We discuss a `negative' way of defining frame classes in (multi)modal logic, and address the question of whether these classes can be axiomatized by derivation rules, the `non-ξ rules', styled after Gabbay's Irreflexivity Rule. The main result of this paper is a metatheorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formulas and Λ+ is the extension of Λ with a set of non-ξ rules, then Λ+ (...) is strongly sound and complete with respect to the class of frames determined by the axioms and the rules. (shrink)

In previous articles we presented a simple set of axioms named “Contexts, Systems and Modalities”, where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain Born’s rule within this framework. Our approach is compared with other former and recent derivations, and its strong links (...) with Gleason’s theorem are particularly emphasized. (shrink)

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state. Unlike Gleason’s theorem, the argument applies even if probabilities are de…ned for only a single resolution of the identity, so it applies to a variety of foundational approaches to quantum mechanics. It also provides a probability rule for state spaces that are not Hilbert spaces.

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they (...) are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level. (shrink)

In the paper we focus upon the problem of derivability of rulesfrom rule complexes. The notion of a rule complex is the main mathematicalnotion of generalized game theory . Derivability of rules, asdefined here, comprises the concept of an extension from a default theory [9]as well as the classical notion of derivability of rules in logic. The idea oflocalness of reasoning, reasoning with a limited access to rules, is realizedby the concept of relative derivability. Starting with derivability of (...) rules, wenext touch upon the questions of the activation of rules and consistencyof rule complexes. (shrink)

If a certain semantic relation (which we call 'local consequence') is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call 'global consequence'), suggested by work of J.W. Garson, turns out to provide a much better - indeed a perfectly accurate - guide to derivability.

We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures, as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, (...) we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered. (shrink)

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing experimentally observable properties of probability distributions for the outcome of measurements. Axioms I, II, III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by von Neumann (in Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955) and independently by Turing (Teuscher and Hofstadter, Alan Turing: Life and Legacy of a Great Thinker, Springer, (...) Berlin, 2004), in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for any finite dimension. (shrink)

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...) in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be encoded (...) into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn’t. (shrink)

