In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin of an electron (along some axis) to be 100. We argue that the disturbance caused by the weak measurement, while small, is sufficient to significantly affect the measurement result, and that this is the most reasonable explanation of anomalous (...) class='Hi'>weak values. (shrink)

Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y?”, may result in different answers depending on which (...) methods are used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al., the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned. (shrink)

We clarify the significance of quasiprobability in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov’s weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. (...) We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality. (shrink)

We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values—the output of weak measurements—goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall (...) the usual form of property ascription, based on the eigenstate-eigenvalue link and the existence of “elements of reality”. We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system. (shrink)

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that “strange” weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from (...) the multiple-time application of Lüders’ Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. (...) As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given. (shrink)

A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. (...) I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations. (shrink)

Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner, Kastner seems to take us many years backwards in the the debate, casting doubt on the very term “weak value” and the meaning of weak measurements. Kastner appears to ignore both the (...) basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by projective measurements, without the need of employing weak measurements. (shrink)

ABSTRACT: A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained (...) from the multiple-time application of Luders' Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for (...) a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

Ben-Israel and Vaidman have raised objections to my arguments that there are cases where a quantum mechanical weak value can be said not to represent the system to which it pertains. They are correct in pointing out that some of my conclusions were too general. However, for weak values of projection operators my conclusions still stand.

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. The (...) generalized law is illustrated for two interesting choices of post-selection. (shrink)

The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of modular momentum associated with such phenomena cannot be directly observed, it has been suggested that effects induced by this exchange can be measured experimentally using weak measurements of pre- and post-selected ensembles of particles. This paper reports on such an optical experiment that yielded measured weak (...) class='Hi'>values that were consistent with the theoretical prediction of an effect induced by a non-local exchange of modular momentum. (shrink)

Svensson argued that the concept of the weak value of an observable of a pre- and post-selected quantum system cannot be applied when the expectation value of the observable in the initial state vanishes. Svensson’s argument is analyzed and shown to be inconsistent using several examples.

This paper evaluates a recent method proposed by Jeremy Gwiazda for calculating the value of gambles that fail to have expected values in the standard sense. I show that Gwiazda’s method fails to give answers for many gambles that do have standardly defined expected values. However, a slight modification of his method (based on the mathematical notion of the ‘Cauchy principal value’ of an integral), is in fact a proper extension of both his method and the method of (...) ‘weak expectations’. I show that this method gives an appropriate value when the ‘tails’ of the gambles that are eliminated in the truncation are ‘stable’, but that the value is not appropriate when the tails are not stable. I do not attempt to give an argument for the use of this method, but just note that it is more general than Gwiazda’s method, and is mathematically quite natural. (shrink)

In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming that every logic can be presented in a two-valued fashion. In this paper, we provide two-valued semantics for the Weak Kleene logics and for a number of four-valued subsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking (...) at them as Logics of Formal Inconsistency and Logics of Formal Underterminedness. Our aim with this work, rather than arguing for Suszko’s thesis, is to show that two-valued presentations of these peculiar logics enlighten the non-standard behavior of their logical connectives. More specifically, the two-valued presentations of paraconsistent logics illustrate and clarify the disjunctive flavor of the conjunction, and dually, the two-valued presentations of paracomplete subsystems of Weak Kleene logics reveal the conjunctive flavor of the disjunction. (shrink)

What does it mean that an object has instrumental value? While some writers seem to think it means that the object bears a value, and that instrumental value accordingly is a kind of value, other writers seem to think that the object is not a value bearer but is only what is conducive to something of value. Contrary to what is the general view among philosophers of value, I argue that if instrumental value is a kind of value, then it (...) is a kind of extrinsic final value. (shrink)

This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each system, we provide a (...) three-valued Kripke-style semantics with and without star operation . We prove soundness and completeness theorems in each case. Note that wB logics may be equivalent to logics with Baaz’s projection Δ. We finally introduce the G3 and the S53pB both with Δ and show that they are equivalent to G3wB and S53wB, respectively. (shrink)

