Quod Erat Demonstrandum Research Articles

Quod erat demonstrandum? - Towards a typology of the concept of explanation for the design of explainable AI

In this paper, we present a fundamental framework for defining different types of explanations of AI systems and the criteria for evaluating their quality. Starting from a structural view of how explanations can be constructed, i.e., in terms of an explanandum (what needs to be explained), multiple explanantia (explanations, clues, or parts of information that explain), and a relationship linking explanandum and explanantia, we propose an explanandum-based typology and point to other possible typologies based on how explanantia are presented and how they relate to explanandia. We also highlight two broad and complementary perspectives for defining possible quality criteria for assessing explainability: epistemological and psychological (cognitive). These definition attempts aim to support the three main functions that we believe should attract the interest and further research of XAI scholars: clear inventories, clear verification criteria, and clear validation methods.

A free mind cannot be digitally transferred

AbstractThe digital transfer of the mind to a computer system (i.e., mind uploading) requires representing the mind as a finite sequence of bits (1s and 0s). The classic “stored-program computer” paradigm, in turn, implies the equivalence between program and data, so that the sequence of bits themselves can be interpreted as a program, which will be algorithmically executed in the receiving device. Now, according to a previous proof, on which this paper is based, a computational or algorithmic machine, however complex, cannot be free (in the sense of ‘self-determined’). Consequently, a finite sequence of bits cannot adequately represent a free mind and, therefore, a free mind cannot be digitally transferred, quod erat demonstrandum. The impossibility of making this transfer, as demonstrated here, should be a concern especially for those who wish to achieve it. Since we intend this to be a rigorous demonstration, we must give precise definitions and conditions of validity. The most important part of the paper is devoted to explaining the meaning and reasonableness of these definitions and conditions (for example that being truly free means being self-determined). Special attention is paid, also, to the philosophical implications of the demonstration. Finally, this thesis is distinguished from other closely related issues (such as other possible technological difficulties to “discretize” the mind; or, whether it is possible to transfer the mind from one material support to another one in a non-digital way).

Quod erat demonstrandum: A comparative study of narrative technique in Ama Ata Aidoo’s Changes and Albert Camus’ Les justes (The Just Ones)

Authors of fictional works often have recourse to irony whereby they subtly indicate their disapproval of certain ideas or courses of action. Irony is a rather complex and wide-ranging phenomenon. However, in both Ama Ata Aidoo‟s Changes and Albert Camus Les justes, the authors resort to a specific form of irony to bring the discussion of issues raised to a conclusion. The technique consists in demonstrating clearly a huge discrepancy between a “fine” idea and its practical usefulness. This study, through textual analysis, aims to show how the two aforementioned authors successfully use this narrative technique. Albert Camus demonstrates the hollowness of the idea of fighting for justice through revolutionary violence and Ama Ata Aidoo similarly demonstrates the fatuousness of the theory of women- emancipation-through-polygamy.

Why Sextus? The Pros logikous as Reliable Source for Gorgias’ Peri tou me ontos

Two versions of Peri tou mē ontos ptmo by Gorgias, related by an Anonymous Author MXG and by Sextus Empiricus SE, have been alternatively accredited by scholars according to their disposition to seek a doctrine or a rhetorical- communicational dimension respectively with the first tendency prevailing. Comparing the ptmo to the rest of Gorgiasʼ works, we verify and clearly demonstrate how SE manages to convey a precise modus argumentandi. In effect, SE shows Gorgias’ demonstrative reasoning as employing: 1 the application of demonstrandum and quod erat demonstrandum typical of Gorgiasʼ speeches, reinforced by a substantial and abundant use of verbs of explanation and demonstration, especially in comparison to the rest of the same Against the Logicians’ section. Otherwise, MXG reduces this lexicon to the more generic phēmi; 2 the continuous employment of the reductio ad absurdum, like in all of Gorgias’ works; 3 a very refined formulation of the principle of non-contradiction §67, similar to the one seen in Pal. 25. In addition, MXG is accurate in the discussion of some arguments as in the third kephalaion, however, presents as an overcorrected interpreter, more interested in questioning Gorgias than reporting his original text, also directly referring to Zeno, Melissus, and Leucippus. The context of the ptmo in SE’s work the structure presented leads us to believe that SE had the text or at least an accurate summary of the ptmo different from MXG. The aims of this paper are: 1 to demonstrate that SE shows well the Gorgianic demonstrative reasoning and, for this specific reason, he is reliable and valuable resource for us; 2 to hypothesise that SE’s version is based on and independent as yet unknown source.

