The objective of this case study concentrated on examining the learning gap, going through some components of the transformation process, and coming up with some ways for aiding students who were experiencing lost learning. A qualitative research design was utilized by the researchers to understand and solve the cases related to Mathematics learning difficulties. Creswell (2008) asserts that qualitative research can be used to discover and comprehend the significance that certain people or groups assign to social or human issues. The (...) researchers used purposive sampling to determine 15 student participants to understand the cases of learning loss and prescribe better interventions to the students. To solve the problems associated with loss of learning experienced by the learners after remote learning, a case study will be utilized as the strategy of inquiry since it fits the situation that is to focus the said key cases, discuss some transforming process, and develop interventions. After analyzing the interviews, researchers identified three common themes across the three cases which serve to clarify the learners' experiences after the post-remote learning: the learners' learning experiences during remote learning, factors that caused learning loss in Mathematics, and learners' coping strategies. In a deeper analysis, the impact of distance learning on students during the pandemic goes beyond just the difficulties in learning and understanding lessons which resulted in difficulty in learning math during in-person classes. The lack of in-person interaction with classmates and teachers also contributes to a sense of isolation and boredom, negatively affecting students' overall well-being and mental health. (shrink)

El debate por una Epistemología del Diseño en Argentina ha coincidido en sostener que estas disciplinas afrontan una diversidad de variables y producen una serie de beneficios que la posicionan como una categoría autónoma, diferente del Arte, la Tecnología y la Ciencia; argumento circular que impide una epistemología sin contradicciones. Forzando el cientificismo de M. Bunge, el objetivo de este trabajo fue indagar el posicionamiento de la Arquitectura como una multi-disciplina científica, análogamente al concepto bungeano sobre la medicina: parte C. (...) Básica, parte C. Aplicada, parte Tecnología y su ejercicio una Artesanía de alto fuste. Sin renunciar a su dimensión artística, ni proponer estéticas, axiologías o dinámicas proyectuales como los antecedentes hallados en la literatura, el posicionamiento como una multi-disciplina abarca la gran variedad de prácticas disciplinares actuales y puede ser el punto de partida para su criba desde las distintas disciplinas científicas y la formulación de su Epistemología. (shrink)

Today, biomedical technoscience has evolved beyond the reach of the past. Its evolution makes our societies complex and thus places us in the face of a paradox that is difficult to overcome. As technoscience arouses by its development, a real need for support, as much it makes impossible any formulation of this support. So much so that in the present text, we wonder with Gilbert Hottois: is it possible to develop a universally valid form of accompaniment to techno-scientific dynamics in (...) postmodern societies as complex as ours? To this question, Hottois answers in the affirmative, but on the condition that one ¨re-think¨ the accompaniment of the technoscience while actualizing the philosophical discourse which is the origin of it. (shrink)

Functional decomposition is an important goal in the life sciences, and is central to mechanistic explanation and explanatory reduction. A growing literature in philosophy of science, however, has challenged decomposition-based notions of explanation. ‘Holists’ posit that complex systems exhibit context-sensitivity, dynamic interaction, and network dependence, and that these properties undermine decomposition. They then infer from the failure of decomposition to the failure of mechanistic explanation and reduction. I argue that complexity, so construed, is only incompatible with one notion of decomposition, (...) which I call ‘atomism’, and not with decomposition writ large. Atomism posits that function ascriptions must be made to parts with minimal reference to the surrounding system. Complexity does indeed falsify atomism, but I contend that there is a weaker, ‘contextualist’ notion of decomposition that is fully compatible with the properties that holists cite. Contextualism suggests that the function of parts can shift with external context, and that interactions with other parts might help determine their context-appropriate functions. This still admits of functional decomposition within a given context. I will give examples based on the notion of oscillatory multiplexing in systems neuroscience. If contextualism is feasible, then holist inferences are faulty—one cannot infer from the presence of complexity to the failure of decomposition, mechanism, and reductionism. (shrink)

The standard assumption for what perception must do in order to represent a “higher level” content—say, tiger—is that it must represent the kind as such. I argue that this “as such condition” is not constitutive of what it means for a content to be “higher‐level”, and that embracing it produces a range of unfortunate dialectical consequences. After offering this critique, I give an alternative construal, the “extended perceptual space” view of higher‐level contents. This view captures the phenomena targeted by the (...) “higher‐level content” thesis, is empirically supported, and avoids the negative dialectical consequences of the as such condition. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...) are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

Various prominent theories of pain assume that it is pain’s biological function to inform organisms about damage to their bodies. I argue that this is a mistake. First, there is no biological evidence to support the notion that pain was originally selected for its informative capacities, nor that it currently contributes to the fitness of organisms in this specific capacity. Second, neurological evidence indicates that modulating mechanisms in the nociceptive system systematically prevent pain from serving a primarily informative role. These (...) considerations threaten to undermine standard perceptual and representational accounts of pain. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

A discussion of a number of ways that information can be present in a computer program without being explicitly represented.

