Conceptualism is the thesis that, for any perceptual experience E, (i) E has a Fregean proposition as its content and (ii) a subject of E must possess a concept for each item represented by E. We advance a framework within which conceptualism may be defended against its most serious objections (e.g., Richard Heck's argument from nonveridical experience). The framework is of independent interest for the philosophy of mind and epistemology given its implications for debates regarding transparency, relationalism and representationalism, demonstrative (...) thought, phenomenal character, and the speckled hen objection to modest foundationalism. (shrink)

Reconstructability analysis (RA) decomposes wholes, namely data in the form either of set theoretic relations or multivariate probability distributions, into parts, namely relations or distributions involving subsets of variables. Data is modeled and compressed by variable-based decomposition, by more general state-based decomposition, or by the use of latent variables. Models, which specify the interdependencies among the variables, are selected to minimize error and complexity.

In this talk, I want to present a conception that I have been working on for a number of years (Zwick, 1983, 1995) about the use of systems ideas. I start from the negative and proceed to the positive. The negative assertion is that systems ideas by themselves , unsupplemented by more specific and concrete knowledge (e.g., from the various disciplines), are insufficient for practical application, either for obtaining knowledge about the world or for solving problems. The reason for this (...) is the inherent abstractness of these ideas. The positive assertion is that this metaphysics can be a rich source of insights needed to improve the human condition and a component of a new scientific world view. (shrink)

Surveys the ideals of friendship in ancient Greco-Roman philosophy. The notion of the best friendship inevitably reflects the various conceptions of a good life.

The Platonic dialogues contain passages that seem to point in quite opposite directions on the question of the moral equality of women with men. Rep. V defends the view that sexual difference need not be relevant to a person’s capacity for philosophy and thus for virtue. Tim. 42a-c, however, makes incarnation in a female body a punishment for failure to master the challenges of embodiment. This paper examines the different ways in which two subsequent Platonists, Proclus (d. 485 CE) and (...) Theodore of Asine (d. c. 360 CE), dealt with this tension. (shrink)

This has been available under Teaching Materials, but items in that category are not easily located, so I have added it here. This short dialogue can be used to introduce students to the core claims of Stoic moral philosophy and to position Stoic moral philosophy in relation to its ancient alternatives: Cynicism, Epicureanism, and Peripatetic thought. The dialogue form is meant to make this fun and easy. -/- This little dialogue may also be of interest to readers who have encountered (...) various popular books on "How to Stoic". Such readers should know that Stoicism is a school of _philosophy_. The Stoics themselves would not recommend that you try to Stoic Yourself unless and until you were convinced of the _truth_ of the central claims of the school -- a truth that the ancient Stoics sought to establish by _arguments_. To treat Stoicism simply as self-help, without due regard to whether its central claims can be shown to be true, would be to treat those ancient philosophers with contempt. (shrink)

‘Know-that’, like so many natural language expressions, exhibits patterns of use that provide evidence for its context-sensitivity. A popular family of views – call it prag- matic invariantism – attempts to explain the shifty patterns by appeal to a pragmatic thesis: while the semantic meaning of ‘know-that’ is stable across all contexts of use, sentences of the form ‘S knows [doesn’t know] that p’ can be used to communicate a pragmatic content that depends on the context of use. In this (...) paper, the author argues that pragmatic invariantism makes inaccurate predictions for a wide range of well- known use data and is committed to attributing systematic pragmatic error to ordinary speakers. But pragmatic error is unprecedented, and it is doubtful that speakers are systematically wrong about what they intend to communicate. (shrink)

In Plato’s dialogues we often find Socrates talking at length about poetry. Sometimes he proposes censorship of certain works because what they say is false or harmful. Other times we find him interpreting the poets or rejecting potential interpretations of them. This raises the question of whether there is any consistent account to be given of Socrates’ practice as a literary critic. One might think that Plato himself in the Ion answers the question that I have raised. Rhapsody, at least (...) in the Ion , is portrayed as the activity of interpreting and evaluating the works of the poets. At first glance at least, Plato seems to conclude that this activity cannot meet the standards of a τέχνη. Rhapsodes are divine madmen. Thus, there cannot be a systematic Platonic account of literary criticism because this activity is inherently irrational and, subsequently, not something that one could engage in in a systematic way, guided by a theory of any sort. In the first part of the paper I argue that the Ion does not simply consign the Interpretation of poetry to the irrational and, as a result, does not pose an obstacle to the possibility of a Platonic literary criticism. In the second part of the paper I turn to the task of finding an account of the purpose of reading poetry and strategies for fulfilling this purpose that make systematic sense of Socrates’ multifarious remarks about poetry. (shrink)

Entangled quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure way than possible in the realm of classical physics. Given this resource character of entanglement, it is an important problem to characterize ways to manipulate it and meaningful approaches to its quantification. This is the objective of entanglement theory.

