This paper argues that challenges that are grand in scope such as "lifelong health and wellbeing", "climate action", or "food security" cannot be addressed through scientific research only. Indeed scientific research could inhibit addressing such challenges if scientific analysis constrains the multiple possible understandings of these challenges into already available scientific categories and concepts without translating between these and everyday concerns. This argument builds on work in philosophy of science and race to postulate a process through which non-scientific notions become (...) part of science. My aim is to make this process available to scrutiny: what I call founding everyday ideas in science is both culturally and epistemologically conditioned. Founding transforms a common idea into one or more scientifically relevant ones, which can be articulated into descriptively thicker and evaluatively deflated terms and enable operationalisation and measurement. The risk of founding however is that it can invisibilise or exclude from realms of scientific scrutiny interpretations that are deemed irrelevant, uninteresting or nonsensical in the domain in question-but which may remain salient for addressing grand-in-scope challenges. The paper considers concepts of "wellbeing" in development economics versus in gerontology to illustrate this process. (shrink)

The broad spectrum revolution brought greater dependence on skill and knowledge, and more demanding, often social, choices. We adopt Sterelny's account of how cooperative foraging paid the costs associated with longer dependency, and transformed the problem of skill learning. Scaffolded learning can facilitate cognitive control including suppression, whereas scaffolded exchange and trade, including inter-temporal exchange, can help develop resolve.

Since Boorse [Philos Sci 44(4):542–573, 1977] published his paper “Health as a theoretical concept” one of the most lively debates within philosophy of medicine has been on the question of whether health and disease are in some sense ‘objective’ and ‘value-free’ or ‘subjective’ and ‘value-laden’. Due to the apparent ‘failure’ of pure naturalist, constructivist, or normativist accounts, much in the recent literature has appealed to more conciliatory approaches or so-called ‘hybrid accounts’ of health and disease. A recent paper by Matthewson (...) and Griffiths [J Med Philos 42(4):447–466, 2017], however, may bear the seeds for the revival of purely naturalist approach to health and disease. In this paper, I defend their idea of Biological Normativity against recent criticism by Schwartz [J Med Philos Forum Bioethics Philos Med 42(4):485–502, 2017] and hope to help it flower into a revival of naturalist approaches in the philosophy of medicine. (shrink)

Recognizing the variety of dystopian science-fiction novels and movies, from Brave New World to Gattaca and more recently Star Trek, on the future of humanity in which eugenic policies are implemented, genetic engineering has been getting a bad reputation for valid but arguably, mostly historical reasons. In this paper, I critically examine the claim from Mehlman & Botkin (1998: ch. 6) that human enhancement will inevitably accentuate existing inequality in a free market and analyze whether prohibition is the optimal public (...) policy for this objection as egalitarians might advise (Lamont and Favor, 2014). (shrink)

This paper introduces and defends an account of model-based science that I dub model pluralism. I argue that despite a growing awareness in the philosophy of science literature of the multiplicity, diversity, and richness of models and modeling practices, more radical conclusions follow from this recognition than have previously been inferred. Going against the tendency within the literature to generalize from single models, I explicate and defend the following two core theses: any successful analysis of models must target sets of (...) models, their multiplicity of functions within science, and their scientific context and history and for almost any aspect x of phenomenon y, scientists require multiple models to achieve scientific goal z. (shrink)

This article introduces and defends the “pathological complexity thesis” as a hypothesis about the evolutionary origins of minimal consciousness, or sentience, that connects the study of animal consciousness closely with work in behavioral ecology and evolutionary biology. I argue that consciousness is an adaptive solution to a design problem that led to the extinction of complex multicellular animal life following the Avalon explosion and that was subsequently solved during the Cambrian explosion. This is the economic trade-off problem of having to (...) deal with a complex body with high degrees of freedom, what I call “pathological complexity.” By modeling the explosion of this computational complexity using the resources of state-based behavioral and life history theory we will be able to provide an evolutionary bottom-up framework to make sense of subjective experience and its function in nature by paying close attention to the ecological lifestyles of different animals. (shrink)

