There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

The paper presents an argument against a "metaphysical" conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...) a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: "the realm of the natural", constituted by the things of our empirical world, and "the realm of the formal", constituted by the structures that we use as "prisms" to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic. (shrink)

It has been argued recently that dialetheist theories are unable to express the concept of naive validity. In this paper, we will show that LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document} can be non-trivially expanded with a naive validity predicate. The resulting theory, LPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}^{\mathbf {Val}}$$\end{document} reaches this goal by adopting a weak self-referential procedure. We show that LPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf (...) {LP}^{\mathbf {Val}}$$\end{document} is sound and complete with respect to the three-sided sequent calculus SLPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {SLP}^{\mathbf {Val}}$$\end{document}. Moreover, LPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}^{\mathbf {Val}}$$\end{document} can be safely expanded with a transparent truth predicate. We will also present an alternative theory LPVal∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}^{\mathbf {Val}^{*}}$$\end{document}, which includes a non-deterministic validity predicate. (shrink)

There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument (...) for CTT by analyzing the processes carried out by a human computer. I then contend that if the Gandy–Sieg account is correct, then the notion of effective computability has changed after 1936. Today computer scientists view effective computability in terms of finite machine computation. My contention is supported by the current formulations of CTT, which always refer to machine computation, and by the current argumentation for CTT, which is different from the main arguments advanced by Turing and Church. I finally turn to discuss Robin Gandy's characterization of machine computation. I suggest that there is an ambiguity regarding the types of machines Gandy was postulating. I offer three interpretations, which differ in their scope and limitations, and conclude that none provides the basis for claiming that Gandy characterized finite machine computation. (shrink)

In 1887 Georg Cantor gave an influential but cryptic proof of theimpossibility of infinitesimals. I first give a reconstruction ofCantor's argument which relies mainly on traditional assumptions fromEuclidean geometry, together with elementary results of Cantor's ownset theory. I then apply the reconstructed argument to theinfinitesimals of Abraham Robinson's nonstandard analysis. Thisbrings out the importance for the argument of an assumption I call theChain Thesis. Doubts about the Chain Thesis are seen to render thereconstructed argument inconclusive as an attack on the (...) infinitelysmall. (shrink)

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the (...) intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand. (shrink)

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such (...) that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation. (shrink)

Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable (...) and that they are true; otherwise a false theory can yield false gödel sentences. (shrink)

Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction strategy, Beall’s paraconsistent (...) strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense. (shrink)

The philosophy of information (PI) is a new area of research with its own field of investigation and methodology. This article, based on the Herbert A. Simon Lecture of Computing and Philosophy I gave at Carnegie Mellon University in 2001, analyses the eighteen principal open problems in PI. Section 1 introduces the analysis by outlining Herbert Simon's approach to PI. Section 2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centers on Hilbert's famous analysis (...) of the central problems in mathematics. The rest of the article is devoted to the eighteen problems. These are organized into five sections: problems in the analysis of the concept of information, in semantics, in the study of intelligence, in the relation between information and nature, and in the investigation of values. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...) 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

Artificial intelligence (AI) research enjoyed an initial period of enthusiasm in the 1970s and 80s. But this enthusiasm was tempered by a long interlude of frustration when genuinely useful AI applications failed to be forthcoming. Today, we are experiencing once again a period of enthusiasm, fired above all by the successes of the technology of deep neural networks or deep machine learning. In this paper we draw attention to what we take to be serious problems underlying current views of artificial (...) intelligence encouraged by these successes, especially in the domain of language processing. We then show an alternative approach to language-centric AI, in which we identify a role for philosophy. (shrink)

According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...) in fact, reasonable and related to Gödel’s proof. (shrink)

The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories as projective geometry; (...) and not only as they were practiced in Kant’s time, but also as architects use them today. (shrink)

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...) the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...) a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

