Between Kantianism and Empiricism: Otto Hölder’s Philosophy of Geometry

La philosophie de la géométrie de Hölder, si l’on s’en tient à une lecture superficielle, est la part la plus problématique de son épistémologie. Il soutient que la géométrie est fondée sur l’expérience à la manière de Helmholtz, malgré les objections sérieuses de Poincaré. Néanmoins, je pense que la position de Hölder mérite d’être discutée pour deux motifs. Premièrement, ses implications méthodologiques furent importantes pour le développement de son épistémologie. Deuxièmement, Poincaré utilise l’opposition entre le kantisme et l’empirisme comme un argument pour justifier son conventionnalisme géométrique. Cependant, Hölder montre qu’une stratégie alternative n’est pas exclue: il sait tirer parti des objections kantiennes pour développer un empirisme cohérent. En même temps, surtout dans Die mathematische Methode [Holder 1924], il adopte aussi bien les expressions que les conceptions de Kant. Dans mon article, je considère d’abord les arguments de Hölder pour la méthode déductive en géométrie dans Anschauung und Denken in der Geometrie [Holder 1900], en relation avec sa façon d’aborder la théorie de la quantité [Holder 1901]. Ensuite, j’examine son rapport avec Kant. À mon sens, les considérations méthodologiques de Hölder lui permettent de préfigurer une relativisation de l’a priori.Hölder’s philosophy of geometry might appear to be the most problematic part of his epistemology. He maintains that geometry depends on experience also after Poincaré’s fundamental criticism of Helmholtz. Nevertheless, I think that Hölder’s view is worth discussing, for two reasons. Firstly, the related methodological considerations were crucial for the development of his epistemology. Secondly, Poincaré uses the opposition between Kantianism and empiricism to argue for his geometrical conventionalism. Nevertheless, Hölder shows that an alternative strategy is not excluded: he profits from Kantian objections in order to develop a consistent empiricism. At the same time, especially in Die mathematische Methode [Holder 1924], he vindicates the Kantian view that mathematics is synthetic. In this paper, I will consider Hölder’s defence of the deductive method in geometry in Anschauung und Denken in der Geometrie [Holder 1900] in connection with his approach to the theory of quantity [Holder 1901]. Moreover, I will discuss his connection with Kant. My suggestion is that Hölder’s methodological considerations enable him to foreshadow a relativized conception of the a priori

Articulating Space in Terms of Transformation Groups: Helmholtz and Cassirer

Hermann von Helmholtz’s geometrical papers (1868–1878) have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences

Latanoprost and Dorzolamide for the Treatment of Pediatric Glaucoma: The Glaucoma Italian Pediatric Study (Gipsy), Design and Baseline Characteristics

INTRODUCTION: To investigate the efficacy of a treatment strategy with latanoprost and dorzolamide in primary pediatric glaucoma patients partially responsive to surgery. METHODS: Single arm, prospective, interventional multicenter study. Primary pediatric glaucoma patients younger than 13 years after a single surgical procedure with IOP between 22 and 26 mmHg were considered eligible. At baseline, patients were allocated to latanoprost monotherapy once daily. Depending on intraocular pressure (IOP) reduction at first visit, the patients were allocated to one of three groups: continuation of latanoprost monotherapy, addition of dorzolamide twice daily, or switch to dorzolamide three times daily. The same approach for allocation in medication groups was used in all subsequent visits. Patients in the dorzolamide monotherapy group with IOP reduction <20% from baseline were considered non-responders and withdrawn. Study treatment and patient follow-up will continue for 3 years or until treatment failure. The primary endpoint is the percentage of responders. Secondary endpoints are time to treatment failure and frequency of adverse events. RESULTS: A total of 37 patients (69 eyes) were enrolled. The mean age was 4.0 ± 3.8 years, the female/male ratio was 1/1.7, and the majority of patients were Caucasian. Eighty percent of patients had bilateral glaucoma. Goniotomy was the most frequently performed surgery (38.6%), followed by trabeculotomy (22.8%), trabeculectomy (21.1%), and trabeculectomy plus trabeculotomy (17.5%). The baseline IOP was 23.6 ± 1.5 mmHg. CONCLUSION: The study population is representative of patients frequently encountered after the first surgery for primary pediatric glaucoma. The study will produce evidence on the medium-term efficacy of a defined pharmacological approach

Self-care in children and young people with complex chronic conditions: a qualitative study using Emotional Text Mining

