Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried out (...) relative to such domains; puzzles about ‘large categories’ and ‘proper classes’ are handled in a uniform way, by relativization, sustaining insights of Zermelo. (shrink)

Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality (...) of MS or a close cousin appears at crucial junctures in both STS and SGS, so that the above outcome is not obviously tendentious. (shrink)

This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically ...

Given a basic conditional of the form, If A then C, individuals usually list three cases as possible: A and C, not‐A and not‐C, not‐A and C. This result corroborates the theory of mental models. By contrast, individuals often judge that the conditional is true only in the case of A and C, and that cases of not‐A are irrelevant to its truth or falsity. This result corroborates other theories of conditionals. To resolve the discrepancy, we devised two new tasks: (...) the “collective” truth task, in which participants judged whether sets of assertions about a specific individual, such as: If A then C, not‐A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not‐C, not‐A and C, and not‐A and not‐C), which summed to over 200%. (shrink)

The object of this paper is to explore the intersection of two issues. The first concerns the role that feasibility considerations play in constraining normative claims – claims, say, about what we (individually and collectively) ought to do and to be. The second concerns whether normative claims are to be understood as applying only to actions in their own right or also non-derivatively to attitudes. In particular, we argue that actions and attitudes may be subject to different feasibility constraints – (...) and hence that how we conceive of the role of feasibility in an account of normativity will depend in part on how we conceive of the role of actions and attitudes in normative theorising. (shrink)

In a Special Issue of Discourse Studies titled ‘The Epistemics of Epistemics’, contributing authors criticize Heritage’s research on participants’ orientations to, and management of, the distribution of knowledge in conversation. These authors claim that the analytic framework Heritage developed for analyzing epistemic phenomena privileges the analysts’ over the participants’ point of view, and rejects standard methods of conversation analysis ; that and are adopted in developing and defending the use of abstract analytic schemata that offer little purchase on either the (...) specific actions speakers accomplish or the understanding others display of them; and that, by virtue of these deficiencies, claims about the systematic relevance of epistemic phenomena for talk-in-interaction breach long-standing norms regarding the relationship between data analysis and generalizing claims. Using a collection of excerpts bearing on the import of epistemics for action formation and action sequencing, I demonstrate that these claims are patently false and suggest that they reflect the authors’ effort to recast CA as a kind of fundamentalist enterprise. I then consider excerpts from a second collection to illustrate how the form of social organization described by Heritage can be used to explicate other phenomena that depend on systematic alterations to its basic features. In conclusion, I suggest that CA’s success in enhancing our grasp of the organization of talk-in-interaction derives from its unique commitment to both generalization and context specificity, collections and single cases, findings plus a continual openness to the ‘something more’ that each particular case can provide. (shrink)

Doing the best we can in the world as it is requires that appropriate account be taken of The object of this essay is to examine what amounts to feasibilitydesirability considerations.feasibilitycoming in degrees objects that the advisee controls feasibility ofought-implies-can” principle, a point of departure that frames feasibility considerations in a dismissive or otherwise inadequate way.

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence (...) of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

Traditional theories of associative learning have found no place for the possibility that the way in which events are perceived might change as a result of experience. Evidence for the reality of perceptual learning has come from those studied by learning theorists. The work reviewed in this book shows that learned changes in perceptual organization can in fact be demonstrated, even in experiments using procedures of the type on which associative theories have been based. These results come from procedures that (...) have been the focus of detailed theoretical and empirical analysis; and from this analysis emerges an outline of the mechanisms responsible. Some of these are themselves associative; others require the addition of nonassociative mechanisms to the traditional theory. The result is an extended version of associative theory which, it is argued, will be relevant not only to the experimental procedures discussed in this book but to the entire range of instances of perceptual learning. (shrink)