Some philosophers argue that the principles of human reasoning are impeccable, and that mistakes are no more than momentary lapses in “information processing”. This article makes a case to the contrary. It shows that human reasoners commit systematic fallacies. The theory of mental models predicts these errors. It postulates that individuals construct mental models of the possibilities to which the premises of an inference refer. But, their models usually represent what is true in a possibility, not what is false. This (...) procedure reduces the load on working memory, and for the most part it yields valid inferences. However, as a computer program implementing the theory revealed, it leads to fallacious conclusions for certain inferences—those for which it is crucial to represent what is false in a possibility. Experiments demonstrate the variety of these fallacies and contrast them with control problems, which reasoners tend to get right. The fallacies can be compelling illusions, and they occur in reasoning based on sentential connectives such as “if” and “or”, quantifiers such as “all the artists” and “some of the artists”, on deontic relations such as “permitted” and “obligated”, and causal relations such as “causes” and “allows”. After we have reviewed the principal results, we consider the potential for alternative accounts to explain these illusory inferences. And we show how the illusions illuminate the nature of human rationality. (shrink)

Certain translational T-schemes of the form True(“f”) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.

Certain translational T-schemes of the form True « f, where f can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.

This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, of a formal (...) grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’s formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change. (shrink)

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a (...) possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations. (shrink)

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore (...) arises whether the notions that are investigated in tense logic can be consistently formalized as predicates. In this paper it is shown that the answer to this question is negative. The logical treatment of the notions of future and past as predicates gives rise to paradoxes due the specific interplay between both notions. For this reason, the tense paradoxes that will be presented are not identical to the paradoxes referred to above. (shrink)

Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.

In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.

The primary purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets certain weak but non-trivial arithmetical theories. It will take almost as long to explain what this means and why it matters as it will to prove the results.

Dan Dennett and Jerry Fodor have recently offered diametrically opposed estimations of the relevance of the theory of natural selection to an adequate theory of intentionality. In this paper, I show, first, how this opposition can be traced largely to differences both in their respective understandings of what the theory of natural selection includes, and in their respective ‘pre-theoretic’ takes on the datum to be explained by a theory of intentionality. These differences, in turn, have been ‘pre-selected’ by contrasting outlooks (...) on the general nature of the explanatory enterprise. While no final adjudication of these large issues is attempted, I argue, second, that it is important to distinguish two rather different questions about the relevance of natural selection to the nature of intentionality, and that, having done so, one can see that, from standpoints purely internal to their respective projects, Dennett and Fodor each in his own way misconstrues the relevance of natural selection. (shrink)

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s (...) results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines. (shrink)

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or (...) will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata. (shrink)

Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency (...) and shows thus, pace Cobreros et al., that the result in McGee does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic. (shrink)

The paper is concerned with Quine's substitutional account of logical truth. The critique of Quine's definition tends to focus on miscellaneous odds and ends, such as problems with identity. However, in an appendix to his influential article On Second Order Logic, George Boolos offered an ingenious argument that seems to diminish Quine's account of logical truth on a deeper level. In the article he shows that Quine's substitutional account of logical truth cannot be generalized properly to the general concept of (...) logical consequence. The purpose of this paper is threefold: first, to introduce the reader to the metamathematics of Quine's substitutional definition of logical truth; second, to make Boolos' result accessible to a broader audience by giving a detailed and self-contained presentation of his proof; and, finally, to discuss some of the possible implications and how a defender of the Quinean concepts might react to the challenge posed by Boolos' result. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

p. cm. — (Zeuthen lecture book series) Includes bibliographical references (p. ) and index. ISBN 0-262-18187-8 (hardcover : alk. paper). — ISBN 0-262-68100-5 (pbk. : alk. paper) 1. Decision-making. 2. Economic man. 3. Game theory. 4. Rational expectations (Economic theory) I. Title. II. Series.

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account of the nature of quantum information. (...) Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view (...) of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought. (shrink)

Roger Penrose is justly famous for his work in physics and mathematics but he is _notorious_ for his endorsement of the Gödel argument (see his 1989, 1994, 1997). This argument, first advanced by J. R. Lucas (in 1961), attempts to show that Gödel’s (first) incompleteness theorem can be seen to reveal that the human mind transcends all algorithmic models of it¹. Penrose's version of the argument has been seen to fall victim to the original objections raised against Lucas (see Boolos (...) (1990) and for a particularly intemperate review, Putnam (1994)). Yet I believe that more can and should be said about the argument. Only a brief review is necessary here although I wish to present the argument in a somewhat peculiar form. (shrink)

This paper provides a survey of philosophical discussion of the "the Turing Test". In particular, it provides a very careful and thorough discussion of the famous 1950 paper that was published in Mind.