In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

Cytogenetics was born of the confluence of two so-far independent fields: cytological studies and breeding studies, which merged through the identification of genes with chromosomes. In this paper I argue that genes were introduced as functional entities. Functional explanations are presented here as a subclass of inferences to the best explanation and I argue that abductive arguments do not offer conclusive proof for the existence of the entities postulated through them. However, functional explanations usually follow a scheme laid out by (...) Fodor (1968): there is a first phase where hypothetical entities are postulated and individuated through their effects; there is a second phase where the physical structures responsible for these effects are sought. I analyze the development of both phases in the construction of the chromosome theory of Mendelian inheritance. I will argue that first-phase theories are important to set conditions of identification for the functions played by a certain structure in a given containing system. (shrink)

A method of linguistically-oriented reasoning comprehension is proposed. It is based on semiological principles of text comprehension. Both content and form are essential for comprehending argumentative texts. A text recipient is viewed as a rational judge trying to detect all the components of the argument he/she considers and thus to see if the argument is consistent. Elementary and higher level argumentative units of the text are discovered by applying a modified S. Toulmin's model of argumentative functions. Validity and correctness of (...) arguments are established by means of a new – linguistic – interpretation of traditional syllogistic. (shrink)

Several arguments attempt to show that if traditional, acquaintance-based epistemic internalism is true, we cannot have foundational justification for believing falsehoods. I examine some of those arguments and find them wanting. Nevertheless, an infallibilist position about foundational justification is highly plausible: prima facie, much more plausible than moderate foundationalism. I conclude with some remarks about the dialectical position we infallibilists find ourselves in with respect to arguing for our preferred view and some considerations regarding how infallibilists should develop their account (...) of infallible foundational justification. In particular, I provide an account of how propositions that moderate foundationalists claim are foundationally justified derive their epistemic support from infallibly known propositions. This is possible when a foundational proposition is coarsely-grained enough to correspond to determinable properties exemplified in experience or determinate properties that a subject insufficiently attends to; one may have inferential justification derived from such a basis when a more finely-grained proposition includes in its content one of the ways that the foundational proposition could be true. (shrink)

Earl Conee and Richard Feldman have recently argued that the evidential support relation should be understood in terms of explanatory coherence: roughly, one's evidence supports a proposition if and only if that proposition is part of the best available explanation of the evidence. Their thesis has been criticized through alleged counterexamples, perhaps the most important of which are cases where a subject has a justified belief about the future. Kevin McCain has defended the thesis against Byerly's counterexample. I argue that (...) McCain's defense is inadequate before pointing toward a more promising solution for explanationism. The Byerly–McCain exchange is important because it casts light on the difficult issues of the standards for justification and the nature of epistemic support. Furthermore, McCain's defense of explanationism about epistemic support represents an important recent development of the burgeoning explanationist program in epistemology and philosophy of science. (shrink)

ABSTRACT The argument of inference to the best explanation sets up that, given a phenomenon to be explained, several rival hypotheses race to provide an explanation and the hypothesis that explains the phenomenon better than its rival gives good reasons for the belief in its truth and, therefore, for the acceptance of such hypothesis. The argument supposes that these rival hypotheses share the same phenomenon to be explained. In this paper it is argued that, in a few scientific episodes, scientists (...) with different hypotheses, even if sharing the phenomenon to be explained, have different goals regarding the handling of the phenomenon; but then an issue arises as to the structure of the argument, since setting different aims to handle a phenomenon would result in an axiological targeting by the scientists, one not enclosed in the structure of the argument. In addition, axiological targeting can also show itself as something crucial for the issue of accepting a hypothesis, a state of affair not foreseen in the argument of inference to the best explanation again. The purpose of this paper is, by means of “research programs” principle by Imre Lakatos, and by means of a case study – the acceptance of the DNA double helix model – to sustain the concept that the axiological difference may prove to be crucial for the acceptance of one hypothesis rather than other rival hypotheses. (shrink)

