The paper presents a new theory of perceptual demonstrative thought, the property-dependent theory. It argues that the theory is superior to both the object-dependent theory (Evans, McDowell) and the object-independent theory (Burge).

Demonstrative thoughts are distinguished by the fact that their contents are determined relationally, via perception, rather than descriptively. Therefore, a fundamental task of a theory of demonstrative thought is to elucidate how facts about visual perception can explain how these thoughts come to have the contents that they do. The purpose of this paper is to investigate how cognitive psychology may help us solve this metasemantic question, through empirical models of visual processing. Although there is a dispute (...) between attentional and non-attentional models concerning the best metasemantic mechanism for demonstrative thoughts, in this paper I will argue in favor of a hybrid model, which combines both types of processes. In this picture, attentional and non-attentional mechanisms are not mutually exclusive, and each plays a specific role in determining the singular content of demonstrative thoughts. (shrink)

In this paper I propose a model of demonstrative thought. I distinguish token-demonstratives, that pick out individuals, from type-demonstratives, that pick out kinds, or properties, and provide a similar treatment for both. I argue that it follows from my model of demonstrative thought, as well as from independent considerations, that demonstration, as a mental act, operates directly on mental representations, not external objects. That is, though the relation between a demonstrative and the object or property (...) demonstrated is semantically direct, the mechanism by which a demonstrative acquires its referent involves mediation by a perceptual representation. Finally, I argue that so-called 'demonstrative concepts'—which I treat as type-demonstratives—cannot perform the various philosophical functions that have been assigned to them. (shrink)

How can we explain our capacity to think about particulars in our external environment? Many philosophers have answered this question in terms of a sophisticated conception of space and time and the movement of objects therein. A more recent reaction against this view sought to explain this capacity solely in terms of perceptual mechanisms of object individuation. Neither explanation remains fully satisfactory. This book argues for a more desirable middle ground in terms of a pragmatist approach to demonstrative (...) class='Hi'>thought, where this capacity is explained through graded practical knowledge of objects. This view allows us to do justice to important insights put forward by both positions criticized in the book, while avoiding their potential shortcomings. It also paves the way to a more pragmatist approach to the theory of mental representation, where the notion of practical knowledge is allowed to play a central role in our cognitive life. Finally, it shows how practical knowledge may be firmly rooted in neurobiological processes and mechanisms that conform to what the empirical sciences tell us about the mind. (shrink)

Russellian or singular propositions are very useful in semantics to specify "what has been said" by a literal and serious utterance of a sentence containing a proper name, an indexical or a demonstrative, or for modeling demonstrative thoughts. I3ased on an example given by S. Guttenplan, I construct a case showing that if our only option for modeling demonstrative thoughts is a singular proposition à la Russell, we run the risk of admitting infallible empirical (existential) beliefs. I (...) defend the principle of the fallibility of our (first order) representations by appealing to Perry's notion of a relational mode of presentation that allows us to generalize the proposition which is the content of the perceptual belief in cases of hallucination or misidentification, so that there is no "immunity to error through misidentification" in the province of demonstrative thought. (shrink)

I raise a problem for common-factor theories of experience concerning the demonstrative thoughts we form on the basis of experience. Building on an insight of Paul Snowdon 1992, I argue that in order to demonstratively refer to an item via conscious awareness of a distinct intermediary the subject must have some understanding that she is aware of a distinct intermediary. This becomes an issue for common-factor theories insofar as it is also widely accepted that the general, pre-philosophical or ‘naïve’ (...) view of experience does not accept that in normal perceptual cases one is consciously aware of non-environmental (inner, mental) features. I argue then that the standard common-factor view of experience should be committed to attributing quite widespread referential errors or failures amongst the general, nonphilosophical populace – which seems an unattractively radical commitment. After clarifying the various assumptions I am making about experience and demonstrative thoughts, I consider a number of possible responses on behalf of the common-factor theorist. I finish by arguing that my argument should apply to any common-factor theory, not just avowedly ‘indirect' theories. (shrink)

The nature of perceptual demonstratives, the ‘that F’ component of judgments of the form ‘that F is G’ based on perceptual input, has been a topic of interest for many philosophers. Another related, though distinct, question concerns the nature of demonstrative judgments based not on current perceptual input, but instead derived from memory. I argue that the account put forward by John Campbell fails to adequately account for memory-based demonstrative thought.

