Proof and Reasoning

L’errore giudiziario è una manchevolezza che può derivare, e non di rado deriva, da un uso inadeguato degli strumenti lato sensu logici che il giudice ha a disposizione.
La presente indagine si propone di approfondire proprio il rapporto tra logica del giudice ed errore giudiziario, seguendo un percorso tanto lineare quanto impegnativo.
Innanzitutto, illustrerò le caratteristiche generali dell’errore umano, le peculiarità dell’errore giudiziario e le varie accezioni di “errore giudiziario” che queste consentono di definire (in senso latissimo, lato, stretto e strettissimo) (§ 2).
Inoltre, ponendomi nella prospettiva delle due grandi concezioni della conoscenza giudiziale (intellettualismo e razionalismo), tratterò le cause salienti delle due componenti dell’errore giudiziario (errore qualificatorio ed errore probatorio), in particolare le cause razionali (suddistinte in cause ineluttabili e cause contrastabili dal giudice) (§ 3).

Abstract. Nel dibattito sulla prova specialistica, in particolare scientifica, si evoca spesso una formula, “Iudex peritus peritorum”, per rendere l’idea dell’autonomia valutativa riservata al giudice anche in questa sfera. Tuttavia, non solo l’idea si particolarizza in varianti molteplici e difficili da discernere, ma neppure è chiaro quali di esse siano compatibili con l’epistemologia giudiziaria accolta nel nostro sistema penale. Il presente saggio tenta di affrontare entrambi i problemi. Dopo aver illustrato le grandi articolazioni del ragionamento probatorio specialistico, nonché i principali modi in cui il giudice può contribuire al suo svolgimento, esso sottopone a critica questi ultimi, considerati come altrettante immagini del iudex peritus peritorum.
Abstract. In the debate on the specialized evidence, especially on the scientific one, the formula “Iudex peritus peritorum” is often evoked to express the idea of the evaluation autonomy reserved to the judge also in this sphere. However, not only does the idea differentiate itself into multiple and difficult to discern variants, but it is not even clear which of them are compatible with the judicial epistemology accepted in our criminal system. This essay attempts to address both problems. Having illustrated the great articulations of the specialized evidential reasoning and the main ways in which the judge can contribute to its development, it critically scrutinizes the latter, considered as many images of the iudex peritus peritorum.

The teacher is the decisive factor in the quality of education, the crux of the reform and innovation in modern general education. In order to improve the quality of teaching and learning to adapt to the general education program conditions and objectives, it is necessary to "change" the view, the look and the method to achieve positive and appropriate results in teaching and learning of Fine Art Education. The harmonious combination of theory and practice is a necessary and sufficient condition to help students, lecturers, and art teachers stand firm with their career, so that they are proud and aware of their self-esteem and professional values.

The need for smart e-learning environments is resulting in new challenges for researchers and practitioners to develop intelligent systems that can be used to automate the Higher Education (HE) activities in an intelligent way. Some common examples of such activities are “analyzing, finding, and ranking the right resource to teach a course,” “analyzing and finding the people with common research interests to start joint research projects,” and “using data analytics and machine reasoning techniques for conducting the exams with different levels of complexities.” Ontological reasoning and smart data analytics can play an important role in analyzing and automating these HE activities and processes. In this paper, we present a framework named as Higher Education Activities and Processes Automation Framework (HEAPAF). The HEAPAF framework can be used to identify, extract, process, and produce the semantically enriched data in machine understandable format from different educational resources. We also present the Higher Education Ontology (HEO) that we designed and developed to accommodate the HE data and then to perform analysis and reasoning on it. As a proof of concept, we present a case study on the topic, “analyzing, finding, and ranking the right resources to teach a course,” which can dramatically improve the learning patterns of students in the growing smart educational environment. Finally, we provide the evaluation of our framework as evidence of its competency and consistency in improving academic analytics for educational activities and processes by using machine reasoning.

This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs.

Why do students take the instruction "prove" in examinations to mean "go to the next question"? Because they have not been shown the simple techniques of how to do it. Mathematicians meanwhile generate a mystique of proof, as if it requires an inborn and unteachable genius. True, creating research-level proofs does require talent; but reading and understanding the proof that the square of an even number is even is within the capacity of most mortals.

Proof in Mathematics: an Introduction takes a straightforward, no nonsense approach to explaining the core technique of mathematics.