It is possible to learn multiple layers of non-linear features by backpropagating error derivatives through a feedforward neural network. This is a very effective learning procedure when there is a huge amount of labeled training data, but for many learning tasks very few labeled examples are available. In an effort to overcome the need for labeled data, several different generative models were developed that learned interesting features by modeling the higher order statistical structure of a set of input vectors. One (...) of these generative models, the restricted Boltzmann machine (RBM), has no connections between its hidden units and this makes perceptual inference and learning much simpler. More significantly, after a layer of hidden features has been learned, the activities of these features can be used as training data for another RBM. By applying this idea recursively, it is possible to learn a deep hierarchy of progressively more complicated features without requiring any labeled data. This deep hierarchy can then be treated as a feedforward neural network which can be discriminatively fine-tuned using backpropagation. Using a stack of RBMs to initialize the weights of a feedforward neural network allows backpropagation to work effectively in much deeper networks and it leads to much better generalization. A stack of RBMs can also be used to initialize a deep Boltzmann machine that has many hidden layers. Combining this initialization method with a new method for fine-tuning the weights finally leads to the first efficient way of training Boltzmann machines with many hidden layers and millions of weights. (shrink)

Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the superiority of (...) variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning "diachronic Dutch Book" arguments and "non-Bayesian shifts" are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis. (shrink)

Berkeley is one of the most influential and yet most misunderstood of eighteenth-century philosophers. In this new, revised edition of his classic introduction, G.J. Warnock examines all Berkeley's major philosophical works and discusses his most original and interesting contributions to questions still debated by philosophers today. The aim of the book is to help the reader learn not so much about Berkeley, but rather, through Berkeley, something about philosophy itself.

Background Increase in global health research undertaken in resource poor settings in the last decade though a positive development has raised ethical concerns relating to potential for exploitation. Some of the suggested strategies to address these concerns include calls for providing universal standards of care, reasonable availability of proven interventions and more recently, promoting the overall social value of research especially in clinical research. Promoting the social value of research has been closely associated with providing fair benefits to various stakeholders (...) involved in research. The debate over what constitutes fair benefits; whether those that addresses micro level issues of justice or those focusing on the key determinants of health at the macro level has continued. This debate has however not benefited from empirical work on what stakeholders consider fair benefits. This study explores practical experiences of stakeholders involved in global health research in Kenya, over what benefits are fair within a developing world context. Methods and results We conducted in-depth interviews with key informants drawn from within the broader health research system in Kenya including researchers from the mainstream health research institutions, networks and universities, teaching hospitals, policy makers, institutional review boards, civil society organisations and community representative groups. The range of benefits articulated by stakeholders addresses both micro and macro level concerns for justice by for instance, seeking to engage with interests of those facilitating research, and the broader systemic issues that make resource poor settings vulnerable to exploitation. We interpret these views to suggest a need for global health research to engage with current crises that face people in these settings as well as the broader systemic issues that produce them. Conclusion Global health research should provide benefits that address both the micro and macro level issues of justice in order to forestall exploitation. Embracing the two is however challenging in terms of how the various competing interests/needs should be balanced ethically, especially in the absence of structures to guide the process. This challenge should point to the need for greater dialogue to facilitate value clarification among stakeholders. (shrink)

(2013). The Theological Foundation of Hobbesian Physics: A Defence of Corporeal God. British Journal for the History of Philosophy: Vol. 21, No. 2, pp. 240-261. doi: 10.1080/09608788.2012.692663.

Was Hume here claiming or implying that propositions about what men ought to do are radically different from purely factual propositions, and that they cannot ever be entailed by any purely factual propositions? No, despite Mr Hare, Professor Nowell-Smith, Professor Ayer, Miss Murdoch, Professor Flew, Mr Basson, and The Observer's Brief Guide to philosophy.

This is the second of a pair of papers, of which the first showed how each of the main late phlogistic theories effectively reached impasses due to internal problems or included features which made them unacceptable even to other phlogistians. This paper deals with theory comparison and theory change. It gives an unprecedentedly detailed comparison between the available theories in 1790–1791, and shows that this was overwhelmingly in favour of the new chemistry. This time period correlates well with many chemists (...) changing to the new theory. There was a plurality of views held by individuals and there was freedom of individual choice concerning theories, yet there was also a widespread and rational change to the new chemistry. (shrink)

Overview of some of the key philosophical problems encountered making sense of the notion of "subjective time", with a focus on the experience of duration. The paper unpacks some of the assumptions behind an intuitive picture of duration experience I call the "simple flow" view, highlighting the availability of alternative models. It then considers a number of obstacles to providing an account of the individuation of subjective features of duration experience.

