This work presents a thorough examination of librarianship and the social and economic contexts in which the profession and its institutions operate.

John Searle's Speech Acts (1969) and Expression and Meaning (1979) developed a highly original and influential approach to the study of language. But behind both works lay the assumption that the philosophy of language is in the end a branch of the philosophy of the mind: speech acts are forms of human action and represent just one example of the mind's capacity to relate the human organism to the world. The present book is concerned with these biologically fundamental capacities, (...) and, though third in the sequence, in effect it provides the philosophical foundations for the other two. Intentionality is taken to be the crucial mental phenomenon, and its analysis involves wide-ranging discussions of perception, action, causation, meaning, and reference. In all these areas John Searle has original and stimulating views. He ends with a resolution of the 'mind-body' problem. (shrink)

John Searle's Speech Acts made a highly original contribution to work in the philosophy of language. Expression and Meaning is a direct successor, concerned to develop and refine the account presented in Searle's earlier work, and to extend its application to other modes of discourse such as metaphor, fiction, reference, and indirect speech arts. Searle also presents a rational taxonomy of types of speech acts and explores the relation between the meanings of sentences and the contexts of their utterance. (...) The book points forward to a larger theme implicit in these problems - the basis certain features of speech have in the intentionality of mind, and even more generally, the relation of the philosophy of language to the philosophy of mind. (shrink)

Many economic problems are also ethical problems: should we value economic equality? how much should we care about preserving the environment? how should medical resources be divided between saving life and enhancing life? This book examines some of the practical issues that lie between economics and ethics, and shows how utility theory can contribute to ethics. John Broome's work has, unusually, combined sophisticated economic and philosophical expertise, and Ethics Out of Economics brings together some of his most important essays, (...) augmented with an updated introduction. The first group of essays deals with the relation between preference and value, the second with various questions about the formal structure of good, and the concluding section with the value of life. This work is of interest and importance for both economists and philosophers, and shows powerfully how economic methods can contribute to moral philosophy. (shrink)

In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in (...) logic and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)

The Human Psyche is an in-depth exploration of dualist-interactionism, a concept Sir John Eccles developed with Sir Karl Popper in the context of a wide...

This book explores how and when biology emerged as a science in Germany. Beginning with the debate about organism between Georg Ernst Stahl and Gottfried Leibniz at the start of the eighteenth century, John Zammito traces the development of a new research program, culminating in 1800, in the formulation of developmental morphology. He shows how over the course of the century, naturalists undertook to transform some domains of natural history into a distinct branch of natural philosophy, which attempted not (...) only to describe but to explain the natural world and became, ultimately, the science of biology. (shrink)

John Kulvicki explores the many ways in which pictures can be meaningful, taking inspiration from the philosophy of language. Pictures are important parts of communicative acts. They express a variety of thoughts, and they are also representations. Kulvicki shows how the meanings of pictures let us put them to a wide range of communicative uses.

Is nature all there is? John Haught examines this question and in doing so addresses a fundamental issue in the dialogue of science with religion. The belief that nature is all there is and that no overall purpose exists in the universe is known broadly as 'naturalism'. Naturalism, in this context, denies the existence of any realities distinct from the natural world and human culture. Since the rise of science in the modern world has had so much influence on (...) naturalism's intellectual acceptance, the author focuses on 'scientific' naturalism and the way in which its defenders are now attempting to put a distance between contemporary thought and humanity's religious traditions. Haught seeks to provide a reasonable, scientifically informed alternative to naturalism. His approach will provide the basis for lively discussion among students, scholars, scientists, theologians and intellectually curious people in general. (shrink)

John Rawls begins a Theory of Justice with the observation that "Justice is the first virtue of social institutions, as truth is of systems of thought… Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override"1 (p.3). The COVID-19 pandemic has resulted in lock-downs, the restriction of liberties, debate about the right to refuse medical treatment and many other changes to the everyday behaviour of persons. The justice issues it raises (...) are diverse, profound and will demand our attention for some time. How we can respect the Rawlsian commitment to the inviolability of each person, when the welfare of societies as a whole is under threat goes to the heart of some of the difficult ethical issues we face and are discussed in this issue of the Journal of Medical Ethics. The debate about ICU triage and COVID-19 is quite well developed and this journal has published several articles that explore aspects of this issue and how different places approach it.2–5 Newdick et al add to the legal analysis of triage decisions and criticise the calls for respecting a narrow conception of a legal right to treatment and more detailed national guidelines for how triage decisions should be made.6 They consider scoring systems for clinical frailty, organ failure assessment, and raise some doubts about the fairness of their application to COVID-19 triage situations. Their argument seems to highlight instances of what is called the McNamara fallacy. US Secretary of Defense Robert McNamara used enemy body counts as a measure …. (shrink)

