We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics as K4, S4, S4.1, K4.3, GL, or Grz are undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4,K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, if.

We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such structures expanding (...) over time. The decidability proof is based on Kruskal’s tree theorem, and the proof of non-primitive recursiveness is by reduction of the reachability problem for lossy channel systems. The result is used to show that the dynamic topological logic interpreted in topological spaces with continuous functions is decidable if the number of function iterations is assumed to be finite. (shrink)

We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics asK4,S4,S4.1,K4.3,GL, orGrzare undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4, K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, ifl1andl2are classes of transitive frames such that their depth cannot be (...) bounded by any fixedn< ω, then the logic of the class {5ℑ1× ℑ2∣ ℑ1∈l1, ℑ2, ∈l2} is undecidable. (On the contrary, the product of, say,K4and the logic of all transitive Kripke frames of depth ≤n, for some fixedn< ω, is decidable.) The complexity of these undecidable logics ranges from r.e. to co-r.e. and Π11-complete. As a consequence, we give the first known examples of Kripke incomplete commutators of Kripke complete logics. (shrink)

In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.

In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six (...) classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide. (shrink)

Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In this paper, we show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting–Brouwer logic [math] that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from extensions of [math] to extensions of [math].

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

Provability logics are modal or polymodal systems designed for modeling the behavior of Gödel’s provability predicate and its natural extensions. If Λ is any ordinal, the Gödel-Löb calculus GLPΛ contains one modality [λ] for each λ < Λ, representing provability predicates of increasing strength. GLPω has no non-trivial Kripke frames, but it is sound and complete for its topological semantics, as was shown by Icard for the variable-free fragment and more recently by Beklemishev and Gabelaia for the full logic. (...) In this paper we generalize Beklemishev and Gabelaia’s result to GLPΛ for countable Λ. We also introduce provability ambiances, which are topological models where valuations of formulas are restricted. With this we show completeness of GLPΛ for the class of provability ambiances based on Icard polytopologies. (shrink)

Various U.S. laws, such as the Clean Air Act and the Food Quality Protection Act, require additional protections for susceptible subpopulations who face greater environmental health risks. The main ethical rationale for providing these protections is to ensure that environmental health risks are distributed fairly. In this article, we (1) consider how several influential theories of justice deal with issues related to the distribution of environmental health risks; (2) show that these theories often fail to provide specific guidance concerning policy (...) choices; and (3) argue that an approach to public decision making known as accountability for reasonableness can complement theories of justice in establishing acceptable environmental health risks for the general population and susceptible subpopulations. Since accountability for reasonableness focuses on the fairness of the decision-making process, not the outcome, it does not guarantee that susceptible subpopulations will receive a maximum level of protection, regardless of costs or other morally relevant considerations. (shrink)

The singularity hypothesis is a radical hypothesis about the future of artificial intelligence on which self-improving artificial agents will quickly become orders of magnitude more intelligent than the average human. Despite the ambitiousness of its claims, the singularity hypothesis has been defended at length by leading philosophers and artificial intelligence researchers. In this paper, I argue that the singularity hypothesis rests on scientifically implausible growth assumptions. I show how leading philosophical defenses of the singularity hypothesis (Chalmers 2010, Bostrom 2014) fail (...) to overcome the case for skepticism. I conclude by drawing out philosophical implications of this discussion for our understanding of consciousness, personal identity, digital minds, existential risk, and ethical longtermism. GPI Working Paper No . 19-2022. (shrink)

In both radical and mainstream environmental discourses, anthropocentrism (human centredness) is inextricably linked to modern industrial society's drive to control and dominate nature and the generation of our current environmental crisis. Such environmental discourses frequently argue for a retreat from anthropocentrism and the establishment of a harmonious relationship with nature, often invoking the supposed ecological harmony of indigenous peoples and/or other small-scale societies. In particular, the beliefs and values of these societies vis-à-vis their natural environment are taken to be instrumental (...) in their low environmental impact. Here it is argued that, aside from the empirically problematic nature of such claims, the beliefs of small-scale societies have been seen through an ethnocentric discursive framework which bifurcates belief systems into anthropocentric and ecocentric. Taking a meta-theoretical approach informed by Strong Structuration Theory, it is argued that the beliefs of small-scale societies about their relationship with nature should be recognised as lying on a continuum of anthropocentrism and understood in the context of their attempts to establish ‘environmental ontological security’ in the face of natural uncertainty. (shrink)

