HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied (i.e. theories of formalization). Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments (i.e. the second sub-project). In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize.

Pró-vitaminas A em hortaliças comercializadas no mercado formal e informal de Viçosa (MG), em três estações do ano

Para fornecer dados sobre a influência climática e a forma de comercialização sobre carotenóides de vegetais, este estudo pesquisou o conteúdo de alfa e beta-caroteno e o valor de vitamina A de sete hortaliças (batata-doce, cenoura, moranga, pimentão, quiabo, tomate e vagem), na cidade de Viçosa (MG), utilizando a Cromatografia Líquida de Alta Eficiência. Compararam-se hortaliças comercializadas nos mercados formal (mercados locais) e informal (feira livre) durante primavera, verão e outono. A cenoura apresentou os teores mais elevados de alfa e beta-caroteno (31,17 e 58,18 µg/g, respectivamente), seguida pela moranga (4,33 e 23,16 µg/g, respectivamente), enquanto a batata-doce apresentou o teor mais reduzido de beta-caroteno (0,51 µg/g). O valor de vitamina A variou conforme o perfil de alfa e beta-caroteno. Com exceção da cenoura e do quiabo, não houve influência significativa do local de comercialização sobre o conteúdo de carotenóides. A variação do conteúdo de carotenos nas estações do ano foi inexpressiva, sendo que apenas o pimentão apresentou valores significativamente diferentes. Porções de 100 g das hortaliças analisadas fornecem entre 3 e 78% da recomendação de vitamina A.

The demands of family caregivers of elderly individuals with dementia

The purpose of this cross-sectional observational study was to identify characteristics of caregivers of elderly people with dementia, types of care demands and to relate demands to the stage of dementia. The study was carried out in 2004 with 104 older adults and 90 caregivers in Ribeirão Preto, state of São Paulo. The OARS instrument was utilized and a questionnaire answered by caregivers. Among older adults, 66.3% were female, aged 75.5 years in average and 86.5% had caregivers. Eighty percent of the caregivers were women family members, aged 52.3 years in average. They spent 15.10 hours/day with care, without help. An important relationship was observed between caregiver's burden, physical and emotional effort and stage of dementia. Emotional overburden was higher at dementia early and late stages, this difference was statistically non-significant. Results reveal the urgent need to plan formal and informal support strategies to caregivers of Brazilian elderly people with dementia.

Informalidade no mercado de trabalho brasileiro: uma resenha da literatura

The economic literature relative to Brazilian labor market informality is very disperse and presents a significant lack of organization. In that sense, the purpose of this paper is to organize and discuss on a systematic way the main pieces of literature concerning informality in the Brazilian labor market using, whenever it is possible, the international literature as a comparison point for the existing results relative to Brazil's experience. More specifically, questions related to wage differentials between formal and informal workers, labor market segmentation and the effect of institutions on the informal sector are emphasized.

Non-formal education for schistosomiasis prevention: the experience of the Museu Arqueológico de Central, Bahia, Brazil

The activities described here form part of an extensive programme in place in the Região Arqueológica de Central, state of Bahia, Brazil. After malacological and socio-environmental surveys in the area, a strategy comprising formal and non-formal education with an emphasis on schistosomiasis prevention was developed, introduced, and evaluated. Interviews were conducted of 142 students and 11 teachers, totalling 11 classes at six primary schools. On the basis of those interviews, four display cases and seven panels were prepared. In addition a table was set up where students could participate directly on the subject, drawing and recognising the factors involved in the schistosomiasis cycle. The exhibition was held at the Museu Arqueológico de Central. The endeavours of this paper underline the importance of health education as well as exhibitions to disease prevention activities.

