Several philosophers of science have claimed that the correspondence principle can be generalized from quantum physics to all of (particularly physical) science and that in fact it constitutes one of the major heuristical rules for the construction of new theories. In order to evaluate these claims, first the use of the correspondence principle in (the genesis of) quantum mechanics will be examined in detail. It is concluded from this and from other examples in the history (...) of science that the principle should be qualified with respect to its nature and relativized with respect to its scope of application. At the same time this conclusion implies a qualification and a relativization of the heuristic power of the principle. Generally speaking, intertheoretical correspondence is primarily of a formal-mathematical and empirical but not of a conceptual nature. Moreover, it only applies to certain parts of the theories involved. Finally, a number of philosophical justifications of the principle are discussed and some conclusions are drawn concerning the debates on theory reduction and on the discovery-justification distinction. (shrink)

This paper presents a more clear formulation of the correspondence principle and explores its justification.

The paper argues that Bohr understood his correspondence principle, or at least an aspect of it expressed by the notion of rational generalization, as grounded in Hankel's principle of permanence.

A vast amount of ink has been spilled in both the physics and the philosophy literature on the measurement problem in quantum mechanics. Important as it is, this problem is but one aspect of the more general issue of how, if at all, classical properties can emerge from the quantum descriptions of physical systems. In this paper we will study another aspect of the more general issue-the emergence of classical chaos-which has been receiving increasing attention from physicists but which has (...) largely been neglected by philosophers of science. (shrink)

We formalize various counting principles and compare their strengths over $$V^{0}$$ V 0. In particular, we conjecture the following mutual independence between: a uniform version of modular counting principles and the pigeonhole principle for injections, a version of the oddtown theorem and modular counting principles of modulus p, where p is any natural number which is not a power of 2, and a version of Fisher’s inequality and modular counting principles. Then, we give sufficient conditions to prove them. We (...) give a variation of the notion of PHP-tree and k-evaluation to show that any Frege proof of the pigeonhole principle for injections admitting the uniform counting principle as an axiom scheme cannot have o(n)-evaluations. As for the remaining two, we utilize well-known notions of p-tree and k-evaluation and reduce the problems to the existence of certain families of polynomials witnessing violations of the corresponding combinatorial principles with low-degree Nullstellensatz proofs from the violation of the modular counting principle in concern. (shrink)

Fifteen essays are contained in this collection, all relating to Heinz Post ’ s article ‘ Correspondence, Invariance and Heuristics ’, also reprinted. In this article, written in the heyday of the post - positivist movement, Post aims to convince his fellowphilosophers of science to bring the issue of heuristics back to the philosophical stage. Examining a wealth of theories and models from the physics and chemistry of the last 300 years, Post extracts several strategies of theory construction of (...) which he considers the General Correspondence Principle to be the most important. According to this principle, any acceptable newtheory should explain the well - confirmed part of its predecessor. Later Post states the General Correspondence Principle more precisely and uses it with what he considers its de facto validity to argue against incommensurability, Kuhn - losses, 1 and relativism. Post himself seems to support a kind of convergent realism which is most notably expressed in his credo that science progresses linearly. (shrink)

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, (...) using examples from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

How does a predecessor theory relate to its successor? According to Heinz Post’s General Correspondence Principle, the successor theory has to account for the em- pirical success of its predecessor. After a critical discussion of this principle, I outline and discuss various kinds of correspondence relations that hold between successive scientific theories. I then look in some detail at a case study from contemporary physics: the various proposals for a theory of high-temperature superconductivity. The aim of (...) this case study is to understand better the prospects and the place of a methodological principle such as the Generalized Correspondence Principle. Generalizing from the case study, I will then argue that some such principle has to be considered, at best, as one tool that might guide scientists in their theoriz- ing. Finally I present a tentative account of why principles such as the Generalized Correspondence Principle work so often and why there is so much continuity in scientific theorizing. (shrink)