Logic is traditionally considered to be a purely syntactic discipline, at least in principle. However, prof. David Isles has shown that this ideal is not yet met in traditional logic. Semantic residue is present in the assumption that the domain of a variable should be fixed in advance of a derivation, and also in the notion that a numerical notation must refer to a number rather than be considered a mathematical object in and of itself. Based on his work, the (...) central question of this thesis is what kind of logic, if any, results from removing this semantic residue from traditional logic.We differ from traditional logic in two significant ways. The first is that the assumption that a numerical notation must refer to a number is denied. Numerical notations are considered as mathematical objects in their own right, related to each other by means of rewrite rules. The traditional notion of reference is then replaced by the notion of reduction (by means of the rewrite rules) to a normal form. Two numerical notations that reduce to the same normal form would traditionally be considered identical, as they would refer to the same number, and hence they would be interchangeable salva veritate. In the new system, called Buridan-Volpin (BV), the numerical notations themselves are the elements of the domains of variables, and two numerical notations that reduce to the same normal form need not be interchangeable salva veritate, except when they are syntactically identical (i.e., have the same Gödel number).The second is that we do away with the assumption that the domains of variables need to be fixed in advance of a derivation. Instead we focus on what is needed to guarantee preservation of truth in every step of a derivation. These conditions on the domains of the variables, accumulated in the course of a derivation, are combined in a reference grammar. Whereas traditionally a derivation is considered valid when the conclusion follows from the premisses by way of the derivation rules (and possibly axioms), in the BV system a derivation must meet the extra condition that no inconsistency occurs within the reference grammar. For if the reference grammar were to give rise to inconsistency (i.e., it would be impossible to assign domains to all the variables without breaking at least one of the conditions placed on them in the reference grammar), there is no longer a guarantee that truth has been preserved in every step of the derivation, and hence the truth of the conclusion is not guaranteed by the derivation.In Chapter 2 the BV system is introduced in some formal detail. Chapter 3 gives some examples of derivations, notably totality of addition, multiplication and exponentiation, as well as a lemma needed for the proof of Euclid’s Theorem. These examples, taken from prof. Isles’ First-Order Reasoning and Primitive Recursive Natural Number Notations, show that there is a real proof-theoretical difference between traditional logic and the BV system. Here we also find the first major point of departure between myself and prof. Isles, centered on the notion of inheritance of conditions in the reference grammar by way of lemmata. These different points of view are best illustrated in the sections on the totality of exponentiation and on Euclid’s Lemma: prof. Isles maintains that the proof of totality of exponentiation is not BV valid, while I maintain that it is. But I do agree with him that the traditional proof of Euclid’s Lemma is not BV valid. Chapter 6 also expands the arguments for my choice in this matter.Now that it has been shown that there is a difference between traditional logic and BV, the properties of BV need to be examined. In Chapter 4 we give a proof of Cut-elimination for BV minus induction and the subformula property for BV, which allows us to prove the consistency of BV minus induction. We also expand on the reasons for excluding induction. In Chapter 5 we consider in detail the proof of a finite analog to the Löwenheim–Skolem theorem given by prof. Isles in his article with the same title. He proves that under certain conditions it is always possible, given the existence of a (possibly uncountable) model for a derivation, to give a finite model for this derivation. The system he considers deviates from BV as considered in this thesis in two significant ways: it does not contain the induction rule and the domains contain numbers instead of numerical notations. We then go on to show that it is possible to extend the result to include induction, in the sense that the existence of a possibly uncountable model for a derivation guarantees the existence of a model that is at most countable. We also consider the complications that arise from taking numerical expressions instead of numbers as the elements of domains.Finally, in Chapter 6 we consider the philosophical consequences of the BV system, informed by the formal results from the previous chapters. In particular we discuss the relation between reduction and reference, the status of reference grammars, the notion of induction and its function within BV, and some brief considerations on the consequences of the BV system for the discussion regarding nominalism and realism with regard to mathematical objects. The object of the chapter is twofold. On the one hand applying the formal results to philosophical questions, on the other hand arguing that BV is not just a theoretically acceptable alternative to traditional logic, but is in fact deserving of further development and research into its properties. The latter will probably appeal most to those of a nominalist and/or finitist bent.Abstract prepared by Harrie de Swart and Sven Storms.E-mail:[email protected]:https://research.tilburguniversity.edu/files/6170 1294/Storms_The_Buridan_Volpin_04_05_2022.pdf. (shrink)

Mainstream historians in recent decades have often treated formal categories and rules as something to be 'used' by individuals, as one might use a stick or stone, and the gains of an earlier legal history are often needlessly set aside. Anthropologists, meanwhile, have treated rules as analytic errors and categories as an imposition by outside powers or by analysts, leaving a very thin notion of 'practice' as the stuff of social life. Philosophy of an older vintage, as well as the (...) work of scholars such as Charles Taylor, provides fresh approaches when applied imaginatively to cases beyond the traditional ground of modern Europe and North America. Not only are different kinds of rules and categories open to examination, but the very notion of a rule can be explored more deeply. This volume approaches rules and categories as constitutive of action and hence of social life, but also as providing means of criticism and imagination. A general theoretical framework is derived from analytical philosophy, from Wittgenstein to his critics and beyond, and from recent legal thinkers such as Schauer and Waldron. Case-studies are presented from a broad range of periods and regions, from Amazonia via northern Chad, Tibet, and medieval Russia to the scholarly worlds of Roman law, Islam, and Classical India. As the third volume in the Legalism series, this collection draws on common themes that run throughout the first two volumes: Legalism: Anthropology and History and Legalism: Community and Justice, consolidating them in a framework that suggests a new approach to rule-bound systems. (shrink)

