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.

Remarks on abstract Galois theory

This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva (see da Costa, Rodrigues (2007)). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva's notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some comments are made on the universal theory of (set-theoretic) structures.

The relation between the general maxim of causality and the principle of uniformity in hume's theory of knowledge

ABSTRACT When Hume, in the Treatise on Human Nature, began his examination of the relation of cause and effect, in particular, of the idea of necessary connection which is its essential constituent, he identified two preliminary questions that should guide his research: (1) For what reason we pronounce it necessary that every thing whose existence has a beginning should also have a cause and (2) Why we conclude that such particular causes must necessarily have such particular effects? (1.3.2, 14-15) Hume observes that our belief in these principles can result neither from an intuitive grasp of their truth nor from a reasoning that could establish them by demonstrative means. In particular, with respect to the first, Hume examines and rejects some arguments with which Locke, Hobbes and Clarke tried to demonstrate it, and suggests, by exclusion, that the belief that we place on it can only come from experience. Somewhat surprisingly, however, Hume does not proceed to show how that derivation of experience could be made, but proposes instead to move directly to an examination of the second principle, saying that, "perhaps, be found in the end, that the same answer will serve for both questions" (1.3.3, 9). Hume's answer to the second question is well known, but the first question is never answered in the rest of the Treatise, and it is even doubtful that it could be, which would explain why Hume has simply chosen to remove any mention of it when he recompiled his theses on causation in the Enquiry concerning Human Understanding. Given this situation, an interesting question that naturally arises is to investigate the relations of logical or conceptual implication between these two principles. Hume seems to have thought that an answer to (2) would also be sufficient to provide an answer to (1). Henry Allison, in his turn, argued (in Custom and Reason in Hume, p. 94-97) that the two questions are logically independent. My proposal here is to try to show that there is indeed a logical dependency between them, but the implication is, rather, from (1) to (2). If accepted, this result may be particularly interesting for an interpretation of the scope of the so-called "Kant's reply to Hume" in the Second Analogy of Experience, which is structured as a proof of the a priori character of (1), but whose implications for (2) remain controversial.

The notion of process in nonstandard theory and in Whiteheadian metaphysics

In this article I intend to show that certain aspects of A.N. Whitehead's philosophy of organism and especially his epochal theory of time, as mainly exposed in his well-known work Process and Reality, can serve in clarify the underlying assumptions that shape nonstandard mathematical theories as such and also as metatheories of quantum mechanics. Concerning the latter issue, I point to an already significant research on nonstandard versions of quantum mechanics; two of these approaches are chosen to be critically presented in relation to the scope of this work. The main point of the paper is that, insofar as we can refer a nonstandard mathematical entity to a kind of axiomatical formalization essentially 'codifying' an underlying mental process indescribable as such by analytic means, we can possibly apply certain principles of Whitehead's metaphysical scheme focused on the key notion of process which is generally conceived as the becoming of actual entities. This is done in the sense of a unifying approach to provide an interpretation of nonstandard mathematical theories as such and also, in their metatheoretical status, as a formalization of the empirical-experimental context of quantum mechanics.

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

The application of the Extreme Value Theory (EVT) to model the probability of occurrence of extreme low Standardized Precipitation Index (SPI) values leads to an increase of the knowledge related to the occurrence of extreme dry months. This sort of analysis can be carried out by means of two approaches: the block maxima (BM; associated with the General Extreme Value distribution) and the peaks-over-threshold (POT; associated with the Generalized Pareto distribution). Each of these procedures has its own advantages and drawbacks. Thus, the main goal of this study is to compare the performance of BM and POT in characterizing the probability of occurrence of extreme dry SPI values obtained from the weather station of Ribeirão Preto-SP (1937-2012). According to the goodness-of-fit tests, both BM and POT can be used to assess the probability of occurrence of the aforementioned extreme dry SPI monthly values. However, the scalar measures of accuracy and the return level plots indicate that POT provides the best fit distribution. The study also indicated that the uncertainties in the parameters estimates of a probabilistic model should be taken into account when the probability associated with a severe/extreme dry event is under analysis.

