Several philosophers have argued that intention is conceptually governed by a normative standard of correctness. Intention normativism is supposed to be the practical counterpart of belief normativism, which is widely discussed in the literature. In this paper, I discuss the extant formulations of the norm of intention and find all of them wanting. I then suggest and defend a new formulation of the norm of intention. I argue that the suggested formulation is immune to the problems that beset other candidates (...) for the norm of intention. (shrink)

This article examines how emerging technologies – particularly artificial intelligence – disrupt the moral and institutional foundations of contemporary military practice. While strategic documents from the United States, NATO, and other major actors anticipate profound institutional transformation driven by AI, their treatment of ethics largely confines itself to legal compliance and technical safeguards, leaving the ethical role of military leadership in managing disruptive change underexamined. Drawing on Seumas Miller’s distinction between social institutions that are merely instrumental to collective goods and (...) those whose defining ends are constitutive of such goods, the article argues that the military belongs to the latter category. Because the military’s core function – defending the sovereignty of a polity – is itself morally significant, technological disruption of its organizational structures simultaneously constitutes ethical disruption. The article thus reconceives change management during periods of technological transition as calling for a specific kind of military prudence, a practical wisdom exercised within and through the institution’s role-mediated ethical practices. By analyzing three concrete modes of techno-moral disruption, the article shows how AI may reshape ethical standards, redistribute professional knowledge, and alter organizational ethos, and why navigating these transformations responsibly is a central task of military virtue. (shrink)

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.

The relationship between traumatic experiences and subsequent distress is not well understood, and little research focuses on the lived experience of psychological trauma. I draw on Louis Sass’s phenomenological taxonomy to address this lacuna. I present his differentiation between relations of phenomenological causality and implication and demonstrate that his taxonomy can be applied to experiences of trauma. Relations of phenomenological causality and implication can be identified in the genesis and constitution of post-traumatic distress. My adaptation of Sass’s taxonomy (...) will furthermore offer an extension and development of his account, applying it to the study of post-traumatic experiences and elaborating it in the process. I shall demonstrate that whether experiences occur synchronically or diachronically is not essential to their categorization in terms of phenomenological implication and causality, respectively. I will show that an alteration in perception or behavior post trauma might temporally succeed the traumatizing event while, at the same time, being implied in the experience of the event. Thereby, I demonstrate how phenomenology may contribute to a detailed understanding of experiences of trauma. Scrutiny of traumatic experiences furthermore promises to contribute to the philosophical discourse on causality, implication, and temporal experience. (shrink)

This paper investigates the logic of compatibility as a ground for the logic of conditionals. We identify a family of principles expressing key properties of compatibility, which can be coherently ordered. Assuming that conditionals are definable in terms of incompatibility — the negation of compatibility — each of the principles identified yields corresponding principles governing conditionals. Clarifying these derivability relations provides a new perspective on several existing accounts of conditionals.

Implication barrier theses deny that one can derive sentences of one type from sentences of another. Hume’s Law is an implication barrier thesis; it denies that one can derive an ‘ought’ (a normative sentence) from an ‘is’ (a descriptive sentence). Though Hume’s Law is controversial, some barrier theses are philosophical platitudes; in his Lectures on Logical Atomism, Bertrand Russell claims: You can never arrive at a general proposition by inference particular propositions alone. You will always have to have (...) at least one general proposition in your premises. (Russell, 1918, p. 206) We will refer to this claim—that one cannot derive general sentences from particular sentences—as Russell’s Law.1 A third barrier thesis claims that one cannot derive sentences about the future from sentences about the past or present. Hume’s endorsement of this barrier thesis is well-known: all inferences from experience suppose, as their foundation, that the future will resemble the past . . . if there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any argument from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. (Hume, EHU 4.21/37) We will refer to this barrier thesis as Hume’s Second Law. A fourth barrier thesis says that one cannot derive a necessary sentence from one about the actual world and we will refer to this last thesis Kant’s Law. Such implication barrier theses present a problem. (shrink)

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework (...) for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

