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.

Primary multidrug-resistant tuberculosis and its control implications in the State of Amazonas, Brazil: report of 3 cases

The occurrence of tuberculosis with first-line multidrug resistance leads to the use of alternative medications, often at higher costs, longer treatment periods, and greater clinical complexity. Here, we report 3 patients with multidrug-resistant tuberculosis. One patient with human immunodeficiency virus died before the sensitivity test was performed. The early diagnosis of multidrug-resistant tuberculosis and appropriate treatment should be priorities of the National Tuberculosis Control Program in order to break the chain of transmission. In addition, the possibility of substituting the proportion method with more modern and faster techniques should be urgently evaluated.

Invading freshwater snails and biological control in Martinique Island, French West Indies

Eight alien freshwater snail species were introduced into Martinique Island during the last 50 years. The introduced snails include four planorbids (Biomphalaria straminea, Helisoma duryi, Amerianna carinata and Gyraulus sp.), three thiarids (Melanoides tuberculata, M. amabilis and Tarebia granifera) and one ampullarid (Marisa cornuarietis). Four of these species rapidly colonized the whole Martinican hydrographic system whereas the other four remained restricted to some particular sites. The invasion processes were documented during the last 20 years and showed (i) a rapid invasion of the island by several morphs of M. tuberculata at the beginning of the 80's; (ii) the introduction of T. granifera in 1991 and M. amabilis in 1997; and (iii) the rapid spread of these last two species throughout the island. In the years following its introduction, M. tuberculata was used in biological control experiments against the snail hosts of schistosomiasis, B. glabrata and B. straminea. Experiments were conducted with success in several groups of water-cress beds which constituted the latest transmission sites for schistosomiasis at the beginning of the 80's. A malacological survey carried out in 2000 all over the island showed the absence of B. glabrata but the presence of some residual populations of B. straminea. Long-term studies carried out in Martinique have shown that the thiarids are able to maintain relatively stable populations over a long period of time, thus preventing recolonization by the snail hosts. Within this context the invasion of the hydrographic system of Martinique by thiarid snails has resulted in an efficient and sustainable control of the intermediate hosts of schistosomiasis.

Apparent competition through facilitation between Melanoides tuberculata and Biomphalaria glabrata and the control of schistosomiasis

Interactions between two species that result in reduced growth rates for both and extinction of one of the species are generally considered cases of asymmetric interspecific competition. Exploitative or interference competition is the usual mechanism invoked. Here we describe another mechanism producing the same result, named apparent competition through facilitation (ACF), observed between Melanoides tuberculata and Biomphalaria glabrata populations. The superior competitor actually gives some benefit to the other species, whose population becomes unstable with progressively increasing oscillations, leading to extinction. A model of ACF using difference equations suggests initial dynamics distinct from traditional interspecific competition. The dynamics of two freshwater snails in the field and in laboratory experiments suggest ACF, and these relations should be considered in studies of schistosomiasis control. ACF could occur in natural populations, but might have gone undetected because the final result is similar to traditional interspecific competition.