The goal of this programmatic paper is to highlight a close connection between the core problem in the philosophy of medicine, i.e. the concept of health, and the core problem of the philosophy of mind, i.e. the concept of consciousness. I show when we look at these phenomena together, taking the evolutionary perspective of modern state-based behavioural and life-history theory used as the teleonomic tool to Darwinize the agent- and subject-side of organisms, we will be in a better position to (...) make sense of them both as natural phenomena. (shrink)

Animal welfare has a long history of disregard. While in recent decades the study of animal welfare has become a scientific discipline of its own, the difficulty of measuring animal welfare can still be vastly underestimated. There are three primary theories, or perspectives, on animal welfare - biological functioning, natural living and affective state. These come with their own diverse methods of measurement, each providing a limited perspective on an aspect of welfare. This paper describes a perspectival pluralist account of (...) animal welfare, in which all three theoretical perspectives and their multiple measures are necessary to understand this complex phenomenon and provide a full picture of animal welfare. This in turn will offer us a better understanding of perspectivism and pluralism itself. (shrink)

This book attempts to advance Donald Griffin's vision of the "final, crowning chapter of the Darwinian revolution" by developing a philosophy for the science of animal consciousness. It advocates a Darwinian bottom-up approach that treats consciousness as a complex, evolved, and multidimensional phenomenon in nature rather than a mysterious all-or-nothing property immune to the tools of science and restricted to a single species. -/- The so-called emergence of a science of consciousness in the 1990s has at best been a science (...) of human consciousness. This book aims to advance a true Darwinian science of consciousness in which its evolutionary origin, function, and phylogenetic diversity are moved from the field’s periphery to its very centre, thus enabling us to integrate consciousness into an evolutionary view of life. Accordingly, this book has two objectives: (i) to argue for the need and possibility of an evolutionary bottom-up approach that addresses the problem of consciousness in terms of the evolutionary origins of a new ecological lifestyle that made consciousness worth having and (ii) to articulate a thesis and beginnings of a theory of the place of consciousness as a complex evolved phenomenon in nature that can help us to answer the question of what it is like to be a bat, an octopus, or a crow. -/- A Philosophy for the Science of Animal Consciousness will appeal to researchers and advanced students interested in advancing our understanding of animal minds as well as anyone with a keen interest in how we can develop a science of animal consciousness. (shrink)

In order to develop a true biological science of consciousness, we have to remove humans from the center of reference and develop a bottom-up comparative study of animal minds, as Donald Griffin intended with his call for a “cognitive ethology.” In this article, I make use of the pathological complexity thesis (Veit 2022a, b, c ) to show that we can firmly ground a comparative study of animal consciousness by drawing on the resources of state-based behavioral life history theory. By (...) comparing the different life histories of gastropods and arthropods, we will be able to make better sense of the possible origins of consciousness and its function for organisms in their natural environments. (shrink)

What is it like to be a bat? What is it like to be sick? These two questions are much closer to one another than has hitherto been acknowledged. Indeed, both raise a number of related, albeit very complex, philosophical problems. In recent years, the phenomenology of health and disease has become a major topic in bioethics and the philosophy of medicine, owing much to the work of Havi Carel (2007, 2011, 2018). Surprisingly little attention, however, has been given to (...) the phenomenology of animal health and suffering. This omission shall be remedied here, laying the groundwork for the phenomenological evaluation of animal health and suffering. (shrink)

As scientific progress approaches the point where significant human enhancements could become reality, debates arise whether such technologies should be made available. This paper evaluates the widespread concern that human enhancements will inevitably accentuate existing inequality and analyzes whether prohibition is the optimal public policy to avoid this outcome. Beyond these empirical questions, this paper considers whether the inequality objection is a sound argument against the set of enhancements most threatening to equality, i.e., cognitive enhancements. In doing so, I shall (...) argue that cognitive enhancements can be embraced wholeheartedly, for three separate reasons. However, though the inequality objection does not sufficiently support the conclusion that cognitive enhancements should be prohibited, it raises several concerns for optimal policy design that shall be addressed here. (shrink)