Evaluation of a linear spectral mixture model and vegetation indices (NDVI and EVI) in a study of schistosomiasis mansoni and Biomphalaria glabrata distribution in the state of Minas Gerais, Brazil

This paper analyses the associations between Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) on the prevalence of schistosomiasis and the presence of Biomphalaria glabrata in the state of Minas Gerais (MG), Brazil. Additionally, vegetation, soil and shade fraction images were created using a Linear Spectral Mixture Model (LSMM) from the blue, red and infrared channels of the Moderate Resolution Imaging Spectroradiometer spaceborne sensor and the relationship between these images and the prevalence of schistosomiasis and the presence of B. glabrata was analysed. First, we found a high correlation between the vegetation fraction image and EVI and second, a high correlation between soil fraction image and NDVI. The results also indicate that there was a positive correlation between prevalence and the vegetation fraction image (July 2002), a negative correlation between prevalence and the soil fraction image (July 2002) and a positive correlation between B. glabrata and the shade fraction image (July 2002). This paper demonstrates that the LSMM variables can be used as a substitute for the standard vegetation indices (EVI and NDVI) to determine and delimit risk areas for B. glabrata and schistosomiasis in MG, which can be used to improve the allocation of resources for disease control.

Burden in family caregivers of the elderly: prevalence and association with characteristics of the elderly and the caregivers

A cross-sectional, epidemiological study aimed to estimate the prevalence of burden among family caregivers of impaired elderly residents in the city of João Pessoa, and to identify associations between the mean burden and social and demographic characteristics of the elderly and the caregivers. A total number of 240 elderly residents in a previously drawn census tract participated in this research. The sample was composed of 52 elderly and their caregivers. For data collection, a questionnaire was applied with questions on social and demographic characteristics of elderly and caregivers, and the Burden Interview Scale was used. Results showed a high prevalence of burden among caregivers (84.6%), in which a statistically significant association was found with the following characteristics: retired elderly, elderly as head of family, spousal caregivers, and caregivers with less education. The findings of this study may contribute to the development of activities focused on formal and emotional support for the caregivers.

Trabalho informal, gênero e raça no Brasil do início do século XXI

O artigo analisa a evolução do trabalho informal no Brasil, de 2001 a 2009, com base nas Pesquisas Nacionais por Amostra de Domicílio. Questões como "onde estão" os informais, "quem são", "quanto ganham" orientaram o estudo, tendo, além da comparação entre setor formal e informal, o gênero como foco. A heterogeneidade, marca do setor informal, é visível nos diversos setores econômicos, nas diferentes posições na ocupação, nas desiguais oportunidades de mulheres e negros em relação a homens e brancos. Apesar de o trabalho informal ter diminuído no Brasil durante a década, o pequeno crescimento registrado deveu-se ao ingresso das mulheres e, particularmente, das negras.

Connexin domains relevant to the chemical gating of gap junction channels

Most cells exchange ions and small metabolites via gap junction channels. These channels are made of two hemichannels (connexons), each formed by the radial arrangement of six connexin (Cx) proteins. Connexins span the bilayer four times (M1-M4) and have both amino- and carboxy-termini (NT, CT) at the cytoplasmic side of the membrane, forming two extracellular loops (E1, E2) and one inner (IL) loop. The channels are regulated by gates that close with cytosolic acidification (e.g., CO2 treatment) or increased calcium concentration, possibly via calmodulin activation. Although gap junction regulation is still unclear, connexin domains involved in gating are being defined. We have recently focused on the CO2 gating sensitivity of Cx32, Cx38 and various mutants and chimeras expressed in Xenopus oocytes and studied by double voltage clamp. Cx32 is weakly sensitive to CO2, whereas Cx38 is highly sensitive. A Cx32 chimera containing the second half of the inner loop (IL2) of Cx38 was as sensitive to CO2 as Cx38, indicating that this domain plays an important role. Deletion of CT by 84% did not affect CO2 sensitivity, but replacement of 5 arginines (R) with sparagines (N) at the beginning of CT (C1) greatly enhanced the CO2 sensitivity of Cx32. This suggests that whereas most of CT is irrelevant, positive charges of C1 maintain the CO2 sensitivity of Cx32 low. As a hypothesis we have proposed a model that involves charge interaction between negative residues of the beginning of IL1 and positive residues of either C1 or IL2. Open and closed channels would result from IL1-C1 and IL1-IL2 interactions, respectively

Binding sites and actions of Tx1, a neurotoxin from the venom of the spider Phoneutria nigriventer, in guinea pig ileum

