The Applicability of Mathematics as a Philosophical Problem: Mathematization as Exploration

This paper discerns two types of mathematization, a foundational and an explorative one. The foundational perspective is well-established, but we argue that the explorative type is essential when approaching the problem of applicability and how it influences our conception of mathematics. The first part of the paper argues that a philosophical transformation made explorative mathematization possible. This transformation took place in early modernity when sense acquired partial independence from reference. The second part of the paper discusses a series of examples from the history of mathematics that highlight the complementary nature of the foundational and exploratory types of mathematization.     

Kant on anatomy and the status of the life sciences

This paper contributes to recent interest in Kant's engagement with the life sciences by focusing on one corner of those sciences that has received comparatively little attention: physical and comparative anatomy. By attending to remarks spread across Kant's writings, we gain some insight into Kant's understanding of the disciplinary limitations but also the methodological sophistication of the study of anatomy and physiology. Insofar as Kant highlights anatomy as a paradigmatic science guided by the principle of teleology in the Critique of the Power of Judgment, a more careful study of Kant's discussions of anatomy promises to illuminate some of the obscurities of that text and of his understanding of the life sciences more generally. In the end, it is argued, Kant's ambivalence with regard to anatomy gives way to a pessimistic conclusion about the possibility that anatomy, natural history, and, by extension, the life sciences more generally might one day become true natural sciences.     

Taming theory with thought experiments: Understanding and scientific progress

I claim that one way thought experiments contribute to scientific progress is by increasing scientific understanding. Understanding does not have a currently accepted characterization in the philosophical literature, but I argue that we already have ways to test for it. For instance, current pedagogical practice often requires that students demonstrate being in either or both of the following two states: 1) Having grasped the meaning of some relevant theory, concept, law or model, 2) Being able to apply that theory, concept, law or model fruitfully to new instances. Three thought experiments are presented which have been important historically in helping us pass these tests, and two others that cause us to fail. Then I use this operationalization of understanding to clarify the relationships between scientific thought experiments, the understanding they produce, and the progress they enable. I conclude that while no specific instance of understanding (thus conceived) is necessary for scientific progress, understanding in general is.     

The PHYTOCHROME C photoreceptor gene mediates natural variation in flowering and growth responses of Arabidopsis thaliana

Light has an important role in modulating seedling growth and flowering time. We show that allelic variation at the PHYTOCHROME C (PHYC) photoreceptor locus affects both traits in natural populations of A. thaliana. Two functionally distinct PHYC haplotype groups are distributed in a latitudinal cline dependent on FRIGIDA, a locus that together with FLOWERING LOCUS C explains a large portion of the variation in A. thaliana flowering time. In a genome-wide scan for association of 65 loci with latitude, there was an excess of significant P values, indicative of population structure. Nevertheless, PHYC was the most strongly associated locus across 163 strains, suggesting that PHYC alleles are under diversifying selection in A. thaliana. Our work, together with previous findings, suggests that photoreceptor genes are major agents of natural variation in plant flowering and growth response.     

Mutations in embryonic myosin heavy chain (MYH3) cause Freeman-Sheldon syndrome and Sheldon-Hall syndrome

The genetic basis of most conditions characterized by congenital contractures is largely unknown. Here we show that mutations in the embryonic myosin heavy chain (MYH3) gene cause Freeman-Sheldon syndrome (FSS), one of the most severe multiple congenital contracture (that is, arthrogryposis) syndromes, and nearly one-third of all cases of Sheldon-Hall syndrome (SHS), the most common distal arthrogryposis. FSS and SHS mutations affect different myosin residues, demonstrating that MYH3 genotype is predictive of phenotype. A structure-function analysis shows that nearly all of the MYH3 mutations are predicted to interfere with myosin's catalytic activity. These results add to the growing body of evidence showing that congenital contractures are a shared outcome of prenatal defects in myofiber force production. Elucidation of the genetic basis of these syndromes redefines congenital contractures as unique defects of the sarcomere and provides insights about what has heretofore been a poorly understood group of disorders.     

Irf6 is a key determinant of the keratinocyte proliferation-differentiation switch

The epidermis is a highly organized structure, the integrity of which is central to the protection of an organism. Development and subsequent maintenance of this tissue depends critically on the intricate balance between proliferation and differentiation of a resident stem cell population; however, the signals controlling the proliferation-differentiation switch in vivo remain elusive. Here, we show that mice carrying a homozygous missense mutation in interferon regulatory factor 6 (Irf6), the homolog of the gene mutated in the human congenital disorders Van der Woude syndrome and popliteal pterygium syndrome, have a hyperproliferative epidermis that fails to undergo terminal differentiation, resulting in soft tissue fusions. We further demonstrate that mice that are compound heterozygotes for mutations in Irf6 and the gene encoding the cell cycle regulator protein stratifin (Sfn; also known as 14-3-3sigma) show similar defects of keratinizing epithelia. Our results indicate that Irf6 is a key determinant of the keratinocyte proliferation-differentiation switch and that Irf6 and Sfn interact genetically in this process.     

Truncating mutations in the Fanconi anemia J gene BRIP1 are low-penetrance breast cancer susceptibility alleles

We identified constitutional truncating mutations of the BRCA1-interacting helicase BRIP1 in 9/1,212 individuals with breast cancer from BRCA1/BRCA2 mutation-negative families but in only 2/2,081 controls (P = 0.0030), and we estimate that BRIP1 mutations confer a relative risk of breast cancer of 2.0 (95% confidence interval = 1.2-3.2, P = 0.012). Biallelic BRIP1 mutations were recently shown to cause Fanconi anemia complementation group J. Thus, inactivating truncating mutations of BRIP1, similar to those in BRCA2, cause Fanconi anemia in biallelic carriers and confer susceptibility to breast cancer in monoallelic carriers.