John D. Caputo explores the very roots of religious thinking in this thought-provoking book. Compelling questions come up along the way: 'What do I love when I love my God?' and 'What can Star Wars tell us about the contemporary use of religion?' Why is religion for many a source of moral guidance in a postmodern, nihilistic age? Is it possible to have 'religion without religion'? Drawing on contemporary images of religion, such as Robert Duvall's film _The Apostle_, Caputo (...) also provides some fascinating and imaginative insights into religious fundamentalism. (shrink)

The journal of Cognitive Computation is defined in part by the notion that biologically inspired computational accounts are at the heart of cognitive processes in both natural and artificial systems. Many studies of various important aspects of cognition (memory, observational learning, decision making, reward prediction learning, attention control, etc.) have been made by modelling the various experimental results using ever-more sophisticated computer programs. In this manner progressive inroads have been made into gaining a better understanding of the many components of (...) cognition. Concomitantly in both science and science fiction the hope is periodically re-ignited that a manmade system can be engineered to be fully cognitive and conscious purely in virtue of its execution of an appropriate computer program. However, whilst the usefulness of the computational metaphor in many areas of psychology and neuroscience is clear, it has not gone unchallenged and in this article I will review a group of philosophical arguments that suggest either such unequivocal optimism in computationalism is misplaced—computation is neither necessary nor sufficient for cognition—or panpsychism (the belief that the physical universe is fundamentally composed of elements each of which is conscious) is true. I conclude by highlighting an alternative metaphor for cognitive processes based on communication and interaction. (shrink)

Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the effect. (...) First, Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations. (shrink)

The religious autobiography of John Henry Newman (1801-1890), in which he discusses his conversion to Roman Catholicism.

Steven Nadler has argued that Spinoza can, should, and does allow for the possibility of suicide committed as a free and rational action. Given that the conatus is a striving for perfection, Nadler argues, there are cases in which reason guides a person to end her life based on the principle of preferring the lesser evil. If so, Spinoza’s disparaging statements about suicide are intended to apply only to some cases, whereas in others he would grant that suicide is dictated (...) by reason. Here, I object to Nadler’s interpretation by showing that it conflicts with Spinoza’s metaphysical psychology. Even given Nadler’s interpretation of the conatus doctrine, the possibility that reason could guide a person to commit suicide is incompatible with the conatus of the mind. Spinoza holds that the mind cannot contain an adequate idea ‘that excludes the existence of our body’. Yet, as I argue, in order for reason to guide a person voluntarily to end her life, she would need to have an adequate idea representing her death – an idea that excludes the existence of her body. For this reason, Spinoza's system rules out the possibility of rational suicide. (shrink)

We offer a reconstruction of Richard Price’s intuition-based epistemology of normative essences, highlighting its key elements and showing how it differs from the approaches taken by other intuitionists such as Thomas Reid and G. E. Moore, as well as sentimentalists such as Francis Hutcheson and David Hume. While our analysis aims to shed light on Price’s moral epistemology, it also seeks to contribute to contemporary debates about the epistemology of essence, advancing a general intuition-based theory. These two goals are related, (...) for the former operates in the service of the latter. In this way, our discussion illustrates the role that historical research might play in contemporary inquiries into intuition. (shrink)

[Editor's introduction: The following are excerpts from three talks given at the conference "Policies and Publics for Science and Technology, " London, April 1990. They introduce a British research initiative in public understanding of science and point to early results. The program was developed and coordinated by the Science Policy Support Group. At the meeting, a new journal for specialists in this area was launched: Public Understanding of Science, to be edited by John Durant, Science Museum, London SW7 2DD, (...) UK. The first issue of the journal is expected to appear in April 1991. Science, Technology, & Human Values reaffirms its long commitment to publishing research on public attitudes toward science and particularly welcomes articles on this topic of general interest to the field of science and technology studies.]. (shrink)

I evaluate Patrick Todd's critique of the idea accepted by many, including (in contemporary philosophy) Nelson Pike and John Martin Fischer, that there can be non‐causal constraints on human actions (including basic actions). I suggest that Todd's critical reflections, although illuminating, are not persuasive. I defend non‐causal constraints in part by putting forward an interpretation of the intuitive idea of the fixity of the past following Carl Ginet: our freedom is the power to add to the given past.

