We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa $, the existence of a strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is a theorem of $\textsf{ZFC}$. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly (...) unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is independent of $\textsf{ZFC}$. We connect the existence of subadditive strongly unbounded colorings with a number of other infinitary combinatorial principles, including the narrow system property, the existence of $\kappa $ -Aronszajn trees with ascent paths, and square principles. In particular, we show that the existence of a closed, subadditive, strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is equivalent to a certain weak indexed square principle $\boxminus ^{\operatorname {\mathrm {ind}}}(\kappa, \theta )$. We conclude the paper with an application to the failure of the infinite productivity of $\kappa $ -stationarily layered posets, answering a question of Cox. (shrink)

ABSTRACTNo longer capable of serving as a nodal point of a single coherent narrative or as a marker for parallel events across national borders, “1968” is best understood in a tense relation to “1967”. Juxtaposed rather than reconciled, they can only be brought together in a dynamic field of conflicting forces still in play even after a half century has passed. Such an approach alerts us to the relativization of what seems to be a punctual moment in a single (...) historical space–time continuum. To understand the role of the Frankfurt School in the German “1968” is therefore to situate its history in the expanded field that includes the very different events of “1967”, which resist incorporation into a unified narrative. It is to register the importance of 1967 in generating its negative relationship to aspects of the German 1968, and in colouring its attitude towards post-colonial struggles and the discourse they have spawned. By expanding the field in this way, we will avoid turning 1968 into an isolated monument on a pedestal that masks its connection to the multiple historical contexts that can set it into motion and help us understand its importance today. (shrink)

We show that the Abraham–Rubin–Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with [Formula: see text]. This answers one of the main open questions from [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206]. As in [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems (...) for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206], we need to construct names for the so-called preassignments of colors in order to add the necessary homogeneous sets. However, the known constructions of preassignments (ours in particular) only work assuming the [Formula: see text]. In order to address this difficulty, we show how to construct such names with very strong symmetry conditions. This symmetry allows us to combine them in many different ways, using a new type of poset called a partition product. Partition products may be thought of as a restricted memory iteration with stringent isomorphism and coherent-overlap conditions on the memories. We finally construct, in [Formula: see text], the partition product which gives us a model of [Formula: see text] in which [Formula: see text]. (shrink)

The paper argues that colouring is a conventional ingredient of literal meaning characterized by a considerable degree of semantic under-determination and a high degree of context-sensitivity. The positive, though tentative, suggestion made in the paper is that whereas in the case of words such as "but" and "damn" we are dealing with words lacking in specificity, in the case of pejoratives in general, and racist jargon in particular, we are dealing with words that express concepts that purport to describe the (...) world as being in a certain way. The circumstance that in certain contexts of utterance colouring can be cancelled out, does not show that it forms a detachable part of a word's literal meaning. It only shows that to account for the interplay between context, literal meaning and assertoric content is much trickier than meets the eye. (shrink)

We prove that colouring of pairs from 2 with strong properties exists. The easiest to state problem it solves is: there are two topological spaces with cellularity 1 whose product has cellularity 2; equivalently, we can speak of cellularity of Boolean algebras or of Boolean algebras satisfying the 2-c.c. whose product fails the 2-c.c. We also deal more with guessing of clubs.

This article examines the early modern household's importance for producing experimental knowledge through an examination of the Halifax household of Margery and Henry Power. While Henry Power has been studied as a natural philosopher within the male-dominated intellectual circles of Cambridge and London, the epistemic labour of his wife, Margery Power, has hitherto been overlooked. From the 1650s, this couple worked in tandem to enhance their understanding of the vegetable world through various paper technologies, from books, paper slips and recipe (...) notebooks to Margery's drawing album and Henry's published Experimental Philosophy. Focusing on Margery's practice of hand-colouring flower books, her copied and original drawings of flowers and her experimental production of ink, we argue that Margery's sensibility towards colour was crucial to Henry's microscopic observations of plants. Even if Margery's sophisticated knowledge of plants never left the household, we argue that her contribution was nevertheless crucial to the observation and representation of plants within the community of experimental philosophy. In this way, our article highlights the importance of female artists within the history of scientific observation, the use of books and paperwork in the botanical disciplines, and the relationship between household science and experimental philosophy. (shrink)