To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it (...) is argued that any mentalist-based radical constructivism suffers from a kind of neo-Kantian apriorism. It would be at best a lucky accident if objective spacetime structure mirrored mentalist mathematics. the latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but is it doubtful if implementation of such a view would overcome the objection. As a result, an anti-realist view of physics seems forced on the radical constructivist. (shrink)

Eye movements were recorded during the display of two images of a real-world scene that were inspected to determine whether they were the same or not . In the displays where the pictures were different, one object had been changed, and this object was sometimes taken from another scene and was incongruent with the gist. The experiment established that incongruous objects attract eye fixations earlier than the congruous counterparts, but that this effect is not apparent until the picture has been (...) displayed for several seconds. By controlling the visual saliency of the objects the experiment eliminates the possibility that the incongruency effect is dependent upon the conspicuity of the changed objects. A model of scene perception is suggested whereby attention is unnecessary for the partial recognition of an object that delivers sufficient information about its visual characteristics for the viewer to know that the object is improbable in that particular scene, and in which full identification requires foveal inspection. (shrink)

This paper examines how communities of naturalists in mid-nineteenth-century Britain were formed and solidified around the shared practices of public meetings, the publication and reading of periodicals, and the making and printing of images. By focusing on communities of naturalists and the sites of their communication, this article undermines the distinction between amateur and professional scientific practice. Building on the notion of imagined communities, this paper also shows that in some cases the editors and illustrators utilized imagery to construct a (...) specifically British naturalist community. Following three ‘amateur’ natural-history periodicals (Science Gossip,Midland Naturalistand theJournal of the Quekett Microscopical Club) the article demonstrates how the production and reproduction of natural history in the nineteenth century was contingent on community debate – and that this debate both was highly visual and moved across printed and geographical boundaries. This paper investigates images both for their purported success and for their ascribed value to natural history. Additionally, it considers the debates over their limitations and alleged failures of printing. Altogether, the article argues that investigating the communal practices of observation, writing, drawing and engraving allows for a better understanding of the shared practices of nineteenth-century natural history. (shrink)

Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of "stochastic" hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist ("realist") interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reasoning, similar to the original EPR, is used to derive determinateness (of all spin components (...) of two spin- 1 / 2 particles in the singlet state) from just (a form of) weak locality, result definiteness, and an assumption on propensities based on conservation. Theories meeting these conditions are therefore constrained by the Bell inequalities. Neither controversial assumptions of "strong locality" ("factorability") nor of determinism are employed in the derivation. The categories of "stochastic hidden variables" are then analyzed; one can focus on "quasi-definite" theories, without loss of generality. A means of excluding these is proposed, based on a demand that certain ideal cases be accurately treated. Theorems from quantum measurement theory, sometimes cited as showing that such cases are not physically possible, are found inapplicable. (shrink)

Descartes and William Harvey engaged in a polite dispute about the cause of the heart's motion. Descartes saw the heart's motion of passive; Harvey saw it as active. I criticize three prominent explanations for Descartes' opposition to Harvey's theory. I argue that Descartes found Harvey's model to be inconsistent with mind-body dualism and this was the reason he opposed it.

Social theorists in recent years have concerned themselves with the matter of the kind and intensity of people’s everyday reflective capacities. In this respect, Bourdieu has mostly been found wanting. This article seeks to counter this sentiment with recourse to an ‘anti-mechanistic’ reading of Bourdieu’s theory of practice. It begins by arguing that in imposing a strict delineation between consciousness and habitus, Bourdieu and his critics alike at times unwittingly conflate habitus and mechanistic habit, at once vaunting conscious deliberation and (...) neglecting the non-habitual acts that habitus makes possible. Next it turns to the treatment, within the mechanistic reading, of the notion of the ‘social world’. The argument is that in this reading the social world is reified and rendered the mere background or setting for social practices rather than the product of those practices. Without recognition of this latter quality, the social world becomes hypostatized and exists outside of time. The secondary aim, then, is to argue for a thoroughgoing temporal relation to social reality in Bourdieu’s theory. (shrink)

The articles that comprise this special issue of Intellectual History Review are briefly described.