The Correspondence Principle of old quantum theory is commonly considered to be the requirement that quantum and classical theories converge in their empirical predictions in the appropriate asymptotic limit. That perception has persisted despite the fact that Bohr and other early proponents of CP clearly did not intend it as a mere requirement, and despite much recent historical work. In this paper, I build on this work by first giving an explicit formulation to the mentioned asymptotic requirement ) (...) and then discussing various possible formulations of CP for emission on the basis of the primary literature as well as general physical and metaphysical considerations. I shall then show that, in all of the most probable interpretations of CP that consider quantum theory as a universal theory, any system incorporating both CR and CP for emission would in fact be inconsistent. Old quantum theory measurably contradicts classical physics in the classical regime. (shrink)

How does a predecessor theory relate to its successor? According to Heinz Post's General Correspondence Principle, the successor theory has to account for the empirical success of its predecessor. After a critical discussion of this principle, I outline and discuss various kinds of correspondence relations that hold between successive scientific theories. I then look in some detail at a case study from contemporary physics: the various proposals for a theory of high-temperature superconductivity. The aim of this (...) case study is to understand better the prospects and the place of a methodological principle such as the Generalized Correspondence Principle. Generalizing from the case study, I will then argue that some such principle has to be considered, at best, as one tool that might guide scientists in their theorizing. Finally I present a tentative account of why principles such as the Generalized Correspondence Principle work so often and why there is so much continuity in scientific theorizing. (shrink)

Given a sequence of sets An⊆{0,…,n−1}, the Furstenberg correspondence principle provides a shift-invariant measure on2N that encodes combinatorial information about infinitely many of the An's. Here it is shown that this process can be inverted, so that for any such measure, ergodic or not, there are finite sets whose combinatorial properties approximate it arbitarily well. The finite approximations are obtained from the measure by an explicit construction, with an explicit upper bound on how large n has to be (...) to yield a sufficiently good approximation. We draw conclusions for computable measure theory, and show, in particular, that given any computable shift-invariant measure on 2N, there is a computable element of 2N that is generic for the measure. We also consider a generalization of the correspondence principle to countable discrete amenable groups, and once again provide an effective inverse. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous localization” has (...) been derived from the Schrödinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments. (shrink)

In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, (...) including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity, the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change. (shrink)

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.

Organizational research constitutes a differentiated, complex and fragmented field with multiple contradicting and incommensurable theories that make fundamentally different claims about the social and organizational reality. In contrast to natural sciences, the progress in this field can’t be attributed to the principle of truthlikeness where theories compete against each other and only best theories survive and prove they are closer to the truth and thus demonstrate scientific knowledge accumulation. We defend the structural realist view on the nature of organizational (...) theories in order to demonstrate that despite the multiplicity of isolated and competing explanations of organization-environment relations these theories are still logically compatible and mutually consistent which, in turn, assures theoretical progress in the field. Although postulating different and incompatible ontologies, three most successful organization-environments theories, namely, contingency theory, new institutionalism and population ecology share the same explanations of the relations between organizations and environments at the structural level. Without this principle one would say that what occurs in the field of organization theory is a change rather than a progress. (shrink)

Schrödinger's original quantization procedure is extended to include observables with classical counterparts described in generalized coordinates and momenta. The procedure satisfies the superposition principle, the correspondence principle, Hermiticity requirements, and gauge invariance. Examples are given to demonstrate the derivation of operators in generalized coordinates or momenta. It is shown that separation of variables can be achieved before quantization.