It is an axiom of late neoplatonic metaphysics that all things are in all, but in each in an appropriate manner (ὀικείως, ET 103). These manners or modes of being are indicated by adverbial forms such as παραδειματικῶς or εἰκονικῶς. Thus, for example, the Forms are in the World Soul in the mode of images, while the objects in the sensible realm below Soul are in it in the manner of paradigms (in Tim. II 150.27). Among the many modes of (...) being distinguished by Proclus we find existence ὁλικῶς and μερικῶς – in the manner of a whole and in the manner of a part. This paper investigates the nature and significance of these mereological modes of being. (shrink)

The author puts forward and defends a new argument for indirect realism called the argument from pain. The argument is akin to a well-known traditional argument to the same end, the argument from hallucination. Like the latter, it contains one premise stating an analogy between veridical perceptions and certain other states and one premise stating that those states are states of acquaintance with sense-data. The crucial difference is that the states that are said to be analogous to veridical perceptions are (...) pain-states instead of hallucinations. This difference makes the argument from pain immune to the standard objections against the argument from hallucination. (shrink)

How should we account for the contextual variability of knowledge claims? Many philosophers favour an invariantist account on which such contextual variability is due entirely to pragmatic factors, leaving no interesting context-sensitivity in the semantic meaning of ‘know that.’ I reject this invariantist division of labor by arguing that pragmatic invariantists have no principled account of embedded occurrences of ‘S knows/doesn’t know that p’: Occurrences embedded within larger linguistic constructions such as conditional sentences, attitude verbs, expressions of probability, comparatives, and (...) many others, I argue, give rise to a threefold problem of embedded implicatures. (shrink)

Later versions of Platonic ethics fit the frame of eudaimonism and specify a telos based on Theaetetus 176B and Timaeus 90A-D: 'likeness to god in so far as possible'. This paper examines the development of this idea from the middle Platonist Alcinous to the Neoplatonist Proclus. It examines the way in which Proclus makes this specification of human happiness a bit less "other worldy".

The idea that there is a coherent and morally relevant concept of sexual perversions has been increasingly called into question. In what follows, I will be concerned with two recent attacks on the notion of sexual perversion: those of Graham Priest and Igor Primoratz. Priest’s paper is the deeper of the two. Primoratz goes methodically through various accounts of sexual perversion and finds difficulties in them. This is no small task, of course, but unlike Priest he does not attempt to (...) provide any diagnosis of why any attempt to analyse the concept of sexual perversion must fail. Priest argues that sexual perversion is an “inapplicable concept”: the presuppositions that would allow us to make sense of the notion have been rightly rejected. Without the theoretical backdrop of an Aristotelian moral teleology, we cannot provide a satisfactory account of sexual perversion, for only such a teleological world-view allows us to give some sense to the idea that a sexual practice might be morally wrong because it is unnatural. Priest surveys accounts of perversion that don’t appeal to any idea of unnaturalness and rejects them—rightly I believe. But, Priest argues, Aristotle’s own moral teleology is part and parcel of his wider views about purpose in nature. This natural teleology has been shown to be explanatorily superfluous. Though some sciences still talk of functions, this can be understood in terms of contributions to evolutionary survival. Though there is considerable disagreement about the details of the right account of function, all versions of this scientifically respectable teleology are morally neutral: it would not follow from the fact that homosexual intercourse does nothing to propagate the agents’ genetic material to future generations that it is therefore morally wrong. Here too I think Priest is right. He also considers what he calls “Aristotelian revivalism” in Roger Scruton’s account of sexual perversion. I think Priest sells Aristotelianism short. I have no interest in defending Scruton’s own understanding of the Aristotelian moral framework nor his particular account of sexual perversion. I shall, however, argue that Aristotelian moral philosophy provides a more useful framework for thinking about these issues than Priest implies, and attempt to defend an account of sexual perversion within the context of this framework. (shrink)