In this paper, I take a closer look at Hans Reichenbach’s relation to metaphysics and work out some interesting parallels between his account and that of the proponents of inductive metaphysics, a tradition that emerged in the mid- and late 19th century and the early 20th century in Germany. It is in particular Hans Reichenbach’s conception of the relation between the natural sciences and metaphysics, as displayed in his treatment of the question of the existence of the external world, that (...) shows some very interesting similarities with inductive metaphysics. By a comparison with the position of the inductive metaphysician Erich Becher and his handling of the problem of realism, I work out the parallels between Reichenbach’s program and inductive metaphysics. I come to the conclusion that while there are certainly some respects in which Reichenbach’s logical empiricism is closer to the positions of the representatives of the Vienna Circle, it turns out that with regard to his views on metaphysics there is a greater affinity with the program of inductive metaphysics. (shrink)

This article describes abductions as special patterns of inference to the best explanation whose structure determines a particularly promising abductive conjecture and thus serves as an abductive search strategy. A classification of different patterns of abduction is provided which intends to be as complete as possible. An important distinction is that between selective abductions, which choose an optimal candidate from given multitude of possible explanations, and creative abductions, which introduce new theoretical models or concepts. While selective abduction has dominated the (...) literature, creative abductions are rarely discussed, although they are essential in science. The article introduces several kinds of creative abductions, such as theoretical model abduction, common cause abduction and statistical factor analysis, and illustrates them by various real case examples. It is suggested to demarcate scientifically fruitful abductions from purely speculative abductions by the criterion of causal unification. (shrink)

Peter Lipton has attempted to flesh out a model of Inference to the Best Explanation (IBE) by clarifying explanation in terms of a causal model. But Lipton's account of explanation makes an adequate explanation depend on a principle which is virtually identical to Mill's Method of Difference. This has the result of collapsing IBE on Lipton's account of it into causal inference as conceived by the Causal-Inference model of induction. According to this model, many of our inductions are inferences from (...) effects to their probable causes, and Mill's Methods are canons to guide such inferences. Thus, Lipton's account of IBE fails to represent an advance over the already familiar Causal-Inference Model of induction. (shrink)

Charles S. Peirce argued that, besides deduction and induction, there is a third mode of inference which he called " hypothesis " or " abduction." He characterized abduction as reasoning " from effect to cause," and as " the operation of adopting an explanatory hypothesis." Peirce ' s ideas about abduction, which are related also to historically earlier accounts of heuristic reasoning, have been seen as providing a logic of scientific discovery. Alternatively, abduction is interpreted as giving reasons for pursuing (...) a hypothesis. Inference to the best explanation has also been regarded as an important mode of justification, both in everyday life, detective stories, and science. In particular, scientific realism has been defended by an abductive nomiracle argument, while the critics of realism have attempted to show that this appeal to abduction is question - begging, circular, or incoherent. This paper approaches these issues by distinguishing weaker and stronger forms of abduction, and by showing how these types of inferences can be given Peircean and Bayesian probabilistic reconstructions. (shrink)

According to a widely shared generic conception of inferential justification—‘the standard conception’—an agent is inferentially justified in believing that p only if she has antecedently justified beliefs in all the non-redundant premises of a good argument for p. This conception tends to serve as the starting-point in contemporary debates about the nature and scope of inferential justification: as neutral common ground between various competing, more specific, conceptions. But it’s a deeply problematic starting-point. This paper explores three questions that haven’t been (...) given the attention they deserve, that complicate the application of the standard conception to cases, and that reveal it to be underspecified at the core—in ways that aren’t resolved but inherited by more specific (extant) versions of it. The goal isn’t to answer the questions, but to articulate them, explain what turns on them, and invite a critical re-examination of the standard conception. (shrink)

Attempts to evaluate a belief or argument on the basis of its cause or origin are usually condemned as committing the genetic fallacy. However, I sketch a number of cases in which causal or historical factors are logically relevant to evaluating a belief, including an interesting abductive form that reasons from the best explanation for the existence of a belief to its likely truth. Such arguments are also susceptible to refutation by genetic reasoning that may come very close to the (...) standard examples given of supposedly fallacious genetic reasoning. (shrink)