Demonstrative thoughts are distinguished by the fact that their contents are determined relationally, via perception, rather than descriptively. Therefore, a fundamental task of a theory of demonstrative thought is to elucidate how facts about visual perception can explain how these thoughts come to have the contents that they do. The purpose of this paper is to investigate how cognitive psychology may help us solve this metasemantic question, through empirical models of visual processing. Although there is a dispute (...) between attentional and non-attentional models concerning the best metasemantic mechanism for demonstrative thoughts, in this paper I will argue in favor of a hybrid model, which combines both types of processes. In this picture, attentional and non-attentional mechanisms are not mutually exclusive, and each plays a specific role in determining the singular content of demonstrative thoughts. (shrink)

Attention plays a role in demonstrative thought: It sets the targets. Visual experience also plays a role. I argue here that it makes visual information available for use in the voluntary control of focal attention. To do so I use both introspection and neurophysiological evidence from projections between areas of attentional control and neural correlates of consciousness. Campbell and Smithies also identify roles for experience, but they further argue that only experience can play those roles. In contrast, I (...) argue that experience is not the only way in which visual information could be accessed for the voluntary control of attention. (shrink)

Perception enables us to think demonstrative thoughts about the world around us, but what must perception be like in order to play this role? Does perception enable demonstrative thought only if it is conscious? This paper examines three accounts of the role of consciousness in demonstrative thought, which agree that consciousness is essential for demonstrative thought, but disagree about why it is. First, I consider and reject the accounts proposed by Gareth Evans in (...) The Varieties of Reference and by John Campbell in Reference and Consciousness before offering an alternative proposal of my own. My proposal is that consciousness plays an essential epistemic role in explaining the capacity for demonstrative thought about an object by enabling the subject to form immediately justified beliefs about the object. (shrink)

Starting with Gareth Evans, there’s an important tradition of theorizing about perception-based demonstrative thought which assigns necessary epistemic conditions to it. Its core idea is that demonstrative reference in thought is grounded in information links, understood as links which carry reliable information about their targets and which a subject exploits for demonstrative reference by tokening the mental files fed by these links. Perception, on these views, is not fundamental to perception-based demonstrative thought but (...) is only the information link exploited in these cases. Evans himself assigns a further epistemic condition, while more recently Imogen Dickie has expanded the reliability requirement into a more complex account centered around justification. In this paper I synthesize three central proponents of this approach and show that the epistemic conditions they place on perception-based demonstrative thought are not actually required. My argument gives two examples in which there is perceptual contact with an object but this perceptual contact fails to do the epistemic work in question. The first case is stimulus-incorporating dream experiences, the second involves multimodal binding failures. I argue that this perceptual contact still affords demonstrative thought in these cases. (shrink)

Suppose you are a blindsighted subject and an experimenter sitting opposite you says of an object in your functionally blind field ‘that peach looks delicious’. Unless you move your head to encompass the object within your normal field of vision you will not know which object she is talking about. Suppose now she reverts to the strategy used by neurophsychologists who work with blindsighted subjects and simply tells you that there is an object there and asks you either to reach (...) for it or guess its shape, colour and so forth. If you are one of the well-trained blindsighted subjects who have been worked over for many years by psychologists you may well be able to do so, while denying you have any visual experience of the object and insisting you are only guessing. And, in concurrence with the existential formulation the experimenter now uses, instead of the demonstrative, it is natural to think that your singular reference, based on your perceptual input, is descriptive, as in ‘the object she maintains is there’ or ‘the object I am guessing about’ or ‘the object in my blind field’, etc. (shrink)