"Mathematics teaches you to think" is often an empty marketing slogan. With this book, it can become a reality.

This article discusses the challenges posed by the scope and volume of the evidential record to fact-finding and the presentation of cases in international criminal trials. To this end, it introduces a modified version of a technique first developed by John Henry Wigmore at the start of the 20th century, which provides a device for mapping complex arguments based on mixed masses of evidence. The potential benefits of the method to both lawyers and judges are illustrated with examples from international criminal trials. This discussion is timely, given a recent debate that has arisen in international criminal law on the analysis of evidence in general, and the standard of proof to be applied to individual facts in particular. The article concludes by offering some observations on that debate and arguing in favour of a method that might be seen as excessively fragmentary to some, but ultimately enables a rigorous analysis of the arguments that support or weaken conclusions on the guilt or innocence of the accused.

Romano Guardini was highly valued by Joseph Ratzinger as a lecturer and author of inspiring books. They shared the zealous pursuit for truth, the courage to ask fundamental questions, the boldness to confront the Christian faith with the challenges of contemporary culture, the conviction that the human mind has high cognitive capacities, and the emphasis on the primate of truth in theology. Both authors highlight the reasonable aspect of the Christian faith. After all, faith relies on the fact that God is Truth. Faith and reason are not contradictory. They can complement one another in the process of in-depth cognition. Naturally, as the human mind tries to understand God, it struggles with its own limitations in the face of the mystery which exceeds the capacities of the creation.

This paper brings up some important points about logic, e.g., mathematical logic, and also an inconsistence in logic as per Gödel's incompleteness theorems which state that there are mathematical truths that are not decidable or provable. These incompleteness theorems have shaken the solid foundation of mathematics where innumerable proofs and theorems have a place of pride. The great mathematician David Hilbert had been much disturbed by them. There are much long unsolved famous conjectures in mathematics, e.g., the twin primes conjecture, the Goldbach conjecture, the Riemann hypothesis, etc. Perhaps, by Gödel's incompleteness theorems the proofs for these famous conjectures will not be possible and the numerous mathematicians attempting to find the solutions for these conjectures are simply banging their heads against the metaphorical wall. Besides mathematics, Gödel's incompleteness theorems will have ramifications in other areas involving logic. This paper looks at the ramifications of the incompleteness theorems, which pose the serious problem of inconsistency, and offers a solution to this dilemma. The paper also looks into the apparent inconsistence of the axiomatic method in mathematics. [Published in international mathematics journal. Acknowledgments: The author expresses his gratitude to the referees and the Editor-in-Chief for their valuable comments in strengthening the contents of this paper.]

O Supremo Tribunal Federal teria aparentemente alterado seu anterior entendimento de que qualquer constatação de um crime em estado de flagrância dentro do domicílio era capaz de validar uma busca domiciliar realizada sem mandado judicial. Desde final de 2015 as buscas domiciliares são inválidas se não era possível divisar a ocorrência de um crime em estado de flagrância a partir do exterior do domicílio. No entanto, se o estado de flagrância for percebi-do apenas de dentro do domicílio e a entrada tenha se dado por consentimento do morador, é válida a prisão em flagrante dela decorrente? O direito fundamental da inviolabilidade domi-ciliar pode ser renunciado? Como deve ocorrer a renúncia à inviolabilidade do domicílio para que se entenda o consentimento como válido? Palavras-chave: BUSCA DOMICILIAR SEM MANDADO. LEGALIDADE. CONSENTI-MENTO. RENÚNCIA A DIREITOS FUNDAMENTAIS. RENÚNCIA À INVIOLABILI-DADE DOMICILIAR. REQUISITOS. ABSTRACT The Brazilian Federal Supreme Court seems to have altered its previous holding that any crime in flagrante state found within a house was able to validate a search and seizure conducted in a house without a court order. Since the end of 2015 warrantless house search and seizure are invalid if the flagrante state of a crime was not perceivable from the outside of the house. However, if the flagrante state is perceived only within the house and the entrance occurred by resident's consent, is it valid the arrest made that arises from the consented en-trance? Can the fundamental right of house inviolability be waived? How should a waiver of the house inviolability occur in order to be valid? Keywords: WARRANTLESS SEARCH AND SEIZURE. LEGALITY. CONSENT. WAIVER OF FUNDAMENTAL RIGHTS. WAIVER OF THE HOUSE INVIOLABILITY. REQUIREMENTS. Introdução Este estudo de caso tenta responder se e como o consentimento pode ser utilizado para autorizar a realização de busca e apreensão em domicílio sem mandado judicial e, por conseguinte, validando a prisão em flagrante dela decorrente e se há razão na nova ratio decidendi aparentemente adotado pelo STF.

