By weakening an inference rule satisfied by logic daC, we define a new paraconsistent logic, which is weaker than logic \ and G′ 3, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism. Besides, daC ' helps to understand the relationships among other logics, in particular daC, \ and PH1.

Recently, several authors have pointed out that substructural logics are adequate for developing naive theories that represent semantic concepts such as truth. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, nowhere in the substructural literature has anyone proposed rejecting the structural rule of weakening, while accepting the other rules. Some theorists have even argued that this task was not possible, since weakening plays no role in the derivation of semantic paradoxes. In (...) this article, I introduce a theory for naive truth based on the logic resulting from dropping the rule of weakening from classical logic, and maintaining the other structural rules. (shrink)

Opioid and sedative use are common ‘active’ practices in the provision of mainstream palliative care services, and are typically distinguished from euthanasia on the basis that they do not shorten survival time. Even supposing that they did, it is often argued that they are justified and distinguished from euthanasia via appeal to Aquinas’ Doctrine of Double Effect. In this essay, I will appraise the empirical evidence regarding opioid/sedative use and survival time, and argue for a position of agnosticism. I will (...) then argue that the Doctrine of Double Effect is a useful ethical tool but is ultimately not a sound ethical principle, and even if it were, it is unclear whether palliative opioid/sedative use satisfy its four criteria. Although this essay does not establish any definitive proofs, it aims to provide reasons to doubt—and therefore weaken—the often-claimed ethical distinction between euthanasia and palliative opioid/sedative use. (shrink)

In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. (...) After that, we define Kripke-style semantics based on possible worlds and derive from it many-valued semantics based on truth-functional valuations for these two paraconsistent logics. Finally, we demonstrate that this model-theoretic inference system is adequate—sound and complete with respect to the axiomatic da Costa-like systems for these two logics. (shrink)

Despite suggestions that the end of metaphysics leaves us with nothing but history, essential questions about the place of history in a post-metaphysical culture have been neglected. In one sense history "weakens" as the scope for "realism" or a teleological master narrative fall away. But it invites overreaction to suggest that history becomes a "process of weakening" insofar as things have come to be as they are not as the resultants of full, meaningful origins, but only through the "dread (...) accident" of the historical process. The world that has resulted from history is the only one we have, and it weighs on us; in that sense history does not weaken but strengthens. Still, the historical process enveloping us is not Hegelian and necessary but weak and contingent, its outcomes subject to further contest. Conversely, although truth is weak, finite, and provisional, it is not merely consensual or relative precisely because it is historical. To grasp the sense it which history both weakens and strengthens enables us to grasp the scope for learning more deeply from our historical experience. A fuller range of historical questions about modernity would enable us better to understand the ongoing dangers and possibilities of modern politics. (shrink)

. In this paper we present a proposal that (i) could validate more relations in the square than those allowed by classical logic (ii) without a modification of canonical notation neither of current symbolization of categorical statements though (iii) with a different but reliable semantics.

We examine the performance of some standard causal discovery algorithms, both constraint-based and score-based, from the perspective of how robust they are against failures of the Causal Faithfulness Assumption. For this purpose, we make only the so-called Triangle-Faithfulness assumption, which is a fairly weak consequence of the Faithfulness assumption, and otherwise allows unfaithful distributions. In particular, we allow violations of Adjacency-Faithfulness and Orientation-Faithfulness. We show that the PC algorithm, a representative constraint-based method, can be made more robust against unfaithfulness by (...) incorporating elements of the GES algorithm, a representative score-based method; similarly, the GES algorithm can be made less error-prone by incorporating elements of the conservative PC algorithm. As our simulations demonstrate, the increased robustness seems to matter even when faithfulness is not exactly violated, for with only finite sample, distributions that are not exactly unfaithful may be sufficiently close to being unfaithful to make trouble. (shrink)

A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of (...) Berman’s variety \. Every linearly ordered frame is logically equivalent to its dual algebra. It is proved that \ is the logic of a nine-element distributive lattice with a negation. Moreover, \ is embedded into \ by Glivenko’s double-negation translation. (shrink)