The status of the laws of nature in Hobbes’s Leviathan has been a continual point of disagreement among scholars. Many agree that since Hobbes claims that civil philosophy is a science, the answer lies in an understanding of the nature of Hobbesian science more generally. In this paper, I argue that Hobbes’s view of the construction of geometrical figures sheds light upon the status of the laws of nature. In short, I claim that the laws play the same role as (...) the component parts – what Hobbes calls the “cause” – of geometrical figures. To make this argument, I show that in both geometry and civil philosophy, Hobbes proceeds by a method of synthetic demonstration as follows: 1) offering a thought experiment by privation; 2) providing definitions by explication of “simple conceptions” within the thought experiment; and 3) formulating generative definitions by making use of those definitions by explication. In just the same way that Hobbes says that the geometer should “put together” the parts of a square to learn its cause, I argue that the laws of nature are the cause of peace. (shrink)

Suppose you are a blindsighted subject and an experimenter sitting opposite you says of an object in your functionally blind field ‘that peach looks delicious’. Unless you move your head to encompass the object within your normal field of vision you will not know which object she is talking about. Suppose now she reverts to the strategy used by neurophsychologists who work with blindsighted subjects and simply tells you that there is an object there and asks you either to reach (...) for it or guess its shape, colour and so forth. If you are one of the well-trained blindsighted subjects who have been worked over for many years by psychologists you may well be able to do so, while denying you have any visual experience of the object and insisting you are only guessing. And, in concurrence with the existential formulation the experimenter now uses, instead of the demonstrative, it is natural to think that your singular reference, based on your perceptual input, is descriptive, as in ‘the object she maintains is there’ or ‘the object I am guessing about’ or ‘the object in my blind field’, etc. (shrink)

What determines the reference of first-person thoughts—thoughts that one would express using the first-person pronoun? I defend a model on which our ways of gaining knowledge of ourselves do, in much the way that our ways of gaining knowledge of objects in the world determine the reference of perceptual demonstrative thoughts. This model—the Demonstrative Model of First-Person Thought—can be motivated by reference to independently plausible general principles about how reference is determined. But it faces a serious objection. (...) There seems to be an explanatory rival to it with a great deal of plausiblility. The rival is The Simple Rule Model, which says that first-person thoughts are governed by the simple rule that any token of one will be about the person whose token it is. I pinpoint a crucial unclarity in The Simple Rule Model, hinging on how we understand the notion of a rule, and argue that no version of the Simple Rule Model is both plausible and a genuine explanatory rival to the Demonstrative Model. I also provide an argument that the Demonstrative Model is extensionally adequate. (shrink)

Matheus Valente presents a number of examples designed to show that my theory of reference fixing for demonstratives violates the desideratum that demonstrative thoughts should be transparent to speakers. In this note I argue that the alleged desideratum is not really such and defend my theory against other criticisms made by Valente.

Jeffrey King has famously argued that there are several prima facie problems with the direct reference theory of the semantics of complex demonstratives, three of which apparently resist solution. King concludes by observing that, if these outstanding problems cannot be solved, then the prospects for a direct reference semantics for complex demonstratives will be poor. I shall focus on just one of these outstanding problems—the objection from belief attributions—and suggest that it, at least, can be answered.

In the basis of the subject which we try to deal with, it stands two worldviews based on expository and demonstrative epistemologies that formalize the intellectual building of Islamic culture. It seems that the main point here is about discussions between exposition and demonstration. Methodological discussions enlighten how are used on the one hand exposition as religious method and on the other hand demonstration as rational or intellectual method. Keywords: , , , , ,.

This paper defends a version of the old empiricist claim that to think about unobservable physical properties a subject must be able to think perception-based thoughts about observable properties. The central argument builds upon foundations laid down by G. E. M. Anscombe and P. F. Strawson. It bridges the gap separating these foundations and the target claim by exploiting a neglected connection between thought about properties and our grasp of causation. This way of bridging the gap promises to introduce (...) substantive constraints on right accounts of perception and perception-based thought. (shrink)

This paper presents a semantic and pragmatic theory of complex demonstratives. According to this theory, the semantic content of a complex demonstrative, in a context, is simply an object, and the semantic content of a sentence that contains a complex demonstrative, in a context, is a singular proposition. This theory is defended from various objections to direct reference theories of complex demonstratives, including King's objection from quantification into complex demonstratives.

