We define intuitionistic subatomic natural deduction systems for reasoning with elementary would-counterfactuals and causal since-subordinator sentences. The former kind of sentence is analysed in terms of counterfactual implication, the latter in terms of factual implication. Derivations in these modal proof systems make use of modes of assumptions which are sensitive to the factuality status of the formula that is to be assumed. This status is determined by means of the reference proof system on top of which a modal proof system (...) is defined. The introduction and elimination rules for counterfactual (resp. factual) implication draw on this status. It is shown that derivations in the systems normalize and that normal derivations have the subexpression/subformula property. An intuitionistically acceptable proof-theoretic semantics is formulated in terms of canonical derivations. The systems are applied to so-called counterpossibles and to related constructions. (shrink)

The ontology of decision theory has been subject to considerable debate in the past, and discussion of just how we ought to view decision problems has revealed more than one interesting problem, as well as suggested some novel modifications of classical decision theory. In this paper it will be argued that Bayesian, or evidential, decision-theoretic characterizations of decision situations fail to adequately account for knowledge concerning the causal connections between acts, states, and outcomes in decision situations, and so they are (...) incomplete. Second, it will be argues that when we attempt to incorporate the knowledge of such causal connections into Bayesian decision theory, a substantial technical problem arises for which there is no currently available solution that does not suffer from some damning objection or other. From a broader perspective, this then throws into question the use of decision theory as a model of human or machine planning. (shrink)

The task of Philosophy in Science (PinS) is to use philosophical tools to help solve scientific problems. This article describes how I stumbled into this line of work and then addressed several topics in philosophy of biology—units of selection, cladistic parsimony, robustness and trade-offs in model building, adaptationism, and evidence for common ancestry—often in collaboration with scientists. I conclude by offering advice for would-be PinS practitioners.

Essay review of John Carroll's book, _Laws of Nature_.

By analyzing the meaning of time I argue, without endorsing operationalism, that time is necessarily related to physical systems which can serve as clocks. This leads to a version of relationism about time which entails that there is no time 'before' the universe. Three notions of metaphysical 'time' (associated, respectively, with time as a mathematical concept, substantivalism, and modal relationism) which might support the idea of time 'before' the universe are discussed. I argue that there are no good reasons to (...) believe that metaphysical 'time' can be identified with what we ordinarily call time. I also briefly review and criticize the idea of time 'before' the big bang, associated with some recent speculative models in modern cosmology, and I argue that if the big bang model is a (roughly) correct description of our universe, then the best current answer to the question in the title is that time did have a beginning. (shrink)

There has been considerable debate regarding the relative merits of two theses about moral obligation known as actualism and possibilism. Both theses seek to give expression to the general idea that one ought to do the best one can. According to actualism, one’s obligations turn on what would happen if one chose some course of action, whereas, according to possibilism, they turn on what could happen if one chose some course of action. There are two strands to the debate: the (...) substantive verdicts that the two theses render in particular cases, and the accounts that they yield of the conceptual structure of moral obligation. Possibilism is conceptually appealing, whereas actualism is not, but the latter may seem to render superior substantive verdicts. In this paper, it is argued that, by turning from the objectivist’s emphasis on what is actually best to the prospectivist’s emphasis on what one’s evidence indicates is best, possibilists can provide an account of moral obligation that is both conceptually and substantively attractive. (shrink)

The paper is about the interpretation of opaque verbs like “seek”, “owe”, and “resemble” which allow for unspecific readings of their (indefinite) objects. It is shown that the following two observations create a problem for semantic analysis: (a) The opaque position is upward monotone: “John seeks a unicorn” implies “John seeks an animal”, given that “unicorn” is more specific than “animal”. (b) Indefinite objects of opaque verbs allow for higher-order, or “underspecific”, readings: “Jones is looking for something Smith is looking (...) for” can express that there is something unspecific that both Jones and Smith are looking for. Given (a) and (b), it would seem that the following inference is hard to escape, if the premisses are construed unspecifically and the conclusion is taken on its under- specific reading: Jones is looking for a sweater. Smith is looking for a pen. Smith is looking for something Jones is looking for. (shrink)

Meinertsen has recently put forward three arguments against disjunctive properties: the arguments from truthmaking, commonality, and causation. In this paper, I argue that all three arguments fail. The argument from truthmaking rests on the problematic notion of different types of truthmakers and is therefore itself problematic. The argument from commonality may hold but only at the cost of losing much of the philosophical significance of its conclusion. The argument from causation essentially collapses into the argument from truthmaking and is therefore (...) problematic for the same reason as the latter is. I conclude that Meinertsen has not made a case against disjunctive properties. (shrink)