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation (...) laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

We discuss at some length evidence from the cognitive science suggesting that the representations of objects based on spatiotemporal information and featural information retrieved bottomup from a visual scene precede representations of objects that include conceptual information. We argue that a distinction can be drawn between representations with conceptual and nonconceptual content. The distinction is based on perceptual mechanisms that retrieve information in conceptually unmediated ways. The representational contents of the states induced by these mechanisms that are available to a (...) type of awareness called phenomenal awareness constitute the phenomenal content of experience. The phenomenal content of perception contains the existence of objects as separate things that persist in time and time, spatiotemporal information, and information regarding relative spatial relations, motion, surface properties, shape, size, orientation, color, and their functional properties. (shrink)

Epistemic paternalism is the thesis that a paternalistic interference with an individual's inquiry is justified when it is likely to bring about an epistemic improvement in her. In this article I claim that in order to motivate epistemic paternalism we must first account for the value of epistemic improvements. I propose that the epistemic paternalist has two options: either epistemic improvements are valuable because they contribute to wellbeing, or they are epistemically valuable. I will argue that these options constitute the (...) foundations of a dilemma: either epistemic paternalism collapses into general paternalism, or a distinctive project of justified epistemic paternalism is implausible. (shrink)

This volume aimed to highlight narrative identities of European cities or city neighbourhoods that have been overlooked, such as mid-sized cities. These cities are neither small towns nor metropolises, cities that are now unveiling their appeal or specificity. The present special issue thus covers a range of representations of cities. The articles investigate more systematically how different texts deal with various cities from different experiential and fictional perspectives. The issue covers the geographical scope across Europe, from east to west or (...) vice versa, as well as a range of different works of national literature(s), but with a clear emphasis on mid-sized European cities that have until now been deemed as lesser-known, secondary, peripheral, ‘other’ cities that are in the focus of the research of the COST project Writing Urban Places. New Narratives of the European City, within which this journal issue is being published. (shrink)

This paper defends the Intention Account of Inquiry. On this account, inquiry is best understood by appeal to a ‘question-directed intention’ (QDI), an intention to answer a question broadly construed. This account’s core commitments help meet recent challenges plaguing extant approaches to characterizing inquiry. First, QDIs are the type of mental state central to inquiry, not attitudes like curiosity or wonder. Second, holding a QDI towards a question and acting in service of it constitutes the start of inquiry. Third, controversial (...) norms which mandate a rational inquirer's ignorance towards the answer to her question can be reformulated and defended by appeal to rational constraints on intention. Fourth, instrumental pressures inquirers face are the standard pressures of plan-rationality. In defending these theses, I show that the Intention Account provides compelling explanations to standing challenges, in ways competitors cannot. It does so by advancing understanding of how our epistemic and practical agency are intertwined. (shrink)

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)

In this introduction, before summarizing the contents of the volume, the authors characterize materialism as it is understood within the philosophy of mind, and they identify three respects in which materialism is on the wane.

This response addresses the excellent responses to my book provided by Heather Douglas, Janet Kourany, and Matt Brown. First, I provide some comments and clarifications concerning a few of the highlights from their essays. Second, in response to the worries of my critics, I provide more detail than I was able to provide in my book regarding my three conditions for incorporating values in science. Third, I identify some of the most promising avenues for further research that flow out of (...) this interchange. (shrink)

Despite their popularity, relatively scant attention has been paid to the upshot of Bayesian and predictive processing models of cognition for views of overall cognitive architecture. Many of these models are hierarchical ; they posit generative models at multiple distinct "levels," whose job is to predict the consequences of sensory input at lower levels. I articulate one possible position that could be implied by these models, namely, that there is a continuous hierarchy of perception, cognition, and action control comprising levels (...) of generative models. I argue that this view is not entailed by a general Bayesian/predictive processing outlook. Bayesian approaches are compatible with distinct formats of mental representation. Focusing on Bayesian approaches to motor control, I argue that the junctures between different types of mental representation are places where the transitivity of hierarchical prediction may be broken, and I consider the upshot of this conclusion for broader discussions of cognitive architecture. (shrink)

We should not be creating conscious, humanoid agents but an entirely new sort of entity, rather like oracles, with no conscience, no fear of death, no distracting loves and hates.