Objectives: To explore: (1) self-care behaviors in children and young people (range: 6 months-24 years) with complex chronic conditions, characterized by the diagnosis of a severe chronic condition, substantial family-identified needs, functional limitations associated with technology dependence, and intensive use of healthcare services; (2) the contribution to self-care of family members and other persons involved in the child's health and daily life context (e.g., health professionals and teachers), and (3) the principal factors that might have influenced the self-care process associated with developmental age. Methods: A qualitative descriptive study was conducted in an Italian academic tertiary pediatric hospital between September 2020 and May 2021. Overall, 25 focus groups and 7 online interviews were conducted via videoconferencing. Textual data were analyzed using Emotional Text Mining to identify three levels of communication: the factors, the main themes (clusters), and the sub-themes. Results: A total of 104 participants were enrolled, including 27 patients with complex chronic conditions (12 males, mean age = 11.1 ± 4.40), 33 parents, 6 siblings, 33 health professionals, and 5 teachers. Participants described the process of self-care through four main factors: "self-care", "external settings", "family", and "management". Five clusters (themes) were identified: (1) Self-care management (device; consulting); (2) Shift of agency (influencing factors; parents; school); (3) Self-care support (normal life and personal development; multidisciplinary support); (4) Daily self-care maintenance/monitoring; (5) Treatment adherence. Self-care management was mostly relevant for parents of children aged between 6 months and 3 years. Conclusion: The self-care process varies according to the needs related to the specific developmental age and the evolution of the clinical condition over time. The contribution of the family, health professionals, and social networks is fundamental for adequate self-care. To help families manage the unstable condition of their children at home, it is necessary to strengthen support networks implement home care, and ensure continuity of care

CHD8 suppression impacts on histone H3 lysine 36 trimethylation and alters RNA alternative splicing

Disruptive mutations in the chromodomain helicase DNA-binding protein 8 gene (CHD8) have been recurrently associated with autism spectrum disorders (ASDs). Here we investigated how chromatin reacts to CHD8 suppression by analyzing a panel of histone modifications in induced pluripotent stem cell-derived neural progenitors. CHD8 suppression led to significant reduction (47.82%) in histone H3K36me3 peaks at gene bodies, particularly impacting on transcriptional elongation chromatin states. H3K36me3 reduction specifically affects highly expressed, CHD8-bound genes and correlates with altered alternative splicing patterns of 462 genes implicated in ‘regulation of RNA splicing’ and ‘mRNA catabolic process’. Mass spectrometry analysis uncovered a novel interaction between CHD8 and the splicing regulator heterogeneous nuclear ribonucleoprotein L (hnRNPL), providing the first mechanistic insights to explain the CHD8 suppression-derived splicing phenotype, partly implicating SETD2, a H3K36me3 methyltransferase. In summary, our results point toward broad molecular consequences of CHD8 suppression, entailing altered histone deposition/maintenance and RNA processing regulation as important regulatory processes in ASD

SINEUPs are modular antisense long non-coding RNAs that increase synthesis of target proteins in cells

Despite recent efforts in discovering novel long non-coding RNAs (lncRNAs) and unveiling their functions in a wide range of biological processes their applications as biotechnological or therapeutic tools are still at their infancy. We have recently shown that AS Uchl1, a natural lncRNA antisense to the Parkinson's disease-associated gene Ubiquitin carboxyl-terminal esterase L1 (Uchl1), is able to increase UchL1 protein synthesis at post-transcriptional level. Its activity requires two RNA elements: an embedded inverted SINEB2 sequence to increase translation and the overlapping region to target its sense mRNA. This functional organization is shared with several mouse lncRNAs antisense to protein coding genes. The potential use of AS Uchl1-derived lncRNAs as enhancers of target mRNA translation remains unexplored. Here we define AS Uchl1 as the representative member of a new functional class of natural and synthetic antisense lncRNAs that activate translation. We named this class of RNAs SINEUPs for their requirement of the inverted SINEB2 sequence to UP-regulate translation in a gene-specific manner. The overlapping region is indicated as the Binding Doman (BD) while the embedded inverted SINEB2 element is the Effector Domain (ED). By swapping BD, synthetic SINEUPs are designed targeting mRNAs of interest. SINEUPs function in an array of cell lines and can be efficiently directed toward N-terminally tagged proteins. Their biological activity is retained in a miniaturized version within the range of small RNAs length. Its modular structure was exploited to successfully design synthetic SINEUPs targeting endogenous Parkinson's disease-associated DJ-1 and proved to be active in different neuronal cell lines. In summary, SINEUPs represent the first scalable tool to increase synthesis of proteins of interest. We propose SINEUPs as reagents for molecular biology experiments, in protein manufacturing as well as in therapy of haploinsufficiencies