The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.

Philosophy Compass, Volume 17, Issue 8, August 2022.

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap''s system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis'' theory of causation, Lewis'' dyadic deontic logic, and Chellas'' dyadic deontic logic.

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...) some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.

This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.

Bioethics, Volume 36, Issue 3, Page 243-251, March 2022.

In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.

Carrying out research on brains is important for medical advances in various diseases. However, such research ought not be carried out on human brains because the benefits do not outweigh the potential risks. A possible alternative is the use of brain surrogates. Nevertheless, some scholars who uphold a threshold account of moral status suggest the possibility that, with technological advances in the near future, more advanced brain surrogates will have very similar features to humans. This may suffice for these having (...) the same moral status as humans, and as a result, the situation may have implications for brain research, indeed, leading to the implication that this ought also not to be carried out upon brain surrogates. In this article, we present a relational approach to moral status which upholds that brain surrogates do not have the same moral status as human beings. Hence, brain research ought not be rejected on the grounds of equality of moral status between humans and brain surrogates. (shrink)

ABSTRACT In this article, I will carry out an epistemic and interpretative project, drawing out the implications of African values for the morality of war. More precisely, I wish to interpret the African value system and tease out some conclusions as to what this value system entails in terms of the following: the morality of when to enter war, how to act in war, and what to do after war. I carry out this inquiry by articulating the African value of (...) Ubuntu in light of the actions and speeches of two prominent African leaders, Nelson Mandela and Amilcar Cabral. (shrink)

RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.

Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (shrink)

This important collection of essays details some of the more significant methodological and philosophical differences that have separated the two traditions, as ...

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.

Models are constructed for a variety of systems of quantified relevance logic with identity. Models are given for systems with different principles governing the transitivity of identity and substitution, and the relative merits of these principles are discussed. The models in this paper are all extensions of the semantics of Fine's Semantics for Quantified Relevance Logic (Journal of Philosophical Logic 17 (1988)).

The Portuguese animal rights movement has been extremely active in campaigning against bullfighting. Indeed, from 2002 to 2014, this was their main priority in terms of campaigns. In this article, I assess how these campaigns have been carried out, arguing that the animal rights movement in Portugal has been othering supporters and practitioners of bullfights in their campaigns. In other words, their campaigns have consisted of drawing a sharp contrast between bullfight supporters and practitioners and the rest of the population. (...) I argue that a consequence of this is that the speciesist practices of the majority of Portuguese have become normalised; consequently, leading to the reinforcement of some speciesist norms. (shrink)

In his thesis 'Para uma Teoria Geral dos Homomorfismos' (1944) the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...) tried to keep in mind, so much as possible, the gist of his standpoint. (shrink)

This chapter contains section titled: Metaphysics and Epistemology Political Philosophy Conclusion.

A main thrust of much of Quine's work is that meaning, belief, desire, motive and other so-called “intentional phenomena” are under-determined by all possible evidence: the totality of possible evidence could not determine whether two persons meant, believed, desired, or had as motives the same thing. One way to identify a person's beliefs, desires and motives is to frame a theory of his meanings, for then we could ask him what he believed and desired; this will be a theory of (...) translation for his language. But such a theory of meaning, according to Quine, is also not uniquely determined by all the evidence. ThusTo accept intentional usage at face value is … to postulate translation relations as somehow objectively valid though indeterminate in principle relative to the totality of speech dispositions… Such postulation promises little gain in scientific insight …. (shrink)

https://deepblue.lib.umich.edu/bitstream/2027.42/156056/1/Mind-Body Union.pdf.

Some philosophers and activists have been sceptical about the relevance of pursuing animal justice to progress racial justice. Routinely, these sceptics have argued that allying animal and racial justice struggles is politically unfeasible, counterproductive, distractive and disruptive for the achievement of racial justice. The conclusion of these sceptics is that animal justice is either a barrier or irrelevant to racial justice and, as such, activists should not ally both struggles. In this article, I wish to contest the arguments that forward (...) the idea that these struggles should not be addressed together, especially in the case of addressing anti-Black racial injustices. I offer a negative argumentative strategy to forward my thesis; namely, I offer reasons to reject the arguments that are sceptical about the relevance of addressing animal justice to achieve progress in racial justice. I contend that racial injustice is partly fuelled by the capacity contract. The capacity contract, in turn, is intertwined with the way humans treat animals. Owing to the fact that speciesism fuels the contract that incites racism, then addressing speciesism is instrumentally relevant for overcoming racial injustices. Moreover, I demonstrate in this article that not only are there various ways that anti-racist and anti-speciesist struggles are interconnected, but also that the project of addressing them together is politically feasible and desirable. (shrink)

The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by the use of restrictions on the ternary accessibility relation, simplified by the use of some definitions, a semantics can be stipulated over which R is complete.

