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.

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)

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 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.

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)

This paper argues against Jon Elster's contention that there is a fundamentalincompatibility between, on one hand, autonomy and rationality and, on theother hand, adaptation to conditions of one's existence in the sense that one'sdesires or preferences are adjusted to what it is possible to achieve. While thefirst part of the paper more narrowly concentrated on Elster's discussion ofthese ideas, this second part goes on to a more general discussion of the conceptof rationality. On the basis of this discussion, it is (...) claimed that Elster's conclusionsconcerning autonomy and adaptation are premised on a defective conceptionof human experience and rationality. Moreover, the claim is made that thesedefects are also characteristic of "rational choice theory" more generally. (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.

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)

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E – the rule of restricted assertion or equivalently Ackermann’s δ-rule – is solely added as a primitiverule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for (...) E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of theternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction◦ – as well as the converse conditional ←. (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)

Democratic backsliding and autocratisation tendencies raise the question of what liberal democracy can do to defend itself. Of particular concern are populists, who are often perceived to have an ambiguous commitment to the principles of liberal democracy. The defence of liberal democracy has often been conceived in legal terms, for example, with party bans and propaganda restrictions. However, legal means are criticized for being elitist because they are directed against irrational and emotionally driven masses and because they allegedly violate the (...) very values that they are supposed to protect by limiting the democratic freedom of some groups. Instead, critics have proposed cultural and socio-economic means as non-elitist and non-exclusionary alternatives more in line with the values of democracy. This article discusses whether the employment of cultural and socio-economic means against groups – in casu populists – who are perceived as a challenge to liberal democracy can avoid the charge of elitism and exclusion by analysing whether these means are consistent with the publicity constraint. It finds that the use of education and money to defend democracy against such groups relies on a form of elitism and exclusion similar to the one that the defence by legal means is charged with. (shrink)

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)

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)

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)

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)

We argue that people may resist temptations not only with the aim of acquiring more self-control, but also because they want to convince others that they are patient and already possess self-control.

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.

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)

Two Hilbert calculi in the use-restricted relevance tradition of Anderson and Belnap are presented. One yields Anderson and Belnap's conjunctive version of the so-called ``entailment theorem,'' whereas the other yields the implication-iterated version. In contrast to previous such use-restricted calculi, those presented in this paper apply to arbitrary strengthenings of the weak contractionless logic B without need for modifying the use-conditions. As such they help to identify the core idea of the ``use-account'' of relevance.

The two ``relevance'' criteria set out by Anderson and Belnap are discussed. It is argued that the motivation backing the variable sharing property is far weaker than it is commonly made out to be, and that the use-criterion does not distinguish between relevant logics such as E and R and ``irrelevant'' logics such as S4, intuitionistic and classical logic. In short, then, the paper argues that Anderson and Belnap's two criteria of relevance are both motivationally unsound, and do not accomplish (...) what they are commonly taken to accomplish. (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)

Langacker's usage-based model provides cognitive linguists with a useful tool for the study of allomorphy. In the present article the model is applied to a central problem in Russian conjugation, viz., the formation of the past passive participle. The analysis demonstrates the restrictiveness of the model, which precludes reference to arbitrary indices and underlying representations. Thus, the analyst is forced to look for surface-true generalizations including phonological, semantic, and symbolic structures and relationships holding between them. This reseach strategy proves fruitful (...) for the Russian past passive participle. The choice of suffixes is shown to be predictable from the shape of the past-tense stem, facilitating the formation of simple generalizations about the distribution of the relevant suffixes. (shrink)

In this article we apply one of the key concepts in cognitive linguistics, the radial category, to inflectional morphology. We advance the Paradigm Structure Hypothesis, arguing that inflectional paradigms are radial categories with internal structure primarily motivated by semantic relationships of markedness and prototypicality. It is possible to construct an expected structure for a verbal paradigm, facilitating an empirical test for our hypothesis. Data tracking an on-going morphological change in Russian documents the distribution of conservative vs. innovative forms across the (...) cells of the verbal paradigm. A logistic regression model that takes into account the sources of variation (the frequencies of individual verbs and paradigm slots, and individual verb preferences) shows that the language change is implemented differently across the paradigm forms, confirming the expected structure. In addition to markedness and prototypicality, we investigate the impact of frequency and show that there is a good, albeit not perfect match between the expected hierarchy and frequency. We conclude that the diachronic change analyzed in this article gives evidence for the structure of paradigms modeled on the radial category. (shrink)

This article argues against Jon Elster’s contention that there is a fundamental incompatibility between, on the one hand, autonomy and rationality, and, on the other hand, adaptation to the conditions of one’s existence in the sense that one’s desires or preferences are adjusted to what it is possible to achieve. It is claimed that Elster’s conclusions are premised on a defective conception of human faculties and powers, including a defective conception of human experience and rationality. Moreover, the claim is made (...) that these defects are also characteristic of “rational choice theory” more generally. (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 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)

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)

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)

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

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)

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)