The safety principle is the view that, roughly, if one knows that p, p could not easily have been false. It is common for safety theorists to relativize safety to belief-formation methods. In this paper, I argue that there is no fixed principle of method-individuation that can stand up to scrutiny. I examine various ways to individuate methods and argue that all of them are subject to serious counterexamples. In the end, I conclude by considering some alternative ways to preserve (...) the insight behind safety without invoking a fixed principle of method-individuation. (shrink)

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. This, we argue, (...) suggests that Pearl’s logic is either too weak or too strong. (shrink)

In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewis’s well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is (...) the weakest logic of causal counterfactuals that respects Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s. (shrink)

The idea of fragmentalism has been proposed by Kit Fine as a non-standard view of tense realism. This paper examines a modal version of the view, called modal fragmentalism, which combines genuine realism and realism of modality. Modal fragmentalism has been recently discussed by Iaquinto. But unlike Iaquinto, who primarily focused on possibilities de re, in this paper, we focus on expressions of possibilities de dicto. We argue that the chief idea of modal realism should be that different worlds are (...) distinguished not just in terms of how things are differently with respect to each world, but also in terms of how things could have been differently with respect to each world. This demands a realism-oriented semantics for suppositional contents, and more specifically, for conditionals. By deploying a multidimensional semantics for conditionals, we show that there are good reasons to consider modal fragmentalism as a serious approach in metaphysics, which shares many similarities with the fragmentalism of tense. (shrink)

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes (...) 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena. (shrink)

In the debate about the nature and identity of possible worlds, philosophers have neglected the parallel questions about the nature and identity of moments of time. These are not questions about the structure of time in general, but rather about the internal structure of each individual time. Times and worlds share the following structural similarities: both are maximal with respect to propositions (at every world and time, either p or p is true, for every p); both are consistent; both are (...) closed (every modal consequence of a proposition true at a world is also true at that world, and every tense-theoretic consequence of a proposition true at a time is also true at that time); just as there is a unique actual world, there is a unique present moment; and just as a proposition is necessarily true iff true at all worlds, a proposition is eternally true iff true at all times. In this paper, I show that a simple extension of my theory of worlds yields a theory of times in which the above structural similarities between the two are consequences. (shrink)

The paper argues against Sosa’s claim that sensitivity cannot be differentially supported over safety as the right requirement for knowledge. Its main contention is that, although all sensitive beliefs that should be counted as knowledge are also safe, some insensitive true beliefs that shouldn’t be counted as knowledge are nevertheless safe.

Lange issues a novel challenge to philosophical accounts of laws of nature. He notes that the laws of nature seem to be themselves governed by laws analogous to the way that the laws govern particular facts. These higher order laws are the meta-laws of nature. He claims that if a philosophical account of laws aims to accurately characterize the laws, it should be able to account for these meta-laws. To generalize this challenge, I introduce the notion of roles played by (...) laws of nature according to a philosophical account, and identify a number of salient roles. I then apply Lange’s challenge to two views: the regularity view and the universals view. I argue that the regularity view may be able to meet the generalized version of Lange’s challenge, and that the universals view is able to meet the challenge. 1 Meta-laws2 Lange’s Challenge3 The Roles Played by Laws and Meta-laws4 Meta-laws and the Regularity View5 Meta-laws and the Universals View6 Summary and Conclusion. (shrink)

Newman’s objection is sometimes taken to be a fatal objection to structural realism (SR). However, ambiguity in the definition of “structure” allows for versions that do not succumb to Newman’s objection. In this paper, I consider some versions of SR that maintain an abstract notion of structure yet avoid Newman’s objection. In particular, I consider versions suggested by Melia and Saatsi. They reject a solution that restricts the domain of the second-order quantifiers, and argue in favor of buttressing the language (...) with intensional operators such as “it is physically necessary that...”. I argue that their favored solution effectively requires the former suggestion that they reject. This argument suggests that a notion of natural properties may be indispensable to SR. (shrink)

Abstract Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in a Reducibility-based reply (...) to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9784-4 Authors Juhani Yli-Vakkuri, Wolfson College, Oxford University, Oxford, OX2 6UD UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