Interpretation -- Introduction -- Interpreting Plato -- The political culture of Plato's early dialogues -- Dialogue -- Character and history -- The mouthpiece principle -- Forms of evidence -- Desire -- Socrates and eros -- The subjectivist conception of desire -- Instrumental and terminal desire -- Rational and irrational desires -- Desire in the critique of Akrasia -- Interpreting Lysis -- The deficiency conception of desire -- Inauthentic friendship -- Platonic desire -- Antiphilosophical desires -- Knowledge -- Excellence as wisdom (...) -- The epistemic unity of excellence -- Dunamis and technê -- Goodness and form -- The epistemological priority of definitional knowledge -- Ordinary ethical knowledge -- Method -- The Socratic fallacy -- Socrates' pursuit of definitions -- Hupothesis -- Two postulates -- The geometrical illustration -- Geometrical analysis -- The method of reasoning from a postulate -- Elenchus and hupothesis -- Knowledge and aitia -- F-conditions -- Cognitive security -- Aporia -- Forms of aporia -- Dramatic aporia -- The example of Charmides -- Charmides as autobiography -- The politics of Sôphrosunê -- Critias' Philotimia -- Self-knowledge and the knowledge of knowledge -- Knowledge of knowledge and knowledge of the good -- Philosophy and the polis. (shrink)

Consciousness and Mind presents David Rosenthal's influential work on the nature of consciousness. Central to that work is Rosenthal's higher-order-thought theory of consciousness, according to which a sensation, thought, or other mental state is conscious if one has a higher-order thought that one is in that state. The first four essays develop various aspects of that theory. The next three essays present Rosenthal's homomorphism theory of mental qualities and qualitative consciousness, and show how that theory fits with and helps (...) sustain the HOT theory. A crucial feature of homomorphism theory is that it individuates and taxonomizes mental qualities independently of the way we're conscious of them, and indeed independently of our being conscious of them at all. So the theory accommodates the qualitative character not only of conscious sensations and perceptions, but also of those which fall outside our stream of consciousness. Rosenthal argues that, because this account of mental qualities makes no appeal to consciousness, it enables us to dispel such traditional quandaries as the alleged conceivability of undetectable quality inversion, and to disarm various apparent obstacles to explaining qualitative consciousness and understanding its nature. Six further essays build on the HOT theory to explain various important features of consciousness, among them the complex connections that hold in humans between consciousness and speech, the self-interpretative aspect of consciousness, and the compelling sense we have that consciousness is unified. Two of the essays, one an extended treatment of homomorphism theory, appear here for the first time. There is also a substantive introduction, which draws out the connections between the essays and highlights their implications. (shrink)

An introduction to ethical reasoning -- Comparative religious perspectives on war -- Just and unjust war in Shakespeare's Henry V -- Anticipating and preventing atrocities in war -- The CIA's original "social contract" -- The KGB: CIA's traditional adversary -- Espionage -- Covert action -- Interrogation -- Concluding reflections.

The philosophical literature that tackles foundational questions about normativity often appeals to normative reasons—or considerations that count in favor of or against actions—and their interaction. The interaction between normative reasons is usually made sense of by appealing to the metaphor of (normative) weight scales. This paper substitutes an argumentation-theoretic model for this metaphor. The upshot is a general and precise model that is faithful to the philosophical ideas.