Los recursos tecnológicos digitales han mostrado la posibilidad de profundizar en la naturaleza del conocimiento matemático y establecer nexos entre diferentes conceptos. La investigación didáctica ha mostrado que es posible usarlos para apoyar el aprendizaje de la demostración en geometría. La investigación en este campo se ha enfocado ampliamente a la geometría plana, dejando poco explorado el contexto de la geometría espacial. En este taller presentamos un conjunto de problemas de construcción de geometría espacial resueltos con GeoGebra 3d, dirigido a estudiantes con alta capacidad matemática de últimos cursos de Primaria y primeros cursos de Secundaria, con los que se pretende ayudarles en el aprendizaje de la demostración.

First days of a logic course
This short paper sketches one logician’s opinion of some basic ideas that should be presented on the first days of any logic course. It treats the nature and goals of logic. It discusses what a student can hope to achieve through study of logic. And it warns of problems and obstacles a student will have to overcome or learn to live with. It introduces several key terms that a student will encounter in logic.

Ante las dificultades probatorias del nexo causal en supuestos de responsabilidad civil o patrimonial el Derecho obliga a que el peso de la incertidumbre recaiga en su conjunto sobre uno solo de los sujetos implicados: sobre el agente (posiblemente) dañoso, cuando el juzgador rebaja el estándar ordinario de prueba para afirmar un nexo causal dudoso y ordena la reparación total del daño padecido; o sobre la víctima, cuando el órgano judicial mantiene ese estándar ordinario y niega el nexo causal y con ello la responsabilidad. Es el principio del " todo o nada ". La teoría de la pérdida de oportunidad o " chance " altera este planteamiento, pues distribuye el peso de la incertidumbre causal entre las dos partes implicadas: el agente responde sólo en proporción a la probabilidad de que fuera autor del menoscabo; y, correlativamente, la víctima obtiene una reparación acomodada a la probabilidad de no haber padecido el daño de no haber mediado el hecho lesivo. De este modo se brinda una solución equilibrada que pretende adaptarse a una sensibilidad justicial a la que repugna la liberación del agente (posiblemente) dañoso por las dificultades probatorias, pero también que se le conmine a reparar la totalidad de un daño que pudo no haber causado. La profesora de filosofía del derecho Marina Gascón Abellán y el profesor de derecho administrativo Luis Medina Alcoz debaten en torno al fundamento de esta solución, empleada cada vez con más frecuencia (pero con poco rigor) por nuestros jueces y tribunales. La primera acude a la teoría de la prueba y el segundo a la teoría de la causalidad. Para la primera la doctrina de la pérdida de oportunidad no entraña ningún cambio significativo en los planteamientos causales tradicionales; para justificarla basta asumir que el conocimiento judicial de los hechos debe basarse en juicios razonados de probabilidad y acudir a la figura de la presunción iuris tantum del nexo causal. Para el segundo esa doctrina implica una corrección parcial de los planteamientos causales tradicionales traducida en una complicación de los sistemas de imputación causal; junto al " todo o nada " basado en la afirmación o negación vínculo etiológico opera el " ni todo ni nada " basado en la afirmación de causalidades solamente posibles. Palabras clave: Responsabilidad por daños; causalidad; responsabilidad patrimonial de la Administración; responsabilidad proporcional; teoría de la pérdida de oportunidad; causalidad; prueba; incertidumbre; causalidad probabilística.

... pro-vides general information on Islam, corrects some misconceptions about it, and answers some commonly asked questions, such as: § What does Islam say about terrorism? § What is the status of women in Islam? A Brief Illustrated Guide To Understanding Islam 4 Contents ...

