A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the (...) assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general phenomenalist tradition (...) as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences. The interesting paper "On the Space-Time Ontology of Physical Theories" by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575-590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions. Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called 'space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.). (shrink)

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...) is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. (...) I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism. (shrink)

Minkowski geometry is axiomatized in terms of the asymmetric binary relation of optical connectibility, using ten first-order axioms and the second-order continuity axiom. An axiom system in terms of the symmetric binary optical connection relation is also presented. The present development is much simpler than the corresponding work of Robb, upon which it is modeled.

The standard coordinate-based formulation of the space-time theory of special relativity (Minkowski geometry) is philosophically unsatisfactory for various reasons. We here present an explicit axiomatic formulation of that theory in terms of primitives with a definitive physical interpretation, prove its equivalence to the standard coordinate formulation, and draw various philosophical conclusions concerning the physical content and assumptions of the space-time theory. The prevalent causal interpretation of physical Minkowski geometry deriving from Reichenbach is criticised on the basis of the present formulation.

The standard mathematical apparatus of classical electromagnetic theory in Minkowski space-time allows an interpretation in terms of retarded distant action, as well as the standard field interpretation. This interpretation is here presented and defended as a scientifically significant alternative to the field theory, casting doubt upon the common view that classical electromagnetic theory provides scientific support for the physical existence of fields as fundamental entities. The various types of consideration normally thought to provide evidence for the existence of the electromagnetic (...) field are surveyed and analyzed in retarded distant action terms, from both a contemporary viewpoint and with regard to the late 19th century context within which the field theory was first generally accepted. It is concluded that acceptance of the field as real is not evidentially justified in either context, and that the customary historical explanation of the triumph of field theory as due to its empirical superiority is inadequate. An alternative explanation is suggested but not developed, appealing to non-empirical factors associated with the research program based on the conservation of energy. (shrink)

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is interpreted as involving (...) arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (shrink)

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the (...) sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

Mundy (1983) presented the formal apparatus of certain relationist theories of space and space-time taking quantitative relations as primitive. The present paper discusses the philosophical and physical interpretation of such theories, and replies to some objections to such theories and to relationism in general raised in Field (1985). Under an appropriate second-order naturalistic Platonist interpretation of the formalism, quantitative relationist theories are seen to be entirely comparable to spatialist ones in respect of the issues raised by Field. Moreover, it (...) appears that even if accepted as sound, Field's general line of criticism would not diminish the significance of relationism for philosophy of science, since this derives primarily from its connection to physical rather than to mathematical or philosophical ontology. (shrink)

Modern mathematical physics uses real-number variables, and therefore presupposes set theory. (A real number is defined as a certain kind of set or sequence of natural or rational numbers.) Set theory is also used to define the operations of differential calculus, needed to state physical laws as differential equations constraining the numerical variables representing physical quantities. The derivative f' = df(t)/dt is defined as the limit of an infinite sequence of terms [f(t+e)-f(t)]/e as e → 0, and this definition can (...) only be expressed in a language allowing reference to infinite sequences. Moreover, closure under these limit operations again requires the underlying field of numbers to be Dedekind complete, hence to include all of the reals.The possibility that mathematical physics depends essentially upon set theory is disturbing, for two distinct reasons. From a logical viewpoint, it is disturbing that an important branch of natural science should depend upon a part of logic or mathematics whose status remains uncertain and controversial. (shrink)

In Mundy [a] I offered an axiomatic analysis of the physical content of the kinematics of special relativity which suggests that, contrary to common belief, there is no incompatibility between special relativity and spacelike (faster-than-light) causation. An anonymous referee pointed out that this conclusion might have some bearing on problems in the interpretation of quantum mechanics such as the Einstein-Podolsky-Rosen problem, since one line of solution to these problems involves the postulation of spacelike causal processes. The present note will (...) develop this idea. (shrink)

