In his milestone textbook Lattice Theory, Garrett Birkhoff challenged his readers to develop a "common abstraction" that includes Boolean algebras and lattice-ordered groups as special cases. In this paper, after reviewing the past attempts to solve the problem, we provide our own answer by selecting as common generalization of ������������ and ������������ their join ������������∨������������ in the lattice of subvarieties of ������ℒ (the variety of FL-algebras); we argue that such a solution is optimal under several respects and we give an (...) explicit equational basis for ������������∨������������ relative to ������ℒ. Finally, we prove a Holland-type representation theorem for a variety of FL-algebras containing ������������∨������������. (shrink)

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice.

The starting point of the present study is the interpretation of intuitionistic linear logic in Petri nets proposed by U. Engberg and G. Winskel. We show that several categories of order algebras provide equivalent interpretations of this logic, and identify the category of the so called strongly coherent quantales arising in these interpretations. The equivalence of the interpretations is intimately related to the categorical facts that the aforementioned categories are connected with each other via adjunctions, and the compositions of the (...) connecting functors with co-domain the category of strongly coherent quantales are dense. In particular, each quantale canonically induces a Petri net, and this association gives rise to an adjunction between the category of quantales and a category whose objects are all Petri nets. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

The central result of this paper provides a simple equational basis for the join, IRLLG, of the variety LG of lattice-ordered groups (-groups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRLLG=IRL×LG. In the process of deriving our result, we will obtain simple axiomatic bases for other products of classes of residuated structures, including the class IRL×s LG, consisting of all semi-direct products of members of IRL by members of LG. We (...) conclude the paper by presenting a general method for constructing such semi-direct products, including wreath products. (shrink)

In this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are constructed by means of alternating applications of disjoint union and ordinal sums with chains. These decompositions are examples of ordinal decompositions in relatively normal lattices as introduced by Snodgrass, Tsinakis, and Hart. We conclude the paper (...) with an application to information systems. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over other (...) methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

According to most accounts of trust, you can only trust other people (or groups of people). To trust is to think that another has goodwill, or something to that effect. I sketch a different form of trust: the unquestioning attitude. What it is to trust, in this sense, is to settle one’s mind about something, to stop questioning it. To trust is to rely on a resource while suspending deliberation over its reliability. Trust lowers the barrier of monitoring, challenging, checking, (...) and questioning. Trust sets up open pipelines between yourself and parts of the external world. Trust permits external resources to have a similar relationship to one as one’s internal cognitive faculties. This creates efficiency, but at the price of exquisite vulnerability. We must trust in this way because we are cognitively limited beings in a cognitively overwhelming world. Crucially, we can hold the unquestioning attitude towards objects and technologies. When I trust my climbing rope, I stop worrying about its reliability. When I trust my online calendaring system, I simply go to the events indicated, without question. But, one might worry, how could one ever hold such a normatively loaded attitude as trust towards mere objects? How could it ever make sense to feel betrayed by an object? Trust is our engine for expanding and outsourcing our agency — for binding external processes into our practical selves. Thus, we can be betrayed by our smartphones in the same way that we can be betrayed by our memory. When we trust, we try to make something a part of our agency, and we are betrayed when our part lets us down. To unquestioningly trust something is to let it in—to attempt to bring it inside one’s practical functioning. This suggests a new form of gullibility: agential gullibility, which occurs when agents too hastily and carelessly integrate external resources into their own agency. (shrink)

Value capture occurs when an agent’s values are rich and subtle; they enter a social environment that presents simplified — typically quantified — versions of those values; and those simplified articulations come to dominate their practical reasoning. Examples include becoming motivated by FitBit’s step counts, Twitter Likes and Re-tweets, citation rates, ranked lists of best schools, and Grade Point Averages. We are vulnerable to value capture because of the competitive advantage that such crisp and clear expressions of value have in (...) our private reasoning and our public justification. There is, however, a price. In value capture, we take a central component of our autonomy — our ongoing deliberation over the exact articulation of our values — and we outsource it. And the metrics to which we outsource usually engineered for the interests of some external force, like a large-scale institution’s interest in cross-contextual comprehensibility and quick aggregability. That outsourcing cuts off one of the key benefits to personal deliberation. In value capture, we no longer adjust our values and their articulations in light of own rich experience of the world. Our values should often be carefully tailored to our particular selves or our small-scale communities, but in value capture, we buy our values off the rack. In some cases – like decreasing CO2 emissions – the costs of non-tailored values are outweighed by the benefit of precise collective coordination. In other cases, like in our aesthetic lives, they are not. This suggests that we should want different values suited to different scales. We should want value federalism. Some values are perhaps best pursued at the largest-scale level, others at smaller scales. The problem occurs when we exhibit an excess preference for the largest-scale values – when we consistently let the universal metrics swamp our quieter interests. (shrink)