Dispositional essentialists argue that physical properties have their causal roles essentially. This is typically taken to mean that physical properties are identical to dispositions. I argue that this is untenable, and that we must instead say that properties bestow dispositions. I explore what it is for a property to have such a role essentially. Dispositional essentialists argue for their view by citing certain epistemological and metaphysical implications, and I appeal to these implications to place desiderata on the concept of essence (...) involved. I argue that the traditional modal theory of essence meets these desiderata, but that the resulting theory wrongly implies that certain dispositions essential to mass are essential to charge, thereby offering a new argument against modal theories of essence. I argue that dispositional essentialism requires a primitive notion of essence, and develop a primitivist theory based on Kit Fine's views. I show that the primitivist theory has all the virtues of the modal alternative, and none of the vices. I develop a novel way of thinking about the relationship between properties, laws and dispositions, and argue that it has distinct advantages over standard dispositional essentialist formulations. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

Modal Dimensionalism is a metaphysical theory about possible worlds that is naturally suggested by the often-noted parallelism between modal logic and tense logic. It says that the universe spreads out not only in spatiotemporal dimensions but also in a modal dimension. It regards worlds as nothing more or less than indices in the modal dimension in the way analogous to the way in which Temporal Dimensionalism regards temporal points and intervals as indices in the temporal dimension. Despite its naturalness and (...) intuitive appeal. Modal Dimensionalism has been largely ignored while the debates between David Lewis and his critics have dominated the discourse on the nature of possible worlds. It is high time that we took Modal Dimensionalism seriously as a viable alternative. (shrink)

We prove some embedding theorems for classical conditional logic, covering 'finitely cumulative' logics, 'preferential' logics and what we call 'semi-monotonic' logics. Technical tools called 'partial frames' and 'frame morphisms' in the context of neighborhood semantics are used in the proof.

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

Laurence BonJour has recently proposed a novel and interesting approach to the problem of induction. He grants that it is contingent, and so not a priori, that our patterns of inductive inference are reliable. Nevertheless, he claims, it is necessary and a priori that those patterns are highly likely to be reliable, and that is enough to ground an a priori justification induction. This paper examines an important defect in BonJour's proposal. Once we make sense of the claim that inductive (...) inference is "necessarily highly likely" to be reliable, we find that it is not knowable a priori after all. (shrink)

When we engage with a work of fiction we gain knowledge about what is fictionally true in that work. Our grasp of what is true in a fiction is central to our engagement with representational works of art, and to our assessments of their merits. Of course, it is sometimes difficult to determine what is fictional – it is a good question whether the main character of American Psycho is genuinely psychotic or merely delusional, for instance. (And even in this (...) case, our ignorance itself is crucial to how we engage with the story and assess its qualities.) But in the vast majority of cases, we have no difficulty distinguishing what is fictionally true from what is not. Every attentive reader of Bleak House knows that it is fictional that Esther is Lady Dedlock’s daughter, but not fictional that Ada is the daughter of John Jarndyce. Moreover, we do not think that our judgements about what is fictional are based on guesswork. We have a folk theory of fictional truth, in the sense that we have a relatively stable framework upon which we rely when we engage with fiction, and we face the challenge of characterizing that theory systematically. (shrink)

The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).

This article examines a popular complaint against the fictionalist account of possible objects bruited by Gideon Rosen. This is the complaint that modal fictionalism is, in some sense or other, hopelessly artificial. I shall separate two different strands to this worry and examine each in turn. As we shall see, neither strand to the objection is intractable.

The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the incompleteness (...) problem. (shrink)

This article defends the use of interventionist counterfactuals to elucidate causal and explanatory claims against criticisms advanced by James Bogen and Peter Machamer. Against Bogen, I argue that counterfactual claims concerning what would happen under interventions are meaningful and have determinate truth values, even in a deterministic world. I also argue, against both Machamer and Bogen, that we need to appeal to counterfactuals to capture the notions like causal relevance and causal mechanism. Contrary to what both authors suppose, counterfactuals are (...) not "unscientific" - a substantial tradition within statistics and the causal modelling literature makes heavy use of them. (shrink)

Counterfactuals all the way down? Content Type Journal Article DOI 10.1007/s11016-010-9437-9 Authors Jim Woodward, History and Philosophy of Science, 1017 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260, USA Barry Loewer, Department of Philosophy, Rutgers University, New Brunswick, NJ 08901, USA John W. Carroll, Department of Philosophy and Religious Studies, North Carolina State University, Raleigh, NC 27695-8103, USA Marc Lange, Department of Philosophy, University of North Carolina at Chapel Hill, CB#3125—Caldwell Hall, Chapel Hill, NC 27599-3125, USA Journal Metascience Online (...) ISSN 1467-9981 Print ISSN 0815-0796 Journal Volume Volume 20 Journal Issue Volume 20, Number 1. (shrink)

Possible worlds represent you as being certain ways, as having a different lives, different hopes, and different friends. A foundational question in the philosophy of modality thus emerges: in virtue of what does a world represent you in these ways? In this paper, we focus on David Lewis's answer to this metarepresentational question: Counterpart Theory.