We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call (...) weak stratified. Finally, we show weak stratified semantics coincides exactly with the three-valued approach on stratifiable programs, though the three-valued version is generally applicable, and does not require stratification assumptions. (shrink)

Weak values are average quantities, therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal and Sonego :1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a (...) class='Hi'>weak value. It also leads naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of ‘subquantum’ theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle. (shrink)

Professional environmental ethics arose directly out of the interest in the environment created by Earth Day in 1970. At that time many environmentalists, primarily because they had read Aldo Leopold’s essay, “The Land Ethic,” were convinced that the foundations of environmental problems were philosophical. Moreover, these environmentalists were dissatisfied with the instrumental arguments based on human use and benefit—which they felt compelled to invoke in defense of nature—because they thought these arguments were part of the problem. Wanting to counter instrumental (...) arguments in some way with non- or even anti-instrumental arguments, and unable to think of anything else to say, they began wistfully suggesting that perhaps nature had or ought to have rights. When professional environmental ethics came into its own in the early 1980s, rights for nature were one of the first subjects to be debated in detail. Unfortunately, however, no one could come up with a theory to support such rights attributions. Nevertheless, because rights had been invoked by environmentalists to challenge the preeminent role of instrumental value arguments, and because the field of environmental ethics developed in support of environmental concerns and arguments, environmental ethicists turned to an examination of noninstrumental or intrinsic value arguments for the preservation of nature. (shrink)

In this paper we focus on some new normativist positions and compare them with traditional ones. In so doing, we claim that if normative judgments are involved in determining whether a condition is a disease only in the sense identified by new normativisms, then disease is normative only in a weak sense, which must be distinguished from the strong sense advocated by traditional normativisms. Specifically, we argue that weak and strong normativity are different to the point that one (...) ‘normativist’ label ceases to be appropriate for the whole range of positions. If values and norms are not explicit components of the concept of disease, but only intervene in other explanatory roles, then the concept of disease is no more value-laden than many other scientific concepts, or even any other scientific concept. We call the newly identified position “value-conscious naturalism” about disease, and point to some of its theoretical and practical advantages. (shrink)

The theory of weak measurements developed by Aharonov and coworkers has been applied by them and others to several interesting problems in which the system of interest is both pre- and post-selected. When the probability of successful post-selection is very small the prediction for the weak value of the measured quantity is often “bizarre” and sometimes controversial, lying outside the range of possibility for a classical system or for a quantum system in the absence of post-selection (e.g. negative (...) kinetic energies associated with particles found immediately after the weak measurement deep inside a classically forbidden region). In Bohmian mechanics a quantum particle is postulated to be a point-like particle which is always accompanied by a wave which probes its environment and guides its motion accordingly. Hence, from the point of view of this theory, it is natural to ask whether the measured weak value under consideration is a property of the point-like particle or of the wave (or of both) and what, if anything, it is that is actually being measured. In this paper, weak measurements of position, momentum and kinetic energy are considered for very simple case studies with these questions in mind. (shrink)

Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.

Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.

Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra (...) WK; we also prove that every involutive bisemilattice is representable as the Płonka sum over a direct system of Boolean algebras. We then study PWK from the viewpoint of AAL. We show that \ is not the equivalent algebraic semantics of any algebraisable logic and that PWK is neither protoalgebraic nor selfextensional, not assertional, but it is truth-equational. We fully characterise the deductive filters of PWK on members of \ and the reduced matrix models of PWK. Finally, we investigate PWK with the methods of second-order AAL—we describe the class \ of PWK-algebras, algebra reducts of basic full generalised matrix models of PWK, showing that they coincide with the quasivariety generated by WK—which differs from \—and explicitly providing a quasiequational basis for it. (shrink)

Suppose that A and B are two kinds of goods such that more of each is better than less. A is strongly superior to B if any amount of A is better than any amount of B. It is weakly superior to B if some amount of A is better than any amount of B. There are many examples of these relations in the literature, sometimes under the labels “higher goods” and “discontinuity.” The chapter gives a precise and generalized statement (...) of Strong and Weak Superiority and discusses different ways in which these relations can be relevant to the aggregation of welfare. It also proves a number of general results. One of the results gives rise to a dilemma: It can be used as an argument against the existence of value superiority or, alternatively, as an argument against the view that superiority entails a radical difference in value. (shrink)

