15,958 research outputs found

    Logical models for bounded reasoners

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    This dissertation aims at the logical modelling of aspects of human reasoning, informed by facts on the bounds of human cognition. We break down this challenge into three parts. In Part I, we discuss the place of logical systems for knowledge and belief in the Rationality Debate and we argue for systems that formalize an alternative picture of rationality -- one wherein empirical facts have a key role (Chapter 2). In Part II, we design logical models that encode explicitly the deductive reasoning of a single bounded agent and the variety of processes underlying it. This is achieved through the introduction of a dynamic, resource-sensitive, impossible-worlds semantics (Chapter 3). We then show that this type of semantics can be combined with plausibility models (Chapter 4) and that it can be instrumental in modelling the logical aspects of System 1 (“fast”) and System 2 (“slow”) cognitive processes (Chapter 5). In Part III, we move from single- to multi-agent frameworks. This unfolds in three directions: (a) the formation of beliefs about others (e.g. due to observation, memory, and communication), (b) the manipulation of beliefs (e.g. via acts of reasoning about oneself and others), and (c) the effect of the above on group reasoning. These questions are addressed, respectively, in Chapters 6, 7, and 8. We finally discuss directions for future work and we reflect on the contribution of the thesis as a whole (Chapter 9)

    Consequence and normative guidance

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    Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would need to produce what John MacFarlane has appropriately called a 'bridge principle', i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper, I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well-motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive

    Modal logic and philosophy

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    Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory
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