Coadaptation and malaria control

Malaria emerges from a disequilibrium of the system 'human-plasmodium-mosquito' (HPM). If the equilibrium is maintained, malaria does not ensue and the result is asymptomatic plasmodium infection. The relationships among the components of the system involve coadaptive linkages that lead to equilibrium. A vast body of evidence supports this assumption, including the strategies involved in the relationships between plasmodium and human and mosquito immune systems, and the emergence of resistance of plasmodia to antimalarial drugs and of mosquitoes to insecticides. Coadaptive strategies for malaria control are based on the following principles: (1) the system HPM is composed of three highly complex and dynamic components, whose interplay involves coadaptive linkages that tend to maintain the equilibrium of the system; (2) human and mosquito immune systems play a central role in the coadaptive interplay with plasmodium, and hence, in the mainten-ance of the system's equilibrium; the under- or overfunction of human immune system may result in malaria and influence its severity; (3) coadaptation depends on genetic and epigenetic phenomena occurring at the interfaces of the components of the system, and may involve exchange of infectrons (genes or gene fragments) between the partners; (4) plasmodia and mosquitoes have been submitted to selective pressures, leading to adaptation, for an extremely long while and are, therefore, endowed with the capacity to circumvent both natural (immunity) and artificial (drugs, insecticides, vaccines) measures aiming at destroying them; (5) since malaria represents disequilibrium of the system HPM, its control should aim at maintaining or restoring this equilibrium; (6) the disequilibrium of integrated systems involves the disequilibrium of their components, therefore the maintenance or restoration of the system's equilibrium depend on the adoption of integrated and coordinated measures acting on all components, that means, panadaptive strategies. Coadaptive strategies for malaria control should consider that: (1) host immune response has to be induced, since without it, no coadaptation is attained; (2) the immune response has to be sustained and efficient enough to avoid plasmodium overgrowth; (3) the immune response should not destroy all parasites; (4) the immune response has to be well controlled in order to not harm the host. These conditions are mostly influenced by antimalarial drugs, and should also be taken into account for the development of coadaptive malaria vaccines.

Vector density and the control of kala-azar in Bihar, India

Bihar, India has been in the grip of kala-azar for many years. Its rampant and severe spread has made life miserable in most parts of the state. Such conditions require a comprehensive understanding of this affliction. The numbers coming out of the districts prone to the disease in the north and south Ganges have provided us with several startling revelations, as there are striking uniformities on both sides, including similar vegetation, water storage facilities, house construction and little change in risk factors. The northern areas have been regularly sprayed with DDT since 1977, but eradication of the disease appears to be a distant dream. In 2007 alone, there were as many as 37,738 cases in that region. In contrast, the southern districts of Patna and Nalanda have never had the disease in its epidemic form and endemic disease has been present in only some pockets of the two districts. In those cases, two rounds of spraying with DDT had very positive results, with successful control and no new established foci. In addition, an eleven-year longitudinal study of the man hour density and house index for the vector Phlebotomus argentipes demonstrated that they were quite high in Patna and Nalanda and quite low in north Bihar. Given these facts, an attempt has been made to unravel the role of P. argentipes saliva (salivary gland) in the epidemiology of kala-azar. It was determined that patchy DDT spraying should be avoided for effective control of kala-azar.

Sooty blotch and flyspeck control with fungicide applications based on calendar, local IPM, and warning system

The objective of this work was to compare fungicide application timing for the control of sooty blotch and flyspeck (SBFS) of 'Fuji' apples in Rio Grande do Sul state, Brazil. The following treatments were evaluated in two growing seasons: two warning system-based (modified version of the Brown-Sutton-Hartmann system) spray of captan plus thiophanate methyl, with or without summer pruning; two calendar/rain-based spray of captan or a mixture of captan plus thiophanate methyl; fungicide spray timing based on a local integrated pest management (IPM) for the control of summer diseases; and a check without spraying. Sooty blotch and flyspeck incidence over time and their severity at harvest were evaluated. The highest number of spray was required by calendar/rain-based treatments (eight and seven sprays in the sequential years). The warning system recommended five and three sprays, in the sequential years, which led to the highest SBFS control efficacy expressed by the reduced initial inoculum and disease progress rate. Summer pruning enhanced SBFS control efficacy, especially by suppressing SBFS signs which tended to be restrained to the peduncle region of the fruit. Sooty blotch and flyspeck can be managed both with calendar and the grower-based IPM practices in Brazil, but a reduced number of sprays is required when the warning system is used.