It is widely held that, as Morgenbesser’s case is usually taken to show, considerations of causal or probabilistic dependence should enter into the evaluation of counterfactuals. This paper challenges that idea. I present a modified version of Morgenbesser’s case and show how probabilistic approaches to counterfactuals are in serious trouble. Specifically, I show how probabilistic approaches run into a dilemma in characterizing probabilistic independence. The modified case also illustrates a difficulty in defining causal independence. I close with a suggestion for (...) a strategy to handle this difficulty. (shrink)

Realists about laws of nature and their Humean opponents disagree on whether laws ‘govern’. An independent commitment to the ‘governing conception’ of laws pushes many towards the realist camp. Despite its significance, however, no satisfactory account of governance has been offered. The goal of this article is to develop such an account. I base my account on two claims. First, we should distinguish two notions of governance, ‘guidance’ and ‘production’, and secondly, explanatory phenomena other than laws are also candidates for (...) governance. My goal is to develop a unified account which captures both guidance and production as well as the governance of phenomena, such as essence and logical consequence. The account of governance I develop belongs to the family of modal accounts, which was popularized by David Armstrong, but it also employs essentialist resources. If successful, this modal-essentialist account not only reveals the costs that proponents of governance incur, but it also puts that important notion on a solid theoretical foundation. (shrink)

This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: the fact that disjunctions scoping under possibility modals give rise to the free choice effect and the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. The analysis explains (...) why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content. (shrink)

In ‘Quiddistic Knowledge’ (Schaffer in Philos Stud 123:1–32, 2005), Jonathan Schaffer argued influentially against the view that the laws of nature are metaphysically necessary. In this reply I aim to show how a coherent and well-motivated form of necessitarianism can withstand his critique. Modal necessitarianism—the view that the actual laws are the laws of all possible worlds—can do justice to some intuitive motivations for necessitarianism, and it has the resources to respond to all of Schaffer’s objections. It also has certain (...) advantages over contingentism in the domain of modal epistemology. I conclude that necessitarianism about laws remains a live option. (shrink)

When does a developing human being acquire moral status? I outline three different positions based on substance ontology that attempt to solve the question by locating some morally salient event in the process of human development question. In the second section, I consider some specific empirical objections to one of these positions, refute them, and then show how similar objections and responses would generalize to the other substance-based positions on the question. The crucial finding is that all the attempts to (...) answer the question that involve substance ontology need to appeal to dispositions. (shrink)

A prominent contemporary anti-skeptical strategy, most famously articulated by Keith DeRose, aims to cage the skeptic′s doubts by contextualizing subjunctive conditional accounts of knowledge through a conversational rule of sensitivity. This strategy, I argue, courts charges of circularity by selectively invoking heavy counterfactual machinery. The reason: such invocation threatens to utilize a metric for modal comparison that is implicitly informed by judgments of epistemic sameness. This gives us reason to fear that said modal metric is selectively cherry-picked in advance to (...) support the very anti-skeptical conclusion for which the contextualist longs. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

The full-text of this book chapter is not available in ORA. Citation: Williamson, T.. Knowledge of counterfactuals. In: O'Hear, A. Epistemology. Cambridge: Cambridge University Press, pp. 45-64.

Could laws of nature be violated, in the sense that some proposition is both a law and false? I argue that opponents of regularity theories of laws should accept the metaphysical possibility of such genuine violations. I begin with a clarification of this claim. The main argument is then developed in three steps. I first argue that opponents of regularity theory should endorse the modal-essence view: certain modal principles are essential to the laws of nature. Second, I argue that the (...) modal-essence view entails sophisticated modal primitivism. Third, I argue from sophisticated primitivism to the metaphysical possibility of genuine violations of laws. (shrink)

In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of ‘decoherence-based’ EQM, and of the ‘consistent histories’ formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both ‘branching worlds’ and ‘parallel worlds’ interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due to Lewis (On (...) the Plurality of Worlds, 1986 ) supports the non-branching interpretation. Belnap et al. (Facing the Future: Agents and Choices in Our Indeterministic World, 2001 ) refer to Lewis’ argument as the ‘Assertion problem’, and propose a pragmatic response to it. I argue that their response is unattractively ad hoc and complex, and that it prevents an Everettian who adopts branching-time semantics from making clear sense of objective probability. The upshot is that Everettians are better off without branching-time semantics. I conclude by discussing and rejecting an alternative possible motivation for branching time. (shrink)