A potential explanation of a fact is a hypothesis such that, if it were true, it would explain the fact in question. Let’s suppose that we become aware of a fact and some potential explanations thereof. Let’s also suppose that we would like to believe the truth. Given this aim, we can ask two questions. First, is it likely that one of these hypotheses is true? Second, given an affirmative answer to the first question, which one is it likely to (...) be? Inference to the best explanation (IBE) offers answers to both questions. To the first, it says ‘Yes’—assuming that at least one of the hypotheses would, if true, provide a satisfactory explanation of the fact under consideration. To the second, it says that the hypothesis most likely to be true is the one that scores best on the explanatory virtues: conservatism, modesty, simplicity, generality, and predictive power. Many philosophers have argued against IBE’s answer to the first question. I am interested in an objection to its answer to the second. Many philosophers seem to think that it is unsustainable: they seem to think that even if we assume that one of the competing hypotheses is true, we should not think that IBE will help us to identify it. Or, more carefully, if these philosophers are doing what they appear to be doing—namely, offering critiques of IBE that don’t depend on assumptions about the field of competing hypotheses—then their claim is that IBE will not help us to identify the truth. I believe that this is mistaken: the argument for believing it assumes a model of IBE that we have no reason to accept. (shrink)

This article offers a simple technical resolution to the problem of induction, which is to say that general facts are not always inferred from observations of particular facts, but are themselves sometimes defeasibly observed. The article suggests a holistic account of observation that allows for general statements in empirical theories to be interpreted as observation reports, in place of the common but arguably obsolete idea that observations are exclusively particular. Predictions and other particular statements about unobservable facts can then appear (...) as deductive consequences of such general observation statements, rather than inductive consequences of other particular statements. This semantic shift resolves the problem by eliminating induction as a basic form of inference, and folding the justification of general beliefs into the more basic problem of perception. (shrink)

One of the main challenges confronting Humean accounts of natural law is that Humean laws appear to be unable to play the explanatory role of laws in scientific practice. The worry is roughly that if the laws are just regularities in the particular matters of fact (as the Humean would have it), then they cannot also explain the particular matters of fact, on pain of circularity. Loewer (2012) has defended Humeanism, arguing that this worry only arises if we fail to (...) distinguish between scientific and metaphysical explanations. However, Lange (2013, 2018) has argued that scientific and metaphysical explanations are linked by a transitivity principle, which would undercut Loewer's defense and re-ignite the circularity worry for the Humean. I argue here that the Humean has antecedent reasons to doubt that there are any systematic connections between scientific and metaphysical explanations. The reason is that the Humean should think that scientific and metaphysical explanation have disparate aims, and therefore that neither form of explanation is beholden to the other in its pronouncements about what explains what. Consequently, the Humean has every reason to doubt that Lange's transitivity principle obtains. (shrink)

The thesis of this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its premises at all favorably relevant to its conclusion. In support of this thesis I assume two premises and argue for a third. My two assumptions are these: (1) that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion certain relative to its premises (this is widely, if not universally, acknowledged by writers (...) on logic), and (2) premises are favorably relevant to a conclusion only if it is certain or probable relative to them (I argued for this in an earlier paper). The premise I argue for in this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion probable relative to its premises. To establish this third premise, I first refute a defense of the contrary position (namely, that an argument's possessing the form of affirming the consequent suffices to make its conclusion probable relative to its premises), then offer counterexamples to that position, and finally demonstrate the failure of several attempts to save it. (shrink)

While “All events have a cause” is a synthetic statement making a factual claim about the world, “All effects have a cause” is analytic. When we take an event as an effect, no inference is required to deduce that it has a cause since this is what it means to be an effect. Some examples often given in the literature as examples of abduction work in the same way through semantic facts that follow from the way our beliefs represent those (...) effects; from this we may deduce not only that it has a cause, but what that cause is. (shrink)