Much contemporary debate on the nature of mechanisms centers on the issue of modulating negative causes. One type of negative causability, which I refer to as "causation by absence," appears difficult to incorporate into modern accounts of mechanistic explanation. This paper argues that a recent attempt to resolve this problem, proposed by Benjamin Barros, requires improvement as it overlooks the fact that not all absences qualify as sources of mechanism failure. I suggest that there are a number of additional types (...) of effects caused by absences that need to be incorporated to account for the diversity of causal connections in the biological sciences. Furthermore, it is argued that recognizing natural variability in mechanisms, such as attenuation, leads to some interesting line-drawing issues for contemporary philosophy of mechanisms. (shrink)

The essays in Weakening Philosophy, from leading figures such as Umberto Eco and Charles Taylor, introduce his ideas to a wider audience.

. This unique series features the actual keyboard parts transcribed as played on the artists' original recordings, along with sound-alike CD backing tracks so you can master the keyboard part and then play-along like a pro! The audio CD is playable on any CD player, and also enhanced so PC and Mac users can adjust the recording to any tempo without changing pitch. Includes 8 Elvis blockbusters: All Shook Up * A Big Hunk O' Love * Blue Suede Shoes * (...) Can't Help Falling in Love * Don't Be Cruel * I Want You, I Need You, I Love You * Jailhouse Rock * Love Me. (shrink)

My essay ‘Weakening the ethical distinction between euthanasia, palliative opioid use and palliative sedation’ has recently generated some critique which I will attempt to address in this response. Regarding the empirical question of whether palliative opioid and sedative use shorten survival time, Schofield et al raise the three concerns that my literature review contains a cherry-picking bias through focusing solely on the palliative care population, that continuous deep palliative sedation falls beyond the scope of routine palliative care, and that (...) my research may contribute to opiophobia and be harmful to palliative care provision globally. Materstvedt argues that euthanasia ‘ends’ rather than ‘relieves’ suffering and is not a treatment, and that the arguments in my essay are therefore predicated on a ‘category mistake’ and are a non-starter. Symons and Giebel both raise the concern that my Kantian and Millian interpretation of the Doctrine of Double Effect is anachronistic, and that when interpreted from the contemporaneous perspective of Aquinas it is a sound ethical principle. Giebel also argues that palliative opioid and sedative use do meet the Doctrine of Double Effect’s four criteria on this Thomistic account, and that it does not contradict the Doctrine of the Sanctity of Human Life. In this response I will explore and defend against most of these claims, in doing so clarifying my original argument that the empirical and ethical differences between palliative opioid/sedative use and euthanasia may not be as significant as often believed, thereby advancing the case for euthanasia. (shrink)

Much contemporary debate on the nature of mechanisms centers on the issue of modulating negative causes. One type of negative causability, which I refer to as “causation by absence,” appears difficult to incorporate into modern accounts of mechanistic explanation. This paper argues that a recent attempt to resolve this problem, proposed by Benjamin Barros, requires improvement as it overlooks the fact that not all absences qualify as sources of mechanism failure. I suggest that there are a number of additional types (...) of effects caused by absences that need to be incorporated to account for the diversity of causal connections in the biological sciences. Furthermore, it is argued that recognizing natural variability in mechanisms, such as attenuation, leads to some interesting line-drawing issues for contemporary philosophy of mechanisms. (shrink)

Let us use ‘false’ and ‘not true’ in such a way that the latter expression covers the broader territory of the two; in other words, a statement's falsity implies its non-truth but not vice versa. For example, ‘John is ill’ cannot be false without being nontrue; but it can be non-true without being false, since it may not be true when ‘John is not ill’ is also not true, a situation we could describe by saying ‘It is neither the case (...) that John is ill nor the case that John is not ill.’. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the (...) definitions of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

As neuroscience methods begin to dominate emotion research it is critical for researchers to remember that peripheral embodiments are critical to understanding emotional experience and emotion—behavior links. Much of modern emotion research assumes reliable mind—body connections that suggest that changes in emotional states influence bodily responses and, vice versa, that somatovisceral information shapes emotional experiences. However, there may be important qualifications to the link between the mind and the (peripheral) body. For example, the ability to sense internal and external bodily (...) states declines in older age as does activation of physiological systems, all of which may contribute to an impairment in emotional experiences and how emotions influence behavior. I describe this phenomenon as maturational dualism and suggest implications of this for emotion in older adults. (shrink)

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, (...) employing the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms. (shrink)

We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant.