There has been increased interest in developing what I call environmental virtue ethics (EVE). This paper presents some of the centralfeatures of this project. The first part is a general description of EVE, showing why there is a need for it. The second part spells out the central features of EVE including an account of the good life as flourishing in an expanded or mixed biotic community, and provides a tentative list of important environmental virtues. The third part examines one (...) virtue: friendship, showing how an understanding of it provides insight into current issues in environmental ethics. The final section addresses a challenge to the project of EVE. (shrink)

It is a remarkable feature of most contemporary discussions of emotion that they have been conducted without any reference to what it could mean to talk of the expression of emotion in music. This is a crucial absence, I shall argue, since a proper understanding of music's expression of emotion must lead to a correct view of the nature of emotion itself. Such an understanding will yield the view that emotion is a state of consciousness which is both intentional and (...) affective, and at the same time totally undermine the view that emotions are, or necessarily involve, judgments or evaluations. (shrink)

Seventeenth-century authors frequently infer the attributes of time by analogy from already established features of space. The rationale for this can be traced back to Aristotle's analysis of time as ?the number of movement?, where movement requires a prior understanding of spatial magnitude. Although these authors are anti-Aristotelian, they were concerned, contra Aristotle, to establish the existence of ?empty space?, and a notion of absolute space which fit this idea. Although they had no independent rationale for the existence of absolute (...) time, it seemed to go with absolute space, and they drew on a long tradition of space-time parallelism in securing this. (shrink)

The application of evolutionary ideas to socioeconomic systems has been an increasingly prominent theme in the work of Friedrich Hayek, and the motif has become dominant in his recent book. In an earlier issue of this journal, Viktor Vanberg raises two substantive criticisms of Friedrich Hayek' theory of cultural evolution that invoke some important questions concerning use of the evolutionary analogy in social science.

Past research has suggested that those spontaneous movements of the human hand made during talk convey significant semantic information over and above the speech, at least when the unit of speech analyzed is the individual clause. However, no previous research has tested whether this information is represented linguistically elsewhere in the narrative . The first study, reported here, uses an experimental procedure to identify which specific imagistic gestures add semantic information to the speech. The second study analyzes whether the specific (...) gestures still do this when respondents hear the whole narrative. It was found that two thirds of the semantic information, thought to be carried by the gestures, is, in fact, represented in the linguistic discourse, or is inferable from it. However, one third of the additional semantic information contained in the gestures is not represented linguistically in the narrative nor is it inferable from it. In other words, a proportion of the imagistic gestures that accompany speech are absolutely critical to semantic communication. (shrink)

Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functionality of QL ∨ and $\wedge $ . Thus, (...) from within both the classical framework and that of any QL that preserves elementary set theory, two distinct (nonsynonymous) sets of connectives are discernible. Classical derivations of QM paradoxes are all available unless the language of QM is not classically closed. Maintaining this requires a strong and selfdefeating verification theory of meaning, the philosophical cornerstone of the Copenhagen interpretation to which QL was to provide an alternative. (shrink)

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of 'closed operator', this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that may (...) still be possible necessarily involve additional 'incompleteness' in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a 'liberal' stance but not with a 'radical', verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify. (shrink)

We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-a-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empiricists. Part 2 seeks purely ontological formulations, so devised that the empiricist cannot reconstruct them from within. The main task here (...) is to characterize "independence of mind". A pair of notions, "physical invariance" and "anti-determination", seem to work. They enable us to assess anew "the problem of constructing the physical out of the phenomenal" (yielding certain clarifications demanded by Goodman). Modern cosmology, especially, is seen to present insuperable obstacles to such empiricist approaches to science. The final section on epistemological principles reveals a morass better avoided in favor of an elementary claim about perception, together with a rejection of any absolute observation/theory dichotomy. Finally, a positive, realist notion of "observable-in-principle" is sketched, and it is suggested that, from the perspective of relativistic cosmology, even this defines no boundary to potential knowledge. (shrink)