The idea that correspondences relating grammatical relations and semantics (argument structure constructions) are needed to account for simple sentence types is reviewed, clarified, updated and compared with two lexicalist alternatives. Traditional lexical rules take one verb as ‘input’ and create (or relate) a different verb as ‘output’. More recently, invisible derivational verb templates have been proposed, which treat argument structure patterns as zero derivational affixes that combine with a root verb to yield a new verb. While the derivational template perspective (...) can address several problems that arise for traditional lexical rules, it still faces problems in accounting for idioms, which often contain specifications that are not appropriately assigned to individual verbs or derivational affixes (regarding adjuncts, modification, and inflection). At the same time, it is clear that verbs play a central role in determining their distribution. The balance between verbs and phrasal argument structure constructions is addressed via the Principles of Semantic Coherence and Correspondence together with a usage-based hierarchy of constructions that contains entries which can include particular verbs and other lexical material. (shrink)

Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent calculus from a ground sequent, that is, a logical axiom. We discuss the similarities and differences of these derived rules as well as their interaction with the implication right rule under cut and the structural axiom. We further consider the question of analyticity (...) of cuts in calculi using one of the new rules instead of the standard left implication rule. (shrink)

The Prudent Investor Rule creates a potential ethical dilemma for investment advisors selling over-the-counter financial products issued by their firms. The "opportunity" to defraud investors using complex, over-the-counter derivative securities designed for client-specific risk management is much higher than for exchange traded securities. This paper emphasizes the ethical responsibility held by trustees and their organizations to eliminate potential conflict of interests through internal control and monitoring. Independent evaluations of the performance of investment advisors and independent appraisals of complex over-the-counter (...) securities are important in reducing the risks of conflicts of interest. Recent lessons learned from the corporate ethics crisis and requirements of the 2002 Sarbanes Oxley Act would suggest that conflict of interest must be eliminated with third party validation of derivative pricing. By performing due diligence and validation, the trustee is able to satisfy the requirements under the Prudent Investor Rule. (shrink)

The best way to conceive semiotical spaces that are not identical to single buildings, such as a cityscape, is to define the place in terms of the activities occurring there. This conception originated in the proxemics of E. T. Hall and was later generalized in the spatial semiotics of Manar Hammad. It can be given a more secure grounding in terms of time geography, which is involved with trajectories in space and time. We add to this a qualitative dimension which (...) is properly semiotic, and which derives from the notion of border, itself a result of the primary semiotic operation of segmentation. Borders, in this sense, are more or less permeable to different kinds of activities, such as gaze, touch, and movement, where the latter are often not physically defined, but characterized in terms of norms. Norms must be understood along the lines of the Prague school, which delineates as scale going from laws in the legal sense to simple rules of thumb. Such considerations have permitted us to define a number of semio-spatial objects as, most notably, the boulevard, considered as an intermediate level of public space, located between the village square and the coffee house presiding over what Habermas called the public sphere. Urbanity originates as a scene on which the gaze, well before the word, mediates between the sexes, the classes, the cultures, and other avatars of otherness. However, this scenario is seriously upset but the emergence of the cell phone and other technical devices, as well as by the movement of populations. (shrink)

The developing academic field of machine ethics seeks to make artificial agents safer as they become more pervasive throughout society. In contrast to computer ethics, machine ethics is concerned with the behavior of machines toward human users and other machines. This study aims to use an action-based ethical theory founded on the combinational aspects of deontological and teleological theories of ethics in the construction of an artificial moral agent (AMA).,The decision results derived by the AMA are acquired via fuzzy logic (...) interpretation of the relative values of the steady-state simulations of the corresponding rule-based fuzzy cognitive map (RBFCM).,Through the use of RBFCMs, the following paper illustrates the possibility of incorporating ethical components into machines, where latent semantic analysis (LSA) and RBFCMs can be used to model dynamic and complex situations, and to provide abilities in acquiring causal knowledge.,This approach is especially appropriate for data-poor and uncertain situations common in ethics. Nonetheless, to ensure that a machine with an ethical component can function autonomously in the world, research in artificial intelligence will need to further investigate the representation and determination of ethical principles, the incorporation of these ethical principles into a system’s decision procedure, ethical decision-making with incomplete and uncertain knowledge, the explanation for decisions made using ethical principles and the evaluation of systems that act based upon ethical principles.,To date, the conducted research has contributed to a theoretical foundation for machine ethics through exploration of the rationale and the feasibility of adding an ethical dimension to machines. Further, the constructed AMA illustrates the possibility of utilizing an action-based ethical theory that provides guidance in ethical decision-making according to the precepts of its respective duties. The use of LSA illustrates their powerful capabilities in understanding text and their potential application as information retrieval systems in AMAs. The use of cognitive maps provides an approach and a decision procedure for resolving conflicts between different duties.,This paper suggests that cognitive maps could be used in AMAs as tools for meta-analysis, where comparisons regarding multiple ethical principles and duties can be examined and considered. With cognitive mapping, complex and abstract variables that cannot easily be measured but are important to decision-making can be modeled. This approach is especially appropriate for data-poor and uncertain situations common in ethics. (shrink)