In this essay I consider Kaplan’s challenge to Frege’s so-called dictum: “Logic (and perhaps even truth) is immune to epithetical color”. I show that if it is to challenge anything, it rather challenges the view (attributable to Frege) that logic is immune to pejorative colour. This granted, I show that Kaplan’s inference-based challenge can be set even assuming that the pejorative doesn’t make any non-trivial truth-conditional (descriptive) contribution. This goes against the general tendency to consider the truth-conditionally inert logically irrelevant. (...) But I take it that Kaplan is right and take his examples to show that truth-conditional inertness need not entail inferential inertness. I end up assessing the Kaplan-Frege “debate” as giving edge to the former to the extent that clarity is achieved through Kaplanian inferences on what should be considered part of the explanandum. (shrink)

© The Authors 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] Colour is a welcome work in history and philosophy of science.1 The opening chapters offer a fresh take on the history of perceptual theory and a broad overview of contemporary philosophy of colour. This is followed by the central fourth chapter, which introduces readers to a cluster of empirical data that to this point have not received explicit (...) treatment in philosophy. The core message is that instead of thinking of colour vision as filling in or painting the experienced world of primary qualities, we should think of colour vision as helping us to experience primary qualities. The colour visual system does not colour in an experiential world of primary qualities, it uses colour for the experience of those qualities. This colouring... (shrink)

Many scholars claim that Frege's theory of colouring is committed to a radical form of subjectivism or emotivism. Some other scholars claim that Frege's concept of colouring is a precursor to Grice's notion of conventional implicature. I argue that both of these claims are mistaken. Finally, I propose a taxonomy of Fregean colourings: for Frege, there are purely aesthetic colourings, communicative colourings or hints, non-communicative colourings.

A common view in both philosophy and the vision sciences is that, in human vision, wavelength information is primarily ‘for’ colouring: for seeing surfaces and various media as having colours. In this article we examine this assumption of ‘colour-for-colouring’. To motivate the need for an alternative theory, we begin with three major puzzles from neurophysiology, puzzles that are not explained by the standard theory. We then ask about the role of wavelength information in vision writ large. How might wavelength information (...) be used by any monochromat or dichromat and, finally, by a trichromatic primate with object vision? We suggest that there is no single ‘advantage’ to trichromaticity but a multiplicity, only one of which is the ability to see surfaces and so on as having categorical colours. Instead, the human trichromatic retina exemplifies a scheme for a general encoding of wavelength information given the constraints imposed by high spatial resolution object vision. Chromatic vision, like its partner, luminance vision, is primarily for seeing. Viewed this way, the ‘puzzles’ presented at the outset make perfect sense. 1 Reframing the Problem1.1 Introduction1.2 Three puzzles1.2.1 Why is trichromatic vision an anomaly in diurnal mammals?1.2.2 Why does the colour system occupy such a large and central part in human vision?1.2.3 Why are the blue cones so rare?1.3 Recasting the question2 The Costs and Benefits of Spectral Vision2.1 Spectral information and object vision2.2 Encoding the spectral dimension of light2.2.1 ‘General’ versus ‘specific’ encoding2.2.2 Spectral encoding and the monochromat2.2.3 Spectral encoding and the dichromat2.2.4 Spectral encoding and the human trichromat2.3 Three puzzles revisited2.3.1 Why is trichromatic vision an anomaly in diurnal mammals?2.3.2 Why does the colour system occupy such a large and central part in human vision?2.3.3 Why are the blue cones so rare3 Conclusion. (shrink)

Colour shapes our world in profound, if sometimes subtle, ways. It helps us to classify, form opinions, and make aesthetic and emotional judgements. Colour operates in every culture as a symbol, a metaphor, and as part of an aesthetic system. Yet archaeologists have traditionally subordinated the study of colour to the form and material value of the objects they find and thereby overlook its impact on conceptual systems throughout human history.This book explores the means by which colour-based cultural understandings are (...) formed, and how they are used to sustain or alter social relations. From colour systems in the Mesolithic, to Mesoamerican symbolism and the use of colour in Roman Pompeii, this book paints a new picture of the past. Through their close observation of monuments and material culture, authors uncover the subtle role colour has played in the construction of past social identities and the expression of ancient beliefs. Providing an original contribution to our understanding of past worlds of meaning, this book will be essential reading for archaeologists, anthropologists and historians, as well as anyone with an interest in material culture, art and aesthetics. (shrink)

Colour plays a fundamental role in the philosophical treatments of painting. Colour while it is an essential part of the work of art cannot be divorced from the account of painting within which it is articulated. This paper begins with a discussion of the role of colour in Schelling's conception of art. Nonetheless its primary concern is to develop a critical encounter with Jean-François Lyotard's analysis of the Dutch painter Karel Appel. The limits of Lyotard's writings on painting, which this (...) paper will attribute in part to Lyotard's ‘empiricism’, becomes most apparent in his treatment of colour. (shrink)