Occurence of thrips on Niagara table grape and its control with the insecticides thiacloprid and methiocarb associated with Metarhizium anisopliae

Thrips are reported as important pests on table grapes in United States and several countries of Europe. Damage caused by thrips, particulary Frankliniella occidentalis, was observed on niagara table grape crop in Limeira-SP, Brazil. During the blooming period, high thrips densities were observed feeding on pollen and small berries. The symptoms left were more visible after the development of the berries and were characterized by dark scars and suberized surface on berries, sometimes causing the berry to crack, and the seed to prolapse. The effect of insecticides thiacloprid or methiocarb, associated or not with the entomopathogenic fungus Metarhizium anisopliae were evaluated during the blooming period. For evaluation of thrips damage on fruits, the treatments were applied three additional times, 7, 14 and 21 days after the first application. The treatments were: a) M. anisopliae (strain 1037) 1x10(7) conidia/mL; b) thiacloprid 20mL/100L; c-d) methiocarb 100 and 150mL/100L; e) methiocarb 100mL/100L + M. anisopliae 1x10(7) conidia/mL. Only methiocarb, associated or not with the fungus, was effective in reducing thrips infestation, and no phytotoxic damage was observed. The efficiency of methiocarb 150mL/100L and the insecticide associated with the fungus for the control of the thrips population was 84.2 and 95.5%, respectively. In both cases, there was a reduction of approximately 70% in the number of berries with scars symptoms. For control of thrips on table grapes, chemical insecticides associated or not with M. anisopliae should be applied during the blooming period of the crop.

Speed Control of an Autonomous Mobile Robot: Comparison between a PID Control and a Control Using Fuzzy Logic

An Autonomous Mobile Robot battery driven, with two traction wheels and a steering wheel is being developed. This Robot central control is regulated by an IPC, which controls every function of security, steering, positioning localization and driving. Each traction wheel is operated by a DC motor with independent control system. This system is made up of a chopper, an encoder and a microcomputer. The IPC transmits the velocity values and acceleration ramp references to the PIC microcontrollers. As each traction wheel control is independent, it's possible to obtain different speed values for each wheel. This process facilities the direction and drive changes. Two different strategies for speed velocity control were implemented; one works with PID, and the other with fuzzy logic. There were no changes in circuits and feedback control, except for the PIC microcontroller software. Comparing the two different speed control strategies the results were equivalent. However, in relation to the development and implementation of these strategies, the difficulties were bigger to implement the PID control.

Nitrogen doses and weed control via intercropping with gliricidia for corn production

Many studies have demonstrated the beneficial influence of nitrogen doses on corn dry grain yield and green ear yield. Due to a growing concern with environmental degradation, many agricultural practices, adopted in the past, are being reexamined. With regard to weed control, strategies that employ mechanical control, including intercrops, are being the object of renewed interest. The purpose of this study was to evaluate the effects of the application of nitrogen doses (0, 40, 80, and 120 kg N ha-1; as ammonium sulfate) and weed control on the growth, green ear yield, and grain yield of the AG 1051 corn cultivar. A randomized block experimental design with split-plots and nine replications was adopted. In addition to nitrogen rates, the AG 1051 cultivar was submitted to the following treatments, applied to subplots: no weeding, two hoeings (at 20 and 40 days after sowing), and intercropping with gliricídia (Gliricidia sepium). Gliricidia was sowed at corn planting, between the corn rows, using two seedlings per pit, in pits spaced 0.30 m apart. Gliricidia did not provide weed control, and gave plant growth, green ear yield and grain yield values similar to the no weeding treatment. However, regarding the number of mature ears got, intercropping with gliricidia did not differ from the two-hoeing treatment. Weed control did not have an effect on plant height and number of marketable, husked green ears, with the application of 120 kg N ha-1; indicating that nitrogen improved the corn's competitive ability. The two-hoeing treatment provided the best means for total green ears weight, number of marketable husked ears, both unhusked and husked marketable ear weight, grain yield and its components than the other treatments. Nitrogen application increased corn growth, green ear yield, and grain yield, as well as weed green biomass, but reduced the stand and growth of gliricidia.