Recent conversation has blurred two very different social epistemic phenomena: echo chambers and epistemic bubbles. Members of epistemic bubbles merely lack exposure to relevant information and arguments. Members of echo chambers, on the other hand, have been brought to systematically distrust all outside sources. In epistemic bubbles, other voices are not heard; in echo chambers, other voices are actively undermined. It is crucial to keep these phenomena distinct. First, echo chambers can explain the post-truth phenomena in a way that epistemic (...) bubbles cannot. Second, each type of structure requires a distinct intervention. Mere exposure to evidence can shatter an epistemic bubble, but may actually reinforce an echo chamber. Finally, echo chambers are much harder to escape. Once in their grip, an agent may act with epistemic virtue, but social context will pervert those actions. Escape from an echo chamber may require a radical rebooting of one's belief system. (shrink)

In his celebrated masterpiece, Symposium, Plato imagines a high-society dinner-party in Athens in 416 BC at which the guests - including the comic poet Aristophanes and, of course, Plato's mentor Socrates - each deliver a short speech in praise of love. The sequence of dazzling speeches culminates in Socrates' famous account of the views of Diotima, a prophetess who taught him that love is our means of trying to attain goodness. And then into the party bursts the drunken Alcibiades, the (...) most popular and notorious Athenian of the time, who insists on praising Socrates himself rather than love, and gives us a brilliant sketch of this enigmatic character. The power, humour, and pathos of Plato's creation engages the reader on every page. This new translation is complemented by full explanatory notes and an illuminating introduction. (shrink)

"This edition, which replaces the original Loeb edition..., offers text, translation, and annotation that are fully current with modern scholarship"--Front flap of dust jacket, volume 1.

Why do moral people so often fail to act morally? Standard scientific answers point to poor moral judgment (based on deficient character development, reason, or intuition) or to situational pressure. I consider a third possibility: a relative lack of truly moral motivation and emotion. What has been taken for moral motivation is often instead a subtle form of egoism. Recent research provides considerable evidence for moral hypocrisy—motivation to appear moral while, if possible, avoid the cost of actually being moral—but very (...) little evidence for moral integrity—motivation to actually be moral. The lack of truly moral motivation may, in turn, be linked to a lack of truly moral emotion, at least in response to violation of certain moral standards. (shrink)

forthcoming in R. Cameron, B. Hale and A. Hoffmann (ed.s), The Logic, Epistemology and Metaphysics of Modality, Oxford University Press. Presents a concept-grounding account of modal knowledge.

Анотація. У статті проаналізовані досягнення Соціального Вчительства Католицької Церкви, репрезентовані працями Лева ХІІІ, Пія ХІ, Пія ХІІ, Івана Павла ІІ, що розкривають змістовні характеристики поняття «принцип субсидіарності», його роль і значення в системі християнських цінностей. Принцип субсидіарності робить можливими такі взаємовідносини в соціальному житті, коли спільнота вищого порядку не втручається у внутрішнє життя спільноти нижчого порядку, перебираючи на себе належні тій функції; заради спільного добра, спільного блага вона надає їй у разі потреби підтримку й допомогу, узгоджуючи у такий спосіб її (...) взаємодію з іншими соціальними структурами. Принцип субсидіарності скеровує соціальну практику на утвердження спільного блага в людському співтоваристві. Поширення і застосування принципу субсидіарності протистоїть небезпеці «одержавлення» суспільства та найзагрозливіших проявів колективізму, обмежує абсолютизацію влади, бюрократизацію державних і соціокультурних структур, стає одним із гарантів дотримання прав і свобод громадян своєї країни. (shrink)

We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras.

Philosophers of biology typically pose questions about individuation by asking “what is an individual?” For example, we ask, “what is an individual species”, “what is an individual organism”, and “what is an individual gene?” In the first part of this chapter, I present my account of the gene concept and how it is used in investigative practices in order to motivate a more pragmatic approach. Instead of asking “what is a gene?”, I ask: “how do biologists individuate genes?”, “for what (...) purposes?”, and “do their practices of individuating genes serve these purposes?" In the second part of this chapter, I propose that we use this approach when analyzing concepts of organisms and biological individuals. Following philosophical pragmatism, I argue that we should abstain from attempts to situate individuation of Darwinian individuals or of holobionts in a philosophy of nature. Instead, we should analyze practices of individuating organisms in terms of three-place relations between the world, ideas, and human purposes and actions. I conclude with three lessons: an ontological, an epistemological, and a meta-philosophical lesson, which I suggest, apply to philosophy of science generally and to philosophy and metaphysics at large. (shrink)

In this critique, Martha Nussbaum argues that our dominant theories of development have given us policies that ignore our most basic human needs for dignity and self-respect.

This edition of Martin Ostwald's revised version of J. B. Skemp's 1952 translation of _Statesman_ includes a new selected bibliography, as well as Ostwald's interpretive introduction, which traces the evolution in Plato's political philosophy from _Republic_ to _Statesman to Laws_--from philosopher-king to royal statesman.