Relationist theories of space or space-time based on embedding of a physical relational system A into a corresponding geometrical system B raise problems associated with the degree of uniqueness of the embedding. Such uniqueness problems are familiar in the representational theory of measurement (RTM), and are dealt with by imposing a condition of uniqueness of embeddings up to composition with an "admissible transformation" of the space B. Friedman (1983) presents an alternative treatment of the uniqueness problem for embedding relationist theories, (...) developed independently of RTM. Friedman's approach differs from that of RTM in securing uniqueness by adding new primitives to the physical system A in contrast to the RTM approach which adds new axioms. Friedman's proposal has recently been developed and defended by Catton and Solomon (1988). This method of solving the uniqueness problem is here argued to be substantially inferior to the RTM method, both in practice and in principle. In practice we find that in none of the concrete examples offered to illustrate the method is the uniqueness problem actually solved in general. Moreover we find that in the most interesting case (addition to the system A of a finite number of relations of finite degree) the method is in principle incapable of success for mathematical reasons. In addition to these technical difficulties there are compelling methodological reasons for preferring the RTM method to the method of adding primitives. (shrink)

I outline an intrinsic (coordinate-free) formulation of classical particle mechanics, making no use of set theory or second-order logic. Physical quantities are accepted as real, but are constrained only by elementary axioms. This contrasts with the formulations of Field and Burgess, in which space-time regions are accepted as real and are assumed to satisfy second-order comprehension axioms. The present formulation is both logically simpler and physically more realistic. The theory is finitely axiomatizable, elementary, and even quantifier-free, but is provably empirically (...) equivalent to the standard coordinate formulations. (shrink)

The view that scientific theories are partially interpreted deductive systems (theoretical deductivism) is defended against recent criticisms by Hempel. Hempel argues that the reliance of theoretical inferences (both from observation to theory and also from theory to theory) uponceteris paribus conditions orprovisos must prevent theories from establishing deductive connections among observations. In reply I argue, first, that theoretical deductivism does not in fact require the establishing of such deductive connections: I offer alternative H-D analyses of these inferences. Second, I argue (...) that when the refined character of scientific observation is taken into account, we find that a theorymay after all establish such deductive connections among scientific observations, without reliance on provisos.These conclusions are based on the multi-level Popperian contextualist account of empirical interpretation sketched in a previous paper. As before, I claim that the supposed objections to theoretical deductivism depend upon questionable empiricist theses unnecessarily conjoined with theoretical deductivism by the Logical Positivists. Theoretical deductivism itself is unaffected by these arguments, and remains (when empirical interpretation is properly analyzed) the best account of scientific theories. (shrink)

This chapter contains sections titled: Historical and Current Views of Species Return to a Darwinian View of Species Practical Implications Postscript: Counterpoint References.

The work reported in this monograph was begun in the winter of 1967 in a graduate seminar at Berkeley. Many of the basic data were gathered by members of the seminar and the theoretical framework presented here was initially developed in the context of the seminar discussions. Much has been discovered since1969, the date of original publication, regarding the psychophysical and neurophysical determinants of universal, cross-linguistic constraints on the shape of basic color lexicons, and something, albeit less, can now also (...) be said with some confidence regarding the constraining effects of these language-independent processes of color perception and conceptualization on the direction of evolution of basic color term lexicons. (shrink)

The debate between faith and reason has been a dominant feature of Western thought for more than two millennia. This book takes up the problem of the relation between philosophy and theology and proposes that this relation can be reconceived if both philosophy and theology are seen as different ways of organising affects. Brent Adkins and Paul R. Hinlicky break new ground in this timely debate in two ways. Firstly, they lay bare the contemporary dependence on Kant and propose (...) that our Kantian inheritance leaves us with an insuperable dualism. Secondly, the authors argue that the philosophy of Gilles Deleuze provides a way of resolving the debate between faith and reason that does justice to philosophy and theology by reconceiving of both as assemblages. Deleuze's philosophy differentiates domains of thought in terms of what they create. This seems like a particularly fruitful way to pursue the problem of the relations among philosophy and theology because it allows their distinction without at the same time placing them in opposition to one another. (shrink)