Abstract: According to Laurence BonJour, the problem of induction can be solved by recognizing the a priori necessity that inductive conclusions constitute the best explanations of inductive premises. I defend an interpretation of the key probability claims BonJour makes about inductive premises and show that they are not susceptible to many of the objections that have been lodged against them. I then argue that these purportedly necessary probability claims nevertheless remain deeply problematic and that, as a result, BonJour's proposal fails (...) to provide a satisfactory resolution of the problem of induction. (shrink)

Several authors believe that there are certain facts that are striking and cry out for explanation—for instance, a coin that is tossed many times and lands in the alternating sequence HTHTHTHTHTHT…. According to this view, we have prima facie reason to believe that such facts are not the result of chance. I call this view the striking principle. Based on this principle, some have argued for far-reaching conclusions, such as that our universe was created by intelligent design, that there are (...) many universes other than the one we inhabit, and that there are no mathematical or normative facts. Appealing as the view may initially seem, I argue that we lack sufficient reason to accept it. (shrink)

After a period of inactivity, interest in explanationism as a thesis about the nature of epistemic justification has been renewed. Poston and McCain have both recently offered versions of explanationist evidentialism. In this paper, we pose two objections to explanationist evidentialism. First, explanationist evidentialism fails to state a sufficient condition for justification. Second, explanationist evidentialism implies a vicious regress.

This thesis explores attempts to characterise the structure of reality. Three notions stand out: Lewisian naturalness, Sider’s ‘structure’, and grounding, where the latter has become the most popular way to characterise the structure of reality in the contemporary literature. I argue that none of these notions, as they are currently understood, are suited for limning the metaphysical structure of reality. In the first part of the thesis I argue that, by the lights of the relevant theories, both naturalness and structure (...) fall short of the theoretical role carved out for those posits. In the second part of the thesis I present two challenges to the ‘orthodox’ conception of grounding. The first contests the standard assumption that grounding is asymmetric, both by citing what I take to be best described as symmetric instances of grounding, and by developing and arguing for a new theory of metaphysical structure – ‘metaphysical interdependence’ – which takes grounding to be nonsymmetric. The second challenge concerns the relationship between grounding and explanation, and leads to a dilemma for the grounding theorist. My proposed resolution to the dilemma is to adopt an antirealist approach to grounding, which I further motivate and develop in the final chapter. (shrink)