This chapter contains sections titled: The Idea of an Exceptionless Moral Norm The Role of Exceptionless Precepts in Moral Thinking Exceptionless Rules and Consequentialism The Casuistry of Exceptionless Rule Approaches References.

Frank Hindriks has attempted to derive a variant of Timothy Williamson’s knowledge rule for assertion on the basis of a more fundamental belief expression analysis of that speech act. I show that his attempted derivation involves a crucial equivocation between two senses of ‘must,’ and therefore fails. I suggest two possible repairs; but I argue that even if they are successful, we should prefer Williamson’s fully general knowledge rule to Hindriks’s restricted moral norm.

Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace (...) formula, one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). (shrink)

Pavel Materna proposed valuable explications of concept and conceptual system. After their introduction, we contrast conceptual systems with (a novel notion of) derivation systems. Derivation systems differ from conceptual systems especially in including derivation rules. This enables us to show close connections among the realms of objects, their concepts, and reasoning with concepts.

In a quiet London office, a software designer muses on the algorithms that will make possible the risk flags to be visualized on the screens of border guards from Heathrow to St Pancras International. There is, he says, ‘real time decision making’ – to detain, to deport, to secondarily question or search – but there is also the ‘offline team who run the analytics and work out the best set of rules’. Writing the code that will decide the association rules (...) between items of data, prosaic and mundane – flight route, payment type, passport – the analysts derive a novel preemptive security measure. This paper proposes the analytic of the data derivative – a visualized risk flag or score drawn from an amalgam of disaggregated fragments of data, inferred from across the gaps between data and projected onto an array of uncertain futures. In contrast to disciplinary and enclosed techniques of collecting data to govern population, the data derivative functions via ‘differential curves of normality’, imagining a range of potential futures through the association rule, thus ‘opening up to let things happen’ ( Foucault 2007 ). In some senses akin to the risk orientation of the financial derivative, itself indifferent to actual underlying people, places or events by virtue of modulated norms, the contemporary security derivative is not centred on who we are, nor even on what our data say about us, but on what can be imagined and inferred about who we might be – on our very proclivities and potentialities. (shrink)

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a rule is (...) derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

In this paper Section 1 distinguishes between two modes of interpreting legal rules: rehearsal and discourse, arguing that the former takes priority over the latter in law, as in many other contexts. Section 2 offers two arguments that following a legal rule in the rehearsing mode presents a riddle. The first argument develops from law, and submits that legal rules do not tell us anything, because they are tautological. The second one develops from philosophy (Wittgenstein's later works), confronting us (...) with the paradox that incompatible courses of action may be derived from any rule. My solution presents a theory of rules as icons (Section 3). I use “icon” rather than “picture,” partly to avoid confusion with what is known among philosophers as “the picture theory of meaning.” Interpretation in the rehearsing mode hinges on imagination: imagining oneself in the space of reasons for action rather than reasoning oneself. In this act of imagination, we project ourselves into the rule in ways that are similar to the way we grasp the sense of paintings, music, stories, or poems. Finally (Section 4) I will defend the position that my view solves the puzzles in the second section, by arguing (a) that it is a better account of what Wittgenstein wrote than two competing theories (intuitionism and conventionalism), and (b) that it provides a more satisfactory account of how lawyers deal with legal rules in actual practice. (shrink)

The connection between the rules and derivations of Gentzen’s calculiNJandLJwill be explained by several steps (i.e., systems), and an analysis of the well-known problems of the connection between reduction steps of normalization and cut elimination, from Zucker (1974) and Urban (2014), will be given.

