Ethics and Science: Is Plausibility in the Eye of the Beholder?

This paper argues that morality is objective in a specific sense that accords with a broadly expressivist stance in metaethics. The paper also explains that although there is a kind of subjectivity in moral inquiry, the same holds for other kinds of normative inquiry, including epistemic and even scientific inquiry, and moreover that this kind of subjectivity is no threat to morality’s objectivity. The argument for the objectivity of morality draws strong parallels between ethics, epistemology, and science, but does not depend on equally strong parallels between ethics and mathematics. I argue that there is more to learn from a comparison between ethics and mathematics than I used to think, but the difference between the issues that come up in thinking about objectivity in ethics and those that come up in thinking about objectivity in mathematics is substantial, and we cannot carry over results from the philosophy of mathematics to the case of morality.     

From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition

Topoi - One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to...     

VOLKER PECKHAUS (ed.), Oskar Becker und die Philosophie der Mathematik.

It has been contended that it is unjustified to believe, as Weyl did, that formalism's victory against intuitionism entails a defeat of the phenomenological approach to mathematics. The reason for this contention, recently put forth by Paolo Mancosu and Thomas Ryckman, is that, unlike intuitionistic Anschauung, phenomenological intuition could ground classical mathematics. I argue that this indicates a misinterpretation of Weyl's view, for he did not take formalism to prevail over intuitionism with respect to grounding classical mathematics. I also point out that the contention is false: if intuitionism fails, in the way Weyl thought it did, i.e. with respect to supporting scientific objectivity, then one should also reject the phenomenological approach, in the same respect.     

Degrees of Objectivity? Mathemata and Social Objects

Topoi - A down-to-earth admission of abstract objects can be based on detailed explanation of where the objectivity of mathematics comes from, and how a ‘thin’ notion of object emerges...     

Transforming objectivity to promote equity in transplant candidate selection

It is necessary to recognize the variety of levels at which values and norms may inappropriately affect the equity of the transplantation process, including candidate selection. Using a revised, richer concept of objectivity, adopted from Longino's work in the philosophy of science and empirical studies of candidate selection, this paper examines what sort of objectivity can be obtained in the transplant candidate selection process, and the closely related question of how selection can occur in an equitable manner. This concept of objectivity requires that transformative criticism occur so that (1) the conceptual and normative commitments underlying selection may be articulated and perhaps challenged, and (2) the relationship between those commitments and criteria for candidate selection may be examined and justified, or revised. Through such transformative criticism, a greater degree of objectivity may be attained, which in turn will increase the likelihood of equity.     

Subjectivity and objectivity in analytic listening.

Analysts use the concepts of subjectivity and intersubjectivity to support many different technical recommendations; this represents a misuse of theory. The dichotomy between subjectivity and objectivity is a false one. Arguing against the notion of objectivity, analysts conflate it with the idealized notion of pure objectivity and then eliminate various technical devices in its name. One cannot have a concept of subjectivity without a concept of objectivity, or an intersubjective perspective that does not include some agreed-upon concept of objectivity. The simplest definition of objectivity is a directional one. Objectivity is the perception or experience of the external; subjectivity is the perception or experience of the internal. Subjectivity and objectivity are both necessary pathways to knowledge and are dependent on each other. Any form of looking or listening does to some extent preclude another, but to speak solely from a subjective or an objective perspective represents a regression in thinking to a form of naive objectivism or naive subjectivism. Clinical examples illustrate how the forming and testing of hypotheses require the cooperation of both subjective and objective listening.     

Expanding the rasch model to a general model having more than one dimension

The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.     

Performance Indicators in Math: Implications for Brief Experimental Analysis of Academic Performance

Brief experimental analysis (BEA) can be used to specify intervention characteristics that produce positive learning gains for individual students. A key challenge to the use of BEA for intervention planning is the identification of performance indicators (including topography of the skill, measurement characteristics, and decision criteria) that meaningfully relate to longer term success in the learning environment. This study investigates the utility of various curriculum-based assessment and measurement estimates of mathematics performance for predicting functional outcomes (i.e., retention of learned skills over time and faster learning of related content in the future). All children in grades 2–5 at the participating school participated in protocol-based computational fluency-building intervention 4 days per week for an entire school year. Specific criteria were applied each week to systematically increase intervention difficulty classwide according to a pre-established sequence of computational skill objectives. Three measurements were routinely obtained. Each week children completed a timed probe of the skill for which intervention was currently occurring and a timed probe of previously mastered skills from the sequence of computational skill objectives. Each month, all children completed a timed probe of mathematics skills representing computational skills that students were expected to master by year’s end at each grade level. At all grade levels, learning a skill that appeared early in the hierarchy or sequence of skills related positively to learning of future related and more complex computational skills. Fluency criteria were specified that predicted retention of the skill over several months.     