This book puts forward a revisionist view of Japanese wartime thinking. It seeks to explore why Japanese intellectuals, historians and philosophers of the time insisted that Japan had to turn its back on the West and attack the United States and the British Empire. Based on a close reading of the texts written by members of the highly influential Kyoto School, and revisiting the dialogue between the Kyoto School and the German philosopher Heidegger, it argues that the work of Kyoto (...) thinkers cannot be dismissed as mere fascist propaganda, and that this work, in which race is a key theme, constitutes a reasoned case for a post-White world. The author also argues that this theme is increasingly relevant at present, as demographic changes are set to transform the political and social landscape of North America and Western Europe over the next fifty years. (shrink)

In this book, which thoroughly revises and greatly expands his classic work Sameness and Substance, David Wiggins retrieves and refurbishes in the light of twentieth-century logic and logical theory certain conceptions of identity, of substance and of persistence through change that philosophy inherits from its past. In this new version, he vindicates the absoluteness, necessity, determinateness and all or nothing character of identity against rival conceptions. He defends a form of essentialism that he calls individuative essentialism, and then a (...) form of realism that he calls conceptualist realism. In a final chapter he advocates a human being-based conception of the identity and individuation of persons, arguing that any satisfactory account of personal memory must make reference to the life of the rememberer himself. This important book will appeal to a wide range of readers in metaphysics, philosophical logic, and analytic philosophy. (shrink)

What is going on when we are consciously aware of a visual scene, or hear sounds, or otherwise enjoy sensory experience? David Papineau argues controversially for a purely qualitative account: conscious sensory experiences are intrinsic states with no essential connection to external circumstances or represented properties.

A number of philosophers endorse, without argument, the view that there’s something it’s like consciously to think that p, which is distinct from what it’s like consciously to think that q. This thesis, if true, would have important consequences for philosophy of mind and cognitive science. In this paper I offer an argument for it, and attempt to induce examples of it in the reader. The argument claims it would be impossible introspectively to distinguish conscious thoughts with respect to their (...) content if there weren’t something it’s like to think them. This argument is defended against several objections. Then I use what I call “minimal pair” experiences—sentences read without and with understanding—to induce in the reader an experience of the kind I claim exists. Further objections are considered and rebutted. (shrink)

Liberal thinkers of the eighteenth and nineteenth centuries were alert to the political costs and human cruelties involved in European colonialism, but they also thought that European expansion held out progressive possibilities. In Progress, Pluralism, and Politics David Williams examines the colonial and anti-colonial arguments of Adam Smith, Immanuel Kant, Jeremy Bentham, and L.T. Hobhouse. Williams locates their ambivalent attitude towards European conquest and colonial rule in a set of tensions between the impact of colonialism on European states, the (...) possibilities of progress in distant and diverse places, and the relationship between universalism and cultural pluralism. In so doing he reveals some of the central ambiguities that characterize the ways that liberal thought has dealt with the reality of an illiberal world. Of particular importance are appeals to various forms of universal history, attempts to mediate between the claims of identity and the reality of difference, and the different ways of thinking about the achievement of liberal goods in other places. Pointing to key elements in still ongoing debates within liberal states about how they should relate to illiberal places, Progress, Pluralism, and Politics enriches the discussion on political thought and the relationship between liberalism and colonialism. (shrink)

The relationship between philosophy and science has always been complementary. Today, while science moves increasingly fast and philosophy shows some problems in catching up with it, it is not always possible to ignore such relationships, especially in some disciplines such as philosophy of mind, cognitive science, and neuroscience. However, the methodological procedures used to analyze these data are based on principles and assumptions that require a profound dialogue between philosophy and science. Following these ideas, this work aims to raise the (...) problems that a classical connectionist theory can cause and problematize them in a cognitive framework, considering both philosophy and cognitive sciences but also the disciplines that are near to them, such as AI, computer sciences, and linguistics. For this reason, we embarked on an analysis of both the computational and theoretical problems that connectionism currently has. The second aim of this work is to advocate for collaboration between neuroscience and philosophy of mind because the promotion of deeper multidisciplinarity seems necessary in order to solve connectionism’s problems. In fact, we believe that the problems that we detected can be solved by a thorough investigation at both a theoretical and an empirical level, and they do not represent an impasse but rather a starting point from which connectionism should learn and be updated while keeping its original and profoundly convincing core. (shrink)

Through Narcissus' Glass Darkly presents a genealogy and critique of the ideal of conscience in modern philosophical theology, particularly in the writings of ...

The arithmetical -- Tripartite city, tripartite soul -- The one, the two, and the three -- The arithmetical character of Kallipolis -- Eros -- Intimations of Eros -- The three waves -- Kallipolis v. The republic -- Democracy, psychology, poetry -- Democracy -- Narrative psychology -- Psychological narrative -- Appendix -- The meaning of "dialectical" -- The technical meaning of "dialectic" -- The non-technical of "dialectic" -- Dialectic in The republic.