For decades Darwinian processes were framed in the form of the Lewontin conditions: reproduction, variation and differential reproductive success were taken to be sufficient and necessary. Since Buss and the work of Maynard Smith and Szathmary biologists were eager to explain the major transitions from individuals to groups forming new individuals subject to Darwinian mechanisms themselves. Explanations that seek to explain the emergence of a new level of selection, however, cannot employ properties that would already have to exist on that (...) level for selection to take place. Recently, Hammerschmidt et al. provided a ‘bottom-up’ experiment corroborating much of the theoretical work Paul Rainey has done since 2003 on how cheats can play an important role in the emergence of new Darwinian individuals on a multicellular level. The aims of this paper are twofold. First, I argue for a conceptual shift in perspective from seeing cheats as a ‘problem’ that needs to be solved for multi-cellularity to evolve to the very ‘key’ for the evolution of multicellularity. Secondly, I illustrate the consequences of this shift for both theoretical and experimental work, arguing for a more prominent role of ecology and the multi-level selection framework within the debate then they currently occupy. (shrink)

Unlike any other field, the science of morality has drawn attention from an extraordinarily diverse set of disciplines. An interdisciplinary research program has formed in which economists, biologists, neuroscientists, psychologists, and even philosophers have been eager to provide answers to puzzling questions raised by the existence of human morality. Models and simulations, for a variety of reasons, have played various important roles in this endeavor. Their use, however, has sometimes been deemed as useless, trivial and inadequate. The role of models (...) in the science of morality has been vastly underappreciated. This omission shall be remedied here, offering a much more positive picture on the contributions modelers made to our understanding of morality. (shrink)

Imagine a world where everyone is healthy, intelligent, long living and happy. Intuitively this seems wonderful albeit unrealistic. However, recent scienti c breakthroughs in genetic engineering, namely CRISPR/Cas bring the question into public discourse, how the genetic enhancement of humans should be evaluated morally. In 2001, when preimplantation genetic diagnosis (PGD) and in vitro fertilisation (IVF), enabled parents to select between multiple embryos, Julian Savulescu introduced the principle of procreative bene cence (PPB), stating that parents have the obligations to choose (...) the child that is expected to have the best life. In this paper I argue that accepting the PPB and the consequentialist principle (CP) that two acts with the same consequences are morally on par, commits one to accepting the parental obligation of genetically enhancing one's children. (shrink)

Metaphors abound in both the arts and in science. Due to the traditional division between these enterprises as one concerned with aesthetic values and the other with epistemic values there has unfortunately been very little work on the relation between metaphors in the arts and sciences. In this paper, we aim to remedy this omission by defending a continuity thesis regarding the function of metaphor across both domains, that is, metaphors fulfill any of the same functions in science as they (...) do in the arts. Importantly, this involves the claim that metaphors in arts as well as science have both epistemic and aesthetic functions. (shrink)

Darwin provided us with a powerful theoretical framework to explain the evolution of living systems. Natural selection alone, however, has sometimes been seen as insufficient to explain the emergence of new levels of selection. The problem is one of “circularity” for evolutionary explanations: how to explain the origins of Darwinian properties without already invoking their presence at the level they emerge. That is, how does evolution by natural selection commence in the first place? Recent results in experimental evolution suggest a (...) way forward: Paul Rainey and his collaborators have shown that Darwinian properties could be exogenously imposed via what they call “ecological scaffolding.” This could solve the “black box” dilemma faced by Darwinian explanations of new levels of organization. Yet, despite “scaffolding” recently becoming a popular term in the study of cognition, culture, and evolution, the concept has suffered from vagueness and ambiguity. This article aims to show that scaffolding can be turned into a proper scientific concept able to do explanatory work within the context of the major evolutionary transitions. Doing so will allow us to once again extend the scope of the Darwinian model of evolution by natural selection. (shrink)

There has been much criticism of the idea that Friston's free-energy principle can unite the life and mind sciences. Here, we argue that perhaps the greatest problem for the totalizing ambitions of its proponents is a failure to recognize the importance of evolutionary dynamics and to provide a convincing adaptive story relating free-energy minimization to organismal fitness.