The letters in this volume continue to cover Ricardo's correspondence while a member of the House of Commons and provide subtle refinements and elaborations to his political economic thoughts. This volume includes a complete index to volumes 6 through 9, which contain Ricardo's correspondence. The index is cross-referenced by name and topic. Ricardo's letters remain a permanent legacy to the development of his many contributions to the political economy and a record of his endearing friendships.The entire series includes: (...) Volume 1 "On the Principles of Political Economy and Taxation"Volume 2 "Notes on Malthus's Principles of Political Economy"Volume 3 "Pamphlets and Papers 1809-1811 "Volume 4 "Pamphlets and Papers 1815-1823"Volume 5 "Speeches and Evidence"Volume 6 "Letters 1810-1815"Volume 7 "Letters 1816-1818"Volume 8 "Letters 1819-1821"Volume 9 "Letters 1821-1823"Volume 10 "Biographical Miscellany"Volume 11 "General Index". (shrink)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

Landauer's principle, often regarded as the basic principle of the thermodynamics of information processing, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. Conversely, it is generally accepted that any logically reversible transformation of information can in principle be accomplished by an appropriate physical mechanism (...) operating in a thermodynamically reversible fashion. These notions have sometimes been criticized either as being false, or as being trivial and obvious, and therefore unhelpful for purposes such as explaining why Maxwell's Demon cannot violate the second law of thermodynamics. Here I attempt to refute some of the arguments against Landauer's principle, while arguing that although in a sense it is indeed a straightforward consequence or restatement of the Second Law, it still has considerable pedagogic and explanatory power, especially in the context of other influential ideas in nineteenth and twentieth century physics. Similar arguments have been given by Jeffrey Bub. (shrink)

In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary von Neumann algebra. (...) A transfer principle is established that enables us to transfer theorems of ZFC to their quantum counterparts holding in the model. The set of real numbers in the model is shown to be in one-to-one correspondence with the set of self-adjoint operators affiliated with the von Neumann algebra generated by the logic. Despite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model. It is also shown that any observational proposition in quantum mechanics can be represented by a corresponding statement for real numbers in the model with the truth value consistent with the standard formulation of quantum mechanics, and that the equality relation between two real numbers in the model is equivalent with the notion of perfect correlation between corresponding observables (self-adjoint operators) in quantum mechanics. The paper is concluded with some remarks on the relevance to quantum set theory of the choice of the implication connective in quantum logic. (shrink)

The correspondence in 1680 and 1681 between John Flamsteed and Isaac Newton on Flamsteed’s theory of the comet of 1680 tells half the story. Related manuscripts reveal Newton was pursuing his own comprehensive line of inquiry based on principles that were the antithesis of Flamsteed’s procedures. Following generally accepted views in England, Newton’s work was marked by critical evaluation of data but marred by uncritical use of simple calculating techniques based on what might be termed Platonic archetypes of straightness. (...) Flamsteed’s intervention provided useful data and allowed Newton to seek additional information. Although Newton supposedly briefly considered a solution that vaguely resembled his parabolic approximation of the path of the comet determined 5 years later, the evidence Newton provided (based on simple hypotheses) did not support such a highly curved path or one in which the sun apart from the solar vortex exerted influence. Newton’s work, including an alleged harmonic law of tails, was quietly abandoned in favor of other work. With new insight, Newton revived work on comets as fully gravitational objects immediately following Halley’s visit in 1684. This little known side of the episode provides a fresh opportunity to examine Newton’s sources and actual practice in developing a new line of inquiry. An appendix dating sections of Newton’s Waste Book entries on comets is included. (shrink)

Norris, McQueen & Cutler argue that there is no need for feedback in word recognition. Given the accumulating evidence in favor of feedback as a general mechanism in the brain, I will question the utility of a model that is at odds with such a general principle. Correspondence:a2 Laboratoire de Neurosciences Intégratives et Adaptatives, Université de Provence, 13397 Marseille, cedex 13, France.