What are the principles that ground our moral obligations? One obvious answer is that they are prescriptive rules that govern conduct by imposing obligations much like (certain) legal rules govern conduct by imposing legal obligations. This "rule conception of moral principles" merits our attention for at least three reasons. It's the obvious and most straightforward way to develop the analogy between morality and law, and between moral principles and legal rules. It appears to fit some prominent theories of morality (...) and justice (e.g., Brad Hooker's rule-consequentialism, David Gauthier's contractarianism, and John Rawls's contractualism), and thus to possibly derive support from its fit with them. And it promises to account for the ability of moral principles to do the explanatory, counterfactual-supporting, and necessity-grounding work that they do. Moreover, it seems to be an integral part of some prominent theories (e.g., those of Gauthier, Kant, and Christine Korsgaard). However, I will argue that we should reject it. Moreover, by warranting the rejection of an obvious rival, the arguments presented herein strengthen the case for a dispositional (or powers) conception of moral principles, and perhaps for certain other conceptions, as well. (shrink)

Among moral rules, Some are seen as having inherent moral authority, Others as sustained by our decision and conceivably susceptible of replacement "salva moralitate". But how can a "chosen" rule have moral authority? one familiar (utilitarian) way: the rule is justified by the supposed consequences of having it not by its content: its authority for us derives from our (revisable) factual judgments as to these consequences. This article seeks to explore another way: we (individual or community) adopt a (...) rule as a symbolic way of expressing a moral conviction. The impulsion here may be to express our conviction to others; or to ourselves--To realize the theoretical conviction in our living (as such a conviction demands of us). Rules justified in terms of "respect for life" are sustained as symbolic rules. Other examples of such rules are considered, Along with questions about the practice of adopting rules as symbols. (shrink)

In intersystemic cases, a court applies the law of a foreign system. Scholars have argued that the court ought to use the interpretive methodology of the foreign system’s courts. I argue against that intuitive position. First, interpretive methodology is not bound up with primary rights and duties such that it constitutes substantive law for conflict of laws purposes. Second, although interpretive methodology has epistemic value and may affect case outcomes, a given methodology might not have the same epistemic value or (...) the same effect on outcomes for differently situated interpreters. Further, the approach that the foreign judges take to interpreting their own law is necessarily anchored to the foreign system’s rule of recognition, which is not true of the approach of external judges. Descriptive facts might align such that external interpreters would have to use the internal methodology to identify the applicable law, but that’s an empirical question the answer to which will vary from case to case. (shrink)

We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction to atomic formulas relieves the need to concern logical rules in the (...) derivation. (shrink)

It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the time-reversal symmetry of quantum equations of motion. The derivation is based on a simple functional equation that takes into account properties of probability, as well as the linearity and time-reversal symmetry of quantum equations of motion. The derivation presented in this (...) work also allows to determine certain limits to applicability of the Born Rule. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

Inference to the best explanation (IBE) is considered to be the main means of discovery and justification of scientific hypotheses and theories. The article investigates this inference and its relationship to the main kinds of inference: deduction, induction and abduction. IBE has an abductive inference mechanism, but, contrary to abduction, infers not a possible, but a true conclusion. IBE is an inductive inference, because it is underdetermined by the rules of deduction and by evidence. The article claims that despite its (...) abductive and inductive features which demonstrate that it is not and cannot be deductive inference, IBE nevertheless makes pretense to an absolute truth of its inference, i.e. claims for an almost deductive validity. (shrink)

This chapter concerns Hume's account in Book I of the Treatise of Human Nature (1739) of the operation of ‘general rules’. It considers their relation to conceptions of regularity, probability, circumstance, and experience that obtained in early modern logic and natural philosophy, taking occasion to reflect upon the significance of Hume's claim, in the Enquiry Concerning Human Understanding, that natural philosophy and moral philosophy are ‘derived from the same principles’. It concludes by suggesting that a number of Hume's essays are (...) structured as reflections and refinements upon commonly-held general rules. (shrink)

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of (...) generalizing Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