In his paper, ìRight Weakening and Right Contraction in LK î, Hirokawa investigates the properties of the structural rules of contraction and weak- ening as they appear in a certain sequent calculus formulation of Örst order classical logic. In what follows we explore the notion of correspondence, in particular with reference to the structural rules in the succedent, and in doing so critically examine the sensitivity of Hirokawaís results to the formulation of the calculus, both with respect to the (...) formulations of the rules governing the connectives present and to the choice of the connectives themselves. (shrink)

In this paper we examine interactions of the reciprocal with distributive and collective operators, which are encoded by prefixes on verbs expressing the reciprocal relation: namely, the Czech distributive po and the collectivizing na-. The theoretical import of this study is two-fold. First, it contributes to our knowledge of how word-internal operators interact with phrasal syntax/semantics. Second, the prefixes po and na generate (a range of) readings of reciprocal sentences for which the Strongest Meaning Hypothesis (SMH) proposed by Dalrymple et (...) al. (1998) does not make the right predictions. The distributive prefix po prefers the Strong Reciprocity reading, although the SMH predicts that a weakening should take place, while with the prefix na we find cases where weaker reciprocal readings are preferable to the stronger ones predicted by the SMH. This behavior of po and na is, we propose, due to the way in which they modulate two factors that are crucial in the interpretation of reciprocal sentences: (i) the relevant subpluralities in the group denoted by the reciprocal's antecedent, and (ii) the strength of reciprocal relations. We provide a detailed analysis of the semantics of the prefixes po and na and their contribution to the meaning of reciprocal sentences within the general framework of event semantics with lattice structures. (shrink)

. A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. In an earlier paper [Notre Dame J. Form. Log. 49, 401–424], we developed the systems of weakening of intuitionistic negation logic, called and, in the spirit of da Costa's approach by preserving, differently from da Costa, the fundamental properties of negation: antitonicity, inversion and additivity for distributive lattices. Taking into account these results, we make some observations on the modified systems of (...) and, and their paraconsistent properties. (shrink)

The shriek modality \s! of linear logic performs two tasks: it restores in annotated from both weakening and contraction. We separate these tasks by introducing two modalities: for weakening and for contraction. These give rise to two logics which are “inbetween” linear and intuitionistic logic: in affine logic one always has a weakening and a for contraction and in relevant logic one always has a contraction and a weakening. The semantics of these logics is obtained from (...) special kinds of monads, introduced by Anders Kock in the early seventies. As subtle point is how to retrieve the \s! of linear logic from and . Technically this will be achieved in terms of distributive laws—introduced by Jon Beck. We find models where one has \s! = and also models with \s! = . It will be shown that on the category of complete lattices one has comonads and with = \s!=. (shrink)

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation (...) of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...) and the relationships between them, and have classified them according to several standard criteria of Abstract Algebraic Logic. One of the logics is protoalgebraic but neither equivalential nor weakly algebraizable, a rare situation where very few natural examples were hitherto known. In passing we have found new, alternative presentations of positive implicative logic, both in Hilbert style and in Gentzen style, and have characterized it in terms of the restricted Deduction Theorem: it is the weakest logic satisfying Modus Ponens and the Deduction Theorem restricted to at most 2 side formulas. The algebraic part of the work has lead to the class of quasi-Hilbert algebras, a quasi-variety of implicative algebras introduced by Pla and Verdú in 1980, which is larger than the variety of Hilbert algebras. Its algebraic properties reflect those of the corresponding logics and Gentzen systems. (shrink)