The American Institute of certified public accountants (AICPA) has promulgated a Code of Professional Conduct , which has served as the primary ethical standard for public accountants in the United States for more than 20 years. It is now out of date and needs to be replaced with a code of ethics. Just as U.S. generally accepted accounting principles are being migrated toward “principles-based accounting” as part of a convergence with international financial reporting standards, a similar process needs to occur (...) with ethics. This article organizes the primary rules of the AICPA Code around five essential virtues: objectivity, integrity, inquisitiveness, loyalty, and trustworthiness. These virtues correspond to the general principles set forth in the Code of Ethics for Professional Accountants of the International Federation of Accountants (IFAC). From this virtue ethics perspective, various rules of the AICPA Code are critiqued as being inadequate at best, and poorly crafted at worst. The article concludes with the proposition that principles-based ethics serves the profession and the financial reporting process better than the current rules-based approach. (shrink)

A generalized Veltman semantics developed by de Jongh is used to investigate correspondences between several extensions of intepretability logic . In this paper we present some new results on independences.

The new critical edition of the works and correspondence of Jeremy Bentham is being prepared and published under the supervision of the Bentham Committee of University College London. In spite of his importance as jurist, philosopher, and social scientist, and leader of the Utilitarian reformers, the only previous edition of his works was a poorly edited and incomplete one brought out within a decade or so of his death. Eight volumes of the new Collected Works, five of correspondence, (...) and three of writings on jurisprudence, appeared between 1968 and 1981, published by the Athlone Press. Further volumes in the series since then are published by Oxford University Press. The overall plan and principles of the edition are set out in the General Preface to The Correspondence of Jeremy Bentham, vol. 1, which was the first volume of the Collected Works to be published.An Introduction to the Principles of Morals and Legislation, Jeremy Bentham's best-known work, is a classic text in modern philosophy and jurisprudence. First published in 1789, it contains the important statement of the foundations of utilitarian philosophy and a pioneering study of crime and punishment, both of which remain at the heart of contemporary debates in moral and political philosophy, economics, and legal theory. Printed here in full is the definitive edition, edited by the distinguished scholars J. H. Burns and H. L. A. Hart. An introductory essay by Hart, first published in 1982 and a widely acknowledged classic in its own right, is reprinted here. It contains an important analysis of Bentham's principle of utility, theory of action, and an account of the relationship between law and morality.A new introduction by the leading Bentham scholar F. Rosen, specially written for this Clarendon Paperback edition, provides students with a helpful survey of Bentham's main ideas and an extensive bibliographical study of recent critical work on Bentham. Professor Rosen's essay also contains a new analysis of the principle of utility in Bentham's philosophy which is compared with its use in Hume and J. S. Mill. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a (...) class='Hi'>generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

This paper investigates three morphosyntactic alternations in Estonian – those between the exterior locative cases allative, adessive and ablative and the corresponding postpositionspeale‘onto’,peal‘on’ andpealt‘off’. Based on the Complexity Principle (e.g., Rohdenburg, Günter. 2002. Processing complexity and the variable use of prepositions in English. In Hubert Cuyckens & Günter Radden (eds.),Perspectives on prepositions, 79–100. Tübingen: Niemeyer), we expect cognitively more complex constructions to use more explicit (i.e., morphologically more substantial) marking by means of a postposition. Further, we expect variation to (...) be conditioned similarly in all three semantic categories. For each of the three alternations, a random sample of the two outcomes (case vs. postposition) from the Estonian National Corpus is used, resulting in 3,000 data points. Using properties of the Landmark phrase as independent variables in Bayesian mixed-effects logistic regression models, we predict the choice of postpositions over case-marked realisations. Of the patterns found, only the frequency-related one supports our complexity-related hypothesis. We conclude that the Complexity Principle, in its general form, has little explanatory power for the Estonian constructions at hand and, in particular, that the derived principle of ‘analytic support’ is not generally applicable. We show, however, that the grammatical knowledge of Estonian exterior locative cases and the corresponding postpositions is regulated by our three factors in a relatively uniform way. (shrink)

