In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions (...) of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

In the present paper, we develop the algorithmic correspondence theory for hybrid logic with binder |$\mathcal {H}(@, \downarrow )$|⁠. We define the class of Sahlqvist inequalities for |$\mathcal {H}(@, \downarrow )$|⁠, and each inequality of which is shown to have a first-order frame correspondent effectively computable by an algorithm |$\textsf {ALBA}^{\downarrow }$|⁠.

The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...) the recursive extension of \sqema\ succeeds on the class of `recursive formulae'. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds. (shrink)

We apply and extend the theory and methods of algorithmic correspondence theory for modal logics, developed over the past 20 years, to the language LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document} of relevance logics with respect to their standard Routley–Meyer relational semantics. We develop the non-deterministic algorithmic procedure PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} for computing first-order equivalents of formulae of the language LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document}, in terms of that semantics. PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} is an adaptation of the previously developed algorithmic procedures SQEMA and ALBA. We then identify a large syntactically defined class of inductive formulae in LR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_R$$\end{document}, analogous to previously defined such classes in the classical, distributive and non-distributive modal logic settings, and show that PEARL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PEARL}$$\end{document} succeeds for every inductive formula and correctly computes a first-order definable condition which is equivalent to it with respect to frame validity. We also provide a detailed comparison with two earlier works, each extending the class of Sahlqvist formulae to relevance logics, and show that both are subsumed by simple subclasses of inductive formulae. (shrink)

In the present paper, we study the correspondence and canonicity theory of modal subordination algebras and their dual Stone space with two relations, generalizing correspondence results for subordination algebras in [13–15, 25]. Due to the fact that the language of modal subordination algebras involves a binary subordination relation, we will find it convenient to use the so-called quasi-inequalities and |$\varPi _{2}$|-statements. We use an algorithm to transform (restricted) inductive quasi-inequalities and (restricted) inductive |$\varPi _{2}$|-statements to equivalent first-order (...) correspondents on the dual Stone spaces with two relations with respect to arbitrary (resp. admissible) valuations. (shrink)

This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring similarities between objects in the conceptual space being based on the Newtonian potential function. The notion of a fuzzy prototype, which generalizes the previous definition of a prototype, is introduced. Furthermore, the (...) necessary conditions that a natural concept must meet are discussed. Instead of convexity, as proposed by Gärdenfors, the notion of geodesically convex sets is used. Thus, if a concept corresponds to a set which is geodesically convex, it is a natural concept. This definition applies, for example, if the conceptual space is an Euclidean space. As a by-product of the construction of the algorithm, an extension of the conceptual space to d-dimensional Riemannian manifolds is obtained. (shrink)

The prospective introduction of autonomous cars into public traffic raises the question of how such systems should behave when an accident is inevitable. Due to concerns with self-interest and liberal legitimacy that have become paramount in the emerging debate, a contractarian framework seems to provide a particularly attractive means of approaching this problem. We examine one such attempt, which derives a harm minimisation rule from the assumptions of rational self-interest and ignorance of one’s position in a future accident. We contend, (...) however, that both contractarian approaches and harm minimisation standards are flawed, due to a failure to account for the fundamental difference between those ‘involved’ and ‘uninvolved’ in an impending crash. Drawing from classical works on the trolley problem, we show how this notion can be substantiated by reference to either the distinction between negative and positive rights, or to differences in people’s claims. By supplementing harm minimisation with corresponding constraints, we can develop crash algorithms for autonomous cars which are both ethically adequate and promise to overcome certain significant practical barriers to implementation. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k (...) : Is there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

Traffic congestion is a common problem in many countries, especially in big cities. At present, China’s urban road traffic accidents occur frequently, the occurrence frequency is high, the accident causes traffic congestion, and accidents cause traffic congestion and vice versa. The occurrence of traffic accidents usually leads to the reduction of road traffic capacity and the formation of traffic bottlenecks, causing the traffic congestion. In this paper, the formation and propagation of traffic congestion are simulated by using the improved medium (...) traffic model, and the control strategy of congestion dissipation is studied. From the point of view of quantitative traffic congestion, the paper provides the fact that the simulation platform of urban traffic integration is constructed, and a feasible data analysis, learning, and parameter calibration method based on RBF neural network is proposed, which is used to determine the corresponding decision support system. The simulation results prove that the control strategy proposed in this paper is effective and feasible. According to the temporal and spatial evolution of the paper, we can see that the network has been improved on the whole. (shrink)