Le seguenti riflessioni hanno un fine teorico-pratico: imparare a trattare adeguatamente i due giudizi in cui si articola la decisione del giudice. Esse nascono da un’esperienza personale, che forse può essere utile comunicare. Nel corso della mia attività di giudice penale, ho notato che, sebbene la differenza concettuale tra giudizio probatorio e giudizio sussuntivo sia alquanto chiara, grazie alla netta differenza di senso delle quaestiones che essi mirano a risolvere, nondimeno tali giudizi interferiscono variamente tra di loro, in modi non sempre afferrabili. In particolare, in diverse occasioni mi sono trovato disorientato, in quanto ciò che credevo di star facendo o di aver fatto in funzione sussuntiva (in fase di istruzione, di deliberazione o di motivazione1) mi sembrava servire, al contempo, a fini probatori, o viceversa. Donde il desiderio di comprendere se queste interferenze siano di vari tipi, quali sono le loro cause, se siano tutte patologiche, se siano in parte evitabili e così via. D’altro canto, nello svolgimento dell’indagine, mi propongo di resistere alle opposte, diffuse tentazioni di far valere visioni astratte dell’attività del giudice o semplici intuizioni professionali: tentazioni parimenti incompatibili con un’aspirazione davvero teorica. Così, il contributo che vorrei offrire costituirà l’esito di un percorso graduale, articolato nei seguenti passaggi. Nel § 1, indicherò i principali fattori di complicazione del rapporto tra prova e sussunzione e cercherò di mostrare il carattere in buona misura apparente della problematicità che ne deriva. Nel § 2, sulla scorta di tale analisi preliminare, suddistinguerò in due tipi le principali tesi formulate sul nostro rapporto, tesi sovrappositive e tesi discretive. Nel § 3, col corredo di vari esempi tratti dal processo penale, proverò a sviluppare una delle tesi discretive, quella dell’Ermeneutica Giuridica Continentale, che tratta prova e sussunzione come attività di giudizio e si interessa al loro svolgimento naturale. Nel § 4, infine, ricapitolerò in forma poco più che stenografica i risultati dell’intera indagine.

A teoria da argumentação, que nas últimas décadas experimentou tão espetacular desenvolvimento, tem dedicado uma escassa atenção ao juízo de fato. Prova do que se acaba de dizer é que ao folhar as bibliotecas jurídicas constata-se que a maior parte das preocupações dos juristas tem se concentrado nos problemas de interpretação das normas, assumindo –implícita ou explicitamente-que o conhecimento de fatos não suscita problemas especiais ou que, suscitando-os, está irremediavelmente destinado à discricionariedade extrema e quando não, à pura e simples arbitrariedade judicial. Uma análise minimamente reflexiva não pode deixar de destacar, no entanto, que o juízo de fato é tão ou mais problemático do que o juízo de direito; que nele a discricionariedade do juiz é freqüentemente maior do que na interpretação das normas; que é, enfim, o momento de exercício do Poder Judicial onde o juiz é mais soberano e onde, conseqüentemente, pode ser mais arbitrário. Por isso, se a teoria da argumentação pretende ser minimamente completa não pode deixar de prestar atenção ao juízo de fato.

Sumário: 1. Duas concepções da prova: cognoscitivismo e concepção persuasiva: 1.1 Concepção cognoscitivista. 1.2 concepção persuasiva. 1.3 As relações verdade-prova. 2. A prova judicial como prova prevalecentemente indutiva: 2.1 Prova dedutiva e prova indutiva. 2.2 A valoração da prova. 3 Algumas construções doutrinais e jurisprudenciais. Considerações críticas: 3.1 A distinção prova direta/prova indireta. 3.2 Os requisitos da prova indireta ou indiciária. 4. Caráter institucionalizado da prova judicial. 5. A motivação da prova: 5.1 A necessidade de motivação da prova. 5.2. Em que consiste a motivação. 5.3. O estilo da motivação. 5.4. Resumo: regras sobre a motivação.

A finalidade da prova é permitir o convencimento. Ocorre que nem sempre o elemento de prova é recepcionado com perfeição. É preciso diferenciar duas situações: a prova perfeitamente produzida que não convence e a prova cuja produção é defeituosa. O perito é parte importante do diálogo processual e a prova pericial, caracterizada por aportar ao processo conhecimento especializado, exige que fundamente as suas razões, apresentando um laudo perfeito e completo. O perito é, portanto, parte da cooperação. Caso seu múnus não seja bem exercido, será necessário realizar nova perícia, ou seja, um segundo exame para complementar o anterior. A perícia imperfeita demanda que se ordene nova perícia, ao tempo em que a perícia perfeita admite que o juiz chegue a conclusões a respeito do thema probandum. A chave é compreender a fundamentação como elemento legitimador da atividade jurisdicional, instância adequada para se decidir sobre a repetição da prova ou sua interpretação em conjunto com as demais provas do processo. Tratam-se de situações distintas, exploradas no desenvolvimento do presente trabalho, a partir de metodologia voltada à pesquisa bibliográfica nacional e internacional especializada.