On a view most secularists accept, the deceased individual goes out of existence. How, then, can death be a bad thing for, or harm, the deceased? I consider the doctrine of subsequentism, according to which the bad thing for the deceased, or the harm of death to the deceased, takes place after he or she has died. The main puzzle for this view is to explain how we can predicate a property at a time (such as having a misfortune or (...) being harmed) to an individual who does not exist at that time. This is the Problem of Predication. I consider alternative attempts to solve this puzzle, including one suggested by Ben Bradley, and I argue that they do not succeed. I go on to provide a new way of addressing the Problem of Predication and thus defending subsequentism against this specific threat, contrasting my approach with others currently on offer. (shrink)

This volume examines the psychological basis of moral judgments and what theories of concepts apply to moral ones. It considers what mental states not only influence but also constitute our moral concepts and judgments by combining philosophical reasoning and empirical insights from the fields of moral psychology, cognitive science, evolutionary psychology, and neuroscience. On this basis, Park proposes a novel pluralistic theory of moral concepts which includes three different cognitive structures and emotions. Thus, our moral judgments are a hybrid that (...) express both cognitive and conative states. -/- In part through analysis of new empirical data on moral semantic intuitions, gathered via cross-cultural experimental research, Park draws on this to reveal that the referents of individuals’ moral judgments and concepts vary across time, contexts, and groups. Due to this, he contends for moral relativism, where moral judgments cannot be universally true across time and location but only relative to groups. -/- This text will benefit researchers, academics, and educators with an interest in cognitive science, moral theory, philosophy of psychology, and moral psychology more broadly. Those interested in ethics, applied social psychology, and moral development will also benefit from the volume. (shrink)

This chapter examines Soren Kierkegaard's thoughts about selfhood and spirit. It analyses Kierkegaard's conceptions of self, passion, and will in his psychological works The Concept of Anxiety and The Sickness Unto Death, suggesting that these works offer more direct or dialectical analyses of different conscious states. The chapter also considers Kierkegaard's view about existentialism and personalism, and his belief that selfhood is the goal rather than the presupposition of existence.

I can say that a building is tall and you can understand me, even if neither of us has any clear idea exactly how tall a building must be in order to count as tall. This mundane fact poses a problem for the view that successful communication consists in the hearer’s recognition of the proposition a speaker intends to assert. The problem cannot be solved by the epistemicist’s usual appeal to anti-individualism, because the extensions of vague words like ‘tall’ are (...) contextually fluid and can be constrained significantly by speakers’ intentions. The problem can be seen as a special case of a more general problem concerning what King has called “felicitous underspecification.” Traditional theories of vagueness offer nothing that can help with this problem. Appeals to diagonalization do not help either. A more radical solution is needed. (shrink)

[John Hawthorne] We examine some well-known disjunctivist projects in the philosophy of perception, mainly in a critical vein. Our discussion is divided into four parts. Following some introductory remarks, we examine in part two the link between object-dependent contents and disjunctivism. In part three, we explore the disjunctivist's use of discriminability facts as a basis for understanding experience. In part four, we examine an interesting argument for disjunctivism that has been offered by Michael Martin. /// [Scott Sturgeon] The paper (...) aims to do five things: sketch the backbone of disjunctivism about visual experience, explore the view of our title, defend a version of that view from two objections, press two more objections of my own, and sketch a more radical variety of disjunctivism which avoids much of the bother. (shrink)

'This book is a model of philosophical and Heideggerian scholarship.

Intergenerational ethics is the study of our responsibilities to future individuals—individuals who are not now alive but will be. The term “future” characterizes, not the kind of a thing, but rather the temporal perspective from which it is being described. Future people, as such, therefore differ from us neither intrinsically nor in moral status. Our responsibilities to them are best understood by attempts to see things from their perspective, not from ours. Though intergenerational ethics takes various forms, the credible forms (...) in conjunction with known facts yield two great practical conclusions: we must reduce human population, and we must keep most fossil fuels in the ground. The demandingness of these conclusions is no objection against them, but rather an accurate measure of the moral burdens of our godlike knowledge and power. (shrink)

John Laird was a Scottish philosopher who specialised in metaphysics and moral philosophy. In this early work, which was originally published in 1920, Laird set out to analyse some of the more perplexing problems of philosophical realism. The text includes a brief survey of philosophical realism at the beginning and critical notes throughout. This book will be of value to anyone with an interest in the works of Laird and the history of philosophy.