This article seeks to explain the correspondence between human intelligibility and that of the physical world by synthesizing the contributions of Jean Ladrière. Ladrière shows that the objectification function of formal symbolism in mathematics as an artificial language has operative power acquired through algorithm to represent physical reality. In physical theories, mathematics relates to observations through theoretic and empirical languages mutually interacting in a methodological circle, and nonmathematical anticipatory intention guides mathematical algorithmic exploration. Ladrière reasons that mathematics can (...) make the physical world comprehensible because of the presence of a rational principle in both kinds of intelligibility. (shrink)

The computational approach to psychiatric disorders, including delusions, promises explanation and treatment. Here, we argue that an information processing approach might be misleading to understand psychopathology and requires further refinement. We explore the claim of computational psychiatry being a bridge between phenomenology and physiology while focussing on the ontological commitments and corresponding methodology computational psychiatry is based on. Interconnecting ontological claims and methodological practices, the paper illustrates the structure of theory-building and testing in computational psychiatry.First, we will explain the (...) ontological commitments computational psychiatry is grounded in, theBayesian Brain hypothesis(BBH) of unconscious inference, paired with normative deontic approaches applied to gauge psychopathology. We then turn to the steps taken in empirical paradigms, from definitions, which are used as starting points, to the operationalisation and isolation of cognitive processes and hypothesis testing based on algorithmic models, to consecutive interpretations regarding the aetiology of psychiatric disorders. We outline how experimental paradigms in computational psychiatry are specifically designed to confirm aberrations in assumed inferential processes, which are thought of as being the underlyingcore invariant features.We will illustrate a gap between the ontological commitments of computational psychiatry and the operationalisation and testing of the cognition assumed to be relevant for psychopathology. This conceptual gap is of utmost importance when designing computational paradigms and may impede a crisp understanding of the approach. Lastly, in evaluating the conceptual gap, it becomes apparent that the information processing formalism used in computational psychiatry is still grounded in rational cognitive psychology. (shrink)

The problem of algorithmic fairness is typically framed as the problem of finding a unique formal criterion that guarantees that a given algorithmic decision-making procedure is morally permissible. In this paper, I argue that this is conceptually misguided and that we should replace the problem with two sub-problems. If we examine how most state-of-the-art machine learning systems work, we notice that there are two distinct stages in the decision-making process. First, a prediction of a relevant property is made. (...) Secondly, a decision is taken based (at least partly) on this prediction. These two stages have different aims: the prediction is aimed at accuracy, while the decision is aimed at allocating a given good in a way that maximizes some context-relative utility measure. Correspondingly, two different fairness issues can arise. First, predictions could be biased in discriminatory ways. This means that the predictions contain systematic errors for a specific group of individuals. Secondly, the system’s decisions could result in an allocation of goods that is in tension with the principles of distributive justice. These two fairness issues are distinct problems that require different types of solutions. I here provide a formal framework to address both issues and argue that this way of conceptualizing them resolves some of the paradoxes present in the discussion of algorithmic fairness. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

The correspondence theory of truth is a precise and innovative account of how the truth of a proposition depends upon that proposition's connection to a piece of reality. Joshua Rasmussen refines and defends the correspondence theory of truth, proposing new accounts of facts, propositions, and the correspondence between them. With these theories in hand, he then offers original solutions to the toughest objections facing correspondence theorists. Addressing the Problem of Funny Facts, Liar Paradoxes, and (...) traditional epistemological questions concerning how our minds can access reality, he challenges recent objections, and defends what has traditionally been the most popular theory of truth. Written with clarity, precision, and sensitivity to a range of philosophical backgrounds, his book will appeal to advanced students and scholars seeking a deeper understanding of the relationship between truth and reality. (shrink)

