In her recent book, Russell (2023) examines various so-called “barriers to entailment,” including Hume’s law, roughly the thesis that an ‘ought’ cannot be derived from an ‘is.’ Hume’s law bears an obvious resemblance to the proscription on fallacies of modality in relevance logic, which has traditionally formally been captured by the so-called Ackermann property. In the context of relevant modal logic, this property might be articulated thus: no conditional whose antecedent is box-free and whose consequent is box-prefixed is valid (for (...) the connection, interpret box deontically). While the deontic significance of Ackermann-like properties has been observed before, Russell’s new book suggests a more broad-scoped formal investigation of the relationship between barrier theses of various kinds and corresponding Ackermann-like properties. In this paper, I undertake such an investigation by elaborating a general relevant bimodal logical framework in which several of the barriers Russell examines can be given formal expression. I then consider various Ackermann-like properties corresponding to these barriers and prove that certain systems satisfy them. Finally, I respond to some objections Russell makes against the use of relevance logic to formulate Hume’s law and related barriers. (shrink)

Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation—in symbols, ¬(¬φ→φ)—has gone by the name of Aristotle’s thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3–14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle’s argument from this passage and show that (...) he accepts this thesis. Further, I show that the argument he gives is, making plausible assumptions, a correct proof in a consistent fragmentary nonclassical metalogic for a metatheorem he previously states concerning his assertoric syllogistic. In this way, Aristotle’s argument emerges as a fascinating case study in the use of a nonclassical metalogic to prove a result about a nonclassical object system. (shrink)

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...) the systems discussed. (shrink)

In On the Trinity 15.12.21, Augustine appears to endorse the KK principle (that if one knows that φ, then one knows that one knows that φ) in the course of giving an argument – the Multiplicity Argument – against the Academic skeptics. Gareth Matthews has disputed Augustine’s endorsement of the KK principle and presented a different reading of the Multiplicity Argument. In this note, I show that Matthews’s construal of the Multiplicity Argument is both interpretively and technically defective and defend (...) the attribution of some form of the KK principle to Augustine. (shrink)

We propose a descriptive version of the classical multi-attribute utility model; to that end, we add a new parameter, momentary salience, to the customary formulation. The addition of this parameter allows the theory to accommodate changes in the decision maker’s mood and circumstances, as the saliencies of anticipated consequences are driven by concerns of the moment. By allowing for the number of consequences given attention at the moment of decision to vary, the new model mutes the criticism that SEU models (...) call for an omniscient decision maker. Use of the model is illustrated with a large-scale longitudinal study showing that adolescent smokers have higher utility for smoking than nonsmokers. We also propose to use the model hierarchically to describe everyday decisions that people deal with repeatedly. Big decisions, which set policy, guide a host of nested little decisions, which in turn lead to action. For a little decision, one of the options will be consistent with the policy, and will inherit its high utility. Accordingly, most little decisions will be made quickly and will follow the policy. However, people do sometimes decide to violate their own policies, and we describe how these lapses can lead to collapse of the policy. (shrink)

This paper is an attempt so to construe the arguments of the Hippias Minor as to remove the justification for regarding it as unworthy of Plato either because of its alleged fallaciousness and Sophistic mode of argument or because of its alleged immorality. It focuses, therefore, only on the arguments and their conclusions, steering clear of the dialogue's dramatic and literary aspects. Whereas I do not wish to deny the importance of these aspects to a proper understanding of the dialogue (...) – on the contrary, in a dialogue so heavily laden with irony and caricature, these aspects are necessarily more significant than they are in other dialogues – I do think there is something to be gained from concentrating on the arguments themselves. Although there can be little doubt that Socrates is up to something in the Hippias Minor, the task of determining just what he is up to can only be simplified by clarifying the arguments first.The Hippias Minor has traditionally been thought to contain two independent arguments, each having its own paradoxical conclusion. The first argument begins, it is said, when Hippias characterizes the two Homeric heroes Achilles and Odysseus as the true man and the false man respectively. Through its discovery that both the false man and the true man have δύναμις, it results in the paradox that the false man and the true are identical. The second argument, on this view, leaves the subject of ⋯ ⋯ληθ⋯ς and ⋯ ψευδ⋯ς and compares instead all sorts of agents in intentional and unintentional action. Finding that the intentional agent is in every case better than the unintentional, the argument concludes that the intentional evil-doer is also better than the unintentional. Viewing the dialogue as thus containing two distinct topics treated in two self-sufficient arguments is perhaps not the best way to understand it. (shrink)