In the Western theist tradition, the conception of a person tends to be understood as an intrinsic property. Hence, the classification of someone as a person does not depend on relational aspects of that person. From this, Western theists often understand that their conception of God as a person does not clash with the idea of immutability. In this article, I challenge the idea that being a person and being immutable are compatible properties by using Afro-communitarian philosophy and, more specifically (...) Afro-communitarian metaphysics of personhood. Afro-communitarian metaphysics is fundamentally relational, i.e. it understands that most properties of the world depend on the existence of other entities. More precisely, personhood is a property that depends on the existence of relatable beings. But if this is true, then it is not possible to hold that an entity that has the property of personhood also has the property of immutability. More specifically, an entity that is a person has to change due to the fact that personhood is a relational property. This is because it is a necessary condition for being a person that one relates to others, i.e. one only becomes a person when this relation occurs. Hence, the process of becoming a person requires a moment before the relation with another and one after; thereby, the feature of being a person requires the feature of change. With respect to the Christian conception of God, what this implies is that if theist philosophers wish to understand Him as a person, they have to also accept that God is not immutable. For if other beings besides Him are not eternal, then it is only possible that He can be a person when these other beings first started existing. This is the case because the kind of relationality needed to be a person is not simply to relate to something (like emptiness), but to do something that makes Him addressable (which requires that the thing He relates to has the capacity to address Him). This means there are two moments of existence where He has distinct properties and, therefore, is mutable. (shrink)

This paper extends the theory of situated inference from Mares to treat two weak relevant logics, B and DJ. These logics are interesting because they can be used as bases for consistent naïve theories, such as naïve set theory. The concepts of a situation and of information that are employed by the theory of situated inference are used to justify various aspects of these logics and to give an interpretation of the notion of set that is represented in the naïve (...) set theories that are based on them. (shrink)

With the current pandemic, many scholars have contended that clinical criteria offer the best way to implement triage. Further, they dismiss the criteria of social value as a good one for triage. In this paper, I respond to refute this perspective. In particular, I present two sets of arguments. Firstly, I argue that the objections to the social value criteria they present apply to the clinical criteria they favor. Secondly, they exaggerate the negative aspects of the social value criteria, while (...) I suggest it is reasonable to use this. I end the article by recommending how operative public values can be a good way to make triaging decisions. (shrink)

This chapter contains sections titled: Non‐Sequiturs are Bad The Real Use of Premises Implication From Proof Theory to Semantics Adding Conjunction The Problem of Disjunction Routley and Meyer's Ternary Relation Rules for Disjunction The Semantics of Negation Rules for Negation Disjunctive Syllogism Logics Stronger than R Logics Weaker than R Relevant Logics and Natural Language Conditionals Theory of Properties Summary.

Bob Fischer has written a reply to my article ‘Animal Abolitionism and ‘Racism without Racists’’. In this article, Fischer contends that my arguments whereby animal abolitionism engages in acts of racism without racists are mistaken. I wish to reply to Fischer’s objections in this article, through four sets of contentions: Fischer’s arguments reveal some misunderstandings in terms of the concept of racism and, particularly, of ‘racism without racists’; his arguments also underestimate the burdens suffered by individuals who wish to become (...) vegan; Fischer’s views on infantilisation lead to counter-intuitive conclusions; and Fischer’s counter-argument against my neo-colonial critique of abolitionism misunderstands the points made in my previous article. (shrink)

This paper presents a probabilist paraconsistent theory of belief revision. This theory is based on a very general theory of probability, that fits with a wide range of classical and nonclassical logics. The theory incorporates a version of Jeffrey conditionalisation as its method of updating. A Dutch book argument is given, and the theory is applied to the problem of choosing a logical system.

The logic CE (for "Classical E") results from adding Boolean negation to Anderson and Belnap's logic E. This paper shows that CE is not a conservative extension of E.

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.

Philosophy Compass, Volume 17, Issue 3, March 2022.