Proclus' commentary on Plato's dialogue Timaeus is arguably the most important commentary on a text of Plato, offering unparalleled insights into eight centuries of Platonic interpretation. It has had an enormous influence on subsequent Plato scholarship. This edition offers the first new English translation of the work for nearly two centuries, building on significant recent advances in scholarship on Neoplatonic commentators. It provides an invaluable record of early interpretations of Plato's dialogue, while also presenting Proclus' own views on the meaning (...) and significance of Platonic philosophy. The present volume, the fifth in the edition, presents Proclus' commentary on the Timaeus, dealing with Proclus' account of static and flowing time; we see Proclus situating Plato's account of the motions of the stars and planets in relation to the astronomical theories of his day. The volume includes a substantial introduction, as well as notes that will shed new light on the text. (shrink)

The aim of the first part of the article is to elucidate the nature of (modern) philosophical scepticism. The author defends the view that scepticism is not a homogenous doctrine, but a general label for heterogenous ways of sceptical argumentation. Sceptical argumentation is, in turn, understood to include any kind of philosophically relevant argument which aims at calling into doubt epistemically-valued qualities, especially knowledge. In the second part of the article the author focuses on the question of what constitutes the (...) intrinsic value of philosophical scepticism. The author defends the thesis that philosophical scepticism has instrumental value as a tool for understanding knowledge. This thesis is the result of the application of a particularist approach to the problem of knowledge. Scepticism provides the material for thought experiments in the context of which findings about epistemic intuitions connected with knowledge can be revealed. In spite of this, scepticism is of value only in the form of a means and its value cannot be reduced to the value of other elements. (shrink)

In this paper we look at two kinds of relations that give rise to reasons for action of a distinctive sort: friendship and erotic love. We argue that what is common to these different relations of affection is that the people in them exhibit dispositions toward mutual direction by one another and interpretation of one another (in a sense that we describe in detail below). This mutual responsiveness is, in part, a matter of responding to reasons that arise from the (...) relation of love or friendship. These reasons are frequently distinct from – and may be opposed to – normative reasons arising from prudence or even morality. Yet reasons of love are normative: they too may obligate us. They may make demands on us that conflict with our present desires and require considerable sacrifice. (shrink)

Plato’s Phaedrus is a dialogue of journeys, a tale of transitions. It begins with Socrates’ question, ‘Where to and from whence, my dear Phaedrus?’ and concludes with the Socrates’ decision, ‘Let’s go’ (sc. back into the city from whence they’ve come). In the speech that forms its centre-piece Socrates narrates another famous journey—the descent of the soul into the body and its reascent to the realm of Forms through erotic madness. It is not too implausible to suppose that Plato himself (...) saw fit to relate his powerful images of the human soul’s fall and re-ascent by dramatic means that highlight the movement from one place to another. This explains how Hermias of Alexandria -- author of the longest sustained work on the Phaedrus to survive from antiquity related the physical journey to the Ilissus to the soul's descent and ascent. This seemingly implausible allegorising gains a certain kind of sense when we consider that the Neoplatonic commentary tradition formed part of a philosophic way of life with an ethical telos. (shrink)

Plato's Tim. 90b1-c6 describes a pathway to the soul's salvation via the study of the heavens. This paper poses three questions about this theme in Platonism: 1. The epistemological question: How is the paradigmatic function of the visible heavenly bodies to be reconciled with various Platonic misgivings about the faculty of perception? 2. The metaphysical question: How can »assimilation« to the motions of bodies in the realm of Becoming provide for the salvation of souls when souls are »higher«- a mid-point (...) between Being and Becoming? 3. The psychological question: What can it mean for an incorporeal soul to utilise the motions of a body for an ethical and cognitive paradigm? And provides an account of how Proclus and some of his fellow Neoplatonists answered these questions. (shrink)

Translation and commentary on the only surviving sustained work on Plato's Phaedrus from antiquity.

In his commentary on Aristotle's Metaphysics, Alexander of Aphrodisias quotes from Aristotle's now-lost work On the Ideas -- his account of the arguments offered by Plato for the theory of Forms and his criticisms of those arguments. This paper considers one of these arguments, the Argument from Relatives (ta pros ti). It considers how Plato argued for Forms or Ideas such as the Large Itself, the Just Itself and so on and whether Plato supposed that there were Forms corresponding to (...) sortal terms like Man. (shrink)

Lengthy review of the 2020 Brill Companion to Hellenistic Astronomy with special reference to Neoplatonism.

