism is grounded in ontological and epistemological naturalism, and is developed on the basis of semantic externalism, this conception of foundational semantics rests on internalist premises, and therefore should be construed as Cartesian. Theories and their interrelations that are assumed by semantic naturalism are explicated by relying on the tripartite (...) interpretation of “the problem of intentionality”. The Cartesian aspects of the assumed theories – and thus of the form of semantic naturalism that is analysed – are then specified in the context of Hilary Putnam’s version of semantic externalism. (shrink)

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)