The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in (...) the algebraic counterpart of a logic \ with suitable infinitary definability properties of \, while not making the standard but awkward assumption that \ comes furnished with a proper class of variables. (shrink)

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...) for every integer $n \geq 2$ , the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics. (shrink)

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

A quasivariety of algebras has the joint embedding property (JEP) if and only if it is generated by a single algebra A. It is structurally complete if and only if the free ℵ0‐generated algebra in can serve as A. A consequence of this demand, called ‘passive structural completeness’ (PSC), is that the nontrivial members of all satisfy the same existential positive sentences. We prove that if is PSC then it still has the JEP, and if it has the JEP and (...) its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if is relatively semisimple then it is generated by one ‐simple algebra. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC if and only if its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics. (shrink)

Two essays on utilitarianism, written from opposite points of view, by J. J. C. Smart and Bernard Williams. In the first part of the book Professor Smart advocates a modern and sophisticated version of classical utilitarianism; he tries to formulate a consistent and persuasive elaboration of the doctrine that the rightness and wrongness of actions is determined solely by their consequences, and in particular their consequences for the sum total of human happiness. In Part II Bernard Williams offers a sustained (...) and vigorous critique of utilitarian assumptions, arguments and ideals. He finds inadequate the theory of action implied by utilitarianism, and he argues that utilitarianism fails to engage at a serious level with the real problems of moral and political philosophy, and fails to make sense of notions such as integrity, or even human happiness itself. This book should be of interest to welfare economists, political scientists and decision-theorists. (shrink)

In this article I try to refute the so-called "libertarian" theory of free will, and to examine how our conclusion ought to modify our common attitudes of praise and blame. In attacking the libertarian view, I shall try to show that it cannot be consistently stated. That is, my dscussion will be an "analytic-philosophic" one. I shall neglect what I think is in practice an equally powerful method of attack on the libertarian: a challenge to state his theory in such (...) a way that it will fit in the modern biology and psychology, which are becoming increasingly physicalistic. (shrink)

In twelfth-century Europe schools flourished in many centres. There were schools in monasteries and cathedrals, primarily for the education of monks and priests but often open also to laymen. In Italian towns, especially, there were lay schools teaching law and commercial skills to fee-paying students. In France, especially, also in England and other countries, there were schools for feepaying students of the liberal arts. The traditional list of the liberal arts included seven: grammar, logic and rhetoric (the "trivium"), and arithmetic, (...) geometry, astronomy and music (the "quadrivium"): most of the schools we're talking about taught the trivium, grammar, logic and rhetoric. These three disciplines in one way or other taught language skills; they were sometimes called the artes sermocinales. Students who had completed these "trivial" studies sometimes moved on to theology, or sometimes set up as teachers themselves of grammar, logic and rhetoric. Some students travelled from country to country looking for a good school, and sometimes made their living for a while by teaching before becoming students again. (shrink)

In this essay I propose to offer some observations in due course on how Christian thought and practice in general might profit from a central theme in the theology of Rāmānuja, a Tamil Vaisnava Brahmin whose traditional date straddles the eleventh and twelfth centuries of the Christian era. The central theme I have in mind is expressed in Rāmānuja's view that the ‘world’ is the ‘body’ of Brahman or God. We shall go on to explain what this means, but let (...) me state first that my overall aim is to further inter-religious understanding, especially between Christian and Hindu points of view. In professing a concern for inter-religious dialogue I know that I reflect a longstanding interest of Professor H. D. Lewis. I shall seek to show that the Christian religion can profit both from the content and the method of Rāmānuja's body-of-God theology. To this end this essay is divided into two sections. Section I is the longer: it contains an analysis of what Rāmānuja did mean by his body-of-God theme – doubtless unfamiliar ground for most of the readers of this essay – and serves as a propaedeutic for what follows in section 2. In section 2 I shall attempt to ‘extrapolate’ Rāmānuja's thinking into a Christian context, with dialogue in mind. Section 2 cannot be appreciated for the promise I hope it holds out without the detail of the first section. (shrink)

J.S. Mill's plural voting proposal in Considerations on Representative Government presents political theorists with a puzzle: the elitist proposal that some individuals deserve a greater voice than others seems at odds with Mill's repeated arguments for the value of full participation in government. This essay looks at Mill's arguments for plural voting, arguing that, far from being motivated solely by elitism, Mill's account is actually driven by a commitment to both competence and participation. It goes on to argue that, for (...) Mill, much of the value of political participation lies in its unique ability to educate the participants. That ability to educate is not, however, a product of participation alone; rather, for Mill, the true educative benefits of participation obtain only when competence and participation work together in the political sphere. Plural voting, then, is a mechanism for allowing Mill to take advantage of the educative benefits that arise from the intersection of competence and participation. (shrink)

This paper begins with a Davidsonian puzzle in the epistemology of perception and introduces two solutions to that puzzle: the Truth-Maker View (TMV) and the Content Model. The paper goes on to elaborate (TMV), elements of which can be found in the work of Kalderon (2011) and Brewer (2011). The central tenant of (TMV) is the claim that one's reason for one's perceptual belief should, in all cases, be identified with some item one perceives which makes the proposition believed true. (...) I defend an argument against (TMV) which appeals to (a) the claim that the reason for which one believes should always to be identified with the explanans of the rationalising explanation to which one's belief is subject and (b) the claim that the explanantia of rationalising explanations must be identified with truths. I finish by replying to two objections to the argument. (shrink)

Abstractabstract:Vaccine hesitancy continues to pose a formidable obstacle to increasing national COVID-19 vaccination rates in the US, but this is not the first time that American vaccination efforts have confronted resistance and apathy. This study examines the history of US vaccination efforts against smallpox, polio, and measles, highlighting persistent drivers of vaccine hesitancy as well as factors that helped overcome it. The research reveals that logistical barriers, negative portrayals in the media, and fears about safety stymied inoculation efforts as early (...) as the 18th century and continue to do so. However, vaccine hesitancy has been markedly diminished when trusted community leaders have guided efforts, when ordinary citizens have felt personally invested in the success of the vaccine, and when vaccination efforts have been tied to broader projects to improve public health and social cohesion. Deliberately cultivating such factors could be an effective strategy for lessening opposition today, when COVID-19's distinctive characteristics make addressing vaccine hesitancy more urgent than it has ever been. (shrink)

This article engages various critiques of Fair Trade, from its participation in commodification to providing a cover for "Fair-washing" corporations, and argues that Fair Trade has the potential to answer the challenges contained within them if and when it initiates an ongoing process of developing the "ethical valuedadded" content of the label. This argument is made in a number of ways. First, by distinguishing between economic and human development impacts and ethics, this article argues that these impacts are necessary but (...) not sufficient conditions for ethical trade. Second, it engages the question of the possibility of ethical practice in economics generally; developing the idea that when economics is concerned with securing the material basis of a broad range of life capacities it becomes ethical. Third, Fair Trade practice itself is examined from this standpoint, and is conceived of as both comprising a promising ethical value-added practice as well as posing a problem in its current formulation that the framework of ethical valueadded can help understand and resolve. Finally, an examination of these theoretical ideas in practice is undertaken through a case study of Café Femenino, a Fair Trade coffee produced in Peru. In conclusion it is argued that for Fair Trade to build upon its economic and human impacts, and therefore remain a meaningful ethical and economic alternative to corporate capitalism and globalization, it must distinguish itself clearly in ethics from those market relations it wishes, explicitly or implicitly, to challenge. (shrink)