It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.

Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong (...) relevant logic R with a S5 modal operator, all fail to be conservatively extended by Boolean negation. The proof, therefore, also covers Meyer and Mares’ proof that NR—R with a primitive S4-modality added—also fails to be conservatively extended by Boolean negation. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...) overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics (...) which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence. (shrink)

Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic (...) to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing. (shrink)

Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean extended (...) logic. (shrink)

This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.

Restall set forth a "consecution" calculus in his "An Introduction to Substructural Logics." This is a natural deduction type sequent calculus where the structural rules play an important role. This paper looks at different ways of extending Restall's calculus. It is shown that Restall's weak soundness and completeness result with regards to a Hilbert calculus can be extended to a strong one so as to encompass what Restall calls proofs from assumptions. It is also shown how to extend the calculus (...) so as to validate the metainferential rule of reasoning by cases, as well as certain theory-dependent rules. (shrink)

Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained (...) center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppression-freedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do. (shrink)

Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of (...) consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context. (shrink)

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that Substitution ought (...) to fail. (shrink)

Ackermann’s motivational spin on his theory of rigorous implication is analyzed and it is shown to contain en equivalent idea to Plumwood’s notion of suppression freedom. The formal properties these ideas back turn out to be properly weaker than Belnap’s variable sharing property, but it is shown that they can be strengthen in various ways. Some such strengthenings, it is shown, yield properties which are equivalent to Belnap’s, and thus provide for new ways of motivating Belnap’s fundamental relevance principle.

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.

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

Cheyne and Girard characterize felt presence during sleep paralysis attacks as a pre-hallucinatory expression of a threat-activated vigilance system. While their results may be consistent with this interpretation, they are nonetheless correlational and do not address a parsimonious alternative explanation. This alternative stipulates that FP is a purely spatial, hallucinatory form of a common cognitive phenomenon—social imagery—that is often, but not necessarily, linked with threat and fear and that may induce distress among susceptible individuals. The occurrence of both fearful and (...) non-fearful FPs in a multiplicity of situations other than sleep paralysis attacks supports the notion that FPs are hallucinatory variants of social imagery and that they are not necessarily bound to threat-activated vigilance. Evidence linking FPs with anxiety disorders supports the notion that the distress they evoke may be mediated by a more general affective distress personality factor. To illustrate the predominantly spatial character of FP hallucinations, similarities between FP and phantom limbs are summarized and the possibility that these two phenomena are parallel expressions of a mirror neuron system is considered. (shrink)

Artificial intelligence receives attention in media as well as in academe and business. In media coverage and reporting, AI is predominantly described in contrasted terms, either as the ultimate solution to all human problems or the ultimate threat to all human existence. In academe, the focus of computer scientists is on developing systems that function, whereas philosophy scholars theorize about the implications of this functionality for human life. In the interface between technology and philosophy there is, however, one imperative aspect (...) of AI yet to be articulated: how do intelligent systems make inferences? We use the overarching concept “Artificial Intelligent Behaviour” which would include both cognition/processing and judgment/behaviour. We argue that due to the complexity and opacity of artificial inference, one needs to initiate systematic empirical studies of artificial intelligent behavior similar to what has previously been done to study human cognition, judgment and decision making. This will provide valid knowledge, outside of what current computer science methods can offer, about the judgments and decisions made by intelligent systems. Moreover, outside academe—in the public as well as the private sector—expertise in epistemology, critical thinking and reasoning are crucial to ensure human oversight of the artificial intelligent judgments and decisions that are made, because only competent human insight into AI-inference processes will ensure accountability. Such insights require systematic studies of AI-behaviour founded on the natural sciences and philosophy, as well as the employment of methodologies from the cognitive and behavioral sciences. (shrink)

En el mundo actual, en el que se está reduciendo la abundancia y la inalterabilidad de la diversidad cultural, nuestras barreras culturales se pueden salvar —aunque no adulterar— si todo el mundo en todas partes se acoge a los derechos humanos. En el presente artículo intento defender la idea de que, para conseguirlo, tenemos que elaborar una pluralidad de aprobaciones de los derechos humanos universalmente aplicables que sea diversa pero bien cimentada culturalmente; en resumidas cuentas, deberíamos adoptar una justificación plural (...) de los derechos humanos. (shrink)

In recent years, semantical partiality has emerged as an important explanatory concept in philosophical logic as well as in the study of natural language semantics. Despite the many applications, however, a number of mathematically intriguing questions associated with this concept have received only very limited attention. ;The present dissertation aims to present a systematic study of certain types of partiality in the area of basic model theory. Two types of issues are given special attention: Introducing partially defined models, there are (...) many ways to generalize the classical truth definition for sentences of a simple first order language relative to standard, complete models. Different interpretations of the formal framework motivate conflicting truth definitions between language and partial models: A partial model can be taken to represent a part of the world, or a partial information set. The truth of a sentence can be supported directly by a part of the world, but can also follow indirectly from an information set. These notions are related, and the relation motivates a comparison between various weaker and stronger alternative truth definitions. Results are obtained about the extent to which these truth definitions differ, and a number of characterization results are deduced. ;Among other conditions that are not expressible in the framework of standard, complete model theory, a condition of monotonicity or persistence of truth relative to partial models is argued to follow under both the given interpretations of the formal framework. The final chapter investigates the relation between such conditions and expressibility properties in general. These discussions culminate with a combined Lindstrom and persistence characterization theorem. (shrink)