Recent evidence in cognitive neuroscience indicates that the visual system is influenced by the outcome of an early appraisal mechanism that automatically evaluates what is seen as being harmful or beneficial for the organism. This indicates that there could be valence in perception. But what could it mean for one to see something positively or negatively? Although most theories of emotions accept that valence involves being related to values, the nature of this relation remains highly debated. Some explain valence in (...) terms of evaluative content, others in terms of evaluative attitude. Here I shall argue that an account of affective perception in terms of attitude has more chance of succeeding. To do so, I will first highlight the difficulties that a content-based approach faces, considering the many forms that it might take. I will conclude that seeing the world positively or negatively involves more than a positive or negative content; it involves a distinctive attitude, but which one? Should it be conceived of in imperative or evaluative terms? And what makes this attitude distinct from a proper emotion? (shrink)

Studies of linguistic synaesthesias in English have shown a range of fine-grained language mechanisms governing the associations between colours on the one hand, and graphemes, phonemes and words on the other. However, virtually nothing is known about how synaesthetic colouring might operate in non-alphabetic systems. The current study shows how synaesthetic speakers of Mandarin Chinese come to colour the logographic units of their language. Both native and non-native Chinese speakers experienced synaesthetic colours for characters, and for words spelled in the (...) Chinese spelling systems of Pinyin and Bopomo. We assessed the influences of lexical tone and Pinyin/Bopomo spelling and showed that synaesthetic colours are assigned to Chinese words in a non-random fashion. Our data show that Chinese-speaking synaesthetes with very different native languages can exhibit both differences and similarities in the ways in which they come to colour their Chinese words. (shrink)

Summary Colourful plant images are often taken as the icon of natural history illustration. However, so far, little attention has been paid to the question of how this beautiful colouring was achieved. At a case study of the eighteenth-century Nuremberg doctor and botanist, Christoph Jacob Trew, the process of how illustrations were hand-coloured, who was involved in this work, and how the colouring was supervised and evaluated is reconstructed, mostly based on Trew's correspondence with the engraver and publisher of his (...) books, Johann Jacob Haid in Augsburg. Furthermore, the question of standardizing colours, their uses and their recipes is discussed at two examples of the same time period: the colour charts of the Bauer brothers, arguably the most renowned botanical draughtsmen of the period, and the colour tables by the Regensburg naturalist, Jacob Christian Schaeffer. Hand-colouring botanical illustrations, it is argued, was far from a straightforward task but confronted botanists and their employees with a plethora of practical and methodological problems, to which different solutions were developed in the course of time. Analysing these problems and solutions reveals some new and interesting aspects of the practices of eighteenth-century botany and of the production of scientific illustrations in general. (shrink)

My subject is what I will call the “Myth of Formal Coherence.” In its normative telling, the Myth is that there are “requirements of formal coherence as such,” which demand just that our beliefs and intentions be formally coherent.1 Some examples are.

A critical examination of the Reflection principle in Bayesian epistemology, and of the diachronic Dutch-book-style arguments that have been invoked to support Reflection and Conditionalization.

In this study we analyze the overlapping perspectives of legitimacy theory, institutional theory, resource dependence theory, and stakeholder theory. Our purpose is to explore how these theories can inform and be built upon by one another. Through our analysis we provide a broader theoretical understanding of these theories that may support and promote social and environmental accounting research. This article starts with a detailed analysis of legitimacy theory by bringing some recent critical discussions on legitimacy and corporations in the management (...) literature into accounting research. The notion forwarded by legitimacy theory then serves as an overarching concept to examine the relationship between and among theories. We conclude that two theoretical considerations are important for future social and environmental accounting research. First, it must be acknowledged that some business entities initiate social activities based on direct interactions with stakeholders, whereas others may also undertake similar activities to manage their societal level of legitimacy. Second, from analyzing the perspectives of legitimacy theory, institutional theory, resource dependence theory, and stakeholder theory, it is possible to reach compatible interpretations of business social phenomena, and the selection and application of these theories should depend upon the focus of study. (shrink)

One of the main problems about is that whether a coherent Suslin tree forces that there are no S‐spaces under. We analyze a forcing notion related to this problem, and show that under, S forces that every topology on ω1 generated by a basis in the ground model is not an S‐topology. This supplements the previous work due to Stevo Todorčević [25].

In this article, I discuss an argument that purports to prove that probability theory is the only sensible means of dealing with uncertainty. I show that this argument can succeed only if some rather controversial assumptions about the nature of uncertainty are accepted. I discuss these assumptions and provide reasons for rejecting them. I also present examples of what I take to..