Inventions of Teaching: A Genealogy is a powerful examination of current metaphors for and synonyms of teaching. It offers an account of the varied and conflicting influences and conceptual commitments that have contributed to contemporary vocabularies--and that are in some ways maintained by those vocabularies, in spite of inconsistencies and incompatibilities among popular terms. The concern that frames the book is how speakers of English invented (in the original sense of the word, "came upon") our current vocabularies for teaching. Conceptually, (...) this book is unique in the educational literature. As a whole, it presents an overview of the major underlying philosophical and ideological concepts and traditions related to knowledge, learning, and teaching in the Western world, concisely introducing readers to the central historical and contemporary discourses that shape current discussions and beliefs in the field. Because the organization of historical, philosophical, theoretical, and etymological information is around key conceptual divergences in Western thought rather than any sort of chronology, this text is not a linear history, but several histories--or, more precisely, it is a genealogy. Specifically, it is developed around breaks in opinion that gave or are giving rise to diverse interpretations of knowledge, learning, and teaching--highlighting historical moments in which vibrant new figurative understandings of teaching emerged and moments at which they froze into literalness. The book is composed of two sorts of chapters, "branching" and "teaching." Branching chapters include an opening treatment of the break in opinion, separate discussions of each branch, and a summary of the common assumptions and shared histories of the two branches. Teaching chapters offer brief etymological histories and some of the practical implications of the terms for teaching that were coined, co-opted, or redefined within the various traditions. Inventions of Teaching: A Genealogy is an essential text for senior undergraduate and graduate courses in curriculum studies and foundations of teaching and is highly relevant as well for students, faculty, and researchers across the field of education. (shrink)

We all experience loneliness at some time in our lives and it often motivates people, consciously or otherwise, to enter treatment. Yet it is rarely explicitly addressed in psychoanalytic literature. Loneliness and Longing rectifies this oversight by thoroughly exploring this painful psychological state. In this book contributors address the inner sense of loneliness âe" that is feeling alone even in the company of others âe" by drawing on different aspects of loneliness and longing. Topics covered include: loneliness in the consulting (...) room the relationship between loneliness and love the effects of social networking and the internet how loneliness changes throughout the life-cycle healing the analystâe(tm)s loneliness. Loneliness and Longing draws on both theory and practice to discuss ways to help people to understand and cope with this important emotional state, encouraging them to make loneliness and longing less pervasive in their lives. This will be ideal reading for analysts, psychotherapists, and related practitioners facing the challenges of loneliness in their consulting rooms. (shrink)

For much of the past two centuries, religion has been understood as a universal phenomenon, a part of the “natural” human experience that is essentially the same across cultures and throughout history. Individual religions may vary through time and geographically, but there is an element, religion, that is to be found in all cultures during all time periods. Taking apart this assumption, Brent Nongbri shows that the idea of religion as a sphere of life distinct from politics, economics, or (...) science is a recent development in European history—a development that has been projected outward in space and backward in time with the result that religion now appears to be a natural and necessary part of our world. Examining a wide array of ancient writings, Nongbri demonstrates that in antiquity, there was no conceptual arena that could be designated as “religious” as opposed to “secular.” Surveying representative episodes from a two-thousand-year period, while constantly attending to the concrete social, political, and colonial contexts that shaped relevant works of philosophers, legal theorists, missionaries, and others, Nongbri offers a concise and readable account of the emergence of the concept of religion. (shrink)

In information societies, operations, decisions and choices previously left to humans are increasingly delegated to algorithms, which may advise, if not decide, about how data should be interpreted and what actions should be taken as a result. More and more often, algorithms mediate social processes, business transactions, governmental decisions, and how we perceive, understand, and interact among ourselves and with the environment. Gaps between the design and operation of algorithms and our understanding of their ethical implications can have severe consequences (...) affecting individuals as well as groups and whole societies. This paper makes three contributions to clarify the ethical importance of algorithmic mediation. It provides a prescriptive map to organise the debate. It reviews the current discussion of ethical aspects of algorithms. And it assesses the available literature in order to identify areas requiring further work to develop the ethics of algorithms. (shrink)