This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...) and the relationships between them, and have classified them according to several standard criteria of Abstract Algebraic Logic. One of the logics is protoalgebraic but neither equivalential nor weakly algebraizable, a rare situation where very few natural examples were hitherto known. In passing we have found new, alternative presentations of positive implicative logic, both in Hilbert style and in Gentzen style, and have characterized it in terms of the restricted Deduction Theorem: it is the weakest logic satisfying Modus Ponens and the Deduction Theorem restricted to at most 2 side formulas. The algebraic part of the work has lead to the class of quasi-Hilbert algebras, a quasi-variety of implicative algebras introduced by Pla and Verdú in 1980, which is larger than the variety of Hilbert algebras. Its algebraic properties reflect those of the corresponding logics and Gentzen systems. (shrink)

This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise (...) to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis’ axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus. (shrink)

Believing in free will may arise from a biological need for control. People induced to disbelieve in free will show impulsive and antisocial tendencies, suggesting a reduction of the willingness to exert self-control. We investigated whether undermining free will affects two aspects of self-control: intentional inhibition and perceived self-control. We exposed participants either to anti-free will or to neutral messages. The two groups then performed a task that required self-control to inhibit a prepotent response. No-free will participants showed less intentional (...) inhibitions than controls, suggesting a reduction of self-control. We assessed perceived self-control by asking participants whether the response resulted from a deliberate intention or from an impulsive reaction. Perceived self-control was lower in the no-free will group than in control group. Our findings show that undermining free will can degrade self-control and provide insights into how disbelieving in free will leads to antisocial tendencies. (shrink)

This paper introduces two new paradoxes for standard deontic logic (SDL). They are importantly related to, but distinct from Ross' paradox. These two new paradoxes for SDL are the simple weakening paradox and the complex weakening paradox. Both of these paradoxes arise in virtue of the underlaying logic of SDL and are consequences of the fact that SDL incorporates the principle known as weakening. These two paradoxes then show that SDL has counter-intuitive implications related to disjunctive obligations (...) that arise in virtue of deontic weakening and in virtue of decisions concerning how to discharge such disjunctive obligations. The main result here is then that theorem T1 is a problematic component of SDL that needs to be addressed. (shrink)