Within and among societies, there are competing understandings of the status of children, including debates over whether they can bear rights and, if so, which rights they bear and against whom, and their capacity to make decisions and be held responsible and accountable for actions. There also are different understandings of what constitutes a family; what authority parents have over and regarding their children; and what should happen to children who are without parents because of death, desertion, or imprisonment. These (...) and other related debates reflect deep differences in worldviews, in how one understands the legitimate role of the state, in how one comes to know the proper way to raise children, and so on. The United Nations Convention on the Rights of the Child purports to reflect international convergence on the rights of children, on how decisions concerning children should be made, and on how children ought to be treated by the state and by their parents. This paper examines whether the Convention's framework for decision making concerning children is an appropriate framework for pediatric bioethics. Questions about how to make health care decisions for children ultimately are questions of who is in authority to make and judge such decisions. Establishing who is in authority, determining whether there are any limits to that authority and, if so, defining those limits should be the focus of efforts to develop and implement a pediatric decision-making framework. (shrink)

An individualized and coherent life story has been described as the form of identity that is required by highly mobile individualistic Western societies, whereas more family-oriented, traditional societies require more role-based, synchronic identities. Therefore entire life narratives can be expected to be more coherent and to contain more autobiographical arguments that contribute to life narrative coherence in individualistic cultures. This cultural group difference is expected to be mediated by individuals’ conformity to their respective cultural normative concept of biography. (...) We tested these expectations by eliciting entire life narratives and cultural life scripts from students of technical universities from provincial and metropolitan Turkey, as well as from students with a Turkish migrant and a German background in urban Germany (N= 96). Expectations were confirmed for global life narrative coherence and autobiographical arguments with self-event connections. Conformity with a normative concept of biography indeed mediated cultural influences on life narrative coherence. Life narratives from Turkey also contained more family-related events and, unexpectedly, were more negative. Thus creating a coherent life narrative is more typical for cultures that require autonomous, individualized selves rather than for cultures requiring more related selves, reflecting the life story’s suitability for expressing individualized identities and its lesser suitability for expressing interdependent identities. (shrink)

The idea that an utterance of a basic (nondeviant) declarative sentence expresses a single true-or-false proposition has dominated philosophical discussions of meaning in this century. Refinements aside, this idea is less of a substantive theses than it is a background assumption against which particular theories of meaning are evaluated. But there are phenomena (noted by Frege, Strawson, and Grice) that threaten at least the completeness of classical theories of meaning, which associate with an utterance of a simple sentence a truth-condition, (...) a Russellian proposition, or a Fregean thought. And it may well be the case that a framework within which utterances express sequences of propositions provides much of what is needed to account for the relevant phenomena, a better overall picture of the way language works, and an enticingly uniform perspective on a variety of semantic problems. I do not myself take to theories that multiply propositions by appealing to propositions “presupposed” or to pairs of Fregean and Russellian propositions, or theories that show no respect for a distinction between semantics and pragmatics— where the former is the study of propositions whose general form and character is determined by word meaning and syntax—or for theories that blithely abandon general principles of composition and semantic innocence. I would like to sketch a package based on four interconnected ideas: (i) the meaning of an individual word is a sequence of instructions for generating a sequence of propositions (in conjunction with compositional instructions (syntax) and elements of context); (ii) utterances themselves are not bearers of truth or falsity; (iii) judgements of truth, falsity, commitment, and conflict are shaped, in part, by the weights attached to individual 1 propositions that occur in sequences expressed by utterances, weights that may be set (and reset) by contextual considerations; (iv) Fregean senses are superfluous; propositions might as well be Russellian (Mont Blanc and all its snow fields will do as well as any mode of presentation).. (shrink)

We observe a number of connections between recent developments in the study of constraint satisfaction problems, irredundant axiomatisation and the study of topological quasivarieties. Several restricted forms of a conjecture of Clark, Davey, Jackson and Pitkethly are solved: for example we show that if, for a finite relational structure M, the class of M-colourable structures has no finite axiomatisation in first order logic, then there is no set (even infinite) of first order sentences characterising the continuously M-colourable structures amongst compact (...) totally disconnected relational structures. We also refute a rather old conjecture of Gorbunov by presenting a finite structure with an infinite irredundant quasi-identity basis. (shrink)