Because of the difficulty of music feature recognition due to the complex and varied music theory knowledge influenced by music specialization, we designed a music feature recognition system based on Internet of Things technology. The physical sensing layer of the system places sound sensors at different locations to collect the original music signals and uses a digital signal processor to carry out music signal analysis and processing. The network transmission layer transmits the completed music signals to the music signal (...) database in the application layer of the system. The music feature analysis module of the application layer uses a dynamic time regularization algorithm to obtain the maximum similarity between the test template and the reference. The music feature analysis module of the application layer uses the dynamic time regularization algorithm to obtain the maximum similarity between the test template and the reference template to realize the feature recognition of the music signal and determine the music pattern and music emotion corresponding to the music feature content according to the recognition result. The experimental results show that the system operates stably, can capture high-quality music signals, and can correctly identify music style features and emotion features. The results of this study can meet the needs of composers’ assisted creation and music researchers’ analysis of a large amount of music data, and the results can be further transferred to deep music learning research, human-computer interaction music creation, application-based music creation, and other fields for expansion. (shrink)

The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the rule of (...) “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory. (shrink)

Common spatial pattern is an effective algorithm for extracting electroencephalogram features of motor imagery ; however, CSP mainly aims at multichannel EEG signals, and its effect in extracting EEG features with fewer channels is poor—even worse than before using CSP. To solve the above problem, a new combined feature extraction method has been proposed in this study. For EEG signals from fewer channels, wavelet packet transform, fast ensemble empirical mode decomposition, and local mean decomposition were used to decompose the band-pass (...) filtered EEG into multiple time–frequency components, and the corresponding components were selected according to the frequency characteristics of MI or the correlation coefficient between its time–frequency components and the original EEG signal. Furthermore, phase space reconstruction was performed on the selected components after the three time-frequency decompositions, the maximum Lyapunov index was calculated, and the features were reconstructed; then, CSP projection mapping was used for the reconstructed features. The support vector machine probability output model was trained by the obtained three mappings. Probability outputs by three different support vector machines were then obtained. Finally, the classification of test samples was determined by the fusion of the Dempster–Shafer evidence theory at the decision level. The results showed that the accuracy of the proposed method was 95.71% on data set III of BCI competition II, which was 2.88% higher than the existing methods. On data set IIb of BCI competition IV, the average accuracy was 86.60%, which was 2.3% higher than the existing methods. This study verified the effectiveness of the proposed method and provided an approach for the research and development of the MI-BCI system based on fewer channels. (shrink)

This work presents a version of the correspondence theory of truth based on Wittgenstein's Tractatus and Russell's theory of truth and discusses related metaphysical issues such as predication, facts and propositions. Like Russell and one prominent interpretation of the Tractatus it assumes a realist view of universals. Part of the aim is to avoid Platonic propositions, and although sympathy with facts is maintained in the early chapters, the book argues that facts as real entities are not needed. (...) It includes discussion of contemporary philosophers such as David Armstrong, William Alston and Paul Horwich, as well as those who write about propositions and facts, and a number of students of Bertrand Russell. It will interest teachers and advanced students of philosophy who are interested in the realistic conception of truth and in issues in metaphysics related to the correspondence theory of truth, and those interested in Russell and the Tractatus. (shrink)

Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied (...) lambda-calculus. This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises. (shrink)

Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to a fact -- a view that was advocated by Russell and Moore early in the 20 th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be (...) specified). During the last 2300 years this basic idea has been expressed in many ways, resulting in a rather extended family of views, theories, and theory sketches. The members of the family employ various concepts for the relevant relation (correspondence, conformity, congruence, agreement, accordance, copying, picturing, signification, representation, reference, satisfaction) and/or various concepts for the relevant portion of reality (facts, states of affairs, situations, events, objects, sequences of objects, sets, properties, tropes). The resulting multiplicity of versions and reformulations of the theory is due to a blend of substantive and terminological differences. (shrink)

We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem.

Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is (...) set to the lim inf of previous register contents if that limit is finite; otherwise the register is reset to 0. The theory of these machines has several similarities to the infinite time Turing machines (ITTMs) of Hamkins and Lewis. The machines can decide all ${\Pi^1_1}$ sets, yet are strictly weaker than ITTMs. As in the ITTM situation, we introduce a notion of ITRM-clockable ordinals corresponding to the running times of computations. These form a transitive initial segment of the ordinals. Furthermore we prove a Lost Melody theorem: there is a real r such that there is a program P that halts on the empty input for all oracle contents and outputs 1 iff the oracle number is r, but no program can decide for every natural number n whether or not ${n \in r}$ with the empty oracle. In an earlier paper, the third author considered another type of machines where registers were not reset at infinite lim inf’s and he called them infinite time register machines. Because the resetting machines correspond much better to ITTMs we hold that in future the resetting register machines should be called ITRMs. (shrink)

Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.