The theory of constraints in manufacturing

In this paper, a systematic and quantitative view is presented for the application of the theory of constraints in manufacturing. This is done employing the operational research technique of mathematical programming. The potential of the theory of constraints in automated manufacturing is demonstrated.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

A Modified phosphate-carrier protein theory is proposed as a non-target site mechanism For glyphosate resistance in weeds

Glyphosate is an herbicide that inhibits the enzyme 5-enolpyruvyl-shikimate-3-phosphate synthase (EPSPs) (EC 2.5.1.19). EPSPs is the sixth enzyme of the shikimate pathway, by which plants synthesize the aromatic amino acids phenylalanine, tyrosine, and tryptophan and many compounds used in secondary metabolism pathways. About fifteen years ago it was hypothesized that it was unlikely weeds would evolve resistance to this herbicide because of the limited degree of glyphosate metabolism observed in plants, the low resistance level attained to EPSPs gene overexpression, and because of the lower fitness in plants with an altered EPSPs enzyme. However, today 20 weed species have been described with glyphosate resistant biotypes that are found in all five continents of the world and exploit several different resistant mechanisms. The survival and adaptation of these glyphosate resistant weeds are related toresistance mechanisms that occur in plants selected through the intense selection pressure from repeated and exclusive use of glyphosate as the only control measure. In this paper the physiological, biochemical, and genetic basis of glyphosate resistance mechanisms in weed species are reviewed and a novel and innovative theory that integrates all the mechanisms of non-target site glyphosate resistance in plants is presented.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Selection of patients for myocardial perfusion scintigraphy based on fuzzy sets theory applied to clinical-epidemiological data and treadmill test results

Coronary artery disease (CAD) is a worldwide leading cause of death. The standard method for evaluating critical partial occlusions is coronary arteriography, a catheterization technique which is invasive, time consuming, and costly. There are noninvasive approaches for the early detection of CAD. The basis for the noninvasive diagnosis of CAD has been laid in a sequential analysis of the risk factors, and the results of the treadmill test and myocardial perfusion scintigraphy (MPS). Many investigators have demonstrated that the diagnostic applications of MPS are appropriate for patients who have an intermediate likelihood of disease. Although this information is useful, it is only partially utilized in clinical practice due to the difficulty to properly classify the patients. Since the seminal work of Lotfi Zadeh, fuzzy logic has been applied in numerous areas. In the present study, we proposed and tested a model to select patients for MPS based on fuzzy sets theory. A group of 1053 patients was used to develop the model and another group of 1045 patients was used to test it. Receiver operating characteristic curves were used to compare the performance of the fuzzy model against expert physician opinions, and showed that the performance of the fuzzy model was equal or superior to that of the physicians. Therefore, we conclude that the fuzzy model could be a useful tool to assist the general practitioner in the selection of patients for MPS.

Use of magnitude-squared coherence to identify the maximum driving response band of the somatosensory evoked potential

The present study proposes to apply magnitude-squared coherence (MSC) to the somatosensory evoked potential for identifying the maximum driving response band. EEG signals, leads [Fpz'-Cz'] and [C3'-C4'], were collected from two groups of normal volunteers, stimulated at the rate of 4.91 (G1: 26 volunteers) and 5.13 Hz (G2: 18 volunteers). About 1400 stimuli were applied to the right tibial nerve at the motor threshold level. After applying the anti-aliasing filter, the signals were digitized and then further low-pass filtered (200 Hz, 6th order Butterworth and zero-phase). Based on the rejection of the null hypothesis of response absence (MSC(f) > 0.0060 with 500 epochs and the level of significance set at a = 0.05), the beta and gamma bands, 15-66 Hz, were identified as the maximum driving response band. Taking both leads together ("logical-OR detector", with a false-alarm rate of a = 0.05, and hence a = 0.0253 for each derivation), the detection exceeded 70% for all multiples of the stimulation frequency within this range. Similar performance was achieved for MSC of both leads but at 15, 25, 35, and 40 Hz. Moreover, the response was detected in [C3'-C4'] at 35.9 Hz and in [Fpz'-Cz'] at 46.2 Hz for all members of G2. Using the "logical-OR detector" procedure, the response was detected at the 7th multiple of the stimulation frequency for the series as a whole (considering both groups). Based on these findings, the MSC technique may be used for monitoring purposes.

