There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (Necinc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators. (shrink)

This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle (...) which pluralities form sets, the paper concludes by affirming a naturalistic approach to the philosophy of set theory. (shrink)

This book is the first treatment at length of negative, or apophatic, theology within the analytic tradition. Apophatic theology holds that there is a significant sense in which we cannot say what God is. Important negative theological elements are present in a host of Christian thinkers, from Gregory of Nyssa to Aquinas, and yet apophaticism is neglected in philosophical theology as practiced within the analytic tradition. By contrast, Hewitt shows how apophatic theology is integral to how Christians have thought (...) about God, and how it can be defended against standard attacks in the philosophical literature. Hewitt diagnoses the unease with apophaticism amongst contempory philosophical theologicans as rooted in a certain picture of how language functions, here called referentialism. Arguing that this picture is not compulsory, an account of language which sits more comfortably with negative theology (originating from work of later Wittgenstein) is invoked, and applied to key themes in philosophical theology including divine personhood, the Trinity, the Incarnation and the afterlife. (shrink)

This paper transforms a development of an argument against pantheism into an objection to the usual account of God within contemporary analytic philosophy. A standard criticism of pantheism has it that pantheists cannot offer a satisfactory account of God as personal. My paper will develop this criticism along two lines: first, that personhood requires contentful mental states, which in turn necessitate the membership of a linguistic community, and second that personhood requires limitation within a wider context constitutive of the ’setting’ (...) of the agent’s life. Pantheism can, I argue, satisfy neither criterion of personhood. At this point the tables are turned on the Swinburnian theist. If the pantheist cannot defend herself against the personhood-based attacks, neither can the Swinburnian, and for instructively parallel reasons: for neither doctrine is God in the material world; in the pantheist case God is identical with the world, in the Swinburnian case God transcends it. Either way both the pantheist and the Swinburnian are left with a dilemma: abandon divine personhood or modify the doctrine of God so as to block the move to personhood. (shrink)

This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , and with (...) respect to which I wish to contend that the system permits progress. (shrink)

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this note I will pose the difficulty, and (...) then propose a solution. Since my solution appeals to a plausible constraint on the introduction of new expressions to a language, it is of interest independently of the particular case of terms for pairs. Since these provide the occasion for discussion we should nonetheless review the use of abstraction for pairs before the argumentative business of the paper commences. (shrink)

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this short paper I will pose the difficulty, (...) and then propose a solution. (shrink)

A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.

Michael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks (from Devitt, Miller and Williamson). This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has (...) a foundational role with respect to metaphysics. (shrink)

There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett's characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn (...) is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions. (shrink)

An important trend in contemporary metaphysics denies that the structure of natural language is an important datum for investigating fundamental structure. Ted Sider proceeds on this basis to propose a metaphysical semantics for natural language. Within this framework he argues that natural language and a fundamental, ‘jointcarving’, language could be subject to distinct logics. Developing an argument of Hartry Field’s, I show that Sider’s preferred option of fundamental classicality combined with non-fundamental non-classicality trivialises within the framework of Siderian metaphysical semantics. (...) The position can be saved only by revising key claims about truth and metaphysical semantics. This has serious implications for methdology in the metaphysics of logic. (shrink)

It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.

ABSTRACTThe doctrine of the Real Presence of Christ in the Eucharist presents a particular challenge to its defenders: how is it so much as intelligible? This paper explores Dummett’s response to this question, centred on the notion of deeming. Whilst instructive, Dummett’s position is unsustainable as it stands, since it fails to secure the meaningfulness of the doctrine. Once deeming is brought together with an account of bodiliness and an appreciation of the nature of the Eucharist as a meal, however, (...) the way is open to demonstrating the intelligibility of the doctrine. This is a prerequisite even for its rejection as false. (shrink)

There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett’s characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn (...) is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions. (shrink)

Permissivist metaontology proposes answering customary existence questions in the affirmative. Many of the existence questions addressed by ontologists concern the existence of theoretical entities which admit precise formal specification. This causes trouble for the permissivist, since individually consistent formal theories can make pairwise inconsistent demands on the cardinality of the universe. We deploy a result of Gabriel Uzquiano’s to show that this possibility is realised in the case of two prominent existence debates and propose rejecting permissivism in favour of substantive (...) ontology conducted on a cost–benefit basis. (shrink)