In a world dominated by half-truths, illogic, and intellectual laziness, Think Better helps readers understand what reason is and how to use it well.

Reason is a powerful tool not only for finding our way in an increasingly complex world but also for growing intellectually and emotionally. This short, accessible volume unlocks the dynamics of human reason, helping readers to think critically and to use reason confidently to solve problems. It enables readers to think more clearly and precisely about the world and tackles a number of profound philosophical questions without getting bogged down with jargon. Topics include knowledge, identity, leadership, creativity, and empathy.

Written in an accessible style that integrates philosophy, illustrations, personal anecdotes, and statistical data, this book is well suited for use in undergraduate, classical school, and home school contexts. It is an invaluable guide for anyone interested in gaining better reasoning skills and a more rational approach to life.

Se describen cinco prácticas productivas para promover
la enseñanza de las matemáticas a través de los
procesos, es decir, una enseñanza basada en pensar
y hacer. Asumiendo que una ‘práctica productiva’ en
educación matemática es una acción o destreza educativa
útil y provechosa para promover el aprendizaje
de las matemáticas con sentido en todos los niveles, se
consideran cinco prácticas asociadas a las herramientas
que nos proporcionan las matemáticas para lograr
este propósito: pensar, argumentar, comunicar, conectar
y representar. Se concluye que estas prácticas
productivas son una oportunidad y un desafío para
transformar las prácticas centradas en los contenidos,
basadas en memorizar definiciones y procedimientos.

Why is This Book Now?
The Manusmriti, the social doctrine of yore, and the Bhagvad-Gita, the spiritual tome in vogue that lay down the discriminatory dharma (duties) of the four social classes (castes) have been the bugbears of the Hindu backward classes. However, to their chagrin, of late, as the latter is being mindlessly promoted even though the former was constitutionally debunked, they began advocating that it too should be dumped in a dustbin.
Ironically, the improbability of their progenitor Krishna, the architect of the Gita, relegating his own ilk to the social margins failed to dawn upon these that Gita supposedly slights, even to this day! Thus, their intellectuals, instead of seeking to reclaim their priceless heritage, albeit after ridding its interpolative garbage, tend to rubbish it a la throwing the baby with the bathwater, and needless to say they must ponder.
Also, it is high time that the Gita-class stop laying store by the self-aggrandizing verses in this Vyāsa’s classic, evidently inserted by their progenitors that came to bedevil the Hindu spiritual integrity and social harmony. Likewise, the grumblers of the dalit desertions must see the need for setting the Hindu house in order to prevent the fractious poaching by the Church, if not to facilitate the ‘hoped for’ return of the prodigals. So also those who take pride that Hinduism is the only religion that reckons all faith as true, should be concerned about the ‘in vogue’ Gita that belittles some of their caste fellows. Besides, this work beckons the feminists to reckon the second of the two interpolations from it cited in the cover image that degrades them in unspeakable terms. 
This ‘overdue’ work, might lead the ‘denied’ Hindu castes as well as the favored folks for an objective approach to the in vogue Bhagvad-Gita which could dispel the misgivings of the former and the delusions of the latter, thereby bridging the Hindu emotional gulf with its abridged book that restores its original form. Whether or not one concurs with its propositions, this original work could be of interest to the students of logic and reasoning as well.
This work is dedicated to the slighted castes, whose forebear, Krishna, bestowed the invaluable Gita upon the mankind that in due course was fouled by the vested priestly interests:


.

This paper answers some questions central argumentation. Are reasoning and argument essentially the same thing? Or is one a proper subpart of the other? Or can you have reasoning that is not in argument? Or could you have argument without reasoning?

A study of the Ordeals, both bilateral and unilateral, in later Anglo-Saxon England and on into the period of intellectual critique in the 1wth century, and attempted abolition at the 4th Lateran Council of 1215. The aim is to understand how it functioned and in what sense it may have been regarded as both rational and effective before the 12th Century Renaissance. Drawing on the social anthropology of the day, it sought to marry intellectual and sociopolitical explanations for the demise of the old ordeals and (NB) its dating.