This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause (...) for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist. -/- Friends of the KCA have sought to defend their view that physical reality began to exist in two distinct ways. As I discuss in chapter 2, the first way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a priori arguments meant to show that, as a matter of metaphysical necessity, the past must be finite. If the past is necessarily finite, then the past history of physical reality is necessarily finite. And if having a finite past suffices for having a beginning, then, since the past history of physical reality is necessarily finite, physical reality necessarily began to exist. I show that the arguments which have been offered thus far for the view that the past is necessarily finite do not succeed. Moreover, as I elaborate on in chapter 5, having a finite past does not suffice for having a beginning. -/- As I discuss in chapter 3, the second way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a posteriori arguments meant to show that we have empirical evidence that physical reality has a finite past history. For example, the big bang is sometimes claimed to have been the beginning of physical reality and, since we have excellent empirical evidence for the big bang, we have excellent empirical evidence for the beginning of physical reality. The big bang can be understood in two ways. On the one hand, the big bang can be understood as a theory about the history and development of the observable universe. Understood in that sense, then I agree that the big bang is supported by excellent empirical evidence and by a scientific consensus. On the other hand, some authors (particularly science popularizers, science journalists, and religious apologists) have wrongly interpreted big bang theory as a theory about the beginning of the whole of physical reality. As I argue, while a beginning of physical reality may be consistent with classical big bang theory, classical big bang theory does not provide good reason for thinking that physical reality began to exist. -/- In part II, I turn to discussing three necessary, but not necessarily sufficient, conditions for physical reality to have a beginning. Before discussing the three conditions, in chapter 4, I introduce three metaphysical accounts of the nature of time (A-theory, B-theory, and C-theory) as well as some formal machinery that will subsequently become useful in the dissertation. I introduce the first of the three conditions in chapter 5. According to the Modal Condition, physical reality began to exist only if, at the closest possible worlds without time, physical reality does not exist. I show that this condition helps us to make sense of various views in both theology and philosophy of physics. In chapter 6}, I introduce the second of my three conditions, the Direction Condition, according to which, roughly, physical reality began to exist only if all space-time points agree about the direction of time, so that all space-time points can agree that physical reality's putative beginning took place in their objective past. In chapter 7, I discuss the third condition, the Boundary Condition, according to which physical reality began to exist only if there is a past temporal boundary such that physical reality did not exist before the boundary. I show that there are two senses in which physical reality could be said to have had a past temporal boundary. Lastly, in chapter 8, I show that there is a relationship between my three conditions and classical big bang theory, even though the relationship is not the one usually identified in the literature. -/- In part III, I present four arguments for the view that, at the present stage of philosophical and scientific inquiry, we cannot know whether physical reality satisfies the three necessary conditions to have had a beginning and, consequently, we cannot know whether physical reality had a beginning. As I will prove in chapter 9, no set of observations that we currently have, when conjoined with General Relativity, entails that physical reality satisfies the Direction or Boundary Conditions. As I show in chapter 10, considerations in the philosophical foundations of statistical mechanics entail either that the Cosmos violates the Modal Condition or else that there is a transcendental condition on the possibility of our knowledge of the past that prevents our access to data we would need to gather to determine whether physical reality satisfies the Boundary Condition. In chapter 11, I show that there are a number of live cosmological models according to which physical reality does not satisfy the Boundary Condition. As long as we don't know whether any of those cosmological models are correct, we do not know whether physical reality satisfies the Boundary Condition. Lastly, I turn to confirmation theory and show that, at our present stage of inquiry, ampliative inferences for the conclusion that physical reality satisfies the Modal, Direction, and Boundary Conditions are not successful. (shrink)

Philosophical work on explanation has focused on the following two topics: theories of explanation, intended to enumerate necessary and sufficient conditions for explanation, and inference to the best explanation as the strongest form of justification for ontological or metaphysical claims. I critically examine the most important philosophical work in both of these areas and defend my own conclusions about the connections between explanation and ontology. I argue that all of our inferences about the nature of the world, in ontology or (...) metaphysics, presuppose criteria for acceptable explanation. I first examine the metaphysics of Plato, Aristotle, and Leibniz, arguing that their metaphysical reasoning was guided by assumptions about the nature of explanation. I also survey some recent work in ontology and find inference to the best explanation offered as the strongest available method of defending existence claims. To conclude this discussion, I offer an original argument for the thesis that all reasoning about existence claims, being nondeductive, presupposes some criteria for acceptable explanations, or a theory of explanation. Carl Hempel and Wesley Salmon have been two of the most influential philosophers offering theories of explanation, and I examine their work with the intention of discovering ontological or metaphysical assumptions shaping their theories of explanation. I argue that Hempel's theory rests on deterministic assumptions, and I argue the Salmon's theory of causality, which he admits supports his theory of explanation, is subject to empiricist criticisms. Theories of explanation typically rest on assumptions about the nature of the world, I argue, and I explain why this is so with an original theory of explanation connecting it to the psychological phenomenon of understanding. We rely on understanding in the identification of explanations, and understanding requires establishing a metaphysical context for an explanandum-event. I end by indicating the possibility of generating vicious justificatory circles through the reciprocal relationship of support between explanation and ontology, and I argue that vicious circles can be avoided only by grounding all ontological reasoning in a fundamental explanatory task of giving order to experience through a system of categories. (shrink)

I begin by making some distinctions between kinds of response to a skeptical claim, the purpose of which is to explain what I mean by a "dissolution" of the problem of induction, and to focus on one of the ways it can be implemented. I then argue that previous attempts to dissolve the problem in this way fail, present mine, and defend it. Finally, I show that the dissolution of the problem doesn't improve our normative situation and may even worsen (...) it. (shrink)