We welcome Mikhalevich & Powell’s (2020) (M&P) call for a more “‘inclusive”’ animal ethics, but we think their proposed shift toward a moral framework that privileges false positives over false negatives will require radically revising the paradigm assumption in animal research: that there is a clear line to be drawn between sentient beings that are part of our moral community and nonsentient beings that are not.

As a result of the world-wide COVID-19 epidemic, an internal tension in the goals of medicine has come to the forefront of public debate. Medical professionals are continuously faced with a tug of...

In his 2009 monograph, Darwinian Populations and Natural Selection, Peter Godfrey-Smith accuses biologists of demonstrating ‘Darwinian Paranoia’ when they engage in what he dubs ‘agential thinking’. But as Daniel Dennett points out, he offers neither an illuminating set of examples nor an extended argument for this assertion, deeming it to be a brilliant propaganda stroke against what is actually a useful way of thinking. Compared to the dangers of teleological thinking in biology, the dangers of agential thinking have unfortunately rarely (...) been discussed. Drawing on recent work by Samir Okasha, I attempt to remedy this omission, through analyzing the nature of agential thinking, and providing a philosophical treatment of the unexamined dangers in this peculiar, yet tempting way of thinking. (shrink)

While we agree in broad strokes with the characterisation of rationalization as a “useful fiction,” we think that Fiery Cushman's claim remains ambiguous in two crucial respects: (1) the reality of beliefs and desires, that is, the fictional status of folk-psychological entities and (2) the degree to which they should be understood as useful. Our aim is to clarify both points and explicate the rationale of rationalization.

If one had to identify the biggest change within the philosophical tradition in the twenty-first century, it would certainly be the rapid rise of experimental philosophy to address differences in intuitions about concepts. It is, therefore, surprising that the philosophy of medicine has so far not drawn on the tools of experimental philosophy in the context of a particular conceptual debate that has overshadowed all others in the field: the long-standing dispute between so-called naturalists and normativists about the concepts of (...) health and disease. In this paper, I defend and advocate the use of empirical methods to inform and advance this and other debates within the philosophy of medicine. (shrink)

This paper is a response to a recent paper by Bobier and Omelianchuk in which they argue that the critics of Giubilini and Minerva’s defence of infanticide fail to adequately justify a moral difference at birth. They argue that such arguments would lead to an intuitively less plausible position: that late-term abortions are permissible, thus creating a dilemma for those who seek to argue that birth matters. I argue that the only way to resolve this dilemma, is to bite the (...) naturalist bullet and accept that the intuitively plausible idea that birth constitutes a morally relevant event is simply mistaken and biologically misinformed. (shrink)

With increasing publication and data production, scientific knowledge presents not simply an achievement but also a challenge. Scientific publications and data are increasingly treated as resources that need to be digitally ‘managed.’ This gives rise to scientific Knowledge Management : second-order scientific work aiming to systematically collect, take care of and mobilise first-hand disciplinary knowledge and data in order to provide new first-order scientific knowledge. We follow the work of Leonelli, Efstathiou and Hislop in our analysis of the use of (...) KM in semantic systems biology. Through an empirical philosophical account of KM-enabled biological research, we argue that KM helps produce new first-order biological knowledge that did not exist before, and which could not have been produced by traditional means. KM work is enabled by conceiving of ‘knowledge’ as an object for computational science: as explicated in the text of biological articles and computable via appropriate data and metadata. However, these founded knowledge concepts enabling computational KM risk focusing on only computationally tractable data as knowledge, underestimating practice-based knowing and its significance in ensuring the validity of ‘manageable’ knowledge as knowledge. (shrink)