It is often thought that endowing a demonstrative with a Fregean sense leaves no room for maintaining that it is also a rigid designator. In addition, some philosophers claim that indexicals - surely the paradigms of singular reference - pose a serious threat to the Fregean sense/ reference approach as they do not comply with the view that singular terms have Fregean senses. In this paper I argue that neither of these is true.

Complex demonstrative phrases, in English, are phrases such as ‘that woman in the department’ and ‘that car on the corner’. They are of particular interest to philosophers for two related reasons. The first involves the problem of intentionality. If there are phrases that are candidates for “latching directly onto the world,” they are such phrases, and their “simple” counterparts, as in the occurrences of ‘that’ in ‘that is nice’. As a result, philosophers interested in intentionality, from the sense-data theorists (...) to contemporary philosophers of mind, have devoted considerable attention to the question of how a demonstrative thought links to its object. The second reason involves issues in semantics and the philosophy of language. In the course of investigations into the model theory for modal logic in the 1950s and 1960s, philosophers recognized that the simplest way to treat terms was as modally rigid, namely as designating their actual designations relative to any possible world in which they existed, and nothing else in other worlds. It was soon recognized that this semantic property could be elegantly explained by the assumption that the semantics of singular terms reflects the role of singular terms in linking representations directly to the world. If the semantic contribution of a singular term to a thought is simply the object it denotes, and the thought is the object of modal evaluation, then the modal rigidity of the class of terms falls out as a consequence. Demonstrative phrases, both simple and complex, have always been taken to be among the paradigms for this picture of reference, which has come to be known as “the direct reference” model. (shrink)

Sometimes form-meaning mappings in language are not arbitrary, but iconic: they depict what they represent. Incorporating iconic elements of language into a compositional semantics faces a number of challenges in formal frameworks as evidenced by the lengthy literature in linguistics and philosophy on quotation/direct speech, which iconically portrays the words of another in the form that they were used. This paper compares the well-studied type of iconicity found with verbs of quotation with another form of iconicity common in sign languages: (...) classifier predicates. I argue that these two types of verbal iconicity can, and should, incorporate their iconic elements in the same way using event modification via the notion of a context dependent demonstration. This unified formal account of quotation and classifier predicates predicts that a language might use the same strategy for conveying both, and I argue that this is the case with role shift in American Sign Language. Role shift is used to report others’ language and thoughts as well as their actions, and recently has been argued to provide evidence in favor of Kaplanian “monstrous” indexical expressions. By reimagining role shift as involving either quotation for language demonstrations or “body classifier” predicates for action demonstrations, the proposed account eliminates one major argument for these monsters coming from sign languages. Throughout this paper, sign languages provide a fruitful perspective for studying quotation and other forms of iconicity in natural language due to their lack of a commonly used writing system which is otherwise often mistaken as primary data instead of speech, the rich existing literature on iconicity within sign language linguistics, and the ability of role shift to overtly mark the scope of a language report. In this view, written language is merely a special case of a more general phenomenon of sign and speech demonstration, which accounts more accurately for natural language data by permitting more strict or loose verbatim interpretations of demonstrations through the context dependent pragmatics. (shrink)

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks (...) to me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

The Quality of Thought develops and defends the thesis that thinking is a kind of experience, characterized by a sui generis (“cognitive”) phenomenology, determinates of which are thought contents—what I call the phenomenal intentionality of thought thesis. It draws out the implications of this thesis for issues in philosophy of mind, philosophy of language and metaphysics. The view defended is radically internalist and intensionalist, and thus goes against received doctrines in philosophy of mind (externalism) and language (extensionalism). (...) It also advocates for a metaphysically neutral, non-naturalistic approach to the philosophical study of mind—what I call “Analytic Phenomenology”—in combination with agnosticism about the nature of the relationship between consciousness and physical reality. -/- The book identifies persistent problems with Dretske-inspired causal-informational-teleological theories of conceptual content, and diagnoses them as due to leaving out what it’s like to think a thought—to entertain or grasp a propositional (conceptual) content. It is thus a contribution to the increasingly influential Phenomenal Intentionality Research Program. It includes refutations of classic externalism (Putnam and Burge) and arguments that standard motivations for direct reference theories of names (Kripke), indexicals and demonstratives (Kaplan) are not inevitable, and alternative accounts of their (and their conceptual equivalents’) semantics. It also addresses outstanding challenges to the phenomenal intentionalist view of thought content, including the existence of unconscious thought, the elusiveness of conceptual phenomenology, the matching content problem, phenomenal compositionality, and the determination of conceptual reference. (shrink)