The paper offers a critical perspective on some modern studies of Plotinus’ doctrine of Love, which interpret his Eros as more than a guide, leading the soul to the intelligible world and above, to the first Principle, or directing its gaze to the sensible world. They consider Love to be the driving force behind generation from the One and even identify it with the One itself, basing most of their arguments on rare instances of Eros’ appearance at levels above the (...) soul and using an emphatically erotic terminology that is alien to Plotinus. (shrink)

We argue that Rousseau 's defense of the sex-roled family is not based on biological determinism or simple misogyny. Rather, his advocacy of sexual differentiation is based on his understanding of its ability to bring individuals outside of themselves into interdependent communities, and thus to counter natural independence, self-absorption and asociality, as well as social competitiveness and egoism. This political defense of the sex-roled family needs more critique by feminists.

A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I show that even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.

Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

This chapter offers a brief historical overview of the gendered mind/body dualism associated with the rationalist tradition, according to which women’s bodies have been viewed as a threat to reason and to ethics. Taking up critiques of this model offered by Beauvoir and Fanon, I maintain that the body of the Other makes an ethical claim upon us in the form of “bodily imperatives.” I conclude with a critical analysis of contemporary feminist ethics that seeks to move beyond the false (...) dichotomies of mind/body, reason/emotions, transcendence/immanence, and male/female dualisms. Assuming as their starting point the universality of human dependency and the debilitating reality of embodied oppression, contemporary feminist ethicists seek to overturn the sexist, racist, and ableist effects of a philosophical tradition that has always privileged some minds and bodies over others. (shrink)

In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this result where negation is included (...) is also discussed). It is proved that BG satisfies the variable sharing property and is Halldén complete, while failing to satisfy the disjunction property. Sound and complete subscripted tableaux are presented for BG. An axiomatization (in the positive language extended with fusion) is presented, which is sound with respect to BG and, with respect to a related ternary relational semantics, complete; the problem of identifying a complete axiomatization for BG itself is left open. Connections between BG and the quasi-relevance logic KR are also discussed. (shrink)

Volume 24, Issue 10, October 2024, Page 80-82.

In this essay, I argue that a comparison of Derrida’s “Faith and Knowledge” to the texts and thought of classical rabbinic Judaism can illuminate new conceptual connections among the different elements of Derrida’s thought. Both Derrida and the rabbinic texts can be viewed as affirming a type of “holding back” and “allowing the other to be,” stances which Derrida links to “religiosity” and to “messianicity beyond all messianism.” Moreover, the rabbinic texts appear to avoid the “autoimmune” reaction that Derrida sees (...) as stemming from many sacrificial and self-sacrificial logics in which the self is problematically sacrificed in order to preserve the “unscathed” other. In addition, the rabbinic texts’ stance concerning divine authorization for war and capital punishment help to illuminate Derrida’s claim that the ostensibly “secular” wars of modern states are in fact better understood as “wars of religion.”. (shrink)

Anamnesis (Swiatlo Dnia) was written as an aftermath of a six-day performative installation at the twelfth-century castle in Trancoso, Portugal with the participation of local women and men, mainly farmers. It was written concurrently while working on the editing of the video and the sound, which I filmed and recorded on site (or, as I think of it, layering of images, sounds and different time paths). The text addresses the act of drawing as related to speech, mark, trace, scripture, presence (...) and absence as it elaborates on the notion of gesture across the media and time. The vital connections between the performative act of drawing and the desire to mark since time immemorial and the contemporary virtual and cinematic mediums are crucial to the notion of anamnesis in both the physical installation in real time with performative inhabitation of space and in the virtual and altered memory of that occurrence in the resulting video piece. (shrink)

I developed a first-day exercise for my interdisciplinary “Feminist Epistemology” class that calms students’ fears about what they imagine will be the unduly abstract course content, and engages them in easy but revealing conversation about knowledge. Individually and then together, we explore metaphors and proverbs about knowing body parts and bodily images of knowledge that have the potential to teach us something about knowledge itself. From “the nose knows” to having “seminal ideas” to being a “birdbrain,” expressions reveal how we (...) conceive of knowledge, how we value it, what threatens and safeguards it, and how it relates to identity. (shrink)