Gonzalo Rodriguez-Pereyra presents an original study of the place and role of the Identity of Indiscernibles in Leibniz's philosophy. The Principle of the Identity of Indiscernibles rules out numerically distinct but perfectly similar things; Leibniz derived it from more basic principles and used it to establish important philosophical theses. Rodriguez-Pereyra aims to establish what Leibniz meant by the Principle of Identity of Indiscernibles, what his arguments for and from it were, and to assess those arguments and Leibniz's claims (...) about the Principle of Identity of Indiscernibles. He argues that Leibniz had a very strong version of the principle, according to which no possibilia are intrinsically perfectly similar, where this excludes things that differ in magnitude alone. The book discusses Leibniz's arguments for the Identity of Indiscernibles in the Meditation on the Principle of the Individual, the Discourse on Metaphysics, Notationes Generales, Primary Truths, the letter to Casati of 1689, the correspondence with Clarke, as well as the use of the Identity of Indiscernibles in Leibniz's arguments against the Cartesian conception of the material world, atoms, absolute space and time, the Lockean conception of the mind as a tabula rasa, and freedom of indifference. Rodriguez-Pereyra argues that the Identity of Indiscernibles was a central but inessential principle of Leibniz's philosophy. (shrink)

Rousseau's understanding of legislation as the expression of the general will implies a constitutional principle of legislative supremacy. In turn, this should translate to a narrow, mechanical account of adjudication, lest creative judicial interpretation subvert the primacy of legislative power. Yet in his constitutional writings, Rousseau recommends open-textured and vague legislative codes, which he openly admits will require judicial development. Thus he apparently trusts a great deal in judicial discretion. Ostensibly, then, he overlooks the problem of how legislative indeterminacy—and (...) correspondingly, judicial discretion—may undermine the authority of the general will. However, I argue that Rousseau aims to check judicial subversion of legislative supremacy simply by extending his broader social politics—and specifically, his peculiar concept of republican virtue—to the domain of law. His main concern is that the law should not develop as a mystifying expert practice; therefore, he necessarily rejects any understanding of judicial virtue as lying in principled discourse. Instead, he envisages that judicial power will be checked by a more generic sense of republican virtue. In turn this echoes his apprehension of social differentiation and social complexity as sources of domination and hierarchy. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be (...) accepted rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...) and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account. (shrink)

In his Works of Pindar, Vol. II, p. xxiii, Dr. L. R. Farnell discusses the admission of metrical licences into Pindar's text, and pronounces that ‘the “Responsion-law” should not be pressed with over-strained severity.’ In general he agrees with Wilamowitz and Schroeder and disagrees with the stricter school of P. Maas. But none of these scholars have formulated the principles by which long syllables may be equated with short in Pindar's text, or even those by which two short syllables may (...) take the place of one long and vice versa. Such attempts were made by great scholars of the past, notably by Erasmus Schmid, Hermann and Boeckh, but recent developments in metric and textual criticism have created a new attitude towards metrical problems and provided a new vocabulary. It is time that Pindar's practice was re-examined. Only from it can we deduce what his rules of composition were and find out what licences he allowed and what not. The question is important both for the textual critic and for the student of Greek metric. If we can discover the principles on which Pindar used such metrical licences, we shall be more qualified to consider emendations which involve them and to understand the rules which he set before himself when composing an ode. (shrink)

A well-known result states that, over basic Kalmar elementary arithmetic EA, the induction schema for ∑n formulas is equivalent to the uniform reflection principle for ∑n + 1 formulas . We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reflection principles as well. Thus, the closure of EA under the induction rule for ∑n formulas is equivalent to ω times iterated ∑n reflection principle. Moreover, for k < (...) ω, k times iterated ∑n reflection principle over EA precisely corresponds to the extension of EA by k nested applications of ∑n induction rule.The above relationship holds in greater generality than just stated. In fact, we give general formulas characterizing in terms of iterated reflection principles the extension of any given theory by k nested applications of ∑n or Πn induction rules. In particular, the closure of a theory T under just one application of ∑1 induction rule is equivalent to T together with ∑1 reflection principle for each finite Π2 axiomatized subtheory of T.These results have closely parallel ones in the theory of subrecursive function classes. The rules under study correspond, in a canonical way, to natural closure operators on the classes of provably recursive functions. Thus, ∑1 induction rule precisely corresponds to the primitive recursive closure operator, and ∑1 collection rule, introduced below, corresponds to the elementary closure operator. (shrink)