The relationship between mind and matter, mental states and physical states, has occupied the attention of philosophers for thousands of years. Richard Fumerton's primary concern is the knowledge argument for dualism - an argument that proceeds from the idea that we can know truths about our existence and our mental states without knowing any truths about the physical world. This view has come under relentless criticism, but here Fumerton makes a powerful case for its rehabilitation, demonstrating clearly the importance of (...) its interconnections with a wide range of other controversies within philosophy. Fumerton analyzes philosophical views about the nature of thought and the relation of those views to arguments for dualism, and investigates the connection between a traditional form of foundationalism about knowledge, and a foundationalist view about thought that underlies traditional arguments for dualism. His book will be of great interest to those studying epistemology and the philosophy of mind. (shrink)

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a (...) variety of distinct ways. I extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

The paper is a contribution to the debate on the epistemological status of thought experiments. I deal with the epistemological uniqueness of experiments in the sense of their irreducibility to other sources of justification. In particular, I criticize an influential argument for the irreducibility of thought experiments to general arguments. First, I introduce the radical empiricist theory of eliminativism, which considers thought experiments to be rhetorically modified arguments, uninteresting from the epistemological point of view. Second, I present (...) objections to the theory, focusing on the critique of eliminativism by Tamar Szabó Gendler based on the reconstruction of famous Galileo's Pisa experiment. I show that her reconstruction is simplistic and that more elaborate reconstruction is needed for an appropriate assessment of the epistemic power of general argument. I propose such a reconstruction and demonstrate that general version of Pisa experiment is epistemically equal to the particular one. Thus, from an epistemological perspective, Galileo's thought experiment is reducible to a straightforward argument without particular premises. (shrink)

I claim that one way thought experiments contribute to scientific progress is by increasing scientific understanding. Understanding does not have a currently accepted characterization in the philosophical literature, but I argue that we already have ways to test for it. For instance, current pedagogical practice often requires that students demonstrate being in either or both of the following two states: 1) Having grasped the meaning of some relevant theory, concept, law or model, 2) Being able to apply that theory, (...) concept, law or model fruitfully to new instances. Three thought experiments are presented which have been important historically in helping us pass these tests, and two others that cause us to fail. Then I use this operationalization of understanding to clarify the relationships between scientific thought experiments, the understanding they produce, and the progress they enable. I conclude that while no specific instance of understanding (thus conceived) is necessary for scientific progress, understanding in general is. (shrink)

This response was written for the Vth Online Consciousness Conference.

John McDowell (in Mind and World) and Bill Brewer (in Perception and Reason) argue that the content of our perceptual experience is conceptual in the following sense. It is of the type of content that could be the content of a judgement – that is, a content which results from the actualization of two (or more) conceptual abilities. Specifically, they suggest that the conceptual abilities actualized in experience are demonstrative abilities, and thus the resulting content is of the type (...) we may express by means of sentences of the form ‘this is thus’. In this paper I argue that we cannot construe experiential contents in this way. I first outline a construal of the ability to think about a thing being thus which is based on Brewer's discussion of conceptual experiential contents, and which I take to be the best construal available to the conceptualist. I then show that on this construal the demonstrative abilities that account for our experience of properties require intentional focused attention to the relevant properties. The conceptualist is thus committed to holding that we experience only the properties we are intentionally attending to, and I argue that this is implausible. The interest in examining Brewer's conceptualist construal of experiential content and pointing out its shortcoming is not limited merely to an interest in whether there is a workable conceptualist account of experiential content. I suggest that certain aspects of Brewer's construal capture important (and often neglected) aspects of our perceptual experience, and that understanding why the account fails can contribute to our understanding of both experiential content and demonstrative thought. (shrink)

