The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...) Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. (shrink)

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.

The variety \ of implication zroupoids and a constant 0) was defined and investigated by Sankappanavar :21–50, 2012), as a generalization of De Morgan algebras. Also, in Sankappanavar :21–50, 2012), several subvarieties of \ were introduced, including the subvariety \, defined by the identity: \, which plays a crucial role in this paper. Some more new subvarieties of \ are studied in Cornejo and Sankappanavar that includes the subvariety \ of semilattices with a least element 0. An (...) explicit description of semisimple subvarieties of \ is given in Cornejo and Sankappanavar. It is a well known fact that there is a partial order ) induced by the operation ∧, both in the variety \ of semilattices with a least element and in the variety \ of De Morgan algebras. As both \ and \ are subvarieties of \ and the definition of partial order can be expressed in terms of the implication and the constant, it is but natural to ask whether the relation \ on \ is actually a partial order in some subvariety of \ that includes both \ and \. The purpose of the present paper is two-fold: Firstly, a complete answer is given to the above mentioned problem. Indeed, our first main theorem shows that the variety \ is a maximal subvariety of \ with respect to the property that the relation \ is a partial order on its members. In view of this result, one is then naturally led to consider the problem of determining the number of non-isomorphic algebras in \ that can be defined on an n-element chain -chains), n being a natural number. Secondly, we answer this problem in our second main theorem which says that, for each \, there are exactly n nonisomorphic \-chains of size n. (shrink)

The purpose of this paper is to define and investigate the new class of quasi-Stone algebras . Among other things we characterize the class of simple QSA's and the class of subdirectly irreducible QSA's. It follows from this characterization that the subdirectly irreducible QSA's form an elementary class and that the variety of QSA's is locally finite. Furthermore we prove that the lattice of subvarieties of QSA's is an -chain. MSC: 03G25, 06D16, 06E15.

We determine the number of non‐isomorphic semi‐Heyting algebras on an n‐element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non‐isomorphic semi‐Heyting chains of a given size in some important subvarieties of the variety of semi‐Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers of non‐isomorphic semi‐Heyting chains with (...) n elements such that removing the mth element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi‐Heyting chain with elements can be extended to a n element semi‐Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers that provides some extra information. (shrink)

This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary expansion (...) of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH. (shrink)

This paper augments Hailperin's substantial efforts to place Boole's algebra of logic on a solid footing. Namely Horn sentences are used to give a modern formulation of the principle that Boole adopted in 1854 as the foundation for his algebra of logic—we call this principle The Rule of 0 and 1.

Now in a third edition, Introduction to Philosophy: Classical and Contemporary Readings is a highly acclaimed, topically organized collection that covers five major areas of philosophy--theory of knowledge, philosophy of religion, philosophy of mind, freedom and determinism, and moral philosophy. Editor Louis P. Pojman enhances the text's topical organization by arranging the selections into a pro/con format to help students better understand opposing arguments. He also includes accessible introductions to each chapter, subsection, and individual reading, a unique feature for an (...) anthology of this depth. While the book focuses on a compelling sampling of classical material--including selections from Plato, Aristotle, Descartes, Locke, Berkeley, Hume, and Kant--it also incorporates some of philosophy's best twentieth-century and contemporary work, featuring articles by Bertrand Russell, Richard Taylor, John Searle, Thomas Nagel, and others. This third edition contains an expanded glossary, more extensive section introductions, and twelve new selections: Karl Popper: "Epistemology without a Knowing Subject" Richard Rorty: "Dismantling Truth: Solidarity Versus Objectivity" Daniel Dennett: "Postmodernism and Truth" Bruce Russell: "The Problem of Evil: Too Much Suffering" David Chalmers: "Against Materialism: Can Consciousness Be Reductively Explained?" Baron Paul Henri d'Holbach: "A Defense of Determinism" Michael Levin: "A Compatibilist Defense of Moral Responsibility" Plato: Socratic Morality: "Crito" Herodotus: "Custom Is King" J. L. Mackie: "The Subjectivity of Values" Louis P. Pojman: "A Critique of Mackie's Theory of Moral Subjectivism" Thomas Nagel: "Moral Luck". (shrink)

In ”Skepticism,” Peter Klein distinguishes between the “Academic Skeptic” who proposes that we cannot have knowledge of a certain set of propositions and the “Pyrrhonian Skeptic” who refrains from opining about whether we can have knowledge. Klein argues that Academic Skepticism is plausibly supported by a “Closure Principle‐style” argument based on the claim that if x entails y and S has justification for x, then S has justification for y. He turns to contextualism to see if it can contribute to (...) the discussion between one who claims that we can have knowledge about some epistemically interesting class of propositions and the Academic Skeptic. He outlines the background of Pyrrhonian Skepticism, pointing out that the Pyrrhonist withholds assent concerning our knowledge‐bearing status because reason cannot provide an adequate basis for assent. He assesses three possible patterns of reasoning, and concludes that the Pyrrhonist view, that reason cannot resolve matters concerning the nonevident, is vindicated. (shrink)

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

This paper advances the research on personalization of political communication by investigating whether this process of focusing on politicians instead of political issues plays a role on Twitter. Results of a content analysis of 5,530 tweets posted in the run-up to the German federal election provide evidence that Twitter communication refers more often to politicians than to issues. However, tweets containing personal characteristics about political leaders play only a marginal role. When distinguishing among different groups of actors on Twitter (journalists, (...) politicians, citizens), we find that citizens focus more on candidates than do journalists or politicians. Investigating the impact of a televised debate on Twitter communication, we observe that this person-centered event puts the focus on individual politicians instead of issues. (shrink)