The notion of representation in neuroscience has largely been predicated on localizing the components of computational processes that explain cognitive function. On this view, which I call “algorithmic homuncularism,” individual, spatially and temporally distinct parts of the brain serve as vehicles for distinct contents, and the causal relationships between them implement the transformations specified by an algorithm. This view has a widespread influence in philosophy and cognitive neuroscience, and has recently been ably articulated and defended by Shea. Still, I am (...) skeptical about algorithmic homuncularism, and I argue against it by focusing on recent methods for complex data analysis in systems neuroscience. I claim that analyses such as principle components analysis and linear discriminant analysis prevent individuating vehicles as algorithmic homuncularism recommends. Rather, each individual part contributes to a global state space, trajectories of which vary with important task parameters. I argue that, while homuncularism is false, this view still supports a kind of “vehicle realism,” and I apply this view to debates about the explanatory role of representation. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

In this paper we argue that Socrates is a cognitivist about emotions, but then ask how the beliefs that constitute emotions can come into being, and why those beliefs seem more resistant to change through rational persuasion than other beliefs.

Interactive theorem provers might seem particularly impractical in the history of philosophy. Journal articles in this discipline are generally not formalized. Interactive theorem provers involve a learning curve for which the payoffs might seem minimal. In this article I argue that interactive theorem provers have already demonstrated their potential as a useful tool for historians of philosophy; I do this by highlighting examples of work where this has already been done. Further, I argue that interactive theorem provers can continue to (...) be useful tools for historians of philosophy in the future; this claim is defended through a more conceptual analysis of what historians of philosophy do that identifies argument reconstruction as a core activity of such practitioners. It is then shown that interactive theorem provers can assist in this core practice by a description of what interactive theorem provers are and can do. If this is right, then computer verification for historians of philosophy is in the offing. (shrink)

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

Many countries are experiencing increasing levels of demand for access to assisted reproductive technologies. Policies regarding who can access ART and with what support from a collective purse are highly contested, raising questions about what state responses are justified. Whilst much of this debate has focused on the status of infertility as a disease, we argue that this is something of a distraction, since disease framing does not provide the far-reaching, robust justification for state support that proponents of ART seem (...) to suppose. Instead, we propose that debates about appropriate state responses should consider the various implications for health and broader well-being that may be associated with difficulties starting a family. We argue that the harms and disruption to valued life projects of subfertility-related suffering may provide a stronger basis for justifying state support in this context. Further, we suggest that, whilst ART may alleviate some of the harm resulting from subfertility, population-level considerations can indicate a broader range of interventions aimed at tackling different sources of subfertility-related harm, consistent with broader public health aims. (shrink)

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...) and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...) due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

This article explores the meeting of two approaches towards philosophy and education: the philosophy for children approach advocated by Lipman and others, and Schmid’s philosophical concept of Lebenskunst. Schmid explores the concept of the beautiful or good life by asking what is necessary for each individual to be able to develop their own art of living and which aspects of life are significant when shaping a good and beautiful life. One element of Schmid’s theory is the practical application of philosophy (...) through the notions of Bildung, reflection, prudence and practical wisdom, as well as the requirement for each individual to take responsibility for actively shaping their life as an artwork. In this sense, each person is the artist responsible for living their own beautiful life. We argue that there are useful parallels between Schmid’s concept of the art of living and P4C, such as the ideal of a holistic philosophy that is “lived.” The pragmatic approach of P4C focuses on the embodied learner who practices critical, caring and creative thinking. Both P4C and Schmid’s theory are reminiscent of the Aristotelian notion of practical wisdom, which allows for an approach to an education for life that prepares students to develop their own art of living. (shrink)

In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

Ordinary reasoning about space—we argue—is first and foremost reasoning about things or events located in space. Accordingly, any theory concerned with the construction of a general model of our spatial competence must be grounded on a general account of the sort of entities that may enter into the scope of the theory. Moreover, on the methodological side the emphasis on spatial entities (as opposed to purely geometrical items such as points or regions) calls for a reexamination of the conceptual categories (...) required for this task. Building on material presented in an earlier paper, in this work we offer some examples of what this amounts to, of the difficulties involved, and of the main directions along which spatial theories should be developed so as to combine formal sophistication with some affinity with common sense. (shrink)