A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking.

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Truth and Objectivity in Perspectivism

I investigate the consequences of Nietzsche's perspectivism for notions of truth and objectivity, and show how the metaphor of visual perspective motivates an epistemology that avoids self-referential difficulties. Perspectivism's claim that every view is only one view, applied to itself, is often supposed to preclude the perspectivist's ability to offer reasons for her epistemology. Nietzsche's arguments for perspectivism depend on “internal reasons”, which have force not only in their own perspective, but also within the standards of alternative perspectives. Internal reasons allow a perspectivist argument against dogmatism without presupposing aperspectival criteria for theory choice. Nietzsche also offers “internal” conceptions of truth and objectivity which reduce them to a matter of meeting our epistemic standards. This view has pluralistic implications, which conflict with common sense, but it is nevertheless consistent and plausible. Nietzsche's position is similar to Putnam's recent internalism, and this is due to their common Kantian heritage. This revised version was published online in August 2006 with corrections to the Cover Date.     

Academic Achievement Over 8 Years Among Children Who Met Modified Criteria for Attention-deficit/Hyperactivity Disorder at 4–6 Years of Age

The predictive validity of symptom criteria for different subtypes of ADHD among children who were impaired in at least one setting in early childhood was examined. Academic achievement was assessed seven times over 8 years in 125 children who met symptom criteria for ADHD at 4–6 years of age and in 130 demographically-matched non-referred comparison children. When intelligence and other confounds were controlled, children who met modified criteria for the predominantly inattentive subtype of ADHD in wave 1 had lower reading, spelling, and mathematics scores over time than both comparison children and children who met modified criteria for the other subtypes of ADHD. In some analyses, children who met modified criteria for the combined type had somewhat lower mathematics scores than comparison children. The robust academic deficits relative to intelligence in the inattentive group in this age range suggest either that inattention results in academic underachievement or that some children in the inattentive group have learning disabilities that cause secondary symptoms of inattention. Unexpectedly, wave 1 internalizing (anxiety and depression) symptoms independently predicted deficits in academic achievement controlling ADHD, intelligence, and other predictors.     

Epistemological principles for developmental psychology in Frege and Piaget

My main aim is to identify and discuss parallels between the epistemologies of Gottlob Frege and Jean Piaget. Although their work has attracted massive attention individually, parallels in their work have gone unnoticed. My discussion is in four parts and covers psychologism and epistemology; five epistemological criteria in Frege's rational epistemology under an AEIOU mnemonic, namely autonomy, entailment, intersubjectivity, objectivity and universality; the elaboration of these same criteria in Piaget's developmental epistemology; their implications for developmental psychology and epistemology. One main conclusion is that the same criteria fit both Frege's and Piaget's epistemology. A second conclusion is that Piaget's developmental epistemology can be regarded as an elaboration of Frege's rational epistemology in each of these five respects on both methodological and substantive grounds. Both conclusions are compatible with non-psychologism, which was accepted by both Frege and Piaget.     

Drawing the boundary between subject and object: Comments on the mind-brain problem

Physics says that it cannot deal with the mind-brain problem, because it does not deal in subjectivities, and mind is subjective. However, biologists (among others) still claim to seek a material basis for subjective mental processes, which would thereby render them objective. Something is clearly wrong here. I claim that what is wrong is the adoption of too narrow a view of what constitutes ‘objectivity’, especially in identifying it with what a ‘machine’ can do. I approach the problem in the light of two cognate circumstances: (a) the ‘measurement problem’ in quantum physics, and (b) the objectivity of standard mathematics, even though most of it is beyond the reach of ‘machines’. I argue that the only resolution to such problems is in the recognition that closed loops of causation are ‘objective’; i.e. legitimate objects of scientific scrutiny. These are explicitly forbidden in any machine or mechanism. A material system which contains such loops is called ‘complex’. Such complex systems thus must possess nonsimulable models; i.e. models which contain impredicativities or ‘self-references’ which cannot be removed, or faithfully mapped into a single coherent syntactic time-frame. I consider a few of the consequences of the above, in the context of thus redrawing the boundary between subject and object.     