Aquinas's thoughts about the human soul present us with a puzzle. On the one hand, Thomas has been applauded within the analytic tradition as an anti-dualistic thinker, who emphasises the animal nature of human beings and denies that there could be disembodied human persons. Yet on the other hand he holds, as a faithful Catholic theologian, that the human soul survives death, and maintains that the post-mortem soul, prior to its reunification with the body is the subject of characteristically personal (...) intellectual activities. This paper reviews the state of the debate regarding whether these commitments of Aquinas's can be reconciled, and concludes that they cannot in his own terms. However, a recognisably thomist approach to the post-mortem survival of the soul is available, proceeding on the basis that to be rationally ensouled is to have a life-story. (shrink)

It is argued that Gabriel Uzquiano's approach to set-theoretic indefinite extensibility is a version of in rebus structuralism, and therefore suffers from a vacuity problem.

Personhood theism is the view that God exists and is a person. It is often claimed that, whatever conclusions might be reached abstractly by philosophers and theologians, Christianity as lived out practically embodies belief in personhood theism. In this article, I critically examine this claim and argue that Christian prayer and liturgical practice does not in fact embody this belief and that the claim that it does begs the questions against the non-personhood theist.

CraigWilliam Lane.* * God andObjects – The Coherence of Theism : Aseity.Springer, 2017. ISBN: 978-3-319-55383-2 ; 978-3-319-55384-9. Pp. xv + 540.

New Blackfriars, Volume 102, Issue 1101, Page 815-833, September 2021.

It is common for contemporary ontologists to claim that they are not concerned with what exists simpliciter, but rather with what exists ’fundamentally’, or what ’really’ exists. I argue that positions of this sort cannot satisfy reasonable constraints concerning the acquisition of language. I assess and dismiss possible responses to this complaint before commenting on the prospects for a metaphysics without bespoke existence claims.

ABSTRACT Classical and intuitionistic logic both validate Ex Contradictione Quodlibet, according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil. (...) It addresses the key arguments – model-theoretic, proof-theoretic, meaning theoretic and holist – deployed by proponents of ECQ against their standard opponents, and shows that each can be defeated from a position of support for ECN. In the course of answering these arguments, some understanding is developed of possible motivations for ECN and a solid case is built that ECN deserves further investigation. (shrink)

Herbert McCabe was, by widespread acclaim, one of the greatest Catholic thinkers in the English speaking world during the final quarter of the last century. He was also deeply committed to radical left‐wing politics. What is the relationship between these two facts? I lay out what I take to be the key themes in McCabe's politics before arguing that, in contrast to significant strands in present day political theology, he had a keen sense of the respective roles of faith and (...) reason in guiding political action. This allowed him to commit himself to a politics which was more radical than much of what has followed him, whilst having a clear sense of how Christian faith ought to be allowed to condition political engagement. The article concludes by drawing out lessons from McCabe for thinking about faith and politics. Not least of these is that we ought to avoid the lure, often articulated in terms of the ‘unifying’ role of the Church, to eschew conflict. (shrink)

Negation, denial and falsity lie at the heart of debates about logic. We set out the classical account of the relationship between negation and denial, owing to Frege and Geach. We then challenge this on the basis that it does not permit an adequate account of falsity. A dialetheic alternative is minuted and criticised before a novel rejectivist account is proposed according to which falsity is the aim of the speech‐act of denial, whilst negation embeds deniability into assertoric contexts.

On the face of it Aquinas stands in the mainstream of Western mystical theology, and in particular is a noteworthy proponent of negative theology. This view, however, is challenged within anglophone philosophical theology. The clearest attack on the view that Aquinas is an apophatic theologian is to be found in Eleonore Stump's Aquinas. This paper lays out Stump's reasons for reading Aquinas as non-apophatic, and shows that they are not convincing. Aquinas, it concludes, meant what he said when he claimed (...) that we do not know what God is. (shrink)