For the first time in over thirty years a revolution is happening in phonology, with the advent of constraint-based approaches which directly oppose the rule-and-derivation tradition of mainstream Generative Phonology. The success of Optimality Theory and the rapidity of its spread since its official launch in 1993 is remarkable even by the general standards of post-1950s linguistics. Many phonologists appear to have been caught up in the whirlwind, as witnessed by the substance of many current working papers and conferences (...) the world over, and the recent contents of well-established journals. Two questions naturally arise: What is Optimality Theory about? In what way is Optimality Theory superior to traditional theory, if indeed it is? In this book, leading specialists and active researchers address these issues directly, and focus deliberately on the evaluation of the two competing approaches rather than on simple displays of their applicability to limited bodies of data. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice. (shrink)

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of (...) generalizing Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

Animal-derived constituents are frequently used in anaesthesia and surgery, and patients are seldom informed of this. This is problematic for a growing minority of patients who may have religious or secular concerns about their use in their care. It is not currently common practice to inform patients about the use of animal-derived constituents, yet what little empirical data does exist indicates that many patients want the opportunity to give their informed consent. First, we review the nature and scale of the (...) problem by looking at the groups who may have concerns about the use of animal-derived constituents in their care. We then summarise some of the products used in anaesthesia and surgery that can contain such constituents, such as anaesthetic drugs, surgical implants and dressings. Finally, we explore the problem of animal-derived constituents and consent using Beauchamp and Childress’ four principles approach, examining issues of autonomy, beneficence, nonmaleficence and justice. Disclosing the use of animal-derived constituents in anaesthesia and surgery is warranted under Beauchamp and Childress’ four principles approach to the problem. Although there exist systemic and practical challenges to implementing this in practice, the ethical case for doing so is strong. The Montgomery ruling presents additional legal reason for disclosure because it entails that patients must be made aware of risks associated with their treatment that they attach significance to. (shrink)

Born’s quantum probability rule is traditionally included among the quantum postulates as being given by the squared amplitude projection of a measured state over a prepared state, or else as a trace formula for density operators. Both Gleason’s theorem and Busch’s theorem derive the quantum probability rule starting from very general assumptions about probability measures. Remarkably, Gleason’s theorem holds only under the physically unsound restriction that the dimension of the underlying Hilbert space \ must be larger than two. (...) Busch’s theorem lifted this restriction, thereby including qubits in its domain of validity. However, while Gleason assumed that observables are given by complete sets of orthogonal projectors, Busch made the mathematically stronger assumption that observables are given by positive operator-valued measures. The theorem we present here applies, similarly to the quantum postulate, without restricting the dimension of \ and for observables given by complete sets of orthogonal projectors. We also show that the Born rule applies beyond the quantum domain, thereby exhibiting the common root shared by some quantum and classical phenomena. (shrink)

Mental content normativists hold that the mind’s conceptual contents are essentially normative. Many hold the view because they think that facts of the form “subject S possesses concept c” imply that S is enjoined by rules concerning the application of c in theoretical judgments. Some opponents independently raise an intuitive objection: even if there are such rules, S’s possession of the concept is not the source of the enjoinment. Hence, these rules do not support mental content normativism. Call this the (...) “Source Objection.” This paper refutes the Source Objection, outlining a key strand of the relationship between judgments and their contents in the process. Theoretical judgment and mental conceptual content are equally the source of enjoinment; norms for judging with contents do not derive from one at the expense of the other. (shrink)

The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of the (...) GBR. Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution. (shrink)

Are norms of inquiry in tension with epistemic norms? I provide a (largely) negative answer, turning to a picture of epistemic practices as rule-governed games. The idea is that, while epistemic norms are correctness standards for the attitudes involved in epistemic games, norms of inquiry derive from the aims of those games. Attitudes that, despite being epistemically correct, are inadvisable regarding the goals of some inquiry are just like bad (but legal) moves in basketball or chess. I further consider (...) cases in which the aims of inquiry recommend breaking epistemic norms. I compare them to strategic infractions, which are common in many coherent games. Finally, I explore the connections between rules and aims in games and in inquiry. I show that in both cases respecting the rules is constitutively required for satisfying the aims of the practice. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)