Hilbert's "Verunglueckter Beweis," the first epsilon theorem, and consistency proofs

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain 'general consistency result' due to Bernays. An analysis of the form of this so-called 'failed proof' sheds further light on an interpretation of Hilbert's Programme as an instrumentalist enterprise with the aim of showing that whenever a `real' proposition can be proved by 'ideal' means, it can also be proved by 'real', finitary means.Comment: 18 pages, final versio

An Internet-Based Tool for Use in Assessing the Likely Effect of Intensification on Losses of Nitrogen to the Environment

The EU Nitrates, Habitat and National Emissions Ceilings directives and the Kyoto Agreement mean that agricultural losses of NO3, NH3 and N2O are under scrutiny by national and international environmental authorities. When farmers wish to intensify their operations, the authorities must then assess the likely environmental impact of the change in operation. The FARM-N internet tool was developed to help farmers and authorities agree how the farm will be structured and managed in the future, and to provide an objective assessment of the environmental losses that will result

A situational analysis of health information library needs in Tanzania

published_or_final_versio

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Empirical Platform Data Analysis to Investigate how Heat Pumps Operate in Real-Life Conditions

Heat pumps have been widely acknowledged, by academia and industry, as highly efficient thermal energy technologies, for space heating and domestic hot water production. However, there is a lack of information about real performance in residential single family houses with active participation of end-users. In this paper, an analysis based on data from 242 heat pump installations in Denmark gathered over a period up to 4 years (2010 until today) is performed. COP, operating temperatures and socio-demographic data are used as basis for comparing theoretical and actual performance. Six different heat pump configurations are considered depending on source (ground or air) and sink (radiators, floor heating and/or combined systems). This unique study intends to point out the benefits and limitations of such technologies in terms of energy efficiency and comfort delivery, as well as investigating the suitability of heat pumps to support fossil-fuel free energy systems

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Role of immunohistochemistry for interobserver agreement of Peritoneal Regression Grading Score in peritoneal metastasis.

Pressurized intraperitoneal aerosol chemotherapy (PIPAC)-directed therapy is a new treatment option for peritoneal metastasis (PM). The 4-tiered Peritoneal Regression Grading Score (PRGS) has been proposed for assessment of histological treatment response. We aimed to evaluate the effect of immunohistochemistry (IHC) on interobserver agreement of the PRGS. Hematoxylin and eosin (H&E)-stained and IHC-stained slides (n = 662) from 331 peritoneal quadrant biopsies (QBs) taken prior to 99 PIPAC procedures performed on 33 patients were digitalized and uploaded to a web library. Eight raters (five consultants and three residents) assessed the PRGS, and Krippendorff's alpha coefficients (α) were calculated. Results (IHC-PRGS) were compared with data published in 2019, using H&E-stained slides only (H&E-PRGS). Overall, agreement for IHC-PRGS was substantial to almost perfect. Agreement (all raters) regarding single QBs after treatment was substantial for IHC-PRGS (α = 0.69, 95% confidence interval [CI] = 0.66-0.72) and moderate for H&E-PRGS (α = 0.60, 95% CI = 0.56-0.64). Agreement (all raters) regarding the mean PRGS per QB set after treatment was higher for IHC-PRGS (α = 0.78, 95% CI = 0.73-0.83) than for H&E-PRGS (α = 0.71, 95% CI = 0.64-0.78). Among residents, agreement was almost perfect for IHC-PRGS and substantial for H&E-PRGS. Agreement (all raters) regarding maximum PRGS per QB set after treatment was substantial for IHC-PRGS (α = 0.61, 95% CI = 0.54-0.68) and moderate for H&E-PRGS (α = 0.60, 95% CI = 0.53-0.66). Among residents, agreement was substantial for IHC-PRGS (α = 0.66, 95% CI = 0.57-0.75) and moderate for H&E-PRGS (α = 0.55, 95% CI = 0.45-0.64). Additional IHC seems to improve the interobserver agreement of PRGS, particularly between less experienced raters

Calibration to American options: numerical investigation of the de-Americanization method.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe