Several themes of David Lewis's theory of counterfactuals, especially their sensitivity to context, pave the way for a viable theory of non-trivial counterpossibles. If Lewis was successful in defending his account against the early objections, a semantics of counterpossibles can be defended from similar objections in the same way. The resulting theory will be extended to address 'might' counterfactuals and questions about the relative "nearness" of impossible worlds.

Plausibly, no agent ever performs an action without some desire to perform that action. If so, a regress argument shows that, given incompatibilism, we are only rarely free. The argument sidesteps recent objections to this thesis.

Against the historically widespread view that divine conservation is a continuation of the act of creation, William Lane Craig argues that conservation is a different kind of act since, unlike creation ex nihilo, it is diachronic and it acts on a patient. Timothy Miller poses a timing objection against Craig's view, arguing that on such a view either the existence of a conserved entity is discontinuous, or the conserving activity overdetermines its effect, or the conserving activity is not continuous. The (...) present paper explores the options that remain for a diachronic, agent-patient account of conservation. It includes several models of conservation on which divine activity is continuous but not overdetermined since its effect at each time is something less specific than the existence of a created being at a time. (shrink)

The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossible worlds of the same sort. I argue for a theory of impossible worlds on which the impossible worlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossible worlds and explore some of their interesting formal properties.

A recently advanced argument for purgatory hinges on the need for complete sanctification before one can enter heaven. The argument has a modal gap.The gap can be exploited to fashion a competing account of how sanctification occurs in the afterlife according to which it is in part a heavenly process.The competing account usefully complicates the overall case for purgatory and raises questions about how the notion ought to be understood.

In much of Christian thought humans are taken to have an ultimate end, understood as the highest attainable good. Christians also anticipate “the life everlasting.” Together these ideas generate a paradox. If the end can be reached in a finite amount of time, some longer-lasting state will be better still, so the purported end is not the highest good after all. But if the end is to possess some good forever, then it will never be reached. So it seems an (...) everlasting being cannot have an ultimate end—a conclusion that apparently makes human life pointless. How can the paradox be solved? (shrink)

This entry provides a brief exposition and formal reconstruction of the argument for possible worlds in David Lewis's _Counterfactuals_.

The theory of possible worlds has permeated analytic philosophy in recent decades, and its best versions have a consequence which has gone largely unnoticed: in addition to the panoply of possible worlds, there are a great many impossible worlds. A uniform ontological method alone should bring the friends of possible worlds to adopt impossible worlds, I argue, but the theory's applications also provide strong incentives. In particular, the theory facilitates an account of counterfactuals which avoids several of the implausible results (...) of David Lewis's account, and it paves the way for the analogues of Kripkean semantics for epistemic and relevant logics. On the theories of possible worlds as abstract objects, worlds bear a strong resemblance to propositions. I contend that if there are distinct necessarily false propositions, then there are likewise distinct impossible worlds. However, one who regards possible worlds as concrete objects must not recognize impossible worlds, in part because concrete worlds cannot misrepresent certain features of reality, as some impossible worlds must. Accordingly, I defend and develop a theory of impossible worlds as maximal impossible states of affairs. Impossible worlds perform admirably in the analysis of counterfactuals with impossible antecedents. I argue that, contrary to standard accounts, not all counterpossibles are trivially true, and I develop a Lewis-style semantics which allows this result. The point is crucial, since many views presuppose that some counterpossibles are substantive philosophical truths. Finally, I show that impossible worlds hold great promise for doxastic and relevant logics. Epistemic logic needs a domain of propositions which is not closed under strict implication to avoid the problem of logical omniscience, and relevant logic needs such a domain to avoid the famous paradoxes of implication. In sum, impossible world theory promises natural, elegant solutions to philosophical problems in numerous areas where possible worlds alone flounder. These solutions come to most possible world theorists at no cost, since the existence of impossible worlds is entailed by theses they already hold. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called “adverse consequences”. The argument from adverse consequences can be seen as an argument that is intended to be pragmatic ‐ about what we should do, not about what is true ‐ but then comes to the wrong kind of conclusion. In many genuinely pragmatic arguments, however, adverse consequences are relevant to the conclusion and no fallacy is committed. So it is important to notice exactly what the conclusion (...) of the argument is. (shrink)

Whether certain objects compose a whole at a given time does not seem to depend on anything other than the character of those objects and the relations between them. This observation suggests a far-reaching constraint on theories of composition. One version of the constraint has been explicitly adopted by van Inwagen and rules out his own answer to the composition question. The constraint also rules out the other well-known moderate answers that have so far been proposed.

Plausibly, if an object persists through time, then its later existence must be caused by its earlier existence. Many theists endorse a theory of continuous creation, according to which God is the sole cause of a creature's existence at a given time. The conjunction of these two theses rather unfortunately implies that no object distinct from God persists at all. What strategies for resolving this difficulty are available? (Published Online April 7 2006).

Arguments concerning divine conservation and concurrence often assume that actions of certain descriptions would be superfluous if God were to perform them, and it is then concluded that God does not perform such actions. In particular, it often seems that atomic actions cannot be the result of cooperative activity between God and creatures since there is no apparent way to divide the labor between the two. However, the actions that are atomic in one model of divine action may not be (...) atomic on another. On fine-grained models there may be unexpected prospects for nonredundant divine action. (shrink)

In comparison with a highest attainable good, a future of everlasting progress may appear subjectively dissatisfying or objectively deficient. This is the satisfaction problem. I defend the progressive view against three strands of the satisfaction problem and argue that the notion of a highest good faces a satisfaction problem of its own.

A review of Kevin Corcoran's Rethinking Human Nature.

This volume comprises essays presented to Alvin Plantinga on the occasion of his 70th birthday.

According to Brian Leftow's modal voluntarism, some necessary truths about created beings depend on the divine will. One might expect this view to be in tension with Molinism, according to which some contingent truths about creatures' free actions are independent of the divine will. It is argued that modal voluntarism is consistent with a lightly modified Molinism.

Structured interviews were held with 149 registered nurses in seven countries in America, Asia, Australia and Europe concerning the feeding of severely demented patients who do not accept food. The most common reasons for nurses being willing to change their decision to feed or not to feed were an order from the medical head, a request from the patient's husband and/or the staff meeting. There was a connection between the willingness to feed and the ranking of ethical principles. Nurses who (...) were most prone to feed the patient most often gave a high rank to the ethical principle of sanctity of life, while those who primarily chose not to feed the patient gave a high rank to the ethical principle of autonomy. All nurses stressed the ethical principle of beneficence. Des interviews structurés ont eu lieu avec 149 infirmiers/ères dans sept pays en Amérique, Asie, Australie et Europe concernant l'alimentation des malades gravement dément qui refusent de manger. La raison la plus générale pour des infirmiers/ères d'être prêt à changer leures décisions de donner à manger ou non sont: un ordre du médecin, la demande du mari de la malade ou de la réunion du personnel. Il y avait un lien entre la volonté de nourir et le rang des principes éthiques. Les infirmiers/ères les plus enclins de nourir la malade le plus souvent donnaient un rang supérieur au principe éthique de la sainteté de vie, pendant que ceux et celles qui choisissaient de ne pas nourrir la malade donnaient un rang supérieur au principe éthique de l'autonomie. Tous insistaient sur l'importance du principe éthique de la bienfaisance. Konstruktive Interviews wurden mit 149 ausgebildeten Krankenschwestern und Pfleger in sieben Ländern in Amerika, Asien, Australien und Europa gehalten über die Ernährung von schwer von Dementia praecox leidenden Patienten, die das Essen verweigern. Die gewöhnlichsten Gründe des Pflegepersonals für die Bereitwilligkeit, ihre Entscheidung, zu ernähren oder nicht, zu ändern, waren Anordnungen vom medizinischen Chef, Anfragen vom Ehemann der Patientin und/oder einer Personalsitzung. Es bestand ein Zusammenhang zwischen der Bereitwilligkeit zur Ernährung und dem Rang der ethischen Prinzipien. Die Pflegenden, die sich am meisten neigten, die Patientin zu ernähren, gaben dem ethischen Prinzip der Heiligkeit des Lebens einen hohen Rang, während die, die meistens vorzogen, die Patientin nicht zu ernähren, gaben dem ethischen Prinzip der Autonomie einen hohen Rang. Alle Pflegenden legten grossen Wert auf das ethische Prinzip der Wohltätigkeit. (shrink)

Offering a unique and wide-ranging examination of the theory of knowledge, the new edition of this comprehensive collection deftly blends readings from the foremost classical sources with the work of important contemporary philosophical thinkers. Human Knowledge: Classical and Contemporary Approaches, 3/e, offers philosophical examinations of epistemology from ancient Greek and Roman philosophy (Plato, Aristotle, Sextus Empiricus); medieval philosophy (Augustine, Aquinas); early modern philosophy (Descartes, Locke, Leibniz, Berkeley, Hume, Reid, Kant); classical pragmatism and Anglo-American empiricism (James, Russell, Ayer, Lewis, Carnap, Quine, (...) Rorty); and other influential Anglo-American philosophers (Chisholm, Kripke, Moore, Wittgenstein, Strawson, Putnam). Organized chronologically and thematically, Human Knowledge, 3/e, features exceptionally broad coverage and nontechnical selections that are easily accessible to students. An ideal text for both undergraduate and graduate courses in epistemology, it is enhanced by the editors' substantial general introduction, section overviews, and up-to-date bibliographies. The third edition offers expanded selections on contemporary epistemology and adds selections by Thomas Reid, Richard Rorty, David B. Annis, Richard Feldman and Earl Conee, Ernest Sosa, Barry Stroud, and Louise M. Antony. Human Knowledge, 3/e, offers an unparalleled introduction to our ancient struggle to understand our own intellectual experience. (shrink)