Physicalists typically believe that neurophysiology has refuted the thesis that non-physical minds can interact with the brain. In this paper, I argue that it is precisely a closer look at the neurophysiology of volitional actions that suggests otherwise. I start with a clarification of how the present inquiry relates to the main argument for physicalism, and how the most common alternative views relate to the findings of my study. I then give a brief overview of the neurophysiological research about volitional (...) actions, finding that there is no research specifically directed at the pertinent question. I proceed by pointing out what it would take for a complete physical explanation of volitional actions to be true: namely a complete physical explanation of the increase in the firing rate of the neurons with which the sequence leading up to volitional actions starts. Since no dedicated research about this question is available, I offer a study of the known mechanisms of neuronal excitation as a substitute, finding that there is no plausible biochemical or physical mechanism that could explain the causal initiation of volitional actions – at least none that upholds energy conservation. But non-conservation is precisely what interactive dualism, in its most plausible version, predicts. Thus, rather than buttressing physicalism, our empirical knowledge of volitional actions points toward interactive dualism. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...) including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

My goal in this paper is to show that naturalists cannot reasonably endorse moral realism. My argument will come in two parts. The first part aims to show that any plausible and naturalistically acceptable argument in favor of belief in objective moral properties will appeal in part to simplicity considerations (broadly construed)—and this regardless of whether moral properties are reducible to non-moral properties. The second part argues for the conclusion that appeals to simplicity justify belief in moral properties only if (...) either those properties are not objective or something like theism is true. Thus, if my argument is sound, naturalists can reasonably accept moral realism only if they are prepared to accept something like theism. But, as will become clear, naturalists can reasonably accept theism or something like it only if belief in some such doctrine is justified by the methods of science. For present purposes, I’ll assume (what I think virtually every naturalist will grant) that belief in theism and relevantly similar doctrines is not justified by the methods of science. Thus, I will conclude that naturalists cannot reasonably accept moral realism. (shrink)

In the present article, he explains why divine silence poses a serious intellectual obstacle to belief in God, and then goes on to consider ways of overcoming that obstacle. After considering several ways in which divine silence might actually be beneficial to human beings, he argues that perhaps silence is nothing more or less than God’s preferred mode of interaction with creatures like us. Perhaps God simply desires communion rather than overt communication with human beings, and perhaps God has provided (...) ways for us to experience God’s presence richly even amidst the silence. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

ABSTRACT This essay focuses on two underlying presumptions that impinge on the effort of UNESCO to engender universal agreement on a set of bioethical norms: the conception of universality that pervades much of the document, and its disregard of structural inequalities that significantly impact health. Drawing on other UN system documents and recent feminist bioethics scholarship, we argue that the formulation of universal principles should not rely solely on shared ethical values, as the draft document affirms, but also on differences (...) in ethical values that obtain across cultures. UNESCO's earlier work on gender mainstreaming illustrates the necessity of thinking from multiple perspectives in generating universal norms. The declaration asserts the ‘fundamental equality of all human beings in dignity and rights’1 and insists that ‘the highest attainable standard of health is one of the fundamental rights of every human being without distinction of race, religion, political belief, economic or social condition’2 yet it does not explicitly recognize disparities of power and wealth that deny equal dignity and rights to many. Without attention to structural (as opposed to merely accidental) inequities, UNESCO's invocation of rights is so abstract as to be incompatible with its avowed intention. (shrink)

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

The following argument is widely assumed to be invalid: there is a pain in my finger; my finger is in my mouth; therefore, there is a pain in my mouth. The apparent invalidity of this argument has recently been used to motivate the conclusion that pains are not spatial entities. We argue that this is a mistake. We do so by drawing attention to the metaphysics of pains and holes and provide a framework for their location which both vindicates the (...) argument's validity and explains why it appears invalid. To this end, we show that previously proposed explanations for the apparent invalidity of the argument fail. Moreover, we show that our account accommodates and explains seemingly opposing linguistic data. We conclude that the ‘pain-in-mouth argument’ does not undermine the view that pains are spatial entities. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these principles also regulate and control (...) the process of deduction in inquiry, i.e., they are prescriptive for the use of language and thought in inquiry, I argue that logic may, and should, be seen as an instrument or as a way of proceeding (modus procedendi) in inquiry. (shrink)

Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...) discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic. (shrink)

In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I next (...) argue that, if empty worlds are logically possible, then the model-theoretic and truth-functional considerations that are usually given address the problem posed by the first kind of formula, but not the problem posed by the second kind. I then show that Russell’s commitments in 1918 provide an answer to the problem of completely generalized molecular formulas: some truth-makers will be non-atomic facts that have no constituents. This shows that the neo-logical atomist goal of defending the principle of atomicity—the principle that only atomic facts are truth-makers—is not realizable. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...) _Principles_. I distinguish the functions and predicates versions, give a novel reading of the _Principles_, section 85, as a paradox dealing with what Russell calls _assertions_, and show that Russell's logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell's notation had changed in such a way as to make a formulation possible. (shrink)