Weak panpsychism, the view that mindlike qualities are wide-spread in nature, has recently been argued for by the prominent ecofeminist Val Plumwood and has been used by her to ground an ethic of respect for nature. This ethic advocates a principle of respect for difference, the rejection of moral hierarchy and the inclusion of plants, mountains, rivers and ecosystems within the moral community. I argue that weak panpsychism cannot, convincingly, justify the rejection of moral hierarchy, as it is (...) compatible with it. Also the intentional criterion of mind, employed by weak panpsychism, which includes teleology, has the counter-intuitive implication of giving machines moral status. I cast doubt on the claims that (i) intentionality is a necessary condition for moral status and that (ii) it is sufficient for the ascription of agency. It is suggested that any account of intentionality that allows it to be predicated of mountains, rivers etc. would be widely, and correctly regarded as a reduction of that account. Finally an aesthetic reinterpretation of weak panpsychism is offered. (shrink)

The phenomenon of weakness of will – not doing what we perceive as the best action – is not recognized by neoclassical economics due to the axiomatic assumptions of the revealed preference theory (RPT) that people do what is best for them. However, present bias shows that people have different preferences over time. As they cannot be compared by the utility measurements, economists need to normatively decide between selves (short- versus long-term preferences). A problem is that neoclassical economists perceive RPT (...) as value-free and incorporate present bias within the economic framework. The axiomatic assumption that people do what is best for them leads to theoretical and practical dilemmas. This work examines weakness of will to resolve some shortcomings of RPT. The concept of intention is used to provide multiple self conception with the framework to decide between selves, which had not been done before. The paper concludes that individuals should not always follow their revealed preferences (desires) but the intentions (reason) because the latter indicates what people really want. (shrink)

Adversity awakens people to the value of weakness and its role in spiritual growth. Qualitative research was conducted to ascertain ways in which adversity impacts spiritual growth. Semi-structured interviews exploring the lives of 12 mature Christians examined how God worked through adversity to bring depth. Three primary categories of spiritual transformation emerged: Awareness of self, humanity, God, and God’s grace; Openness to engage tension as a catalyst of growth, in accepting and extending grace to others, and in partnering with God; (...) and Realism about the time, process, and pain involved in spiritual growth. Through crises, patterns of self-reliance fail and are exposed, awakening believers to the limits and fallenness of human life in such a way that they gain a greater appreciation for the role weakness plays in catalyzing dependence on God in everyday life leading to deeper spiritual maturity. (shrink)

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. (...) This $6$-valued logic, unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

This paper is a critique of the present mode of capitalist democracy from the ethico-moral viewpoint. The crisis of values is identified as the great bane of free market-led globalization. This trend has aggravated worldwide inequality, promoted terrorism and violence, created psychological anomie and triggered eco logical disasters. Only a few business interests in the wealthier economies are gaining at the expense of humankind. The moral dimension of the government's role has been undermined by such profit-making free market gospel. (...) The author contends that more than beingjust secular, democracy is a pre-social moral force and, as such, is perceived more proximately in the religious temper of a non-industrial society than in a mass industrial society. In the latter democracy is almost a farce with the periodic ritual of public voting as its main act. The paper castigates the global economy and global media which cleverly mastermind our lives, and pleads for a change of values which will make humans self-conscious and will restore their autonomy. (shrink)

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth–functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a “weak” interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure “statability” operators are also examined.