From Aperspectival Objectivity to Strong Objectivity: The Quest for Moral Objectivity

Sandra Harding is working on the reconstruction of scientific objectivity. Lorraine Daston argues that objectivity is a concept that has historically evolved. Her account of the development of “aperspectival objectivity” provides an opportunity to see Harding's “strong objectivity” project as a stage in this evolution, to locate it in the history of migration of ideals from moral philosophy to natural science, and to support Harding's desire to retain something of the ontological significance of objectivity.     

The prevalence of specific learning disorder in mathematics and comorbidity with other developmental disorders in primary school-age children

Mathematics difficulties are common in both children and adults, and they can have a great impact on people's lives. A specific learning disorder in mathematics (SLDM or developmental dyscalculia) is a special case of persistent mathematics difficulties, where the problems with maths cannot be attributed to environmental factors, intellectual disability, or mental, neurological or physical disorders. The aim of the current study was to estimate the prevalence rate of SLDM, any gender differences in SLDM, and the most common comorbid conditions. The DSM-5 provides details regarding these only for specific learning disorders in general, but not specifically for SLDM. We also compared the prevalence rates obtained on the basis of the DSM-IV and DSM-5 criteria. We investigated the performance of 2,421 primary school children on standardized tests of mathematics, English, and IQ, and several demographic factors over the primary school years. We applied the DSM-5 diagnostic criteria to identify children with a potential diagnosis of SLDM. Six per cent of our sample had persistent, severe difficulties with mathematics, and, after applying the exclusion criteria, 5.7% were identified as having an SLDM profile. Both persistent maths difficulties and consistently exceptionally high performance in maths were equally common in males and females. About half of the children with an SLDM profile had some form of language or communication difficulty. Some of these children also had a diagnosis of autism, social, emotional, and behavioural difficulties or attention deficit and hyperactivity disorder. Our findings have important implications for research and intervention purposes, which we discuss in the study.     

Imposters,Tricksters, and Trustworthiness as an Epistemic Virtue

This paper argues that trustworthiness is an epistemic virtue that promotes objectivity. I show that untrustworthy imposture can be an arrogant act of privilege that silences marginalized voices. But, as epistemologists of ignorance have shown, sometimes trickery and the betrayal of epistemic norms are important resistance strategies. This raises the question: when is betrayal of trust epistemically virtuous? After establishing that trust is central to objectivity, I argue for the following answer: a betrayal is epistemically vicious when it strengthens or promotes oppressive, exclusive networks of trust, and a betrayal is epistemically virtuous when it expands trust networks to involve the oppressed. These criteria correctly account for both the epistemic vice of a recent case of Internet imposture and the epistemic virtue of resistant tricksters.     

From Gegenstand to Gegenstehenlassen: On the Meanings of Objectivity in Heidegger and Hegel

ABSTRACT

One of Heidegger’s enduring concerns was to develop an original meditation on the meaning of (the presence of) the present. Integral to this attempt is his critique of the understanding of the being of beings in terms of the objectivity of the object. In this paper, I trace Heidegger’s analyses of objectivity, through which Heidegger consistently establishes objectivity as non-primordial and derivative. In order to do this, however, Heidegger had to identify a specific, narrow (spatio-temporalized) conception of objectivity (in terms of Gegenstehenlassen and Vorstellen) as the hallmark of modern philosophy. I show that it is unclear whether that conception is a justified result or rather an unjustified presupposition of his approach. I then suggest what meanings of objectivity might be lost after Heidegger, by pointing to several aspects of Hegel’s notion of objectivity that are incompatible with Heidegger’s account, to wit: the lack of ‘subject-object’-terminology in his definitions of objectivity; the special language of ‘forms of’ objectivity; Hegel’s critique of representation; his notion of Gegenstand as a content with a categorical form, and, finally, that Aristotle’s notion of hypokeimenon might provide a clue as to how Hegel’s notion of object can be understood.     

Teaching Mathematics for Spatial Justice: An Investigation of the Lottery

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. Local Lotto, a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This article describes findings from the second iteration in a remedial class in a low-income neighborhood. The research questions consider how the spatial focus supported the learning of mathematics and provided opportunities for students to think critically about the lottery using that mathematics. Findings include student interest in and engagement with the theme of the lottery familiar from outside of school with associated social justice implications. Students used mathematics and spatial evidence, at various levels of spatial scale, to support arguments about the lottery with greater success at narrower levels of scale. Suggestions about further innovations to scaffold place in a “critical pedagogy of place” in mathematics are provided.     

Mathematical forms and forms of mathematics: leaving the shores of extensional mathematics

In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according to some speculative research programs.