This article outlines an epistemological perspective to understand the organism as a temporally changing whole. To analyze the mental faculties involved, the organism’s development and persisting existence is differentiated into four interdependent aspects: descent, future existence, persistent species, and environmentally adapted physical appearance. It is outlined that these aspects are recognized by comparative memory, concept-guided anticipation, conceptual thinking, and sensory perception, respectively. Furthermore, it is pointed out that these aspects correspond to the famous four Aristotelian “causes” or principles of explanation. (...) The descent of an organism corresponds to Aristotle’s efficient principle (“where does it come from?”), its future existence to the final principle (“what is if for?”), its physical structure to the material principle (“out of what is it?”) and its persistent species to the formal principle (“what is it?”). Aristotle regarded the unity of the efficient, formal and final principle as the ontological cause of the organism and called it the “soul” (psyche), while the material principle can be understood to represent its “body” (soma). I suggest that Aristotle’s “soul” corresponds to three of the four mental faculties required for cognition of a self-maintaining organism. I argue that in a Kantian perspective, the Aristotelian “soul” represents the condition for recognizing an organism at all. Therefore, the Aristotelian principle of life becomes intelligible and even empirically observable through the inner sense. In summary, I suggest that the four aspects of the organism described here can be viewed as the general, epistemological and ontological principle of the organism, the Bio-Logos. (shrink)

To determine the place that corresponds to a particular author in the process called “the dispute about psychologism” (“Psychologismusstreit”), it is necessary to go beyond his express statements about the relationship between psychology and logic, and pay attention to his statements regarding subjectivity. In the following lines, this general principle is applied to Herbart, which will make it possible to determine the place he occupies in the dispute and clarify the relationship in which he finds himself with respect to (...) other better-known and paradigmatic authors of said dispute, such as Frege. (shrink)

The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. (...) Still working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)

The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper revolves around the question what logic describes the behavior that is present in all theories with a minimum amount of arithmetic; the intersection over all such theories so to say. We denote this target logic by IL.In this paper we present a new principle R in IL. We show that R does not follow from the logic (...) ILP0W* that contains all previously known principles. This is done by providing a modal incompleteness proof of ILP0W*: showing that R follows semantically but not syntactically from ILP0W*. Apart from giving the incompleteness proof by elementary methods, we also sketch how to work with so-called Generalized Veltman Semantics as to establish incompleteness. To this extent, a new version of this Generalized Veltman Semantics is defined and studied. Moreover, for the important principles the frame correspondences are calculated.After the modal results it is shown that the new principle R is indeed valid in any arithmetically theory. The proof employs some elementary results on definable cuts in arithmetical theories. (shrink)

Jan Krajíček posed the following problem: Is there is a generalization result in the theory of real closed fields of the form: If A is provable in length k for all n ϵ ω , then A is provable? It is argued that the answer to this question depends on the particular formulation of the “theory of real closed fields.” Four distinct formulations are investigated with respect to their generalization behavior. It is shown that there is a positive answer to (...) Krajíček's question for 1. the axiom system RCF of Artin-Schreier with Gentzen's LK as underlying logical calculus, 2. RCF with the variant LK B of LK allowing introduction of several quantifiers of the same type in one step, 3. LK B and the first-order schemata corresponding to Dedekind cuts and the supremum principle. A negative answer is given for 4. any system containing the schema of extensionality. (shrink)