In a recent special issue dedicated to Dani Rodrik’s (2015) influential monograph Economics Rules, Grüne-Yanoff and Marchionni (2018) raise a potentially damning problem for Rodrik’s suggestion that progress in economics should be understood and measured laterally, by a continuous expansion of new models. They argue that this could lead to an “embarrassment of riches”, i.e. the rapid expansion of our model library to such an extent that we become unable to choose between the available models, and thus needs to be (...) solved to make ‘model pluralism’ viable. Drawing on Veit’s (2019a) ‘model pluralism’ account, this paper argues that model pluralism as a thesis about the relationship between science and nature undermines the very idea of a general model selection framework for policy making. (shrink)

Phillips et al. make a compelling case for a reversal in the current paradigm in “other minds” research by considering the representation of other people's knowledge more basic than the attribution of belief. Unfortunately, they only discuss primates. In this commentary, I argue that the representation of others' knowledge is an evolutionary ancient trait, first appearing during the Cambrian explosion.

This goal of this thesis in the philosophy of nature is to move us closer towards a true biological science of consciousness in which the evolutionary origin, function, and phylogenetic diversity of consciousness are moved from the field’s periphery of investigations to its very centre. Rather than applying theories of consciousness built top-down on the human case to other animals, I argue that we require an evolutionary bottomup approach that begins with the very origins of subjective experience in order to (...) make sense of the place of mind in nature. To achieve this goal, I introduce and defend the pathological complexity thesis as both a framework for the scientific investigation of consciousness and as a lifemind continuity thesis about the origins and function of consciousness. (shrink)

Assertion plays a crucial dual role in Frege's conception of logic, a formal and a transcendental one. A recurrent complaint is that Frege's inclusion of the judgement-stroke in the Begriffsschrift is either in tension with his anti-psychologism or wholly superfluous. Assertion, the objection goes, is at best of merely psychological significance. In this paper, I defend Frege against the objection by giving reasons for recognising the central logical significance of assertion in both its formal and its transcendental role.

ABSTRACT This paper compares Spinoza with Daniel Dennett and uncovers a number of striking parallels. Genevieve Lloyd’s recent work on Spinoza reveals a picture of a philosopher that anticipated many of Dennett’s later ideas. Both share a fervent opposition to Descartes’ conception of mind and body and endorse a strikingly similar naturalist philosophy. It is the goal of this paper to tease out these connections and once again highlight the richness of a Spinozist lens of the world.

In their thoughtful article, Malm and Navin (2020) raise concerns about a potentially unjust generational welfare tradeoff between children and adults when it comes to chicken pox. We share their c...

The conditions animals experience during the early developmental stages of their lives can have critical ongoing effects on their future health, welfare, and proper development. In this paper we draw on evolutionary theory to improve our understanding of the processes of developmental programming, particularly Predictive Adaptive Responses (PAR) that serve to match offspring phenotype with predicted future environmental conditions. When these predictions fail, a mismatch occurs between offspring phenotype and the environment, which can have long-lasting health and welfare effects. Examples (...) include metabolic diseases resulting from maternal nutrition and behavioral changes from maternal stress. An understanding of these processes and their evolutionary origins will help in identifying and providing appropriate developmental conditions to optimize offspring welfare. This serves as an example of the benefits of using evolutionary thinking within veterinary science and we suggest that in the same way that evolutionary medicine has helped our understanding of human health, the implementation of evolutionary veterinary science (EvoVetSci) could be a useful way forward for research in animal health and welfare. (shrink)