This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, (...) we show how to interpret the theory BTFA in Robinson's theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q. (shrink)

The design argument for God’s existence was critically assessed when in the growth of modern science the cognitive value of teleological categories was called into question. In recent discussions dealing with anthropic principles there has appeared a new version of the design argument, in which cosmic design is described without the use of teleological terms. The weak anthropic principle (WAP), a most critical version of all these principles, describes the fine-tuning of physical parameters necessary to the genesis of carbon-based (...) life. Consequently, a new version of the philosophical design argument can be developed on the basis of the weak anthropic principle.(edited). (shrink)

This paper makes first steps toward a systematic investigation of how pertinence to topic contributes to determine deductively valid reasoning along with preservation of designated values. I start from the interpretation of Weak Kleene Logic WKL as a reasoning tool that preserves truth and topic pertinence, which is offered by Jc Beall. I keep Beall’s motivations and I argue that WKL cannot meet them in a satisfying way. In light of this, I propose an informal definition of a (...) topic-sensitive logic and I proceed to turn it into a formal one by deploying the topic-algebraic framework from the Topic-Sensitive Intentional Modalities project by Francesco Berto. I apply the framework in order to define semantically a ‘classical topic-sensitive logic’ CTSL that meets Beall’s motivations and proves topic-sensitive. Then, I prove results that connect CTSL and any possible topic-sensitive logic to the tradition of containment logics and provide a unification tool for a wide range of recent proposals in philosophical logic. A topic-theoretical interpretation of WKL is then offered without prejudice to the fact that the logic is not topic-sensitive. Finally, the paper discusses some conceptual issues and research perspectives. (shrink)

Extensive measurement is called weak if the axioms allow two objects to have the same scale value without being indifferent with respect to the order. Necessary and/or sufficient conditions for such representations are given. The Archimedean and the non-Archimedean case are dealt with separately.

Economic environmental valuation remains a much debated and contested issue. Concerns have been voiced that it is unable to capture the manifold immaterial values of ecosystems due to conceptual and methodological issues. Thus, additional value categories (social values) as well as novel valuation approaches like deliberative (monetary) valuation are areas of growing interest, yet the theoretical foundations are rather weak. Against this background, this article aims to develop a consistent conceptual framework for making sense of social (...) class='Hi'>values in economic environmental valuation. Based on a holistic view of society and individuals, the role of institutions, the social environment, culture and transcendental values is emphasised. To synthesise diverging concepts of value into an economic concept and to account for the multidimensionality of social values, the framework consists of three spheres: social, natural and contextual. The novel framework demonstrates that social values may be integrated into a preference-based utility framework when denoting a holistic understanding of social preferences and human embeddedness in nature and society. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest (...) in exploring the foundations of multialgebras applied to the study of logic systems. It is well known from universal algebra that, for every signature \, there exist algebras over \ which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of \-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms. Equivalently, the forgetful functor, from the category of \-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor \, from the category of \-multialgebras to Set, does not have a left adjoint. In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices, there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that \ does not have a left adjoint. (shrink)

This study aims to develop and defend an account of practical rationality and intention that explains how weakness of the will is conceptually possible. I first present two sceptical arguments against the possibility of weakness and then distinguish two different responses to scepticism that defends its possibility. Both sceptical arguments are motivated by what many have believed is an analogy between theoretical and practical reasoning. This analogy holds that the conclusion of practical reasoning is an intention just as the conclusion (...) of theoretical reasoning is a belief. The particular version held by what I call the Socratic theorists claims, in addition, that the value of desirability is transferred from premisses to conclusion in practical reasoning, just as probability is transferred from premisses to conclusion in theoretical reasoning. One example of an author who takes the analogy as a basic premise and seek to explain how weakness of the will still may be possible, is Donald Davidson. Critics of Davidson object that the the kinds of difficulties that his account runs into shows that the Socratic version of the analogy must be false; not only is this account phenomenologically implausible, it also exaggerates the degree of irrationality of the weak agent. In this study I suggest the possibility of a weaker version of the Davidsonian account. The main source of difficulty for the Davidsonian account, I argue, may not be its reliance on the Socratic version of the analogy between practical and theoretical reasoning, but rather its particular understanding of this analogy in terms of an analogy between practical and inductive-statistical reasoning. This understanding may lead one to accept too “rationalistic” a picture of the reasoning processes behind weakness of the will which, in effect, may make the account vulnerable to objections that it is phenomenologically implausible and exaggerates the irrationality of the weak agent. The weaker version of the Davidsonian account that I propose, ties in the account of weakness with the notions of “satisficing” and “default reasoning”. Although it preserves the central idea of the stronger version that intentions are unconditional evaluative judgements, it proposes a different view of the contents of these judgements, as well as of the reasoning process that lie behind them. It is not difficult to motivate this weaker view: given our human finitary predicament, both satisficing and default reasoning seem to be likely results of an optimal trade-off between the speed and reliability of our computational processes. The question is how these notions may shape the concepts we use to understand weakness of the will. I argue that if we modify the account usually ascribed to Davidson in the light of these notions, the result is a less rationalistic picture of weakness of the will. The gains are more phenomenological credibility as well as a less extreme view of the degree of irrationality involved. (shrink)