The form of the monostrophic ballata as a frame for a logical demonstration

ABSTRACTThe later Trecento repertoire contains many short, monostrophic ballatas with philosophical or moralising texts. Why should the poets and composers, mostly Florentine, have preferred the ballata over the madrigal when exploring serious subjects, and why did they employ the monostrophic form?It turns out that the text structure of the monostrophic ballata is, in its essentials, comparable to the pattern of the geometric demonstration from Euclid'sElements, comprising premise, argumentation and return to the enhanced, proved premise (quod erat demonstrandum). Considered in light of Florentine Humanism's engagement with philosophy, including Ockham methods of demonstration, this article examines the possibility that Francesco Landini and other composers were sufficiently influenced by philosophy to view the structure of the monostrophic ballata as a means of logical demonstrations of refined arguments.

Quod erat demonstrandum: Understanding and Explaining Equations in Physics Teacher Education

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their master’s degree in two European universities. The course had two main goals: (1) To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and (2) To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived.

Autoimmune diabetes: caught in a NET.

The mantra is “no type 1 diabetes without autoimmunity.” Indeed, it is difficult to resist the evidence that autoimmunity plays a key role in the origins of type 1 diabetes (1,2). Recently, some aspects of that certainty have been shaken. As with other autoimmune diseases, type 1 diabetes is believed to arise from the impact of environmental insults in genetically susceptible individuals (3). The disease is β-cell specific, associated with β-cell autoantigens, which are recognized both by T cells and highly disease-predictive autoantibodies (2,4). Adoptive transfer of T cells from type 1 diabetic donors or of a pancreas from a twin donor to their type 1 diabetic twin induces the disease process (1,5). Moreover, genes associated with genetic susceptibility to the disease have a number of immune-associated functions, including decreasing the threshold of T-cell signaling and activation and modifying antigen presentation, each of which implies an adaptive immune effect (3). Quod erat demonstrandum? Well, not quite, because additional changes occur that coexist or antedate the development of diabetes-predictive autoantibodies; namely, changes in innate effector cells (6–8), decreased pancreatic weight (9), and metabolic dysfunction (10–13). Innate effector cells most likely play a role in causing type 1 diabetes, as macrophages, monocytes, dendritic cells, and neutrophils infiltrate the islets at the onset …

Quod erat demonstrandum! Is it?

ChemPhysChemVolume 14, Issue 3 p. 470-470 News Quod erat demonstrandum! Is it? First published: 11 February 2013 https://doi.org/10.1002/cphc.201300101Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume14, Issue3February 25, 2013Pages 470-470 RelatedInformation

Bigger is bigger. Better is better

Dear editor, First, we would like to thank the editorial board for the interest in our study and the thorough and extensive commentary [18] to our publication, “The impact of provider surgical volumes on survival in children with primary tumours of the central nervous system—a population-based study” [48]. The editorial includes comments on central publications and addresses some of the problems with the available evidence concerning the volume-outcome relationship. We appreciate the opportunity to comment further on the argumentation for and against centralization of paediatric neurosurgery. If a surgeon does not practice surgery, he or she will not master the procedures. This is self-evident. This is why training and licensing is required to become specialists and subspecialists. Although, accepting a volume-outcome relationship, there are still many unanswered questions as to what to gain from centralisation of different neurosurgical procedures. Here, we would like to expand the literary review in the editorial and comment on the specific points in respect to our study. The magnitude and importance of the volume-outcome relationship is difficult to assess from a review of the available literature. Major limitations rise from the fact that the data source are mainly American administrative claims databases or discharge summaries of variable quality that do not contain much clinical data. Usually, such record data only allow for crude adjustments for age, sex, ethnicity, hospital size and socioeconomic status [often just assessed as mean income in the postal code of the patient’s residential address (!)]. The severity and incidence of the treated disease is not corrected for, and there are often considerable limitations in data concerning differences in referral and case mix [28, 29]. It should further be remembered that high volume institutions in the USA more often treat younger patients, whites, patients with private insurance and residents of wealthier areas. Hospitals with the highest volumes typically also have more elective cases. In publications based on American administrative databases, the main outcome is usually surgical mortality, measured as in-house-mortality. Although 30-day mortality has a better face validity, the correlation to in-house mortality rates are generally at least moderate (kappa > 0.40), but with variance across conditions [14]. Surgical mortality has in the USA been endorsed as an Inpatient Quality Indicator (IQI) by the Agency for Healthcare Research and Quality in eight surgical procedures for adults, including craniotomies (the other seven are specific surgical procedures, while craniotomy is the opening of a body part). The line of logic is that since (1) surgical mortality in craniotomies is defined as a quality indicator, and (2) surgical mortality in many publications is lower in high-volume providers of care, then (3) surgical volume is a quality indicator (quod erat demonstrandum). However, studies by the Veterans Affair (VA) National Surgical Quality Improvement Program (NSQIP), which prospectively collects clinical data on all major surgical operations in the VA, do not reach the same conclusions as studies based on administrative claims data: “Unlike retrospective studies that are based on administrative databases, NSQIP studies have failed to demonstrate a direct relationship between volume and risk-adjusted outcomes of surgery across various specialties. These studies have emphasized that the quality of systems of care was more important than volume in determining the overall quality of surgical care at an institution. High-volume hospitals could still deliver poor care in as much as low-volume hospitals could deliver good care. NSQIP studies have also underscored the major limitations of claims data and administrative databases in the provision of adequate risk-adjustment models that are crucial for volume-outcome studies” [35].