In a work entitled On the Generation of Animals, Aristotle remarks that “intellect (nous) alone enters from outside (thurathen)”. Interpretations of this passage as dualistic dominate the history of ideas and allow for a joining together of Platonic and Aristotelian doctrine on the soul. This, however, pulls against the well-known Aristotelian position that soul and body are intertwined and interdependent. The most influential interpretations thereby misrepresent Aristotle’s view on soul and lack any real engagement with his embryology. This paper seeks (...) to extract the account of intellect (nous) in Aristotelian embryology from this interpretative background and place it within the context of his mature biological thought. A clear account of the actual import of this statement in its relevant context is given before explaining how it has been misunderstood by various interpretative traditions. The paper finishes by touching on how early commentary by Christian writers, freed as it was from the imperative to synthesise Greek philosophy, differed from those that came after. While realising that Aristotle’s position would not aid them in their explanations of the soul’s survival after death, their engagement with Aristotle’s science allowed for other aspects of theology concerning the fittingness of soul to body. (shrink)

The ‘psychologist’s green thumb’ refers to the argument that an experimenter needs an indeterminate set of skills to successfully replicate an effect. This argument is sometimes invoked by psychological researchers to explain away failures of independent replication attempts of their work. In this paper, I assess the psychologist’s green thumb as a candidate explanation for individual replication failure and argue that it is potentially costly for psychology as a field. I also present other, more likely reasons for these replication failures. (...) I conclude that appealing to a psychologist’s green thumb is not a convincing explanation for replication failure. (shrink)

Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre-theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.

Discussions of patient-centred care and patient autonomy in bioethics have tended to focus on the decision-making context and the process of obtaining informed consent, leaving open the question of how patients ought to be counselled in the daily maintenance of their health and management of chronic disease. Patient activation is an increasingly prominent counselling approach and measurement tool that aims to improve patients’ confidence and skills in managing their own health conditions. The strategy, which has received little conceptual or ethical (...) analysis, raises important questions about how clinicians ought to foster confidence and a sense of control in their patients without exposing them to blame, stigma and other harms. In this paper, we describe patient activation, discuss its relationship to personal responsibility, autonomy and health disparities, and make recommendations regarding its use and measurement. (shrink)

The way of laws is as much a defining feature of the modern period as the way of ideas; but the way of laws is hardly without its forks. Both before and after Descartes, there are philosophers using the concept to carve out a very different position from his, one that is entirely disconnected from God or God’s will. I argue that Francis Bacon and Baruch Spinoza treat laws as dispositions that derive from a thing’s nature. This reading upends the (...) currently orthodox treatment of Spinoza’s laws as infinite modes, and calls for a re-conception of his metaphysics of causation. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...) paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence. (shrink)

Eliminativism is a position most readily associated with the eliminative materialism of the Churchlands, denying that there are such things as propositional states. This position has created much controversy, despite the fact that intentionality has long been seen as perhaps the core problem for naturalistic philosophy. There is a more radical interpretation of eliminativism, however, denying not only mental states, such as beliefs and desires, but also intentionality (i.e., aboutness) on a global level. This position traces its contemporary origin back (...) to Quine, but has generally been assumed to undermine naturalism or, worse, to be incoherent by the majority of philosophers who maintain that there clearly are things or mental states that are about others. In a recent paper, Hutto and Satne (2015a) offer an update that tries to revive John Haugeland’s baseball analogy from his influential 1990 review paper The Intentionality All-Stars on the state of the game to argue that the failure of Neo-Cartesians, Neo- Behaviorists, and Neo-Pragmatists should urge us to make them work together to naturalize content and “win the game.” But Hutto and Satne misunderstand what the game is ultimately about. The goal of the Intentionality All-Stars is not to naturalize content against eliminativism but to defend a naturalist “thirdperson” view of the problem against first-person phenomenalists. For this goal, a naturalist defense of global content eliminativism would equally enable them to emerge victorious. Revisiting Haugeland, I will offer my own analysis of the current state of play to argue that global content eliminativism has not received sufficient attention and deserves a more prominent place in the debate than it currently occupies. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)