The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...) potential new information, suggesting that conditional propositions should be understood as projections of epistemic policies onto the world.Robert C. Stalnaker is a professor in the Sage School of Philosophy at Cornell University. A Bradford Book. (shrink)

The question I wish to explore is this: Does idealism conflict with common sense? Unfortunately, the answer I give may seem like a rather banal one: It depends. What do we mean by ‘idealism’ and ‘common sense?’ I distinguish three main varieties of idealism: absolute idealism, Berkeleyan idealism, and dualistic idealism. After clarifying what is meant by common sense, I consider whether our three idealisms run afoul of it. The first does, but the latter two don’t. I conclude that while (...) Moore’s famous common sense critique is sound against external world skepticism, against Berkeleyan idealism and dualist idealism it is unavailing. (shrink)

Alasdair MacIntyre explores some central philosophical, political and moral claims of modernity and argues that a proper understanding of human goods requires a rejection of these claims. In a wide-ranging discussion, he considers how normative and evaluative judgments are to be understood, how desire and practical reasoning are to be characterized, what it is to have adequate self-knowledge, and what part narrative plays in our understanding of human lives. He asks, further, what it would be to understand the modern condition (...) from a neo-Aristotelian or Thomistic perspective, and argues that Thomistic Aristotelianism, informed by Marx's insights, provides us with resources for constructing a contemporary politics and ethics which both enable and require us to act against modernity from within modernity. This rich and important book builds on and advances MacIntyre's thinking in ethics and moral philosophy, and will be of great interest to readers in both fields. (shrink)

Монографія "Функціональність релігії: український контекст".

A revolutionary new theory and call to action on animal rights, ethics, and law from the renowned philosopher Martha C. Nussbaum.

What is empiricism and what could it be? Bas . van Fraassen, one of the world’s foremost contributors to philosophical logic and the philosophy of science, here undertakes a fresh consideration of these questions and offers a program for renewal of the empiricist tradition. The empiricist tradition is not and could not be defined by common doctrines, but embodies a certain stance in philosophy, van Fraassen says. This stance is displayed first of all in a searing, recurrent critique of metaphysics, (...) and secondly in a focus on experience that requires a voluntarist view of belief and opinion. Van Fraassen focuses on the philosophical problems of scientific and conceptual revolutions and on the not unrelated ruptures between religious and secular ways of seeing or conceiving of ourselves. He explores what it is to be or not be secular and points the way toward a new relationship between secularism and science within philosophy. (shrink)

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

Aristotle on Practical Wisdom is the first full-scale commentary on Nicomachean Ethics VI to be issued in a century, and the most illuminating ever. A meticulous translation with facing-page analysis enables readers to engage directly with Aristotle's account, while the lucid introduction locates it in the context of his—and later—ethical thought.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

De uma perspectiva comportamentalista radical, o eu é um repertório verbal complexo, que, como tal, tem uma gênese social. O reconhecimento da origem social do “eu” abre caminho para uma análise política, incluindo uma discussão do pa- pel das relações de poder na constituição do eu. Entretanto, uma concepção radicalmente social do “eu”, como a proposta pelo comportamentalismo, suscita um problema político: se o eu é integralmente produto do ambiente social, de onde viria uma eventual “vontade” de romper com esse (...) sistema? Parece que para reconhecer a possibilidade de ação política transformadora seria preciso preservar uma noção descontextualizada de “eu”. Considerando essa dificuldade, o objetivo deste artigo é propor uma interpretação política da constituição do “eu” no âmbito do comportamentalismo radical, mantendo no horizonte a possibilidade de uma ação política transformadora. Para tanto, destacamos como “eus” oprimidos são tornados submissos, mas também como de certas contingências podem emergir “eus” subversivos, que se opõem a um sistema social opressivo. Esse “eu” subversivo é caracterizado por um repertório de autoconhecimento mais amplo, que inclui a discriminação do papel das relações de poder e do controle promovido por instituições. Concluímos, com isso, que um “eu” socialmente constituído pode ser politicamente ativo. (shrink)

The biopolitics of empire : slavery and "the Muslim" -- The biopolitics of settlement : temporality, desire, and civilization -- Foucault and queer theory -- Society must be destroyed -- Queer terror -- Bibliography.

This book offers solutions to two persistent and I believe closely related problems in epistemology. The first problem is that of drawing a principled distinction between perception and inference: what is the difference between seeing that something is the case and merely believing it on the basis of what we do see? The second problem is that of specifying which beliefs are epistemologically basic (i.e., directly, or noninferentially, justified) and which are not. I argue that what makes a belief a (...) perceptual belief, or a basic belief, is not any introspectible feature of the belief but rather the nature of the cognitive system, or "module", that is causally responsible for the belief. Thus, even zombies, who in the philosophical literature lack conscious experiences altogether, can have basic, justified, perceptual beliefs. -/- The theories of perceptual and basic beliefs developed in the monograph are embedded in a larger reliabilist epistemology. I use this theory of basic beliefs to develop a detailed reliabilist theory: Inferentialist Reliabilism, which offers a reliabilist theory of inferential justification and which solves some longstanding problems for other reliabilist views by demanding inferential support for some—but not all—beliefs. The book is an instance of a thoroughgoingly naturalistic approach to epistemology. Many of my arguments have an empirical basis, and the view that I endorse reserves a central role for the cognitive sciences—in particular, cognitive neuroscience—in filling in the details of an applied epistemological theory. (shrink)