"In order to write" said Simone de Beauvoir, "the first essential condition is that reality can no longer be taken for granted." She and four other French women writers of the second half of the twentieth century—Nathalie Sarraute, Marguerite Duras, Monique Wittig, and Maryse Condé—illustrate that producing autobiography is like performing a tightrope act on the slippery line between fact and fiction. Autobiographical Tightropes emphasizes the tension in the works of these major writers as they move in and out of (...) "experience" and "literature," violating the neat boundaries between genres and confusing the distinctions between remembering and creating. Focusing on selected works, Leah D. Hewitt for the first time anywhere explores the connections among the authors. In doing so she shows how contemporary women's autobiography in France links with feminist issues, literary tradition and trends, and postmodern theories of writing. In light of these theories Hewitt offers a new reading of de Beauvoir's memoirs and reveals how her attempt to represent the past faithfully is undone by irony, by literary and "feminine" detours. Other analysts of Nathalie Sarraute's writing have dwelt mainly on formal considerations of the New Novel, but Hewitt exposes a repressed, forbidden feminine aspect in her literary innovations. Unlike Sarraute, Duras cannot be connected with just one literary movement, political stance, style, or kind of feminism because her writing, largely autobiographical, is marked by chameleon like transformations. The chapters on Wittig and Condé show how, within the bounds of feminism, lesbians and women of color challenge the individualistic premises of autobiography. Hewitt demonstrates that, despite vast differences among these five writers, all of them reveal in their autobiographical works the self's need of a fictive other. (shrink)

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which Gibbs’ concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual frequentism (as opposed to hypothetical (...) frequentism) insofar as all the microstates exist, in keeping with the decoherence-based Everett interpretation, and some versions of pilot-wave theory. (shrink)

UK blood services, supported by the Health Protection Agency/Health Protection Scotland, carried out an exercise over the summer of 2005 to notify 110 donors whose blood was transfused to three recipients who later developed vCJD. These donors were to be informed that they were now considered 'at risk of vCJD for public health purposes'. The notification began on 20 July 2005 and was completed (barring follow-up) at the end of the first week of October 2005. Apart from two donors who (...) had died, contact was attempted with all donors, including four who were not currently registered with a GP. The lessons learnt about the conduct of such notification have been reviewed. The limited ad hoc feedback available suggests the process and content of this notification was acceptable to donors and their GPs. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

Marine ecosystems are under increasing pressure from human activity, yet successful management relies on knowledge. The evidence-based policy (EBP) approach has been promoted on the grounds that it provides greater transparency and consistency by relying on ‘high quality’ information. However, EBP also creates epistemic responsibilities. Decision-making where limited or no empirical evidence exists, such as is often the case in marine systems, creates epistemic obligations for new information acquisition. We argue that philosophical approaches can inform the science-policy interface. Using marine (...) biosecurity examples, we specifically examine the epistemic challenges in the acquisition and acceptance of evidence to inform policy, discussing epistemic due care and biases in consideration of evidence. (shrink)

This paper considers a host of definitions and labels attached to the concept of smart cities to identify four dimensions that ground a review of ethical concerns emerging from the current debate. These are: (1) network infrastructure, with the corresponding concerns of control, surveillance, and data privacy and ownership; (2) post-political governance, embodied in the tensions between public and private decision-making and cities as post-political entities; (3) social inclusion, expressed in the aspects of citizen participation and inclusion, and inequality and (...) discrimination; and (4) sustainability, with a specific focus on the environment as an element to protect but also as a strategic element for the future. Given the persisting disagreements around the definition of a smart city, the article identifies in these four dimensions a more stable reference framework within which ethical concerns can be clustered and discussed. Identifying these dimensions makes possible a review of the ethical implications of smart cities that is transversal to their different types and resilient towards the unsettled debate over their definition. (shrink)

As laws are written in 'universal terms' they offer inadequate guidance for those difficult cases that do not fall neatly under one general rule or another. While Aristotle is clear that written laws are essential to secure justice in a political community, he is quick to recognize that alone they are insufficient to achieve this aim. Bridging the gap between legal principle and concrete situation is Aristotle's concept of epieikeia: that virtue which 'corrects' the law where it falls short. Through (...) an acute attentiveness to relevant mitigating factors, epieikeia allows the judge to discern what -- beyond rigid application the law -- a just decision entails. However, though triggered by and tied to particular circumstances, epieikeia does not sanction egregious deviation from established law. This is because it serves the ends of 'universal', or 'natural' justice and so is guided, and therefore constrained by its fixed and unchanging principles. In conclusion, this article explores the normative repercussions of incorporating epieikeia into legal decisions, specifically how it might work to transform justice into a virtue which promotes mercy, kindness, and forgiveness. (shrink)