Living Happily However After

There are an awful lot of stories out there that treat happiness as an experience, as put off to the end, or as both. So let us review two famous, distant, but related narratives of Western literature, each with a remarkable geometry of its own even though they putatively tell the same story: Homer's Odyssey and James Joyce's Ulysses. When Henry James associates his trade with drawing circles, he invokes more than two millennia of studying Euclidean geometry in the classroom. He doesn't insist on proof. The artist resorts to fiction, "a geometry of this own"; nevertheless he or she customarily envisions, within the artificial spatial and temporal confinement of the action, a sort of Q.E.D.: Quod erat demonstrandum. Whatever individual readers of Ulysses conclude about its treatment of happiness, however, it will be clear that Joyce does not subscribe to the convention (or religion) of living happily ever after. As Declan Kiberd argues at length, Ulysses is about "the reality of ordinary people's daily rounds". (Excerpt)

Regional anaesthesia – the bride at last?

Regional anaesthesia – the bride at last?

Predicting memory decline as a risk factor for Alzheimer's disease in older post-menopausal women: quod erat demonstrandum?

Alzheimer's disease (AD) is the major form of age-related dementia worldwide, accounting for more than two-thirds of all dementia cases. The disease is characterized by a progressive loss of cognitive and intellectual functioning (Gilman, 1997). A number of risk factors for AD have been identified. The prevalence of AD increases with age, diabetes, depression, family history of Parkinson's disease and following head injury or exposure to solvents (Jorm et al., 1991; van Duijn et al., 1991; Ott et al., 1995; Yoshitake et al., 1995; Devanand et al., 1996). Published research further suggests that low education levels are associated with increased prevalence of clinical AD (Gatz et al., 2001; Qiu et al., 2001; Ravaglia et al., 2002). Women also have a higher risk for developing the disease than men, with the risk being markedly increased following menopause (Sherwin, 2002; Sherwin 2003). Additionally, slightly more severe cognitive deficits have been reported in AD in women compared to men (Buckwalter et al., 1993, Henderson and Buckwalter, 1994). These epidemiological trends may be a consequence of reproductive hormonal changes. Specifically, menopause results in a marked diminution in gonadal estrogen production in women (see Sherwin, 2003, for a review). Estrogen plays a pivotal role in the maintenance and function of neuronal circuits in the brain and in resistance to neuronal damage (McEwen, 2001). The neuroprotective properties of estrogen are thought to be mediated at least in part by anti-amyloidogenic, anti-oxidative and ant-inflammatory mechanisms (reviewed in Barron et al., 2006a). However, limited and somewhat mixed data exist regarding the association between endogenous levels of estrogen and cognitive decline (Manly et al., 2000; Schupf et al., 2003). Based on some of our own findings, we here consider the factors that may be useful in predicting memory decline as a risk factor for Alzheimer's disease in older post-menopausal women.

Quod erat demonstrandum? A Reaction to Geiger and Schreyögg: ‘Coping with the Concept of Knowledge: Toward a Discursive Understanding of Knowledge’

This short essay is a reply to Geiger and Schreyögg’s reaction to the author’s article and was inspired by the editors and all authors alike. As we agree on the discursive character of (academic) knowledge, dialogue is the silver bullet to clarify meanings and thereby one’s own thinking. I thank the editors for the opportunity to respond and my colleagues for their reply (Geiger and Schreyögg, this issue). The response will be structured in three steps. First, it will delineate the ideas and concepts on which all authors seem to agree. This will be followed by the attempt to elaborate distinctly, on which concepts and/or interpretations the authors seem to disagree. In a third step some consequences of the consensus on concepts as well as on dissent for theories of knowledge and learning will be deduced.