In the present paper, we continue the research in Zhao (2021, Logic J. IGPL) to develop the Sahlqvist completeness theory for hybrid logic with satisfaction operators and downarrow binders |$\mathcal {L}( @, {\downarrow })$|⁠. We define the class of restricted Sahlqvist formulas for |$\mathcal {L}( @, {\downarrow })$| following the ideas in Conradie and Robinson (2017, J. Logic Comput., 27, 867–900), but we follow a different proof strategy which is purely proof-theoretic, namely showing that for every restricted Sahlqvist formula (...) |$\varphi $| and its hybrid pure correspondence |$\pi $|⁠, |$\textbf {K}_{\mathcal {H}( @, {\downarrow })}+\varphi $| proves |$\pi $|⁠; therefore, |$\textbf {K}_{\mathcal {H}( @, {\downarrow })}+\varphi $| is complete with respect to the class of frames defined by |$\pi $|⁠, using a modified version |$\textsf {ALBA}^{{\downarrow }}_{\textsf {Modified}}$| of the algorithm |$\textsf {ALBA}^{{\downarrow }}$| defined in Zhao (2021, Logic J. IGPL). (shrink)

First published in 1975, The Correspondence Theory of Truth examines the simplest statements of empirical fact and establishes what we can mean when we say that such statements are true. In particular, the author has considered whether any or all of beliefs, sentences, statements, or propositions are properly said to be true or false. He proceeds to examine what we mean by the term 'fact' and what possible relation between facts and beliefs could be meant by the term (...) 'correspondence'. The second part of the book is a critical survey of important contemporary accounts of truth. The author examines Tarski's semantic theory to see if it offers a satisfactory reconstruction of the essence of the traditional notion of correspondence, then J.L. Austin's recent and famous version of the correspondence theory and some criticisms of it by Professor P. E. Strawson. A final chapter summarizes the viable content of the correspondence theory and suggests what problems about truth still remain for discussion if the theory is accepted. This book will be an essential read for students and scholars of Philosophy. (shrink)

Two concepts of truth as correspondence of ideas with facts are analyzed. One of them is the thought-external fact relation, and the other is the fact-proposition one. The two maps are then composed, and the resulting map is assumed to formalize the concept of truth as adequacy or correspondence of ideas to facts. Besides, some desiderata for a correspondence theory of partial truth are proposed. Finally, the truth criteria employed in science and technology are recalled.

A novel account of semantic information is proposed. The gist is that structural correspondence, analysed in terms of similarity, underlies an important kind of semantic information. In contrast to extant accounts of semantic information, it does not rely on correlation, covariation, causation, natural laws, or logical inference. Instead, it relies on structural similarity, defined in terms of correspondence between classifications of tokens into types. This account elucidates many existing uses of the notion of information, for example, in the (...) context of scientific models and structural representations in cognitive science. It is poised to open a new research program concerned with various kinds of semantic information, its functions, and its measurement. (shrink)

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets (...) the correspondence intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution (...) of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise. (shrink)

William Dembski claims to have established a decision process to determine when highly unlikely events observed in the natural world are due to Intelligent Design. This article argues that, as no implementable randomness test is superior to a universal Martin-Löf test, this test should be used to replace Dembski's decision process. Furthermore, Dembski's decision process is flawed, as natural explanations are eliminated before chance. Dembski also introduces a fourth law of thermodynamics, his “law of conservation of information,” to argue that (...) information cannot increase by natural processes. However, this article, using algorithmic information theory, shows that this law is no more than the second law of thermodynamics. The article concludes that any discussions on the possibilities of design interventions in nature should be articulated in terms of the algorithmic information theory approach to randomness and its robust decision process. (shrink)

Turing machine An idealized computing device attached to a tape, each square of which is capable of holding a symbol. We write a program (a nite binary string) on the tape, and start the machine. If the machine halts with string o written at a designated place on the tape.