In his work on the moral status of nonhuman animals, David Clough rejects the theory of anthropocentrism while accepting its practical importance. He thus leaves theology in a dilemma: reflection on animals should not support the very concept that practical approaches to animals require. An alternative is a “weak anthropocentrism” along the line of Gianni Vattimo's “weak ontology.” A weak anthropocentrism is better suited to a Neoplatonic theory of participation, not the traditional framework of creation out of (...) nothing, and it also can give new meaning to the idea of imago Dei and a Christocentric affirmation of nonhuman value. (shrink)

This article introduces the three-valuedweakly-intuitionistic logicI 1 as a counterpart of theparaconsistent calculusP 1 studied in [11].I 1 is shown to be complete with respect to certainthree-valued matrices. We also show that in the sense that any proper extension ofI 1 collapses to classical logic.The second part shows thatI 1 is algebraizable in the sense of Block and Pigozzi (cf. [2]) in a way very similar to the algebraization ofP 1 given in [8].

An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all its odd-valued extensions \(\mathbf{RM}_{2n\mathord{-}1}\) satisfy the weak variable sharing property. It is also shown that a proof to the effect that the "fuzzy" version of the relevant logic R satisfies the property is incorrect.

Kolodny and MacFarlane have made a pioneering contribution to our understanding of how the interpretation of deontic modals can be sensitive to evidence and information. But integrating the discussion of information-sensitivity into the standard Kratzerian framework for modals suggests ways of capturing the relevant data without treating deontic modals as “informational modals” in their sense. I show that though one such way of capturing the data within the standard semantics fails, an alternative does not. Nevertheless I argue that we have (...) good reasons to adopt an information-sensitive semantics of the general type Kolodny and MacFarlane describe. Contrary to the standard semantics, relative deontic value between possibilities sometimes depends on which possibilities are live. I develop an ordering semantics for deontic modals that captures this point and addresses various complications introduced by integrating the discussion of information-sensitivity into the standard semantic framework. By attending to these complexities, we can also illuminate various roles that information and evidence play in logical arguments, discourse, and deliberation. (shrink)

The standard account of weakness of will identifies it with akrasia, that is, with action against one's best judgment. Elsewhere I have argued that weakness of will is better understood as over-readily giving up on one's resolutions. Many cases of weak willed action will not be akratic: in over-readily abandoning a resolution an agent may well do something that they judge at the time to be best. Indeed, in so far as temptation typically gives rise to judgment shift -- (...) to a tendency to change one's judgment so that one values the tempting option as the best -- weak willed action will typically be akratic. But conversely, strong willed action now looks as though it will be akratic. I argue though that it need not be, once we distinguish between actual judgment, and dispositions to judge. Within this framework, the issue of inverse akrasia looks rather different. I argue that whilst Huckleberry Finn plausibly does show weakness of will in abandoning his resolve to turn Jim in, it is far from clear that he is akratic: a point brought out well in Twain's later additions to the text. Whilst cases of inverse akrasia are clearly theoretically possible, I suggest that, given cognitive dissonance mechanisms, they are unlikely to be very common. (shrink)

Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...) it exhibits, and use this to define a notion of ‘weak expectation’ that can give values to the Pasadena game and many others, though not to all games that fail to have a strong expectation in the standard sense. CiteULike Connotea Del.icio.us What's this? (shrink)