Wittgenstein famously remarks that ‘the meaning of a word is its use’ (PI §43). Whether or not one views this as gesturing at a ‘theory’ of meaning, or instead as aiming primarily at dissuading us from certain misconceptions of language that are a source of puzzlement, it is clear that Wittgenstein held that for certain purposes the meaning of an expression could profitably be characterised as its use. Throughout his later writings, however, Wittgenstein’s appeal to the notion of use pulls (...) in two directions. In several places, Wittgenstein seems to connect the notion of an expression’s meaning with that of use in the sense of usage or practice. More specifically, he suggests that for an expression to possess meaning is for there to be a practice of employing it according to certain rules. ‘That’, he tells us, ‘is why there exists a correspondence between the concepts “rule” and “meaning”’ (OC §62; cf. PG 68; PO 51; RFM VI §28; VW 103). Indeed, Wittgenstein goes so far as to say, ‘The rule-governed nature of our languages permeates our life’ (RC §303). Call the view that the meaning of an expression is determined by a general principle governing its use, rulism. (shrink)

Cyclic mechanic is intended as a suitable generalization both of quantum mechanics and general relativity apt to unify them. It is founded on a few principles, which can be enumerated approximately as follows: 1. Actual infinity or the universe can be considered as a physical and experimentally verifiable entity. It allows of mechanical motion to exist. 2. A new law of conservation has to be involved to generalize and comprise the separate laws of conservation of classical and relativistic mechanics, and (...) especially that of conservation of energy: This is the conservation of action or information. 3. Time is not a uniformly flowing time in general. It can have some speed, acceleration, more than one dimension, to be discrete. 4. The following principle of cyclicity: The universe returns in any point of it. The return can be only kinematic, i.e. per a unit of energy (or mass), and thermodynamic, i.e. considering the universe as a thermodynamic whole. 5. The kinematic return, which is per a unit of energy (or mass), is the counterpart of conservation of energy, which can be interpreted as the particular case of conservation of action “per a unit of time”. The kinematic return per a unit of energy (or mass) can be interpreted in turn as another particular law of conservation in the framework of conservation of action (or information), namely conservation of wave period (or time). These two counterpart laws of conservation correspond exactly to the particle “half” and to the wave “half” of wave-particle duality. 6. The principle of quantum invariance is introduced. It means that all physical laws have to be invariant to discrete and continuous (smooth) morphisms (motions) or mathematically, to the axiom of choice. The list is not intended to be exhausted or disjunctive, but only to give an introductory idea. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)---although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility---and incredible versatility---of theory reduction. A non-exhaustive (...) list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction---revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (shrink)

The results established in this paper are in connection with the Relative Internal Set Theory (R.I.S.T.). The main result is the general principle of choice: Let α be a level and let Φ(x, y) be anαexternalαbounded formula of the language of R.I.S.T.. Suppose that to each elementx, dominated by α, corresponds an elementy x such that Φ(x, y x ) holds, then there exists a function of choice ψ such that, which is a very general principle of choice, (...) for everyx dominated by α, Φ(x, ψ(x)) holds. More than that, we establish that if all the elementsy x are uniformly dominated by a level β then we can prescribe that the function of choice is also dominated by β. (shrink)

Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk–Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in (...) several different circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system. (shrink)

