Designed for use by philosophy students, this 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues (...) concerning the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers. (shrink)

Designed for use by philosophy students, this book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues concerning (...) the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers. (shrink)

What do the rules of logic say about the meanings of the symbols they govern? In this book, James W. Garson examines the inferential behaviour of logical connectives, whose behaviour is defined by strict rules, and proves definitive results concerning exactly what those rules express about connective truth conditions. He explores the ways in which, depending on circumstances, a system of rules may provide no interpretation of a connective at all, or the interpretation we ordinarily expect for it, or an (...) unfamiliar or novel interpretation. He also shows how the novel interpretations thus generated may be used to help analyse philosophical problems such as vagueness and the open future. His book will be valuable for graduates and specialists in logic, philosophy of logic, and philosophy of language. (shrink)

This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical (...) issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout. (shrink)

Quantified modal logic has reputation for complexity. Completeness results for the various systems appear piecemeal. Different tactics are used for different systems, and success of a given method seems sensitive to many factors, including the specific combination of choices made for the quantifiers, terms, identity, and the strength of the underlying propositional modal logic. The lack of a unified framework in which to view QMLs and their completeness properties puts pressure on those who develop, apply, and teach QML to work (...) with the simplest systems, namely those that adopt the Barcan Formulas and predicate logic rules for the quantifiers. In these systems, the quantifier ranges over a fixed domain of possible individuals, so advocates of these logics are sometimes called possibilists. A literature has grown up rationalizing the choice of possibilist logics despite ordinary intuitions that the resulting theorems are too strong.Williamson even takes the view that the complications to be faced within the weaker logics “are a warning sign of philosophical error”. It is the purpose of this paper to show that abandonment of the weaker QMLs is excessively fainthearted, since most QMLs can be given relatively simple formulations within one general framework. Given the straightforward nature of the systems and their completeness results, the purported complications evaporate, along with any philosophical warnings one might have associated with them. (shrink)

Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, (...) for example by adopting sequent rules with multiple conclusions. Another is to explore what readings the natural deduction rules do enforce. When the notion of a model of a rule is generalized, it is found that natural deduction rules express “intuitionistic” readings of their connectives. A third approach is presented here. The intuitionistic readings emerge when models of rules are defined globally, but the notion of a local model of a rule is also natural. Using this benchmark, natural deduction rules enforce exactly the classical readings of the connectives, while this is not true of axiomatic systems. This vindicates the historical motivation for natural deduction rules. One odd consequence of using the local model benchmark is that some systems of propositional logic are not complete for the semantics that their rules express. Parallels are drawn with incompleteness results in modal logic to help make sense of this. (shrink)

In this paper investigates how natural deduction rules define connective meaning by presenting a new method for reading semantical conditions from rules called natural semantics. Natural semantics explains why the natural deduction rules are profoundly intuitionistic. Rules for conjunction, implication, disjunction and equivalence all express intuitionistic rather than classical truth conditions. Furthermore, standard rules for negation violate essential conservation requirements for having a natural semantics. The standard rules simply do not assign a meaning to the negation sign. Intuitionistic negation fares (...) much better. Not only do the intuitionistic rules have a natural semantics, that semantics amounts to familiar intuitionistic truth conditions. We will make use of these results to argue that intuitionistic connectives, rather than standard ones have a better claim to being the truly logical connectives. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

This paper explores a line of argument against the classical paradigm in cognitive science that is based upon properties of non-linear dynamical systems, especially in their chaotic and near-chaotic behavior. Systems of this kind are capable of generating information-rich macro behavior that could be useful to cognition. I argue that a brain operating at the edge of chaos could generate high-complexity cognition in this way. If this hypothesis is correct, then the symbolic processing methodology in cognitive science faces serious obstacles. (...) A symbolic description of the mind will be extremely difficult, and even if it is achieved to some approximation, there will still be reasons for rejecting the hypothesis that the brain is in fact a symbolic processor. (shrink)

Fodor and Pylyshyn (1988) argue that any successful model of cognition must use classical architecture; it must depend upon rule-based processing sensitive to constituent structure. This claim is central to their defense of classical AI against the recent enthusiasm for connectionism. Connectionist nets, they contend, may serve as theories of the implementation of cognition, but never as proper theories of psychology. Connectionist models are doomed to describing the brain at the wrong level, leaving the classical view to account for the (...) mind.This paper considers whether recent results in connectionist research weigh against Fodor and Pylyshyn's thesis. The investigation will force us to develop criteria for determining exactly when a net is capable of systematic processing. Fodor and Pylyshyn clearly intend their thesis to affect the course of research in psychology. I will argue that when systematicity is defined in a way that makes the thesis relevant in this way, the thesis is challenged by recent progress in connectionism. (shrink)

