Direct products and the contravariant hom-functor

We prove in ZFC that if $G$ is a (right) $R$-module such that the groups \Hom_R(\prod_{i\in I}G_i,G) and \prod_{i\in I}\Hom_R(G_i,G) are naturally isomorphic for all families of $R$-modules $(G_i)_{i\in I}$ then G=0. The result is valid even we restrict to families such that $G_i\cong G$ for all $i\in I$

Assertion: Just One Way to Take It Back

According to Jonathan Kvanvig, the practice of taking back one’s assertion when finding out that one has been mistaken or gettiered fails to speak in favour of a knowledge norm of assertion. To support this claim, he introduces a distinction between taking back the content of the assertion, and taking back the speech act itself. This paper argues that Kvanvig’s distinction does not successfully face close speech-act-theoretic scrutiny. Furthermore, I offer an alternative diagnosis of the target cases sourced in the normativity of action

Semisimplicity and rigidity of the Kontsevich-Zorich cocycle

We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant subbundles must vary polynomially on affine manifolds. All results apply to tensor powers of the cocycle and this implies that the measurable and real-analytic algebraic hulls coincide. We also prove that affine manifolds parametrize Jacobians with non-trivial endomorphisms. Typically a factor has real multiplication. The tools involve curvature properties of the Hodge bundles and estimates from random walks. In the appendix, we explain how methods from ergodic theory imply some of the global consequences of Schmid's work on variations of Hodge structures. We also derive the Kontsevich-Forni formula using differential geometry.Comment: Two appendices, 42 page

Epistemic trouble for engineering ‘woman'

This paper puts forth a functionalist difficulty for Sally Haslanger's proposal for engineering our concept of 'woman.' It is argued that the project of bringing about better political function fulfillment cannot get off the ground in virtue of epistemic failure

The impact of financial informations over per index

Company performances evaluation rated on capital market starts from the assumption that the company value is decisive determined by its financial variables and its growth potential, business risk, profitability, financial liquidity and flexibility as well as its capability to finance on its own its development projects. In the present study we wish to demonstrate the way of using the informations to take a decision for investing in stocks of the listed companies, considering the ratio between current price of one stock rated at the stock-market and the net benefit per stock (PER), as well as the way that this ratio is influenced by the company financial indexes, underlining some.performance, PER ratio, levier effect, profitability