Offering a unique and wide-ranging examination of the theory of knowledge, the new edition of this comprehensive collection deftly blends readings from the foremost classical sources with the work of important contemporary philosophical thinkers. Human Knowledge: Classical and Contemporary Approaches, 3/e, offers philosophical examinations of epistemology from ancient Greek and Roman philosophy ; medieval philosophy ; early modern philosophy ; classical pragmatism and Anglo-American empiricism ; and other influential Anglo-American philosophers. Organized chronologically and thematically, Human Knowledge, 3/e, features exceptionally broad (...) coverage and nontechnical selections that are easily accessible to students. An ideal text for both undergraduate and graduate courses in epistemology, it is enhanced by the editors' substantial general introduction, section overviews, and up-to-date bibliographies. The third edition offers expanded selections on contemporary epistemology and adds selections by Thomas Reid, Richard Rorty, David B. Annis, Richard Feldman and Earl Conee, Ernest Sosa, Barry Stroud, and Louise M. Antony. Human Knowledge, 3/e, offers an unparalleled introduction to our ancient struggle to understand our own intellectual experience. (shrink)

International Rules brings together exemplary works from the most prominent approaches to international rules of International Law and International Relations disciplines. Included are chapters on Natural Law, Legal Positivism, Classical Realism, the New Haven School, Institutionalism, Structural Realism, the New Stream, and Feminist Voices. Each of the eight chapters begins with a brief overview, offers a representative work or works, and concludes with a selected bibliography. From Hugo Grotius to David Kennedy, from George Kennan to Robert Keohane, the featured (...) authors provide valuable insights into their common subject: international rules. Despite divergent methods and objectives, they address fundamentally the same questions: What is the nature of such rules? What is their purpose? How do they originate? What role, if any, do they play in politics? Framing the selections assembled are two original chapter-length essays. The first chapter of this volume assesses the prospects for interdisciplinary collaboration; the final one suggests a direction for future research. (shrink)

Arguments for Restrictivism – the position that we are rarely free– have been proposed by incompatibilists Peter van Inwagen and David Vander Laan among others. This article is concerned much more with these arguments than with quantifying the frequency of free actions. There are two general ways to argue for restrictivism. First, one may take a Negative Strategy, arguing that the situations in which one is not free are common and predominant. Second, one may focus on situations (...) in which one is apparently free, and argue directly that these situations are rare – the Inventory Strategy. I conclude that both types of arguments for restrictivism are unconvincing. (shrink)

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another (...) justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (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)

Do psychological traits predict philosophical views? We administered the PhilPapers Survey, created by David Bourget and David Chalmers, which consists of 30 views on central philosophical topics (e.g., epistemology, ethics, metaphysics, philosophy of mind, and philosophy of language) to a sample of professional philosophers (N = 314). We extended the PhilPapers survey to measure a number of psychological traits, such as personality, numeracy, well-being, lifestyle, and life experiences. We also included non-technical ‘translations’ of these views for eventual use (...) in other populations. We found limited to no support for the notion that personality or demographics predict philosophical views. We did, however, find that some psychological traits were predictive of philosophical views, even after strict correction for multiple comparisons. Findings include: higher interest in numeracy predicted physicalism, naturalism, and consequentialism; lower levels of well-being and higher levels of mental illness predicted hard determinism; using substances such as psychedelics and marijuana predicted non-realist and subjectivist views of morality and aesthetics; having had a transformative or self-transcendent experience predicted theism and idealism. We discuss whether or not these empirical results have philosophical implications, while noting that 68% of our sample of professional philosophers indicated that such findings would indeed have philosophical value. (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)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative (...) principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

While there are many legal textbooks on the laws of armed conflict and academic works on ethical issues in international relations, this is the first text on the relevance of legal and normative issues in military practice. It covers the entire spectrum of military operations and is written with military deicision-makers particularly in mind.

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)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

A collection of 14 essays honoring the life and work of Oxford philosopher Wiggins touching on topics from ancient philosophy to ethics, metaphysics and the theory of meaning. The contributing scholars debate many of the seminal issues of Wiggins' work, including the determinancy of distinctness, relative identity, naturalism in ethics, logic and truth in moral judgments, and the practical wisdom of Aristotle. The collection uniquely features replies by Wiggins to each of the papers. Annotation copyright by Book News, Inc., Portland, (...) OR. (shrink)

The identity of indiscernibles states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to a number of (...) well-known and recent objections to the PII. (shrink)

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)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

What is called ``orthodox'' quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements and that the eigenvalue-eigenvector link implies that virtually all interesting properties are (...) maximally indefinite pretty much always. I present an alternative way of conceptualising quantum mechanics that does a better job of representing quantum mechanics as it is actually used, and in particular that eliminates use of either the projection postulate or the eigenvalue-eigenvector link, and I reformulate the measurement problem within this new presentation of orthodoxy. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (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)

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they come out both (...) necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>. (shrink)