It is widely supposed that Epicurus' identification of aponia (painlessness) and the absence of anxiety (ataraxia) yields as a consequence the claim that the most pleasant life is one that requires little in the way of resources or power. This paper argues that the remarks in Cicero which attempt to reconstruct Epicurus' reasons for thinking that aponia and ataraxia are the limit of pleasure are best interpreted if we suppose that the inference runs the other direction. Epicurus supposed that it (...) was a pre-theoretical constraint on any account of human happiness that it should be natural. Moreover, its naturalness means its in-principle availability to most humans. (shrink)

In previous chapters, it has become clear that Proclus’ metaphysics is often relevant to human life. In this chapter, that relation is elaborated on in detail, starting from the notion of a ‘textual community’. In the first section, the author presents the Neoplatonic goal of human life, assimilation to the divine. In the second section, he elaborates the scale of virtues through which, according to Proclus, one may reach that assimilation. The third section is devoted to establishing the interesting hypothesis (...) that the philosophical curriculum was in fact considered a mystagogy, aimed at internalizing semantic associations and thereby acquiring the different virtues. In the last section the author turns to Proclus’ political philosophy, and specifically the analogical relation between the philosopher-ruler and the demiurge. (shrink)

In the present volume Proclus comments on the creation of the body of the universe in Plato's Timaeus.

The longevity of Aristotelian natural science consists not so much in the fact that Aristotle’s solutions to puzzles were accepted by generations of philosophers, but by the fact that the presuppositions that made these puzzles look puzzling were. In what follows I consider some Neoplatonic responses to two puzzles that Aristotle poses in De Caelo Book 2, Chapter 12. Both Proclus and Simplicius rejected Aristotle’s solutions to the puzzles he posed. In one case, but not in the other, they also (...) reassessed the relative importance of the presuppositions that created the puzzle. (shrink)

This third and final volume concludes Hermias' commentary on Plato's Phaedrus. Here, Plato delivers a celebrated critique of writing, and its relationship to orality. Hermias follows him, and adds a general account of good writing. In addition, this volume offers the first English translation of the brief Introduction to Hermogenes' On Styles, which manuscripts attribute-probably mistakenly-to Hermias' teacher Syrianus. Baltzly and Share discuss the Introduction's authorship and its relation to the genuine commentaries of Syrianus on the rhetorical treatises of Hermogenes. (...) They illuminate the relationship between philosophy and rhetoric in the Neoplatonic schools, and provide a novel explanation of Neoplatonic commentaries as performances of Platonic literacy in ancient elite education. This translation offers novel evidence of interest for students of ancient philosophy, rhetorical education, and literature more broadly. It is accompanied by explanatory notes, an introduction, and scholarly apparatus, including indices, glossaries, and bibliography. (shrink)

The commentary on Plato's Republic by Proclus (d. 485 CE), which takes the form of a series of essays, is the only sustained treatment of the dialogue to survive from antiquity. This three-volume edition presents the first complete English translation of Proclus' text, together with a general introduction that argues for the unity of Proclus' Commentary and orients the reader to the use which the Neoplatonists made of Plato's Republic in their educational program. Each volume is completed by a Greek (...) word index and an English-Greek glossary that will help non-specialists to track the occurrence of key terms throughout the translated text. The second volume of the edition presents Proclus' essays on the tripartite soul and the virtues, female philosopher rulers, and the metaphysics and epistemology of the central books of the Republic. The longest of the essays in Volume II interprets the nature and significance of the 'marriage number' whose miscalculation leads to the degeneration of the ideal city-state. (shrink)

Covers Essays 1 to 6 in Proclus' Commentary and includes a general introduction to the work as a whole.

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

The purpose of this paper is to reconstruct Frege’s argument against the relativity of truth contained in his posthumous writing Logic from 1897. Two points are made. The first is that the argument is a performative version of the common objection that truth relativism is incoherent: it is designed to show that the assertion of the relativity of truth involves a performative incoherence, because the absoluteness of truth is a success condition for making assertions. From a modern point of view, (...) the central premise of the argument, that the successful making of assertions depends on the absoluteness of truth, is highly doubtful. The second point is that this premise can be made plausible within the framework of Frege’s conception of truth and assertion: it can be derived from his thesis that, in order to put something forward as true, we do not need the word ‘true’, but only the assertoric force. (shrink)

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...) The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

This chapter applies ‘The Decline and Fall of the Spectacle-Commodity Economy’ – the Situationist account of the Watts Rebellion (Los Angeles, 1965) – to the August riots (England, 2011) and the global Occupy movement. It draws two conclusions: that both May ’68 and Occupy were formed by the political violence that preceded them; and that, although the Situationist essay makes problematic claims about race, its assessment of the Spectacle-Commodity Economy remains valuable: in fact, if combined with intersectional theory, it can (...) provide a useful counterbalance to identity politics that can prevent what Alain Badiou calls an ‘immediate riot’ from becoming a ‘historical riot’ by fragmenting mass social movements and undermining unity. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a sense an ultimate (...) form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