What does it mean for someone to exist? What is truth? Are we free to choose to think or act? What is consciousness? Is human cloning justifiable? These are just some of the questions philosophers have attempted to answer, striking right at the heart of what it means to be human. This important new books shows that philosophy need not be dry or intimidating. Its highly original treatment, combining philosophical analysis, historical and biographical background and thought-provoking illustrations, simultaneously informs and (...) stimulates the reader. Western Philosophy: An Illustrated Guide is structured thematically, in terms of major issues, with chapters on World, Mind and Body, Knowledge, Faith, Ethics and Aesthetics, and Society. Cutting across this organization by theme is a parallel organization that focuses on the great thinkers and their influence, as well as the schools or "-isms" to which they subscribed. A highly accessible introduction to the subject, founded upon impeccable academic scholarship, Western Philosophy: An Illustrated Guide offers life-changing perspectives on what really matters. (shrink)

The Quality of Thought develops and defends the thesis that thinking is a kind of experience, characterized by a sui generis (“cognitive”) phenomenology, determinates of which are thought contents—what I call the phenomenal intentionality of thought thesis. It draws out the implications of this thesis for issues in philosophy of mind, philosophy of language and metaphysics. The view defended is radically internalist and intensionalist, and thus goes against received doctrines in philosophy of mind (externalism) and language (extensionalism). It also advocates (...) for a metaphysically neutral, non-naturalistic approach to the philosophical study of mind—what I call “Analytic Phenomenology”—in combination with agnosticism about the nature of the relationship between consciousness and physical reality. -/- The book identifies persistent problems with Dretske-inspired causal-informational-teleological theories of conceptual content, and diagnoses them as due to leaving out what it’s like to think a thought—to entertain or grasp a propositional (conceptual) content. It is thus a contribution to the increasingly influential Phenomenal Intentionality Research Program. It includes refutations of classic externalism (Putnam and Burge) and arguments that standard motivations for direct reference theories of names (Kripke), indexicals and demonstratives (Kaplan) are not inevitable, and alternative accounts of their (and their conceptual equivalents’) semantics. It also addresses outstanding challenges to the phenomenal intentionalist view of thought content, including the existence of unconscious thought, the elusiveness of conceptual phenomenology, the matching content problem, phenomenal compositionality, and the determination of conceptual reference. (shrink)

Arguing about origins' great theater and a grand distraction -- Ideas and idea making -- Beauty and the arts -- Suffering and sensation -- The justice paradox -- Life and afterlife.

In the twenty-first century, the debate about life on other worlds is quickly changing from the realm of speculation to the domain of hard science. Within a few years, as a consequence of the rapid discovery by astronomers of planets around other stars, astronomers very likely will have discovered clear evidence of life beyond the Earth. Such a discovery of extraterrestrial life will change everything. Knowing the answer as to whether humanity has company in the universe will trigger one of (...) the greatest intellectual revolutions in history, not the least of which will be a challenge for at least some terrestrial religions. Which religions will handle the discovery of extraterrestrial life with ease and which will struggle to assimilate this new knowledge about our place in the universe? Some religions as currently practiced appear to only be viable on Earth. Other religions could be practiced on distant worlds but nevertheless identify both Earth as a place and humankind as a species of singular spiritual religious importance, while some religions could be practiced equally well anywhere in the universe by any sentient beings. Weintraub guides readers on an invigorating tour of the world's most widely practiced religions. It reveals what, if anything, each religion has to say about the possibility that extraterrestrial life exists and how, or if, a particular religion would work on other planets in distant parts of the universe. (shrink)