Praca stanowi pomoc dydaktyczną, w szczególności dla studentów WPiA UJ. Zaprezentowane są w niej podstawowe zagadnienia teoretyczne dotyczące dowodów założeniowych i praktyczne sposoby rozwiązywania zadań ich dotyczących.
Nie jest to wersja ostateczna tekstu - w przyszłości będą się pojawiać drobne jego uzupełnienia.

Susan Haack, “Legal Probabilism: An Epistemological Dissent,” in Haack, Evidence Matters: Science, Proof, and Truth in the Law (New York: Cambridge University Press, 2014), 47-77. (First published in Spanish in 2013.)

Abstract: In §1, I argue in some detail why legal standards of proof are best understood in terms of the degree to which the evidence presented must warrant the conclusion (of the defendant’s guilt or liability) for a case to be made. In §2, I show that it follows from my epistemological analysis that degrees of warrant cannot be identified with mathematical probabilities; and so, that “legal probabilism”—by which I mean the thesis that legal degrees of proof are to be identified with the probabilities that figure in the mathematical calculus of probability—is misguided. These arguments are completely general, applying to any kind of legal probabilism. The rest of the paper, however, focuses specifically on one popular form of legal probabilism—subjective Bayesianism; and shows how subjective Bayesian accounts fail, and my approach succeeds, in advancing our understanding of the evidence in two famous, and famously complicated, cases. In §3, I show that Kadane and Schum’s subjective-Bayesian analysis of evidence in the Sacco and Vanzetti case is seriously flawed—and that my approach can do significantly better; and in §4, to make clear that, though it isn’t probabilistic, my approach is nonetheless perfectly capable of accommodating statistical evidence appropriately, I turn to Finkelstein and Fairley’s subjective-Bayesian analysis of the evidence in Collins, showing that it, too, is seriously flawed—and, again, that my approach can do significantly better.

POWERPOINTS TO ACCOMPANY THIS PAPER ARE AVAILABLE IN THE SECTION LABELED “SELECTED PRESENTATIONS” BELOW (UNDER “MORE”). A LINK TO A YOUTUBE VIDEO OF HAACK GIVING THIS PRESENTATION CAN BE FOUND UNDER “LINKS” IN THAT SECTION

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle – and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation drawn from past works by the author over a period of eighteen years.

RE: Facades, illusions & ideological concepts created & promoted by ancient royalty out of necessity; effective creation of an alternate version of reality. It is only by knowing this information that the true nature of ancient texts may be understood correctly. Not knowing, means making incorrect assumptions & conclusions. Important!

T anrı Ha kkınd a Düşünmek: ilahi Olanın Peşinde
Dini Tanımlamak
Din Felsefesi Nedir?
Teizmin Tanrısı
Tefekküre Dayanan Araştınna ve Dini İman
Hayatın Dini Bakımdan Müphemliği
Bizim Görevimiz
Dinin  Mahiyeti : Dini lnançların Maksadı Nedir?
Dini Gayrihakikiyecilik
Budist Gayrihakikiyecilik
Dini Hakikiyecilik (Gerçekçilik)
Wıttengstein'ın Dine Bakışı
Bu Mesele Niçin Önemlidir?
D i n i T e c r ü b e : ilahi Olanla Karşılaşmak Ne Demektir?
Dini Tecrübenin Çeşitleri
Hissetme Olarak Dinil ecrübe 
Algısal Tecrübe Olarak Dini Tecrübe
Dini İnançlara Dayalı Yorum Olarak Dini Tecrübe 
Sinir Teolojisi (Neurotheology) 79
Dini Tecrübe Dini İnancı Gerekçelendirebilir mi? 
Safdillik İlkesi
Dini Tecrübenin Çeşitliliği
Dini Tecrübenin Drtak Bir Özü Var Mıdır?

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for acceptable reasoning across domains. We further argue that students' acceptance of these values may be integral to their apprenticeship into proving practice; students who do not perceive or accept these values will likely have difficulty adhering to the norms that uphold them and hence will find proof confusing and problematic. We discuss the implications of mathematical values and norms with respect to proof for investigating mathematical practice, conducting research in mathematics education, and teaching proof in mathematics classrooms. Values and norms in mathematical proof 2

This volume continues the discussion initiated in Part 1 of "Logical Forms" and deals with issues of language, logic, proof, and knowledge. I list the chapter titles:
13. Language, meaning, and reference.
14. Syntax and semantics.
15 Grammar and logical form.
16. Propositional logic.
17. Predicate logic.
18. Grammar and logical truth.
19. Proof and logical deduction.
20. Proof and proving.
21. Proof and truth.
22. The tyranny of belief.
23. Ockham's razor.
24. Knowledge and justification.
25. Logic and knowledge.
Epilogue. Plato, Zeno, Parmenides, and Frege.