It has been over two decades since Miranda Fricker labeled epistemic injustice, in which an agent is wronged in their capacity as a knower. The philosophical literature has proliferated with variants and related concepts. By considering cases in popular music, we argue that it is worth distinguishing a parallel phenomenon of art-interpretive injustice, in which an agent is wronged in their creative capacity as a possible artist. In section 1, we consider the prosecutorial use of rap lyrics in court as (...) a central case of this injustice. In section 2, we distinguish art-interpretive injustice from other categories already discussed in recent literature. In section 3, we discuss the relationship between genre discourse and identity prejudice. The case for recognizing the category of art-interpretive injustice is that it allows one to recognize a class of harms as being importantly related in ways that one would otherwise overlook. (shrink)

The conflict in Gaza and Israel that ignited on October 7, 2023 signals a catastrophic breakdown in the possibility of ethical dialogue in the region. The actions on both sides have revealed a dissolution of ethical restraints, with unimaginably cruel attacks on civilians, murder of children, destruction of health facilities, and denial of basic needs such as water, food, and shelter. There is a need both to understand the nature of the ethical singularity represented by this conflict and what, if (...) any, options are available to allow the reconstruction of communication between the warring parties. This article seeks to address these tasks by analysing the conflict as inherently an ethical one, in the sense that it exposes a rupture in the fabric of communicative relationships that has evolved systematically out of the deep cultural structures from which all protagonists have emerged. Drawing on the work of Levinas, Habermas, Arendt, and others, and referring to the specific circumstances in the region, it examines the ethical sources of the crisis and tries to identify conditions for its resolution. The possibility of reconciliation—that is, of refiguring relationships to open up a space for dialogue to create pathways to heal the ruptures—is examined. The dark legacy of the Holocaust is identified as an abiding cultural vulnerability for both societies. It is concluded, however, that the rich history of partnerships and collaborations between Jews and Palestinians provides a robust infrastructure on the basis of which a sustainable peace might be built, providing a much-needed source of hope. (shrink)

By the time of his death in 2006, Sir Peter Strawson was regarded as one of the world's most distinguished philosophers. Unavailable for many years,_ Scepticism and Naturalism_ is a profound reflection on two classic philosophical problems by a philosopher at the pinnacle of his career. Based on his acclaimed Woodbridge lectures delivered at Columbia University in 1983, Strawson begins with a discussion of scepticism, which he defines as questioning the adequacy of our grounds for holding various beliefs. He then (...) draws deftly on Hume and Wittgenstein to argue that we must distinguish between 'hard', scientific naturalism; or 'soft', humanistic naturalism. In the remaining chapters the author takes up several issues in which sceptical doubts play an important role, in particular the nature of transcendental arguments and including the objectivity of moral philosophy, the mental and the physical, and the existence of abstract entities. _Scepticism and Naturalism_ is essential reading for those seeking an introduction to the work of one of the twentieth century’s most important and original philosophers. This reissue includes a substantial new foreword by Quassim Cassam and a fascinating intellectual autobiography by Strawson, which together form an excellent introduction to his life and work. (shrink)

Pekakak adalah salah satu tokoh yang memiliki pengetahuan mendalam dan perencanaan yang cermat. Saat fajar menyingsing, ia terlihat bertengger di atas pohon. Dengan kemampuan sempurna untuk mengontrol kecepatan penerbangan miliknya, seperti kapan harus memperlambat atau mempercepat, dia dapat dengan mudah menghitung cara optimal untuk menangkap ikan.

This article aims to read feminist new materialisms (Barad), together with ‘postulated’ linguistic or cultural primacy of Queer Theory (Butler), to show how both are engaged in similar critical-ethical endeavours. The central argument is that the criticism of Barad and new materialisms misses Butler’s materialistic insights due to a narrow interpretation of Butler's alleged social-constructivist position. There is, therefore, a specific focus on where they both make similar ethical appeals. Moreover, the article relies on Adorno's negative dialectic to highlight an (...) interpretation of Barad and Butler as being part of the same dialectical movement, in which materialism and idealism fluctuate in their mutual criticisms, thus continuing the procession towards 'new knowledge' and emancipation, or freedom, through their motions back and forth. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

Differential scanning calorimetry (DSC) has been employed to investigate the glass transition activation energy E g, thermal stability and glass-forming ability (GFA) of Se90In10− x Sb x (x = 0, 2, 4, 6, 8, 10) chalcogenide glasses. DSC runs were performed at six different heating rates. Well-defined endothermic and exothermic peaks were obtained at glass transition and crystallization temperature. The dependence of glass transition temperature T g on heating rate (α), as well as composition of Sb, has been studied. From (...) the dependence of glass transition temperature on heating rate, the E g has been calculated on the basis of the Kissinger [Anal. Chem. 29 (1957) p.1702] and Moynihan [J. Phys. Chem. 78 (1974) p.267] models. Thermal stability has been monitored through the calculation of temperature differences T c–T g, the stability parameter S, and the enthalpy released during crystallization H c. The GFA has been investigated on the basis of the Hruby parameter H r, which is strong indicator of GFA. Results for GFA are in good agreement with fragility index F i calculations, indicating that Se90In6Sb4 is an excellent glass-former. (shrink)

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

My topic is personal identity, or rather,ouridentity. There is general, but not, of course, unanimous, agreement that it is wrong to give an account of what is involved in, and essential to, our persistence over time which requires the existence of immaterial entities, but, it seems to me, there is no consensus about how, within, what might be called this naturalistic framework, we should best procede. This lack of consensus, no doubt, reflects the difficulty, which must strike anyone who has (...) considered the issue, of achieving, just in one's own thinking, a reflective equilibrium. The theory of personal identity, I feel, provides a curious contrast. On the one side, it seems highly important to know what sort of thing we are, but, on the other, it is hard to find any answer which has a ‘solid’ feel. (shrink)