Eliminative reasoning is a method that has been employed in many significant episodes in the history of science. It has also been advocated by some philosophers as an important means for justifying well-established scientific theories. Arguments for how eliminative reasoning is able to do so, however, have generally relied on a too narrow conception of evidence, and have therefore tended to lapse into merely heuristic or pragmatic justifications for their conclusions. This paper shows how a broader conception of evidence not (...) only can supply the needed justification but also illuminates the methodological significance of eliminative reasoning in a variety of contexts. (shrink)

Inference to the best explanation—or, IBE—tells us to infer from the available evidence to the hypothesis which would, if correct, best explain that evidence. As Peter Lipton puts it, the core idea driving IBE is that explanatory considerations are a guide to inference. But what is the epistemic status of IBE, itself? One issue of contemporary interest is whether it is possible to provide a justification for IBE itself which is non- objectionably circular. We aim to carve out some new (...) space in this debate. In particular, we suggest that the matter of whether a given rule-circular argument is objectionably circular itself depends crucially on some subtle distinctions which have been made in the recent literature on perceptual warrant. By bringing these debates together, a principled reason emerges for why some kinds of rule-circular justifications for IBE are considerably less objectionable than others. (shrink)

Despite decades of focused philosophical investigation, Inference to the Best Explanation still lacks a precise articulation and compelling defense. The primary reason for this is that it is not at all clear what it means for a hypothesis to be the best available explanation of the evidence. This paper first seeks to rectify this problem by developing a formal explication of the explanatory virtue of power. A resulting account of IBE is then evaluated as a form of uncertain inference. Overall, (...) this paper offers a precise account and novel defense of one important version of IBE. (shrink)

Accounts of modal knowledge are many and varied. How should we choose between them? I propose that we employ inference to the best explanation, and I suggest that there are three desiderata that we should use to rank hypotheses: conservatism, simplicity, and the ability to handle disagreement. After examining these desiderata, I contend that they can’t be used to justify belief in the modal epistemology that fares best, but that they can justify our accepting it in an epistemically significant sense. (...) Finally, I outline a modal epistemology that seems to do well by the standards I’ve recommended. (shrink)

In this dissertation I consider the problem of external world skepticism and attempts at providing an argument to the best explanation against it. In chapter one I consider several different ways of formulating the crucial skeptical argument, settling on an argument that centers on the question of whether we're justified in believing propositions about the external world. I then consider and reject several options for getting around this issue which I take to be inadequate. I finally conclude that the best (...) option available to us at the moment is to argue that the antiskeptical view is the best explanation of our ordinary experiences In chapter two I argue that, if we hope to ground what counts as defending antiskepticism in common sense, there is an argument against the possibility of ever knowing one has succeeded in defending antiskepticism. After showing that common sense is no place to look in setting a goal for our antiskeptical project, I present the view that what will be crucial to settling on our antiskeptical goal is coming to a successful analysis of the nature of physical objects. I suggest some minimal criteria that must be met by a view in order to be antiskeptical based on our intuitions about core skeptical cases, but acknowledge that a fully successful response to external world skepticism will require the antiskeptic to engage in some much more difficult analysis. In chapter three I consider various views of the nature of explanation and conclude, tentatively, that explanation as it interests the antiskeptic is fundamentally causal. In chapter four I consider and reject some of the core views on which best explanation facts are so fundamental that a project of attempting to vindicate probabilistically the virtues which make explanations epistemically good. In this chapter I show that views which analyze justification in terms of best explanation factors fail. In chapter five I attempt to vindicate the various explanatory virtues probabilistically. In doing so I attempt to express or translate the various explanatory virtues in terms of probabilities in order to show that having those virtues makes a view at least prima facie more probable. In chapters six and seven I explain and evaluate the various arguments to the best explanation against skepticism present in current philosophical literature. I attempt to show that extant arguments fail to appreciate the virtues possessed by classical skeptical scenarios. In chapter eight I briefly consider some options that may be open to the antiskeptic moving forward. All routes forward contain considerable obstacles, but there are some fruitful areas of research to pursue. (shrink)