Neil Sinhababu and I presented Backward Clock, an original counterexample to Robert Nozick’s truth-tracking analysis of propositional knowledge. Fred Adams, John Barker and Murray Clarke argue that Backward Clock is no such counterexample. Their argument fails to nullify Backward Clock which also shows that other tracking analyses, such as Dretske’s and one that Adams et al. may well have in mind, are inadequate.

This essay considers some ethical issues of nanotechnology and quantum computing, particularly the issue of privacy, and questions related to artificial intelligence, implants, and virtual reality. It then examines the claim that research in this field should be halted.

In this paper I seek to explore how the idea of modus vivendi might help us to understand political legitimacy. A suitable conception of modus vivendi, I suggest, can represent a way of underpinning a viable and attractive account of political legitimacy. On my account a modus vivendi is basically a set of arrangements that are accepted as basis for conducting affairs by those who are party to them. Political legitimacy, I argue, is ultimately rooted in the judgements of those (...) subject to it, but is mediated through a language in which claims to it are argued and assessed. The thought is that the web of operative beliefs and values in any given society, which constitute the grounds of judgements about political legitimacy, are what sustains a modus vivendi around the basic political institutions and practices. On this view, legitimate political institutions and practices incline towards a modus vivendi in that they are the outcome of an historical and ongoing conglomeration of settlements reflecting shifting and conflicting values and interests, as well relative balances of power, both currently and in the past. The marriage of modus vivendi and political legitimacy, therefore, seeks to reflect the contingent and ‘negotiated’ character of basic political institutions and practices and an understanding of political legitimacy that sees it as mediated through an ongoing and emergent discourse of argument and judgement, which remains nonetheless always vulnerable to challenge and change. (shrink)

Subsidiarity, i.e., “the principle of subsidiarity,” i.e., “the principle of subsidiary function/responsibility,” i.e., the principle that it is unjust for a higher authority to usurp the self-governing authority that lower authorities, acting in the service of their own members, rightly have over those members, is a presumptive and defeasible, not an absolute, principle. But it excludes any general policy or aim of assuming the control or managerial direction of lower groups. Its deepest rationale is the intrinsic desirability of self-direction, a (...) good that is to be favored and respected even at the expense of some efficiency in the pursuit of other goods. Though arising out of Aristotelean moral and political theory, it denies or strongly disambiguates a cardinal principle of Aristotelean political theory. It is reflected in the work of Aquinas, Taparelli, Mill and Maitland, before its articulation by Pius XI. (shrink)

This paper argues for a novel account of deceitful scientific communication, as “wishful speaking”. This concept is of relevance both to philosophy of science and to discussions of the ethics of lying and misleading. Section 1 outlines a case-study of “ghost-managed” research. Section 2 introduces the concept of “wishful speaking” and shows how it relates to other forms of misleading communication. Sections 3–5 consider some complications raised by the example of pharmaceutical research; concerning the ethics of silence; how research strategies—as (...) well as the communication of results—may be misleading; and questions of multiple authorship. The conclusion suggests some more general conclusions. (shrink)

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of (...) a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C − 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between −408 and −397 and probably within a very few years of −400. (shrink)

John Dewey developed sophisticated theories for a liberal civil society and a deliberative democracy. These theories have recently enjoyed renewed attention, discussion, and practical application.1 However, no consensus on Dewey's primary theoretical strategies has yet emerged.2 What precisely was Dewey's justification for democracy and its superiority over other ways of life and forms of government? This essay explains how Dewey attempted to formulate a philosophical justification for democracy on ethical grounds, rather than just epistemic or satisfaction-maximization grounds alone. Provided (...) with a solid ethical foundation, progressive and participatory democracy could become a practical, achievable, and highly .. (shrink)

Maurice Merleau-Ponty’s philosophy of embodiment has been widely adopted by enactivists seeking to provide an account of cognition that is both embodied and embedded. Yet very little attention has been paid to Merleau-Ponty’s later works. This is troubling given that in The Visible and the Invisible Merleau-Ponty revises his conception of embodied subjectivity because he came to the realization that understanding consciousness through the concepts of subject and object imposed a dualistic framework that he was trying to escape. To overcome (...) this dichotomy Merleau-Ponty more fully develops the radically embodied ontology implicit in his earlier work by introducing the concept of flesh. I argue that the enactive account of subjectivity would be improved by “giving flesh” to the enactive subject, given that the enactive account of subjectivity as grounded in pre-reflective bodily self-consciousness is ultimately rooted in accounts of which the later Merleau-Ponty is critical. Incorporating flesh resolves the underlying problems with the enactive account of subjectivity and makes the account more consistent with the ontological commitments to embodiment and embeddedness. (shrink)