The binding problem is to explain how information processed by different sensory systems is brought together to unify perception. The problem has two sides. First, we want to explain phenomenal binding: the fact that we experience a single world rather than separate perceptual fields for each sensory modality. Second, we must solve a functional problem: to explain how a neural net like the brain links instances to types. I argue that phenomenal binding and functional binding require very different treatments. The (...) puzzle of phenomenal binding rests on a confusion and so can be dissolved. So only functional binding deserves explanation. The general solution to that problem is that information to be bound is arrayed along different dimensions. So sensory coding into separate topographic maps facilitates functional binding and there is no need based on the unity of perception for special mechanisms that bring "back together" information in different maps. (shrink)

This paper explores the possibility that chaos theory might be helpful in explaining free will. I will argue that chaos has little to offer if we construe its role as to resolve the apparent conflict between determinism and freedom. However, I contend that the fundamental problem of freedom is to find a way to preserve intuitions about rational action in a physical brain. New work on dynamic computation provides a framework for viewing free choice as a process that is sensitive (...) and unpredictable, while at the same time organized and intelligent. I conclude that this vision of a chaotic brain may make a modest contribution to an intuitively acceptable physicalist account of free will. (shrink)

Over the last forty years, Donald Davidson has been one of the most influential, but least accessible voices in philosophy. There are several reasons why it is hard to come to grips with his work. First, his language is dense, even by the standards of analytic philosophy; while at the same time his thought is highly organic, so that it is difficult to make sense of one idea without an understanding of his whole program. Davidson never attempted to write a (...) book that would provide an easy entry into the interconnections between his many influential and controversial views. Nor did he attempt to record the evolution of his thought, keeping track of how reconsiderations on one point would affect the tenability of the others. It is perhaps a good thing too, for as the volume to be reviewed here makes clear, such a massive project would have left him with little time for his later contributions to philosophy. (shrink)

Simulation has emerged as an increasingly popular account of folk psychological (FP) talents at mind-reading: predicting and explaining human mental states. Where its rival (the theory-theory) postulates that these abilities are explained by mastery of laws describing the connections between beliefs, desires, and action, simulation theory proposes that we mind-read by "putting ourselves in another's shoes." This paper concerns connectionist architecture and the debate between simulation theory (ST) and the theory-theory (TT). It is only natural to associate TT with classical (...) architectures where rule governed operations apply to explicit propositional representations. On the other hand, ST would seem better tuned to procedurally oriented non-symbolic structures found in connectionist models. This paper explores the possible alignment between ST and connectionist architecture. Joe Cruz argues that connectionist models with distributed non-symbolic representations are particularly well suited to simulation theory. The purported linkage between connectionist architecture and simulation theory is criticized in this paper. The conclusion is that there are reasons for thinking that connectionist forms of representation are the enemy of both TT and ST. So the contribution of connectionism may be to suggest the need for an alternative to both views. (shrink)

The purpose of this paper is to explore the merits of the idea that dynamical systems theory (also known as chaos theory) provides a model of the mind that can vindicate the language of thought (LOT). I investigate the nature of emergent structure in dynamical systems to assess its compatibility with causally efficacious syntactic structure in the brain. I will argue that anyone who is committed to the idea that the brain's functioning depends on emergent features of dynamical systems should (...) have serious reservations about the LOT. First, dynamical systems theory casts doubt on one of the strongest motives for believing in the LOT: principle P, the doctrine that structure found in an effect must also be found in its cause. Second, chaotic emergence is a double-edged sword. Its tendency to cleave the psychological from the neurological undermines foundations for belief in the existence of causally efficacious representations. Overall, a dynamic conception of the brain sways us away from realist conclusions about the causal powers of representations with constituent structure. (shrink)

One of the most puzzling things about time is that peculiar experience we all have of the present forever “moving” from the past towards the future. What is now future becomes progressively closer to the present as time goes on, until it becomes present, and finally slips away into the past. Philosophers of time seem to divide themselves into two main camps concerning the ontological status of these phenomena. The objectivist insists that this temporal “becoming” is an objective feature of (...) the real world, that this progression of now is an aspect of reality quite independent of our experience. The subjectivist argues to the contrary that temporal becoming is a subjective phenomenon which has no existence apart from the experience of some sentient being. Richard Gale in Chapters X and XI of The Language of Time takes the objectivist position. He argues for the objectivity of temporal becoming by claiming that the conceptual systems embodied in ordinary language rule out the subjective position. (shrink)

The computational theory of cognition (CTC) holds that the mind is akin to computer software. This article aims to show that CTC is incorrect because it is not able to distinguish the ability to solve a maze from the ability to solve its mirror image. CTC cannot do so because it only individuates brain states up to isomorphism. It is shown that a finer individuation that would distinguish left-handed from right-handed abilities is not compatible with CTC. The view is explored (...) that CTC correctly individuates in an autonomous domain of the mental, leaving discrimination between left and right to some non-cognitive component of psychology such as physiology. I object by showing that the individuation provided by CTC does not properly describe in any domain. An embodied computational taxonomy, rather than software alone, is required for an adequate science of the mind. (shrink)

Another objection to the dynamical hypothesis is explored. To resolve it completely, one must focus more directly on an area not emphasized in van Gelder's discussion: the contributions of dynamical systems theory to understanding how cognition is neutrally implemented.