For much of the past two centuries, religion has been understood as a universal phenomenon, a part of the “natural” human experience that is essentially the same across cultures and throughout history. Individual religions may vary through time and geographically, but there is an element, religion, that is to be found in all cultures during all time periods. Taking apart this assumption, Brent Nongbri shows that the idea of religion as a sphere of life distinct from politics, economics, or (...) science is a recent development in European history—a development that has been projected outward in space and backward in time with the result that religion now appears to be a natural and necessary part of our world. Examining a wide array of ancient writings, Nongbri demonstrates that in antiquity, there was no conceptual arena that could be designated as “religious” as opposed to “secular.” Surveying representative episodes from a two-thousand-year period, while constantly attending to the concrete social, political, and colonial contexts that shaped relevant works of philosophers, legal theorists, missionaries, and others, Nongbri offers a concise and readable account of the emergence of the concept of religion. (shrink)

DigiCat Publishing presents to you this special edition of "The Sixth Sense: Its Cultivation and Use" by Charles Henry Brent. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.

Two studies tested the relationship between three facets of personality—conscientiousness, agreeableness, and openness to experience—as well as moral identity, on individuals’ ethical ideology. Study 1 showed that moral personality and the centralityof moral identity to the self were associated with a more principled (versus expedient) ethical ideology in a sample of female speech therapists. Study 2 replicated these findings in a sample of male and female college students, and showed that ideology mediated therelationship between personality, moral identity, and two organizationally (...) relevant outcomes: organizational citizenship behavior and the propensity to morally disengage. Implications for business ethics are discussed. (shrink)

Two studies tested the relationship between three facets of personality—conscientiousness, agreeableness, and openness to experience—as well as moral identity, on individuals’ ethical ideology. Study 1 showed that moral personality and the centralityof moral identity to the self were associated with a more principled (versus expedient) ethical ideology in a sample of female speech therapists. Study 2 replicated these findings in a sample of male and female college students, and showed that ideology mediated therelationship between personality, moral identity, and two organizationally (...) relevant outcomes: organizational citizenship behavior and the propensity to morally disengage. Implications for business ethics are discussed. (shrink)

Leadership and the Unmasking of Authenticity presents a philosophic treatment of the core concept of authentic leadership theory, with a view toward illuminating how authors in the history of philosophy have understood authenticity as an ideal for humanity. Such an approach requires a broader view of the historical origins of authenticity and the examination of related ideas such as self-knowledge and deception. The chapters of this volume illuminate the conflict between the contemporary understanding of authenticity and traditional philosophy by revisiting (...) the ideas of thinkers who express self-knowledge as a cornerstone of their philosophy. Tracing the origins of our contemporary concern for authenticity to the writings of 18th century philosopher Jean-Jacques Rousseau, this book explores the key thinkers writing in the wake of Rousseau's emphasis on sincerity, namely Friedrich Nietzsche and Martin Heidegger, to show that their acceptance of authenticity as an ideal for humanity was ambiguous at best. This volume also covers representative authors in the earlier history of philosophy, such as Plato, Niccolò Machiavelli, Francis Bacon, and John Locke. The result is a keen, in-depth analysis of works of philosophy and political philosophy that broach questions of authenticity, self-knowledge, and deception. This critical contribution to authentic leadership theory and the theory of authenticity will be a key resource for both undergraduate and graduate students in the fields of leadership studies, political science and philosophy. Contributors include: J.C. Byham, B.E. Cusher, E.A. Dolgoy, J. Fortier, N.W. Harter, M.A. Menaldo, H. Pedersen, J.M. Warner. (shrink)

Recent work on interpretability in machine learning and AI has focused on the building of simplified models that approximate the true criteria used to make decisions. These models are a useful pedagogical device for teaching trained professionals how to predict what decisions will be made by the complex system, and most importantly how the system might break. However, when considering any such model it’s important to remember Box’s maxim that "All models are wrong but some are useful." We focus on (...) the distinction between these models and explanations in philosophy and sociology. These models can be understood as a "do it yourself kit" for explanations, allowing a practitioner to directly answer "what if questions" or generate contrastive explanations without external assistance. Although a valuable ability, giving these models as explanations appears more difficult than necessary, and other forms of explanation may not have the same trade-offs. We contrast the different schools of thought on what makes an explanation, and suggest that machine learning might benefit from viewing the problem more broadly. (shrink)