Perceiving things to be a certain way may in some cases lead directly to action that is intelligent. This phenomenon has not often been discussed, though it is of broad philosophical interest. It also raises a difficult question: how can perception produce intelligent action? After clarifying the question—which I call the question of “practical perception”—and explaining what is required for an adequate answer, I critically examine two candidate answers drawn from work on related topics: the first, inspired by Hubert Dreyfus's (...) phenomenological analysis of absorbed coping, focuses on awareness of situational features; the other, suggested by Gilbert Ryle's classic treatment of knowledge-how, focuses on possession of behavioral dispositions. I argue that neither approach is adequate. Subsequently, I develop and defend an alternative answer that emphasizes the agent's conceptual understanding. (shrink)

The formerly established medically-based idea of disability, with its charity-based approach to treatment and services, is being replaced by a human rights-based approach in which people with impairments are no longer considered medical problems, totally dependent on the beneficence of non-impaired people in society, but have fundamental rights to support, inclusion, and participation. This interdisciplinary book examines the diverse concerns that people with impairments face in the context of human rights, provides insights into new developments on important issues relating human (...) rights to disability, and features new approaches and solutions to vital problems in the current debate. (shrink)

Who or what comes after God? In the wake of God, as the last fifty years of philosophy has shown, God comes back again, otherwise: Heidegger's last God, Levinas's God of Infinity, Derrida's and Caputo's tout autre, Marion's God without Being, Kearney's God who may be.

In this article I discuss how the Greek concept of chōra inspired both Martin Heidegger and Nishida Kitarō. Not only was Plato’s concept an important source, but we can also draw connections to the pre-Platonic understanding of the term as well. I argue that chōra in general entails concretion-cum-indetermination, a space that implaces human existence into its environment and clears room for the presencing-absencing of beings. One aim is to convince Nishida scholars of the significance of chōra in Nishida’s thought (...) vis-a-vis the other Greek concept of place, topos. Another is to convince Heidegger scholars who accuse him of neglecting chōra that, to the contrary, there is evidence of Heidegger’s appropriation of this concept. The point is to show that chōra is significant to the thinking of both while correcting certain misreadings and to show its relevance to us today. (shrink)

How our beliefs about the soul have developed through the ages, and why an understanding of it still matters today The concept of the soul has been a recurring area of exploration since ancient times. What do we mean when we talk about finding our soul, how do we know we have one, and does it hold any relevance in today’s scientifically and technologically dominated society? From Socrates and Augustine to Darwin and Freud, In Search of the Soul takes readers (...) on a concise, accessible journey into the origins of the soul in Western philosophy and culture, and examines how the idea has developed throughout history to the present. Touching on literature, music, art, and theology, John Cottingham illustrates how, far from being redundant in contemporary times, the soul attunes us to the importance of meaning and value, and experience and growth. A better understanding of the soul might help all of us better understand what it is to be human. Cottingham delves into the evolution of our thoughts about the soul through landmark works—including those of Aristotle, Plato, and Descartes. He considers the nature of consciousness and subjective experience, and discusses the psychoanalytic view that large parts of the human psyche are hidden from direct conscious awareness. He also reflects on the mysterious and universal longing for transcendence that is an indelible part of our human makeup. Looking at the soul’s many dimensions—historical, moral, psychological, and spiritual—Cottingham makes a case for how it exerts a powerful pull on all of us. In Search of the Soul is a testimony to how the soul remains a profoundly significant aspect of human flourishing. (shrink)

_Pretendism in Name Only_ By WoodsJohnCambridge University Press, Cambridge, 2015. xii + 273. £22.99.

We explore Shelah's model‐theoretic dividing line methodology. In particular, we discuss how problems in model theory motivated new techniques in model theory, for example classifying theories by their potential (consistently with Zermelo–Fraenkel set theory with the axiom of choice (ZFC)) spectrum of cardinals in which there is a universal model. Two other examples are the study (with Malliaris) of the Keisler order leading to a new ZFC result on cardinal invariants and attempts to clarify the “main gap” by reducing the (...) dependence of certain versions on (highly independent) cardinal arithmetic. (shrink)