This article provides a normative framework for evaluating the moral permissibility of various defences of European Union (EU) values against their violation in EU member states. This requires, first, a coherent interpretation of EU values as the values of liberal democracy; second, a clear notion of when they are violated; third, a theory of how liberal democracy can be defended with measures that are consistent with the values of liberal democracy themselves; and, finally, a discussion of what the EU’s role (...) is in this defence. The article argues that it would be permissible for the EU to combine a number of political, cultural, socio-economic and legal responses in a concentric defence of liberal democracy as long as they respect the separation of powers doctrine and do not rely on problematic notions of collective responsibility. (shrink)

Lautemann et al. (1995) gave a descriptive characterisation of the class of context-free languages, showing that a language is context-free iff it is definable as the set of words satisfying some sentence of a particular logic (fragment) over words. The present notes discuss how to specialise this result to the class of linear languages. Somewhat surprisingly, what would seem the most straightforward specialisation actually fails, due to the fact that linear grammars fail to admit a Greibach normal form. We identify (...) an alternative specialisation, based on an alternative characterisation of context-free languages, also noted by Lautemann et al. (1995). (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Purpose: To survey the attitudes of the general public in Sweden to biobank research and to discuss the findings in the light of some well-known ethical principles.Methods: A questionnaire was used to survey the opinions of the general public in Sweden, and an ethical analysis (using the principles of autonomy, non-maleficence, beneficence and justice) was performed to discuss the possible conditions of such research.Findings: Between 3 and 9% answered that they did not want their samples to be collected and stored (...) in a biobank. Many respondents required information about the purpose of the research and wanted to be able to consent or refuse. About one third of the respondents said they would have answered differently if financial gain was involved and those who commented indicated a more negative attitude. The principle of autonomy maintains that the right to self-determination should be respected, and the principles of non-maleficence and beneficence that the probable harms and benefits resulting from a particular project by using samples from a biobank should be balanced. The general public disagree about how these principles are to be balanced. Interpretation: In the light of the findings different interpretations of the situation as well as possible alternatives are discussed in this paper. (shrink)

This introduction describes the background and reasons why the Mercator-Hondius atlas analysed in this issue became part of the library collection of the Donner Institute.

The aim of this study was to analyse experiences of moral concerns in intensive care nursing. The theoretical perspective of the study is based on relational ethics, also referred to as ethics of care. The participants were 36 intensive care nurses from 10 general, neonatal and thoracic intensive care units. The structural characteristics of the units were similar: a high working pace, advanced technology, budget restrictions, recent reorganization, and shortage of experienced nurses. The data consisted of the participants’ examples of (...) ethical situations they had experienced in their intensive care unit. A qualitative content analysis identified five themes: believing in a good death; knowing the course of events; feelings of distress; reasoning about physicians’ ‘doings’ and tensions in expressing moral awareness. A main theme was formulated as caring about - caring for: moral obligations and work responsibilities. Moral obligations and work responsibilities are assumed to be complementary dimensions in nursing, yet they were found not to be in balance for intensive care nurses. In conclusion there is a need to support nurses in difficult intensive care situations, for example, by mentoring, as a step towards developing moral action knowledge in the context of intensive care nursing. (shrink)

This article discusses fundamental problems in "rational choice theory," as outlined by Jon Elster. Elster's discussion of why institutions may not be said to act shows his fundamental presupposition that only "monolithic," unitary entities are capable of action. This is, for him, a reason why only individual human beings may be said to act. Furthermore, human beings may be said to act only insofar as they "maximize" (their "utility") on the basis of a unitary, complete, consistent "preference structure." All action (...) that is not maximization in this sense is for Elster not really human action, but rather instances of "pure causality." Elster distinguishes between the "real," intentional person, who "maximizes," and "purely causal forces" within the person. This article tries to show that this radical, sharp dichotomy between "intentionality," in this narrow sense, and "pure causality" is inadequate as a basis for understanding human action. This radical dichotomy is central to important arguments made by Elster more generally. (shrink)

Name der Zeitschrift: Cognitive Linguistics Jahrgang: 27 Heft: 4 Seiten: 573-585.

That PTSD nightmares are highly realistic threat simulations triggered by trauma is difficult to reconcile with the disturbed, sometimes debilitating sleep and waking functioning of PTSD sufferers. A theory that accounts for fundamental forms of imagery other than threat scenarios could explain the selection of many more adaptive human functions – some still pertinent to survival today. For example, interactive characters, a virtually ubiquitous form of dream imagery, could be simulations of attachment relationships that aid species survival in many different (...) ways. [Revonsuo]. (shrink)

Nanoscale objects are presented by ever more sophisticated pictures. There is a need to reflect on the status of such nano images, because the “seeing” involved is of a highly indirect kind. The aim of this paper is to complement existing philosophical critique of nano images with a scientific practitioner's perspective. First, we show some reasons to consider seeing and imaging as complex endeavours not only on the micro and nano scale, but also on the macro level. Secondly, we argue (...) that practising scientists are not only accustomed to interpret pictures and other graphical presentations of data as being partial and simplified, but that simplification is deliberate and internal. Rather than requiring that “true” images have to be representational, the paper advocates for the fruitfulness of understanding and judging images by the amount and nature of the information they convey. Scientific literacy could be improved by creative development of visualization techniques, but also by improved public understanding of images and their correct and cautious interpretation. (shrink)