The capacity to collect and analyse data is growing exponentially. Referred to as ‘Big Data’, this scientific, social and technological trend has helped create destabilising amounts of information, which can challenge accepted social and ethical norms. Big Data remains a fuzzy idea, emerging across social, scientific, and business contexts sometimes seemingly related only by the gigantic size of the datasets being considered. As is often the case with the cutting edge of scientific and technological progress, understanding of the ethical implications (...) of Big Data lags behind. In order to bridge such a gap, this article systematically and comprehensively analyses academic literature concerning the ethical implications of Big Data, providing a watershed for future ethical investigations and regulations. Particular attention is paid to biomedical Big Data due to the inherent sensitivity of medical information. By means of a meta-analysis of the literature, a thematic narrative is provided to guide ethicists, data scientists, regulators and other stakeholders through what is already known or hypothesised about the ethical risks of this emerging and innovative phenomenon. Five key areas of concern are identified: informed consent, privacy, ownership, epistemology and objectivity, and ‘Big Data Divides’ created between those who have or lack the necessary resources to analyse increasingly large datasets. Critical gaps in the treatment of these themes are identified with suggestions for future research. Six additional areas of concern are then suggested which, although related have not yet attracted extensive debate in the existing literature. It is argued that they will require much closer scrutiny in the immediate future: the dangers of ignoring group-level ethical harms; the importance of epistemology in assessing the ethics of Big Data; the changing nature of fiduciary relationships that become increasingly data saturated; the need to distinguish between ‘academic’ and ‘commercial’ Big Data practices in terms of potential harm to data subjects; future problems with ownership of intellectual property generated from analysis of aggregated datasets; and the difficulty of providing meaningful access rights to individual data subjects that lack necessary resources. Considered together, these eleven themes provide a thorough critical framework to guide ethical assessment and governance of emerging Big Data practices. (shrink)

This chapter focuses on ethical governance, which speaks to the infrastructure, processes, and practices that decrease the probability of performing ethically wrong actions and ethically bad outcomes resulting from relatively innocent actions. The ethics consultant can help spot gaps or other insufficiencies in ethical infrastructure, process, and practice. Ethics consulting consists in engaging in a due diligence process for ethical risk. The goal is to identify possible sources of ethical risk both in terms of features of the product and the (...) ways it may or may not be used, and to recommend feature changes and best practices for ethical deployment and use of the product. Ethics consulting more generally can be seen as aimed at either doing a bunch of good or avoiding a bunch of bad. Ethical challenges often arise in business because of competing assumptions and commitments that create seemingly irresolvable tensions or obscure the potentially bad consequences of particular decisions. (shrink)

We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these two-cardinal derived (...) topologies can be obtained from certain two-cardinal indescribability hypotheses, which follow from local instances of supercompactness. Additionally, we answer several questions posed by the first author, Holy and White on the relationship between Ramseyness and indescribability in both the cardinal context and in the two-cardinal context. (shrink)

The underlying structures that are common to the world's languages bear an intriguing connection with early emerging forms of “core knowledge” (Spelke & Kinzler, 2007), which are frequently studied by infant researchers. In particular, grammatical systems often incorporate distinctions (e.g., the mass/count distinction) that reflect those made in core knowledge (e.g., the non-verbal distinction between an object and a substance). Here, I argue that this connection occurs because non-verbal core knowledge systematically biases processes of language evolution. This account potentially explains (...) a wide range of cross-linguistic grammatical phenomena that currently lack an adequate explanation. Second, I suggest that developmental researchers and cognitive scientists interested in (non-verbal) knowledge representation can exploit this connection to language by using observations about cross-linguistic grammatical tendencies to inspire hypotheses about core knowledge. (shrink)

The underlying structures that are common to the world's languages bear an intriguing connection with early emerging forms of “core knowledge”, which are frequently studied by infant researchers. In particular, grammatical systems often incorporate distinctions that reflect those made in core knowledge. Here, I argue that this connection occurs because non-verbal core knowledge systematically biases processes of language evolution. This account potentially explains a wide range of cross-linguistic grammatical phenomena that currently lack an adequate explanation. Second, I suggest that developmental (...) researchers and cognitive scientists interested in knowledge representation can exploit this connection to language by using observations about cross-linguistic grammatical tendencies to inspire hypotheses about core knowledge. (shrink)