A translation to Portuguese of chapter 25--Lógica e conhecimento--was published in 2007 and I added the pdf in TRANSLATIONS.

Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue that, when we make claims about those notations, we inevitably get saddled with bivalent commitments. I present several simple inferences to show this. The argument that results from those examples is 'pragmatic', because the inevitability of the principle is revealed in use (not mention); and it is 'semiotic', because this revelation happens in the use of signs.

Paper regarding the idea of "religious tolerance" as propaganda designed to just let religion continue to do harm to society and destroy lives. See my paper 'Religion Is Not Benign' in order to better understand this paper:
http://www.academia.edu/11700742/Religion_Is_Not_Benign

I am Kishlaya Jaiswal, a high school student (at the time of writing this document), and I have a great curiosity in Research and Mathematics. In this paper, I’ll be presenting and proving the Vandermonde’s Identity. I’ll also be discussing some  other interesting consequences of this identity. And any resemblance of my work somewhere else will be purely coincidental.

This is a text for a course that introduces math majors and math-education majors to the basic concepts, reasoning patterns, and language skills that are fundamental to higher mathematics. The skills include the ability to

    read with comprehension,
    express mathematical thoughts clearly,
    reason logically,
    recognize and employ common patterns of mathematical thought, and
    read and write proofs.  To see another section, see Section 2.2 on "Existence Statements and Negation" on Academia.edu.

The text is amazingly inexpensive. See about that at
http://estymath.com/Proof.html

This article is focused on answering the question to what extent one can be a sceptic. Sextus Empiricus’s Outlines of Scepticism serves as a guide. In section 1, it is investigated whether three logical laws have a certain foundation or are subject to doubt. In section 2, Sextus’s way to deal with these laws is examined; the question arises how dogmatic his approach is. After that, a possible ‘reply’ by Sextus to the criticism receives attention. Section 3 is concentrated on a possible alternative to Sextus’s approach. Besides logical laws, some important methods are concerned.

Desde hace décadas, los científicos reclaman insistentemente la necesidad de que los laboratorios forenses abandonen, en la formulación de las conclusiones de los informes periciales, el paradigma de la individualización –que confía en la capacidad de las pruebas científicas para identificar plenamente a un individuo o a un objeto a partir de vestigios– y lo sustituyan por el de la verosimilitud. El presente trabajo pretende ilustrar sobre la trascendencia de este nuevo paradigma y argumentar en favor de este cambio.

La sentenza Cozzini, pronunciata dalla Corte Suprema di Cassazione nel 2010, ha stabilito i principali requisiti di
affidabilità delle informazioni rese dagli esperti (periti e consulenti) nel processo penale. Il presente articolo esamina
contenuti e funzioni di tale regime, anche in confronto all’analoga disciplina vigente nel processo americano, e
affronta alcuni interrogativi che impegneranno nei prossimi anni i giudici chiamati ad applicarlo.
Deciding the Cozzini case in 2010, the Italian Supreme Court of Cassation has ruled the main requirements which
expert witnesses must satisfy to be considered reliable in a criminal trial. The paper investigates contents and
functions of this regulation, on the one hand comparing it with the similar standard in force in the USA, on the
other hand dealing with some questions about it which criminal judges must address in the next years.