For Heidegger, Hegel understands being, ‘the highest actuality’, as the categories which pervade and thereby form all objects and events. Since, Heidegger argues, the categories are, in Hegel, present-at-hand, Hegel conceives of being as presence-at-hand. This is a problem, for Heidegger, because it entails the full transparency and knowability of being, whereas, in his view, being is partially hidden and unknowable. I consider the objection to this Heideggerian critique of Hegel that Hegelian logic understands being not only as the list (...) of categories but also as their derivation and movement from pure being to the absolute idea, which (derivation and movement) establish being not only as presence but also as implication. Since being-as-implication is (a) not presence-at-hand and (b) necessary to being, it cannot be said that Hegel's account of being turns it into full transparency and knowability. Heidegger's critique should, therefore, be rejected. I argue that this objection is unsuccessful because there is strong evidence in the Logic that Hegel ‘subordinates’ being-as-implication to presence-at-hand. Implication's way of being is, in Hegel, only a collapse into presence-at-hand and hence ‘merely a modification of presence’. Consequently, Heidegger's critique of Hegel should not be rejected based on the objection. I conclude the article with a remark on the relation between language and being-as-implication. I argue that Hegel's account of being-as-implication in language disrespects the autonomy of being-as-implication therein and that Haas's argument for such an autonomy based on the phenomenon of the syntactic ellipsis of ‘is’ fails to undermine Hegel's account. (shrink)

An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of (...) the existence of a chain of immediately evident steps linking premises and conclusion. (shrink)

An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of (...) the existence of a chain of immediately evident steps linking premises and conclusion. (shrink)

C. I. Lewis intended his systems S1–S5 as contributions to the study of “strict implication”, but in his formulation, strict implication is so thoroughly intertwined with other notions, such as possibility and negation, that it remains a problem, to separate out the properties of strict implication itself. I shall solve this problem for S2–5 and von Wright's M. The results for S3–5 are given below, while the implicative parts of S2 and M, which are rather more complicated, (...) are given in §5.In this presentation, ‘⊃’ stands for strict implication, and missing brackets for ‘⊃’ are restored by associationtothe right. Astrictformula is one of the form A ⊃ B. Axiom schemes are used throughout. (shrink)

We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

In this contribution, we will present some results concerning the connectives of bi-intuitionistic logic in the setting of Arnold Koslow’s implication structures. Furthermore, we will present soundness and completeness results of Koslow’s implication structures with respect to bi-intuitionistic logic.

Most of the logics of grounding that have so far been proposed contain grounding axioms, or grounding rules, for the connectives of conjunction, disjunction and negation, but little attention has been dedicated to the implication connective. The present paper aims at repairing this situation by proposing adequate grounding principles for relevant implication. Because of the interaction between negation and implication, new grounding principles concerning negation will also arise.

The authors of Beziau and Franceschetto work with logics that have the property of not satisfying any of the formulations of the principle of non contradiction, Béziau and Franceschetto also analyze, among the three-valued logics, which of these logics satisfy this property. They prove that there exist only four of such logics, but only two of them are worthwhile to study. The language of these logics does not consider implication as a connective. However, the enrichment of a language with (...) an implication connective leads us to more interesting systems, therefore we look for one implication for these logics and we study further properties that the logics obtain when this connective is added to these systems. (shrink)

This manuscript presents an English translation of the work titled “Begründung Einer Strengen Implikation” by the German logician and mathematician Wilhelm Ackermann (1896-1962), first published in June 1956.

The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength and \). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system (...) for \, CI\, is definitionally equivalent to the deontic system KD and is intertranslatable with the minimal consequential system for \, CI. The main drawback ot the weaker operator \ is that it lacks unrestricted contraposition, but the final section of the paper argues that \ has some properties which make it a valuable alternative to \, turning out especially plausible as a basis for the definition of operators representing synthetic conditionals. (shrink)

of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.

Suppose P is the conjunction of all truths statable in the austere vocabulary of an ideal physics. Then phsicalists are likely to accept that any truths not included in P are different ways of talking about the reality specified by P. This ‘redescription thesis’ can be made clearer by means of the ‘strict implication thesis’, according to which inconsistency or incoherence are involved in denying the implication from P to interesting truths not included in it, such as truths (...) about phenomenal consciousness. Commitment to the strict implication thesis cannot be escaped by appeal to a posteriori necessary identities or entailments. A minimal physicalism formulated in terms of strict implication is preferable to one based on a priori entailment. (shrink)

The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics (...) for DAI, showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic. This fact sheds further light on the relationship between containment logics and logics of nonsense. (shrink)