The debate over the place of religion in secular, democratic societies dominates philosophical and intellectual discourse. These arguments often polarize around simplistic reductions, making efforts at reconciliation impossible. Yet more rational stances do exist, positions that broker a peace between relativism and religion in people's public, private, and ethical lives. _Christianity, Truth, and Weakening Faith_ advances just such a dialogue, featuring the collaboration of two major philosophers known for their progressive approach to this issue. Seeking unity over difference, Gianni (...) Vattimo and René Girard turn to Max Weber, Eric Auerbach, and Marcel Gauchet, among others, in their exploration of truth and liberty, relativism and faith, and the tensions of a world filled with new forms of religiously inspired violence. Vattimo and Girard ultimately conclude that secularism and the involvement of religion in governance are, in essence, produced by Christianity. In other words, Christianity is "the religion of the exit from religion," and democracy, civil rights, the free market, and individual freedoms are all facilitated by Christian culture. Through an exchange that is both intimate and enlightening, Vattimo and Girard share their unparalleled insight into the relationships among religion, modernity, and the role of Christianity, especially as it exists in our multicultural world. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.2 (2003) 73-79 [Access article in PDF] Does Film Weaken Spectator Consciousness? R.D. Boyd and S.K. Wertz The role of spectator is crucial for an actor, for there are "no actors without spectators." 1 At times the success of the actor depends upon the role taken by the spectator. Thornton Wilder's "Our Town" depends upon an active,creative, involved audience. Other artists expect their audience (...) to be passive,almost unconscious. Whether the medium of creativity is film or the printedpage, examples of both dependencies abound. The focus of this essay is ona classic piece in the literature about film. In the Theory of Film, Siegfried Kracauer provides us with a mesmerizing printed discussion of film. 2 In this essay we wish to examine his reasoning that is in a self-contained argument by analogy. Since Kracauer does not use or mention the argument thereafter, we feel that we can isolate the argument from its context and deal with it as it stands. After an extended analysis of the argument, we will relate some of the points to the literature on film. The following analogical argument is our focus. Films...tend to weaken the spectator's consciousness. Its withdrawal from the scene may be furthered by the darkness in moviehouses. Darkness automatically reduces our contacts with actuality, depriving us of many environmental data needed for adequate judgments and other mental activities. It lulls the mind....Devotees of film and its opponents alike have compared the medium to a sort of drug and have drawn attention to its stupefying effects....Doping creates dope addicts. It would seem a sound proposition that the cinema has its habitues who frequent it out of an all but physiological urge. They are not prompted by a desire to look at a specific film or to be pleasantly entertained; what they really crave is for once to be released from the grip of consciousness, lose their identity in the dark, and let sink in, [End Page 73] with their senses ready to absorb them, the images as they happen to follow each other on the screen. 3To support his main point, "Films...tend to weaken the spectator's consciousness," Kracauer develops three intermediate arguments (IA's), which support his major argument (MA). If each sentence in the above passage were numbered one through nine, with the last full sentence being broken into two sentences at the semicolon, the following schema emerges. In English the chain of reasoning is: IA-1 Some habitues of film are not prompted by a desire to look at a specific film or to be pleasantly entertained. What they really crave is release fromthe grip of consciousness, to lose their identity in the dark, and let sink in, with their senses ready to absorb them, the images as they happen to follow each other on the screen. Therefore, the cinema has its habitues who frequent it out of an all but physiological urge.IA-2 Some habitues of film frequent it out of an all but physiological urge. Doping creates dope addicts. Therefore, devotees of film and its opponents alike have compared the medium to a sort of drug and have drawn attention to its stupefying effects.IA-3 Darkness automatically reduces our contacts with actuality, depriving us of many environmental data needed for adequate judgments and other mental activities. Darkness lulls the mind. Therefore, consciousness withdrawal from the scene may be furthered by the darkness in moviehouses.MA Devotees of film and its opponents alike have compared the medium to a sort of drug and have drawn attention to its stupefying effects. Consciousness withdrawal from the scene may be furthered by the darkness in moviehouses. Therefore, films...tend to weaken the spectator's consciousness. The above chain of arguments influences us, the spectators, to embrace his main point. However, before we are lulled into accepting his reasoning, it will be helpful to examine and evaluate each link. [End Page 74]IA-1 Some habitues of film are not prompted by a desire to... (shrink)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...) distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \. (shrink)

ABSTRACT:This paper re-examines the import of Rawls’s theory of justice for private sector institutions in the face of the decline of the welfare state. The argument is based on a Rawlsian conception of justice as the establishment of a basic structure of society that guarantees a fair distribution of primary goods. We propose that the decline of the welfare state witnessed in Western countries over the past forty years prompts a reassessment of the boundaries of the basic structure in order (...) to include additional corporate institutions. A discussion centered on the primary good of self-respect, but extensible to power and prerogatives as well as income and wealth, examines how the legislator should intervene in private sector institutions to counterbalance any unfairness that results from the decline of the welfare state. (shrink)

Ontologies represent principled, formalised descriptions of agents’ conceptualisations of a domain. For a community of agents, these descriptions may differ among agents. We propose an aggregative view of the integration of ontologies based on Judgement Aggregation (JA). Agents may vote on statements of the ontologies, and we aim at constructing a collective, integrated ontology, that reflects the individual conceptualisations as much as possible. As several results in JA show, many attractive and widely used aggregation procedures are prone to return inconsistent (...) collective ontologies. We propose to solve the possible inconsistencies in the collective ontology by applying suitable weakenings of axioms that cause inconsistencies. (shrink)

Through an exchange that is both intimate and enlightening, Vattimo and Girard share their unparalleled insight into the relationships among religion, modernity, and the role of Christianity, especially as it exists in our multicultural ...