Topographic distribution of the tibial somatosensory evoked potential using coherence

The objective of the present study was to determine the adequate cortical regions based on the signal-to-noise ratio (SNR) for somatosensory evoked potential (SEP) recording. This investigation was carried out using magnitude-squared coherence (MSC), a frequency domain objective response detection technique. Electroencephalographic signals were collected (International 10-20 System) from 38 volunteers, without history of neurological pathology, during somatosensory stimulation. Stimuli were applied to the right posterior tibial nerve at the rate of 5 Hz and intensity slightly above the motor threshold. Response detection was based on rejecting the null hypothesis of response absence (significance level α= 0.05 and M = 500 epochs). The best detection rates (maximum percentage of volunteers for whom the response was detected for the frequencies between 4.8 and 72 Hz) were obtained for the parietal and central leads mid-sagittal and ipsilateral to the stimulated leg: C4 (87%), P4 (82%), Cz (89%), and Pz (89%). The P37-N45 time-components of the SEP can also be observed in these leads. The other leads, including the central and parietal contralateral and the frontal and fronto-polar leads, presented low detection capacity. If only contralateral leads were considered, the centro-parietal region (C3 and P3) was among the best regions for response detection, presenting a correspondent well-defined N37; however, this was not observed in some volunteers. The results of the present study showed that the central and parietal regions, especially sagittal and ipsilateral to the stimuli, presented the best SNR in the gamma range. Furthermore, these findings suggest that the MSC can be a useful tool for monitoring purposes.

Increased coherence among striatal regions in the theta range during attentive wakefulness

The striatum, the largest component of the basal ganglia, is usually subdivided into associative, motor and limbic components. However, the electrophysiological interactions between these three subsystems during behavior remain largely unknown. We hypothesized that the striatum might be particularly active during exploratory behavior, which is presumably associated with increased attention. We investigated the modulation of local field potentials (LFPs) in the striatum during attentive wakefulness in freely moving rats. To this end, we implanted microelectrodes into different parts of the striatum of Wistar rats, as well as into the motor, associative and limbic cortices. We then used electromyograms to identify motor activity and analyzed the instantaneous frequency, power spectra and partial directed coherence during exploratory behavior. We observed fine modulation in the theta frequency range of striatal LFPs in 92.5 ± 2.5% of all epochs of exploratory behavior. Concomitantly, the theta power spectrum increased in all striatal channels (P < 0.001), and coherence analysis revealed strong connectivity (coefficients >0.7) between the primary motor cortex and the rostral part of the caudatoputamen nucleus, as well as among all striatal channels (P < 0.001). Conclusively, we observed a pattern of strong theta band activation in the entire striatum during attentive wakefulness, as well as a strong coherence between the motor cortex and the entire striatum. We suggest that this activation reflects the integration of motor, cognitive and limbic systems during attentive wakefulness.

Optical coherence tomography imaging of the basal ganglia: feasibility and brief review

Optical coherence tomography (OCT) is a promising medical imaging technique that uses light to capture real-time cross-sectional images from biological tissues in micrometer resolution. Commercially available optical coherence tomography systems are employed in diverse applications, including art conservation and diagnostic medicine, notably in cardiology and ophthalmology. Application of this technology in the brain may enable distinction between white matter and gray matter, and obtainment of detailed images from within the encephalon. We present, herein, the in vivo implementation of OCT imaging in the rat brain striatum. For this, two male 60-day-old rats (Rattus norvegicus, Albinus variation, Wistar) were stereotactically implanted with guide cannulas into the striatum to guide a 2.7-French diameter high-definition OCT imaging catheter (Dragonfly™, St. Jude Medical, USA). Obtained images were compared with corresponding histologically stained sections to collect imaging samples. A brief analysis of OCT technology and its current applications is also reported, as well as intra-cerebral OCT feasibility on brain mapping during neurosurgical procedures.

As duas vias do princípio das vantagens comparativas de David Ricardo e o padrão-ouro: um ensaio crítico

This article critically resumes Ricardo's principle of comparative advantages pointing out internal coherence problems that have been neglected by the specialized literature. First, long-lasting disequilibria observed in the balance of trade seem incompatible with the idea that these disequilibria are caused by technical advances that change relative prices. Second, comparative advantages do not seem to work in an economy with a universally accepted commodity-money. Finally, the contradiction between the gold standard mechanisms, ruled by Smith's "Law of Reflux", and the quantitative theory of money, which is a necessary condition for the "second way" of the theory of comparative advantages.