Short-term or working memory provides temporary storage of information in the brain after an experience and is associated with conscious awareness. Neurons sensitive to the multiple stimulus attributes comprising an experience are distributed within many brain regions. Such distributed cell assemblies, activated by an event, are the most plausible system to represent the WM of that event. Studies with a variety of imaging technologies have implicated widespread brain regions in the mediation of WM for different categories of information. Each kind (...) of WM may thus be expected to involve many brain regions rather than a local, uniquely dedicated set of cells. Neurons in a distributed “cell assembly” may be self-selected by their temporally coherent activations. The process by which this fragmented representation of the recent past is reassembled to accomplish essentially automatic and reliable recognition of a recurrent event constitutes an important problem. One plausible mechanism to achieve the identification of past with previous events would require that the representational system mediating WM must coexist in spatial extent and somehow overlap in temporal activation with cell ensembles registering input from subsequent events. The detection of such a postulated mechanism required an experimental approach which would focus upon spatial patterns of coherent activation while information about different events was stored in WM and retrieved, rather than focusing upon the temporal sequences of activation in localized regions of interest. For this purpose, the familiar delayed matching from sample task was modified. A series of information-free flashes, or “noncontingent probes,” was presented before an initial series of visual information items, the Priming Sample, which were to be held in WM during a Delay Period. A second series of visual information items were then presented, the Matching Sample. The task required detection of any item in the second series which had beenabsentfrom the initial series. Thirty such trials with a particular category of visual information constituted a single task. Several DMS tasks with this standardized design, but with different categories of visual information, were presented within each test session. The information categories included letters of the alphabet, single digit numbers, or faces from a school yearbook. Event-related potentials , were computed from 21 standardized electrode placements, separately for information-free probes and for information items in each interval of the trials within a task. Because each electrode is particularly sensitive to coherent activation of neurons in the immediately underlying brain regions, topographic maps were constructed and interpolated across the surface of the scalp. The momentary fluctuations of the resulting voltage “landscapes” throughout the task were then subjected to quantitative analysis. Distinctive landscapes sometimes persisted for prolonged periods, implying sustained engagement of very large populations of neurons. “Difference landscapes” were constructed by subtraction of topographic maps evoked by noncontingent probes during the Delay Period from maps of probe ERPs before the presentation of the initial information in the Priming Sample. Such probe difference landscapes displayed recurrent high similarity to momentary landscapes elicited during subsequent presentation of the information items in the Matching Sample. It seemed as if the distributed cell assembly continuously engaged by mediation of WM of the diverse attributes of the initial stimuli was being dynamically compared to the ensembles engaged by registration of the subsequent stimuli. Spatial Principal Component Analysis was applied to the sequences of momentary voltage landscapes observed throughout trials of each task. This method sought a small number of spatial patterns with which these large sets of inhomogeneous spatial distributions of voltage could be reconstructed. This is the spatial analog of the reconstruction of local ERPs by temporal principal components, as often described previously. Five Spatial Principal Components were found which accounted for about 90% of the total variance of voltage across the surface of the scalp throughout every task. Theloadings,or distinguishing topographic features, of these SPCs, were highly similar during every cognitive task for every subject. However,factor scores,or relative average contribution to the overall voltage distributions, of the different SPCs varied substantially among subjects between the tasks and momentarily within successive intervals of each task. These five SPCs may reflect coherent activation of huge distributed ensembles of neurons which comprise independent but interacting functional brain subsystems. These subsystems may correspond to basic resources available to individuals for allocation to mediate conscious evaluation of information during cognitive activity, providing a filter to bind together fractionated representations of the past to evaluate the present. (shrink)

This commentary describes some extensions of the Phillips & Singer model of contextual interactions to cater for the contrast- and extent-dependency of surround facilitation and suppression. I also comment briefly on some semantic problems with what exactly the role of synchronization might be: input preprocessing or output postprocessing?

More and more people seem to think that constructivism - in political philosophy, in moral philosophy, and perhaps in practical reasoning most generally - is the way to go. And yet it is surprisingly hard to even characterize the view. In this paper, I go to some lengths trying to capture the essence of a constructivist position - mostly in the realm of practical reason - and to pinpoint its theoretical attractions. I then give some reason to suspect that there (...) cannot be a coherent constructivist view about practical reason as a whole, at least not if it is to be interestingly constructivist, in a sense I make reasonably precise. (shrink)

Stochastic forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for different events. Third, the credibility of individual judges might vary, and one would like to pay greater attention to more trustworthy forecasts. These considerations limit the value of simple aggregation (...) methods like linear averaging. In this paper, a new algorithm is proposed for combining probabilistic assessments from a large pool of judges. Two measures of a judge’s likely credibility are introduced and used in the algorithm to determine the judge’s weight in aggregation. The algorithm was tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (∼ 16000 judges). (shrink)