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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

Anna Elisabetta Galeotti?s theory of ?toleration as recognition? has been criticised by Peter Jones for being conceptually incoherent, since liberal toleration presupposes a negative attitude to differences, whereas multicultural recognition requires positive affirmation hereof. The paper spells out Galeotti?s justification for recognition as a requirement of liberal justice in detail and asks in what sense the policies supported by Galeotti are policies of recognition. It is argued that Jones misrepresents Galeotti?s theory, insofar as this sense of recognition actually is compatible (...) with liberal toleration. This does not prove Jones?s criticism to be wrong, since the justification may have implications unacknowledged by Galeotti, which might be liberally problematic. The paper considers this problem and possible ways of responding to it, but concludes that Galeotti?s theory is incomplete in respects that need to be filled out in order to secure compatibility with liberalism, and that this may prove problematic. (shrink)

The paper concerns the specific transnational aspects of the ‘cartoons controversy’ over the publication of 12 drawings of the Prophet Muhammad in the Danish newspaper Jyllands-Posten. Transnationalism denotes the relationships that are not international or domestic. The paper considers whether the specifically transnational aspects of the controversy are normatively significant, that is, whether transnationalism makes a difference for the applicability or strength of normative considerations concerning publications such as the Danish cartoons. It is argued that, although some of the usual (...) arguments about free speech only or mainly apply domestically, many also apply transnationally; that standard arguments for multicultural recognition are difficult to apply transnationally; and that requirements of respect may have problematic implications if applied to transnational relationships. Keywords: civility; Muhammad cartoons; freedom of speech; global civil society; multicultural recognition; respect; transnational relations Citation: Ethics & Global Politics, Vol. 3, No. 2, 2010, pp. 101-121. DOI: 10.3402/egp.v3i2.1977. (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)

Although many ecofeminists acknowledge heterosexism as a problem, a systematic exploration of the potential intersections of ecofeminist and queer theories has yet to be made. By interrogating social constructions of the "natural," the various uses of Christianity as a logic of domination, and the rhetoric of colonialism, this essay finds those theoretical intersections and argues for the importance of developing a queer ecofeminism.

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)

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)

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.

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" 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)

This article provides a normative framework for evaluating the moral permissibility of various defences of European Union 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)

Landgrebe and Smith :2061–2081, 2021) present an unflattering diagnosis of recent advances in what they call language-centric artificial intelligence—perhaps more widely known as natural language processing: The models that are currently employed do not have sufficient expressivity, will not generalize, and are fundamentally unable to induce linguistic semantics, they say. The diagnosis is mainly derived from an analysis of the widely used Transformer architecture. Here I address a number of misunderstandings in their analysis, and present what I take to be (...) a more adequate analysis of the ability of Transformer models to learn natural language semantics. To avoid confusion, I distinguish between inferential and referential semantics. Landgrebe and Smith ’s analysis of the Transformer architecture’s expressivity and generalization concerns inferential semantics. This part of their diagnosis is shown to rely on misunderstandings of technical properties of Transformers. Landgrebe and Smith also claim that referential semantics is unobtainable for Transformer models. In response, I present a non-technical discussion of techniques for grounding Transformer models, giving them referential semantics, even in the absence of supervision. I also present a simple thought experiment to highlight the mechanisms that would lead to referential semantics, and discuss in what sense models that are grounded in this way, can be said to understand language. Finally, I discuss the approach Landgrebe and Smith advocate for, namely manual specification of formal grammars that associate linguistic expressions with logical form. (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)

Political theory is contextualist when factual claims about context are part of the justification of normative political judgments. There are different kinds of contextualism depending on whether context is relevant for the formulation and justification of political principles, whether principles themselves are contextually specific, or whether context is only relevant for the application of principles. An important challenge to contextualism is the problem of critical distance: how can theories ensure a critical perspective if facts about the context to be evaluated (...) are also part of the justification for the normative judgments? Tariq Modood and Simon Thompson have defended what they call iterative contextualism, which combines elements of all three kinds of contextualism in an attempt to avoid the problem of critical distance. The present paper discusses Modood and Thompson’s iterative contextualism and whether it manages to avoid the problem of critical distance. (shrink)

This article argues against the idea that European Union member states that have turned autocratic should be ejected from the EU to ensure that the latter does not itself violate the principle of democracy identified with the all subjected principle. First, the ASP requires that MSs be democratic before a decision to eject them would be acceptable and at that point, there is no reason to eject them. Second, if EU membership is voluntary as the protagonist of the above idea (...) presupposes, any MS can decide to leave at any point in time and other MSs can decide to leave any MS behind and create a new European organization without it. Taken together, this means that the ASP, which pertains to permanent subjection, is irrelevant already from the outset and cannot be used as the main premise for the argument for ejection. Finally, the very disagreement about what kind of organization the EU is and should become, implies that the democratic rights of citizens be given priority over the rights of states. This speaks against the legitimacy of ejecting MSs for democracy protection. (shrink)

This paper interacts specifically with two separate texts, that is Michel de Certeau’s The Possession at Loudun and Carlo Ginzburg’s The Cheese and the Worms: The Cosmos of a Sixteenth Century Miller. Both of these texts present a narrative of religious turmoil, demonic possessions and a heretical Inquisition, respectively, and the events which surround a single religious dissenter. Examining the two heretical men presented within these texts in comparison allows for an understanding of Catholic Church dogma during the age of (...) the Counter Reformation, and how such an institution managed threats, both external and internal. Moreover, this paper also examines the methodologies behind the historical discourse, in order to understand the validity of the narratives presented, and the scope of historical depth sought. Addressing methodology is crucial when one narrows focus to two singular case studies by two separate historians. Thus, this paper intends to illustrate the threats to normative religious discourse which Urbain Grandier and Menocchio possessed in the face of the Catholic Church, while also demonstrating the methodologies by which the two men are presented within their respective histories. (shrink)

Numerous studies have replicated the finding of mentation in both rapid eye movement (REM) and nonrapid eye movement (NREM) sleep. However, two different theoretical models have been proposed to account for this finding: (1) a one-generator model, in which mentation is generated by a single set of processes regardless of physiological differences between REM and NREM sleep; and (2) a two-generator model, in which qualitatively different generators produce cognitive activity in the two states. First, research is reviewed demonstrating conclusively that (...) mentation can occur in NREM sleep; global estimates show an average mentation recall rate of about 50% from NREM sleep – a value that has increased substantially over the years. Second, nine different types of research on REM and NREM cognitive activity are examined for evidence supporting or refuting the two models. The evidence largely, but not completely, favors the two-generator model. Finally, in a preliminary attempt to reconcile the two models, an alternative model is proposed that assumes the existence of covert REM sleep processes during NREM sleep. Such covert activity may be responsible for much of the dreamlike cognitive activity occurring in NREM sleep. Key Words: cognition in sleep; dreaming; NREM sleep; REM sleep; sleep mentation. (shrink)