It can be said that proving activities are an important activity for both mathematicians and mathematics educators. Thus, developing the proving ability is among the aims of many courses in advanced mathematics. However, although the importance of proof is frequently emphasized, studies show that undergraduates have difficulty in this regard. To overcome these difficulties and to make sense of the complex structure of the proof, many theoretical frameworks have been presented. However, it can be said that very few of these frameworks deal with the proving activity from a process perspective. On the other hand, Kidron and Dreyfus (2014), who approaching proof from a knowledge construction perspective and analyzing affective-logical interaction in this process in the micro-analytical level, reached the concept of “proof image” in the context of the Abstraction in Context (AiC) framework. However, despite the elapsed time, it can be seen that the researches on this framework have not reached sufficient numbers. As stated by the authors, it is clear that more research is required to deepen this framework. Because, by making sense of the proof image, which constitutes a significant dimension of the proof process, the multidimensional structure of dynamics of the proof can be clarified, and thus difficulties experienced in this activity can be avoided. In this doctoral study designed with this perspective, it was aimed to deepen the understanding of "proof image" and to shed light on the spots left open in the theoretical framework. Taking into account both the views of Kidron & Dreyfus (2014) and the deficiencies emerged in the practices, the issues of "the relationship between the proof image and the formal proof", "the levels (or types) of the proof image" and "the socio-cultural dimension of the proof image" were examined in this study.
In the study, sophomore pre-service teachers in the primary school mathematics education department were selected by using the criterion sampling method, one of the purposive sampling methods. The reason for the selection of this class level is that the subjects related to Cantorian Set Theory and "infinity" take place at this level. The subject of infinity has been considered to be a suitable context for investigations. Because many studies in the literature indicate that pre-service teachers' understanding of infinity has developed from intuitive to formal just like the proof image. In the study, the case study (for the first two sub-problems) which is one of the qualitative research designs, and discourse analysis (for the third sub-problem) were used together. In addition, individual interview forms developed by Pala (2016) were used as a data collection tool in task-based interviews. On the other hand, while analyzing the data, descriptive analysis was used for the first two questions and, the discourse analysis technique with a socio-cultural interaction perspective was used for the third question.
As a result of the analysis related to the first sub-problem of the study, it was determined that the proof image would not provide a certainty to reach the formal proof. In many tasks, it has been observed that participants cannot make a transition to formal proof even though forming a proof image. Possible reasons for this situation are discussed in detail in the context of subcomponents. On the other hand, some of the prominent reasons for individuals, who formed a proof image, failed to reach the formal proof can be listed as "lack of conceptual knowledge", "frequent use of intuitive assumptions", and "limited perception of the theorem". In the context of the second sub-problem of the study, all these situations that arise between the proof image and the formal proof had been interpreted separately in the context of the role of formal knowledge. Thus, 4 different possibilities were determined for situations that include and do not include the image of proof. It was observed that situations involving a proof image may result in two cases that “result in formal proof” and “result in partial verification”. However, it was observed that situations, which do not contain a proof image, may result from either practice such as memorization and repetition that contain only inauthentic connections (Type 1) or insufficient justification (Type 2) that includes logical connections based on personal understanding. Lastly, in the context of the third sub-problem of the study, an interactive proof process was carried out and discourse analysis was made on the obtained data. In this context, 9 different discourse styles that affect the participants' proving processes were determined. These forms of discourse are "1. Questioning, 2. Making a definition of concepts, 3. Reminding the pre-knowledge, 4. Proposing a proving method, 5. Presenting a confirmatory or falsifying example, 6. Making comments or explanations, 7. Making inferences, 8. Expression of affective experiences, 9. Guessing or predicting”. Besides, with reference to the relationship on the transcription text, the discourse forms associated with each component of the proof image were determined. Consequently, the contributions of both discourses and formal knowledge to the formation of the proof image were explained and, suggestions for proving applications, which may involve a proof image, were presented.

The subject of this thesis is the problem of the many - a problem which presents the challenge of there being many objects in situations in which we putatively take there to be one. The problem demands attention since it is paradoxical, ubiquitous in its extent, prompts a revision of the concepts it invokes (identity, distinctness, vagueness, and indeterminacy), and promises a revelation of the relation between it and other philosophical problems. Chapters 2-3 establish what the problem of the many is and establishes its relationship to other problems and paradoxes. Chapters 3-9 consider the most standard responses to the problem and chapter 10 presents a new response called role theory. There are three main original contributions:

1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy
which are based on alethic modality, such as those supplied by the
supervaluationist and the ontic indeterminist.

2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many.

3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.

This work is the result of research carried out in the Master in Legal Reasoning at the University of Girona, Spain, concluded in January 2019, under the guidance of Prof. Dr. Diego M. Papayannis and approved in defense before a panel composed by Professor Dr. Jordi Ferrer Beltrán, Professor Dr. Carmem Vázquez and Professor Dr. Vitor de Paula Ramos. The research deals with the epistemological problem about standards of the proof with a special focus on Brazilian civil procedural law.