Receiving social support from community and extended family has been typical for mothers with infants in human societies past and present. In non-industrialised contexts, infants of mothers with extended family support often have better health and higher survival through the vulnerable infant period, and hence shared infant care has a clear fitness benefit. However, there is scant evidence that these benefits continue in industrialised contexts. Better infant health and development with allocare support would indicate continued evolutionary selection for allocare. The (...) research reported here used multiple logistic regression analysis to test whether a lack of family and other social support for mothers was associated with an increased risk of developmental delay in 9-month-old infants in the UK Millennium Cohort (analysis sample size, 15,696 infants). Extended family-based childcare during work hours and more maternal time spent with friends were the most influential kin and social support variables: infants of mothers with kin-based childcare versus all other childcare arrangements had a lower risk of developmental delay (OR = 0.61, 95% CIs: 0.46–0.82). Infants of mothers who spent no time with friends when compared with those who saw friends every day had double the odds of delay. Greater paternal involvement in infant care was associated with a lower odds of developmental delay. In conclusion, shared care of infants and social support for mothers may influence fitness-related traits in industrialised societies rather than being factors that influenced selection only in the past and in societies which retain close kin networks and a strong local community focus. (shrink)

This chapter, which is concerned with the phenomenology of perception, especially the role of content and context in the intentionality of perception, tries to provide an account of the structure of perceptual experience and its intentional relation to its objects. In particular, it presents an analysis of consciousness and intentionality in perception. Perceptual experience is sensuous and paradigmatically intentional. The intentional character of a visual experience of an object is different to the successful intentional relation between the experience and the (...) object. The twin-tomatoes experiment reveals that content alone does not settle which tomato is the correct object of perception. Perception gives a direct awareness of an object in the sense that the external object is itself the object of perception, and the object is actually present to the subject and experienced as actually present in the context of perception. (shrink)

A perfect starting point for the exploration of philosophical thought, Philosophy offers life-changing perspectives on some of the great questions, from the nature of the mind to the morality of cloning and stem-cell research. No browser will be able to resist the stunning design here: gorgeous full-color photos, many textboxes, and concise captions that inform and interest. These and the lucid writing, with multiple examples and illuminating analogies, will engage readers and provoke them into thought before they know it.... This (...) most attractive volume makes its discipline irresistible. (shrink)

Introduction -- Sidgwick's metaethics -- Sidgwick's moral epistemology -- Utilitarianism versus dogmatic intuitionism -- Utilitarianism versus egoism.

Prologue : narratocracy and the contours of political life -- From nomos to nomad : Kant, Deleuze, and Rancière on sensation -- The piazza, the edicola, and the noise of the utterance -- Machiavelli's theory of sensation and Florence's vita festiva -- The viewing subject : Caravaggio, Bacon, and the ring -- "You're eating too fast!" slow food's ethos of convivium -- Epilogue : "the photographs tell it all" : on an ethics of appearance.

Cet article offre la toute première édition critique du Quodlibet IV, q. 11, d’Hervé de Nédellec (Hervaeus Natalis ; c. 1250/60-1323), laquelle est précédée d’une étude du contenu doctrinal de cette question quodlibétique qui traite essentiellement de trois choses : une définition de la connaissance intuitive ; une explication de ce que signifie la présence d’une chose ; une analyse des modalités selon lesquelles la connaissance – et en particulier l’intuitive – dépend de la présence de la chose connue.

Introduction -- The commercialisation of science and the construction of the knowledge-based bio-economy -- The KBBE reality--the case of agriculture -- Intellectual property rights and the global commodification of knowledge -- Privatizing Chinese science : national development vs. neoliberal financialization -- Critical realism and the importance of ontological attention -- Critical realism and beyond in economics -- The realist transcendental argument.

Personal Identity and Ethics provides a lively overview of the relationship between the metaphysics of personal identity and ethics. How does personal identity affect our ethical judgments? It is a commonplace to hold that moral responsibility for past actions requires that the responsible agent is in some relevant respect identical to the agent who performed the action. Is this true? On the other hand, can ethics constrain our account of personal identity? Do the practical requirements of moral theory commit us (...) to holding that persons do remain identical over time? Or is it the case that personal identity is not, in fact, relevant to ethics? -/- Shoemaker provides the first comprehensive examination of these issues for the undergraduate audience. Topics include personal identity and prudential rationality; personal identity's significance for moral responsibility and ethical theory; and the practical consequences of accounts of personal identity for issues such as abortion, stem cell research, cloning, advance directives, populations ethics, multiple personality disorder, and the definition of death. (shrink)