Tx1, a neurotoxin isolated from the venom of the South American spider Phoneutria nigriventer, produces tail elevation, behavioral excitation and spastic paralysis of the hind limbs after intracerebroventricular injection in mice. Since Tx1 contracts isolated guinea pig ileum, we have investigated the effect of this toxin on acetylcholine release, as well as its binding to myenteric plexus-longitudinal muscle membranes from the guinea pig ileum. [125I]-Tx1 binds specifically and with high affinity (Kd = 0.36 ± 0.02 nM) to a single, non-interacting (nH = 1.1), low capacity (Bmax 1.1 pmol/mg protein) binding site. In competition experiments using several compounds (including ion channel ligands), only PhTx2 and PhTx3 competed with [125I]-Tx1 for specific binding sites (K0.5 apparent = 7.50 x 10-4 g/l and 1.85 x 10-5 g/l, respectively). PhTx2 and PhTx3, fractions from P. nigriventer venom, contain toxins acting on sodium and calcium channels, respectively. However, the neurotoxin PhTx2-6, one of the isoforms found in the PhTx2 pool, did not affect [125I]-Tx1 binding. Tx1 reduced the [3H]-ACh release evoked by the PhTx2 pool by 33%, but did not affect basal or KCl-induced [3H]-ACh release. Based on these results, as well as on the homology of Tx1 with toxins acting on calcium channels (w-Aga IA and IB) and its competition with [125I]-w-Cono GVIA in the central nervous system, we suggest that the target site for Tx1 may be calcium channels.

Reactive oxygen species and angiotensin II signaling in vascular cells: implications in cardiovascular disease

Diseases such as hypertension, atherosclerosis, hyperlipidemia, and diabetes are associated with vascular functional and structural changes including endothelial dysfunction, altered contractility and vascular remodeling. Cellular events underlying these processes involve changes in vascular smooth muscle cell (VSMC) growth, apoptosis/anoikis, cell migration, inflammation, and fibrosis. Many factors influence cellular changes, of which angiotensin II (Ang II) appears to be amongst the most important. The physiological and pathophysiological actions of Ang II are mediated primarily via the Ang II type 1 receptor. Growing evidence indicates that Ang II induces its pleiotropic vascular effects through NADPH-driven generation of reactive oxygen species (ROS). ROS function as important intracellular and intercellular second messengers to modulate many downstream signaling molecules, such as protein tyrosine phosphatases, protein tyrosine kinases, transcription factors, mitogen-activated protein kinases, and ion channels. Induction of these signaling cascades leads to VSMC growth and migration, regulation of endothelial function, expression of pro-inflammatory mediators, and modification of extracellular matrix. In addition, ROS increase intracellular free Ca2+ concentration ([Ca2+]i), a major determinant of vascular reactivity. ROS influence signaling molecules by altering the intracellular redox state and by oxidative modification of proteins. In physiological conditions, these events play an important role in maintaining vascular function and integrity. Under pathological conditions ROS contribute to vascular dysfunction and remodeling through oxidative damage. The present review focuses on the biology of ROS in Ang II signaling in vascular cells and discusses how oxidative stress contributes to vascular damage in cardiovascular disease.

Cl- and regulation of pH by MDCK-C11 cells

The interaction between H+ extrusion via H+-ATPase and Cl- conductance was studied in the C11 clone of MDCK cells, akin to the intercalated cells of the collecting duct. Cell pH (pHi) was measured by fluorescence microscopy using the fluorescein-derived probe BCECF-AM. Control recovery rate measured after a 20 mM NH4Cl acid pulse was 0.136 ± 0.008 pH units/min (dpHi/dt) in Na+ Ringer and 0.032 ± 0.003 in the absence of Na+ (0 Na+). With 0 Na+ plus the Cl- channel inhibitor NPPB (10 µM), recovery was reduced to 0.014 ± 0.001 dpHi/dt. 8-Br-cAMP, known to activate CFTR Cl- channels, increased dpHi/dt in 0 Na+ to 0.061 ± 0.009 and also in the presence of 46 nM concanamycin and 50 µM Schering 28080. Since it is thought that the Cl- dependence of H+-ATPase might be due to its electrogenic nature and the establishment of a +PD (potential difference) across the cell membrane, the effect of 10 µM valinomycin at high (100 mM) K+ was tested in our cells. In Na+ Ringer, dpHi/dt was increased, but no effect was detected in 0 Na+ Ringer in the presence of NPPB, indicating that in intact C11 cells the effect of blocking Cl- channels on dpHi/dt was not due to an adverse electrical gradient. The effect of 100 µM ATP was studied in 0 Na+ Ringer solution; this treatment caused a significant inhibition of dpHi/dt, reversed by 50 µM Bapta. We have shown that H+-ATPase present in MDCK C11 cells depends on Cl- ions and their channels, being regulated by cAMP and ATP, but not by the electrical gradient established by electrogenic H+ transport.