S.58. Quod Erat Demonstrandum: Clonally Expanded Plasma Cells in the CSF of MS Patients Produce “Oligoclonal Bands”

S.58. Quod Erat Demonstrandum: Clonally Expanded Plasma Cells in the CSF of MS Patients Produce “Oligoclonal Bands”

Clitoral variation says nothing about female orgasm

Clitoral variation says nothing about female orgasm

Carbon isotope composition of fossil leaves – revealing ecophysiological responses to past environmental change

Carbon isotope composition of fossil leaves – revealing ecophysiological responses to past environmental change

Quod erat demonstrandum? The mystery of experimental validation of apparently erroneous computational analyses of protein sequences.

Computational predictions are critical for directing the experimental study of protein functions. Therefore it is paradoxical when an apparently erroneous computational prediction seems to be supported by experiment. We analyzed six cases where application of novel or conventional computational methods for protein sequence and structure analysis led to non-trivial predictions that were subsequently supported by direct experiments. We show that, on all six occasions, the original prediction was unjustified, and in at least three cases, an alternative, well-supported computational prediction, incompatible with the original one, could be derived. The most unusual cases involved the identification of an archaeal cysteinyl-tRNA synthetase, a dihydropteroate synthase and a thymidylate synthase, for which experimental verifications of apparently erroneous computational predictions were reported. Using sequence-profile analysis, multiple alignment and secondary-structure prediction, we have identified the unique archaeal 'cysteinyl-tRNA synthetase' as a homolog of extracellular polygalactosaminidases, and the 'dihydropteroate synthase' as a member of the beta-lactamase-like superfamily of metal-dependent hydrolases. In each of the analyzed cases, the original computational predictions could be refuted and, in some instances, alternative strongly supported predictions were obtained. The nature of the experimental evidence that appears to support these predictions remains an open question. Some of these experiments might signify discovery of extremely unusual forms of the respective enzymes, whereas the results of others could be due to artifacts.

Science as Child's Play: Tales from the Crib

Child's play? Certainly Alison Gopnik is in good company in pointing to connections between science and child development. To mention just a few luminaries: in psychology, Freud (followed by Erikson and Piaget) looked at the developmental connection between children's play and adult work; in philosophy, Thomas Reid may have been the first to ground the faculty of reasoning in developmental stages that “unfold themselves by degrees; so that it [the child] is inspired with the various principles of common sense” (1764, V, 7). As for connecting commonsense reasoning and science, according to Einstein, “The whole of science is nothing more than a refinement of everyday thinking” (1954, 290). Quod erat demonstrandum.

Des passions et de la compétence politique

It is possible to find any consistency in Spinoza's heterogeneous argument leading to the abrupt conclusion (last page of his interrupted « Tractatus politicus ») that « women cannot rule ». A detour through Spinoza's « Ethics » where it is shown that Passions (here Jealousy) tend to interfere with the requirements implied by social agreement, is needed in order to understand the logic underlying Spinoza's argument. While, according to Real-Politik, it is impossible to hold absolute command over passions. It is clear that women are the cause of dissension between men, since they are objects of a contrary desire to social agreement and impossible to share. Thus the reason why women are not suited for government is not some intrinsic inability ; it is rather due to some indirect consequence : since neither desire nor objects of desire can be suppressed, the only way out is to make these objects harmless. Conjugal appropriation is the way found to abolish the real danger inherent to a « free thing ». Once a woman is « in the power of her husband », she does not fulfil the logical and legal conditions required by citizenship. Quod erat demonstrandum. Women are thus expelled out of the political field where they would otherwise be cause of desire, therefore of discord.

The power of appreciation

My heart is filled with a double helping of loving appreciation on this occasion. First, there is the appreciation I feel for the award itself. It affords a rare opportunity for me to celebrate the happy circumstances that have made it possible over so many years to engage with colleagues such as yourselves in the exciting enterprise of practice and discovery in Community Psychology. Second, there is the appreciation I feel for the loving labor that Jim Kelly invested in his introduction of me. He has treated it in the way he always approaches his work -wi th delight, excitement, devotion, and creativity. Through the use of his own Power of Appreciation he has given me a gift that few people ever e n j o y t h e privilege of hearing from so many dear friends, family members, and colleagues about how they experience me and my work. This occasion, including Jim's beautiful overture, is itself a demonstration of my topic, the Power of Appreciation. So much so, in fact, that I am tempted simply to say, QED and sit down. Since I first came across it in high school geometry, the expression QED has fascinated me. At long last I have an opportunity to use it. Quod erat demonstrandum; Thus it has been demonstrated. It has a lovely flourish, does it not, worthy of the Amen corner of any congregation. Though I recall little of the substance of high school geometry, the artistry of QED remains firmly implanted in my mind: a carefully reasoned set of propositions followed by the triumphant: QED, Quod erat demonstrandum. I have been deeply touched by being a recipient of my colleagues award for my work in Community Psychology. In response to this expression of