In On the Genesis of Thought and Language, linguist Alexey Koshelev explores fundamental questions of how human concepts arise in a child, why concepts appear in a child before words, the genesis of language, and why there are so many languages. Chapter One introduces the fundamental dichotomy "visual (exogenous) vs. functional (endogenous)" cognitive units; these units are used to give non-verbal definitions of mental representations of various objects, actions, and situations. In particular, definitions of such concepts as GLASS, CHAIR, (...) BANANA, TREE, LAKE, RUN, and some others are given. Chapter Two discusses how children form concepts, hierarchical relationships, and propositions (conceptual 'utterances'). It is shown that the initial units of the child's representation of the world are pre-conceptual cognitive units--mental representations of whole situations. In the course of two consecutive cycles in the child's cognitive development, these units transform into (a) primary notions--object and motor concepts, and (b) binary role relationships. Together, they constitute the elementary language of thought which, in the process of thinking, is used to build conceptual structures--propositions. It is further demonstrated that, immediately after the formation of thought, the child begins to develop his native language in which concrete and motor concepts become initial meanings of nouns and verbs, while propositions become the meanings of the child's expressions. The chapter concludes with a contrastive analysis of the proposed approach and Aristotle's and Chomsky's views on thought and language. Chapter Three analyzes how a community's culture affects its language. It is demonstrated that the progress of a community, the main constituent of the civilizational component of its culture, enhances the development of the content component of language by extending the range of its lexical and grammatical meanings. In the context of this analysis, Daniel Everett's (2008) hypothesis that culture affects language structure is discussed. In the subsequent sections, models of the development of human and social activity are offered. These models comprise three components: Activity (main component), Thought, and Language (auxiliary components that ensure the successful realization of activities). The models are illustrated with examples of some concrete societies. (shrink)

As research on mind wandering has accelerated, the construct’s defining features have expanded and researchers have begun to examine different dimensions of mind wandering. Recently, Christoff and colleagues have argued for the importance of investigating a hitherto neglected variety of mind wandering: “unconstrained thought,” or, thought that is relatively unguided by executive-control processes. To date, with only a handful of studies investigating unconstrained thought, little is known about this intriguing type of mind wandering. Across two experiments, we (...) examined, for the first time, whether changes in task demand influence rates of constrained versus unconstrained thoughts. In both experiments, participants completed either an easy (0-back) or hard (2-back) task and responded to intermittently presented thought probes that gauged thought constraint throughout the task. In Experiment 1, we found that participants completing the easy task engaged in unconstrained thoughts more frequently than those completing the difficult task. In Experiment 2, we replicated this result and further demonstrated manipulations of unconstrained thought while also measuring task-relatedness (a common dimension of mind wandering). Finally, exploratory analyses showed associations between constrained thought and age, verbal intelligence, and an assessment of flow (‘deep effortless concentration’), thereby adding further evidence to indicate a dissociation between task-relatedness and constraint. We discuss the methodological and theoretical applications of our findings to the burgeoning field of research on unconstrained thought. (shrink)

Demonstratives have been thought to provide counterexamples to theories which analyze the notion of speaker reference in terms of the intentions of the speaker. This paper is a response to three attempts to undermine my efforts to defend such theories against these putative counterexamples. It is argued that the efforts of Howard Wettstein, M. J. More and John L. Biro to show that my own attempt to defuse the putative counterexamples offered by David Kaplan fails, are themselves unsuccessful. The (...) competing view of demonstration which I endorse is clarified further by the discussion. (shrink)

Demonstratives have been thought to provide counterexamples to theories which analyze the notion of speaker reference in terms of the intentions of the speaker. This paper is a response to three attempts to undermine my efforts to defend such theories against these putative counterexamples. It is argued that the efforts of Howard Wettstein, M. J. More and John L. Biro to show that my own attempt to defuse the putative counterexamples offered by David Kaplan fails, are themselves unsuccessful. The (...) competing view of demonstration which I endorse is clarified further by the discussion. (shrink)