Expression of E-cadherin, Snail and Hakai in epithelial cells isolated from the primary tumor and from peritumoral tissue of invasive ductal breast carcinomas

Epithelial intercellular cohesion, mainly mediated by E-cadherin (CDH1) expression and function, may be deregulated during cancer cell invasion of adjacent tissues and lymphatic and vascular channels. CDH1 expression is down-modulated in invasive lobular breast carcinomas but its regulation in invasive ductal carcinomas (IDC) is less clear. CDH1 expression is repressed by transcription factors such as Snail (SNAI1) and its product is degraded after Hakai ubiquitination. We compared CDH1, SNAI1 and HAKAI mRNA expression in IDC and paired adjacent normal breast tissue and evaluated its relation with node metastasis and circulating tumor cells. Matched tumor/peritumoral and blood samples were collected from 30 patients with early IDC. Epithelial cells from each compartment (tumor/peritumoral) were recovered by an immunomagnetic method and gene expression was determined by real time RT-PCR. There were no differences in CDH1, SNAI1 and HAKAI mRNA expression between tumor and corresponding peritumoral samples and no differential tumoral gene expression according to nodal involvement. Another 30 patients with a long-term follow-up (at least 5 years) and a differential prognosis (good or poor, as defined by breast cancer death) had E-cadherin and Snail protein detected by immunohistochemistry in tumor samples. In this group, E-cadherin-positive expression, but not Snail, may be associated with a better prognosis. This is the first report simultaneously analyzing CDH1, SNAI1 and HAKAI mRNA expression in matched tumor and peritumoral samples from patients with IDC. However, no clear pattern of their expression could distinguish the invasive tumor compartment from its adjacent normal tissue.

The methyl ester of rosuvastatin elicited an endothelium-independent and 3-hydroxy-3-methylglutaryl coenzyme A reductase-independent relaxant effect in rat aorta

The relaxant effect of the methyl ester of rosuvastatin was evaluated on aortic rings from male Wistar rats (250-300 g, 6 rats for each experimental group) with and without endothelium precontracted with 1.0 µM phenylephrine. The methyl ester presented a slightly greater potency than rosuvastatin in relaxing aortic rings, with log IC50 values of -6.88 and -6.07 M, respectively. Unlike rosuvastatin, the effect of its methyl ester was endothelium-independent. Pretreatment with 10 µM indomethacin did not inhibit, and pretreatment with 1 mM mevalonate only modestly inhibited the relaxant effect of the methyl ester. Nω-nitro-L-arginine methyl ester (L-NAME, 10 µM), the selective nitric oxide-2 (NO-2) inhibitor 1400 W (10 µM), tetraethylammonium (TEA, 10 mM), and cycloheximide (10 µM) partially inhibited the relaxant effect of the methyl ester on endothelium-denuded aortic rings. However, the combination of TEA plus either L-NAME or cycloheximide completely inhibited the relaxant effect. Inducible NO synthase (NOS-2) was only present in endothelium-denuded aortic rings, as demonstrated by immunoblot with methyl ester-treated rings. In conclusion, whereas rosuvastatin was associated with a relaxant effect dependent on endothelium and hydroxymethylglutaryl coenzyme A reductase in rat aorta, the methyl ester of rosuvastatin exhibited an endothelium-independent and only slightly hydroxymethylglutaryl coenzyme A reductase-dependent relaxant effect. Both NO produced by NOS-2 and K+ channels are involved in the relaxant effect of the methyl ester of rosuvastatin.