Although algorithmic information theory provides a measure of the information content of string of characters, problems of noise and noncomputability emerge. However, if pattern in a noisy string is recognized by reference to a set of similar strings, this article shows that a compressed algorithmic description of a noisy string is possible and illustrates this with some simple examples. The article also shows that algorithmic information theory can quantify the information in complex organized systems where (...) pattern is nested within pattern. (shrink)

One of the most intuitive concepts of truth is the classical correspondence theory of truth. Aside from the theoretical cogency and plausibility, this truth theory has two fundamental problems. I shall explore both of these problems. This will not be to reveal the problematic nature of the classical correspondence theory of truth itself, but to demonstrate the implications it has on Islam. I shall establish that the problems of this truth theory contribute in the (...) failure to determine the truth of a particular notion of an Islamic God. Consequently this truth theory would prove inconsistent with a particular notion of God within the Islamic tradition. (shrink)

This dissertation defends the place of representation in music. Music’s status as a representational art has been hotly debated since the War of the Romantics, which pitted the Weimar progressives (Liszt, Wagner, &co.) against the Leipzig conservatives (the Schumanns, Brahms, &co.) in an intellectual struggle for what each side took to be the very future of music as an art. I side with the progressives, and argue that music can be and often is a representational medium. Correspondence (or resemblance) (...) theories of representation, such as the one I offer, have been much maligned in philosophy since the 1960s. Most theories assimilate representation under “meaning,” which has usually been thought to belong primarily to language. As a result, representational content has been taken to be purely conventional in the way that sentential meaning is. People want to know what music “means,” and these theories interpret this as “what does it refer to?” or “what propositions does it express?” I argue that propositional communication is only one (small) part of the issue. Once we overcome the bias of conceiving of musical works as essentially linguistic items, speech acts (performed) or sentence tokens (written), we can begin to take music on its own terms to discover how it represents—one way in which it “means.” The first step is to “naturalize” music’s representational content. Influenced by recent discussions in the philosophies of mind and science, I argue in Chapter 1 that composers represent extra-musical objects, events, and states of affairs through their works by exploiting antecedent relations (such as similarities in pitch, timbre, and structure) in order to secure reference to them. In Chapter 2, I survey and respond to the main challenges that those skeptical of music’s representational possibilities would raise against my theory of musical representation. In Chapter 3, I explore a number of ways through which music has been claimed to represent in order to show how my theory accounts for these diverse phenomena better than its conventionalist rivals, both in terms of the metaphysics and the epistemology. Chapter 4 extends this discussion by offering an account of how we perceive, understand, appreciate, and interpret sophisticated musical representations. I conclude by teasing out some of my theory’s implications and suggesting areas for further research. (shrink)

Ernst Cassirer claimed that Kant's notion of actual object presupposes the notion of truth. Therefore, Kant cannot define truth as the correspondence of a judgement with an actual object. In this paper, I discuss the relations between Kant's notions of truth, object, and actuality. I argue that's notion of actual object does not presuppose the notion of truth. I conclude that Kant can define truth as the correspondence of a judgement with an actual object.

A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They (...) should abandon the relation and replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)

Ever since the works of Alfred Tarski and Frank Ramsey, two views on truth have seemed very attractive to many people. On the one hand, the correspondence theory of truth seemed to be quite promising, mostly, perhaps, for its ability to accomodate a realistic attitude towards truth. On the other hand, a minimalist conception seemed appropriate since it made things so simple and unmysterious. So even though there are many more theories of truth around - the identity (...) class='Hi'>theory, the prosentential theory, etc. -, it is fair to say that these two views have acquired the status of the main contenders in the field. Most recently, John Searle and David Lewis have taken sides on the issue. Searle defends a new version of the correspondence theory which takes facts to be the correspondents of true statements, whereas Lewis wants to hold on to a minimalist conception of truth - allowing for an appendix of purely ontological claims that he extracts from the correspondence theory. What is new is that both have tried to see the correspondence theory not as a rival to the minimalist conception, but rather as essentially compatible with it. Still, in the end, Searle arrives at his version of the correspondence theory, and Lewis votes for minimalism. Both philosophers have sympathy with the spirit of the correspondence theory, to say the least. So one wonders why it is that they come to so different conclusions. Both start from the spirit of the correspondence theory, and both see it as essentially compatible with the heart of the minimalist conceptions, and still is there no agreement on what theory is to be accepted in the end. (shrink)