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and (...) both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XXII, Number 1, April 1996, pp. 23-48 Fantastick Associations and Addictive General Rules: A Fundamental Difference between Hutcheson and Hume MICHAEL B. GILL The belief that God created human beings for some moral purpose underlies nearly all the moral philosophy written in Great Britain in the seventeenth and early eighteenth centuries. David Hume attacks this theological conception of human nature on all fronts. It is out (...) of these attacks that Hume develops his own "science of man" based solely on "experience and observation."1 Francis Hutcheson is often taken to be the most important positive influence on Hume. And there can be no doubt that Hume does take on board several crucial Hutchesonian elements. But Hutcheson's moral theory, like that of most of his contemporaries, is grounded in a theological conception of human nature to which Hume is adamantly opposed.2 In this paper I will examine how Hume's disagreements with Hutcheson embody the anti-theological purpose that defines Hume's work as a whole. I will look, in particular, at Hume's and Hutcheson's different positions on the principles of association. I hope to show how Hume's use of these principles in the Treatise advances his larger goal of placing "the science of man" on "a foundation almost entirely new" (T xvi). I will proceed, first, by explaining Hutcheson's conception of human nature and his use of the principles of association; second, by sketching in broad outline how Hume's accounts of the origins of justice and natural virtue undermine crucial components of Hutcheson's conception of human nature; and third, by elucidating in more detail an aspect of Hume's associationism that is particularly revealing of his distance from Hutcheson. Michael B. Gill is at the Department of Philosophy, Purdue University, 1360 Liberal Arts and Education Building, West Lafayette IN 47907 USA. email: mbgill@sage.cc.purdue.edu. 24 Michael B. Gill I. Hutcheson and Association Hutcheson discusses the mind's tendency to associate in all of his writings, but his most extensive treatment of the matter comes in his Essay on the Passions.3 Hutcheson begins the Essay by telling us that something is good if and only if the perception of it "Causes, or Occasions" a pleasurable feeling, and that something is evil if and only if the perception of it causes or occasions a painful feeling (EP 2). Crucially, Hutcheson denies that all of our pleasures and pains are of the same type (EP 1-8).4 He holds, rather, that there are at least five distinct types of pleasures and pains and that each of them grounds a different irreducible type of good and evil. There are, first, the pleasures and pains caused by things we perceive through the external senses of taste, touch, smell, etc.; things that cause such pleasures are called naturally good, while things that cause such pains are called naturally evil. Second, there are the "Pleasant Perceptions, arising from regular, harmonious, uniform Objects" (EP 5); the things that cause these pleasures are called beautiful.5 Third, there are the pleasures and pains we feel upon perceiving the happiness or misery of other human beings; the things that cause these pleasures are called public goods while those that cause the corresponding pains are called public evils. Fourth, there are pleasures and pains, usually called approval and disapproval, that we feel upon perceiving the actions of others; the actions that cause approval are called virtuous or morally good, while those that cause disapproval are called vicious or morally evil. Finally, there are the pleasures and pains we feel upon perceiving others' moral perceptions of our own actions; the pleasure of perceiving others' approval of one's actions is called the feeling of honor, while the pain of perceiving others' disapproval is called the feeling of shame. For Hutcheson, then, natural goodness, beauty, the public good, virtue and honor are all defined by our pleasures and pains. He does not think, however, that these are defined by just any of our actual or occurrent pleasures and pains. He holds, rather, that they are defined by the pleasures and pains we feel under certain privileged... (shrink)

The rapid diffusion of artificial intelligence (AI) technologies in the defence domain raises challenges for the ethical governance of these systems. A recent shift from the what to the how of AI ethics sees a nascent body of literature published by defence organisations focussed on guidance to implement AI ethics principles. These efforts have neglected a crucial intermediate step between principles and guidance concerning the elicitation of ethical requirements for specifying the guidance. In this article, we outline the key normative (...) choices and corresponding tradeoffs that are involved in specifying guidance for the implementation of AI ethics principles in the defence domain. These correspond to: the AI lifecycle model used; the scope of stakeholder involvement; the accountability goals chosen; the choice of auditing requirements; and the choice of mechanisms for transparency and traceability. We provide initial recommendations for navigating these tradeoffs and highlight the importance of a pro-ethical institutional culture. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing his ideas (...) through lucid lecturing and writing. The present work, first published in 1845, has been hailed as 'the first systematic account of the theory and policy of public finance'. After a general introductory chapter, the book discusses direct and indirect taxation, before considering national debt and how to deal with it. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)