Content disjunctivism is the view that veridical experience involves contents and objects that differ from those of corresponding hallucinations. On one formulation of this view, we are aware of ordinary material things in our surroundings when we experience veridically, and we are aware of mere appearances when we hallucinate. This paper proposes a way of developing this view and offers some considerations in support. Central to the proposed regimentation will be a distinction between different notions of appearance. We distinguish between (...) the notion of something merely appearing to have a property and the notion of mere appearances, which are types of objects that we can refer to and be aware of. Mere appearances are not sense data or Meinongian non-existent objects but existing objects that do not have the properties that they appear to have. These notions of appearance will be elucidated, in particular by characterizing how they are involved in hallucination and illusion. I argue that the resulting view is supported by how our mental life seems to us when we experience our environment. (shrink)

Kant's 'Staatsrecht' in the "Metaphysik der Sitten" very likely represents the sharpest analysis and critique of democratic modernity after 1789. This, however, had to remain unrecognized as long as the repeatedly lamented problematic nature of this late text was attributed either to the alleged senility of the author, or else confusion created in the course of the printing process was blamed for its inscrutable composition. In fact, however, it is an expression of the brilliance of a philosophical rhetoric that has (...) remained unexplored to this day and must be regarded as the culmination and pièce de résistance of Kant's oeuvre. By focussing the attention to this piece of writing for the first time in the history of Kant scholarship, Martin Welsch uncovers a hitherto unnoticed variant of the notion of radical popular sovereignty that sheds new light on our political present. (shrink)

Tento text se soustřeďuje na prozkoumání vztahu dvou knih Alfreda Northa Whiteheada, Procesu a reality a Funkce rozumu, které byly publikovány ve stejném roce, v roce 1929. Autor textu nejprve představuje Whiteheadovo pojetí spekulativní filosofie, tak jak je představeno na úvodních stránkách Procesu a reality. Poukazuje, že Whitehead pro potřeby konstrukce filosofického schématu odmítl matematickou axiomatickou metodu a metodu rigidního empirismu a představuje Whiteheadovu vlastní filosofickou metodu, metodu deskriptivní generalizace. Ta může být ve stručnosti shrnuta jako imaginativní konstrukce spekulativního schématu, (...) založená na předchozích pozorováních, která je zpětně testována dalšími pozorováními. Text poukazuje na to, že v Procesu a realitě není předvedena imaginativní konstrukce Whiteheadovy filosofie. Jedna z fází deskriptivní generalizace tedy chybí. Text tvrdí, že tuto chybějící fázi deskriptivní generalizace můžeme najít ve Funkci rozumu. (shrink)

The Basics for the Philosophy Dictionary of Arguments - How to find non-mentioned concepts.

In this paper I draw attention to a peculiar epistemic feature exhibited by certain deductively valid inferences. Certain deductively valid inferences are unable to enhance the reliability of one's belief that the conclusion is true—in a sense that will be fully explained. As I shall show, this feature is demonstrably present in certain philosophically significant inferences—such as GE Moore's notorious 'proof' of the existence of the external world. I suggest that this peculiar epistemic feature might be correlated with the much (...) discussed phenomenon that Crispin Wright and Martin Davies have called 'transmission failure'—the apparent failure, on the part of some deductively valid inferences to transmit one's justification for believing the premises. (shrink)

Metaphysical rationalism, the doctrine which affirms the Principle of Sufficient Reason (the PSR), is out of favor today. The best argument against it is that it appears to lead to necessitarianism, the claim that all truths are necessarily true. Whatever the intuitive appeal of the PSR, the intuitive appeal of the claim that things could have been otherwise is greater. This problem did not go unnoticed by the great metaphysical rationalists Spinoza and Leibniz. Spinoza’s response was to embrace necessitarianism. Leibniz’s (...) response was to argue that, despite appearances, rationalism does not lead to necessitarianism. This paper examines the debate between these two rationalists and concludes that Leibniz has persuasive grounds for his opinion. This has significant implications both for the plausibility of the PSR and for our understanding of modality. (shrink)

In 1990 Edward Craig published a book called Knowledge and the State of Nature in which he introduced and defended a genealogical approach to epistemology. In recent years Craig’s book has attracted a lot of attention, and his distinctive approach has been put to a wide range of uses including anti-realist metaepistemology, contextualism, relativism, anti-luck virtue epistemology, epistemic injustice, value of knowledge, pragmatism and virtue epistemology. While the number of objections to Craig’s approach has accumulated, there has been no sustained (...) attempt to develop answers to these objections. In this paper we provide answers to seven important objections in the literature. (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)