Nature Of Proof Research Articles

Mental Health Exemptions to Criminal Responsibility

Ill mental health is a key category for exempting individuals from criminal responsibility. Even in cases where a defendant has been found to have carried out the act, if mentally ‘ill enough’, the person could either be fully exempt from criminal responsibility and found not guilty – or be partially exempt and receive a reduced or special sentence on mental health grounds. Such outcomes might entail diversion into mental health treatment, sectioning – or release. In determining whether a mental health exemption is warranted in individual cases, ordinary practice is that psychologists or psychiatrists forensically assess the severity and nature of the accused’s impairment or disorder. While this might seem like a straightforward medical-juridical procedure of establishing evidence, this article uses a modified ‘genealogy of the present’ to show how mental health exemptions to criminal responsibility involve significantly more complexity. Looking to Norway and the UK, this article highlights differences in frameworks and implementation, including on matters of burden and nature of proof, and on causality. The article uses as an example the particular category of terrorism-related cases to bring out some of the contingencies involved. By doing so, the article shows the tensions inherent to the principle and practice of mental health exemptions, and its location between law, medicine, politics and security. Funding AcknowledgementThis research was made possible by a STAIRS grant from the Norwegian Institute of International Affairs (NUPI), as well as by funding from C-REX (Centre for Research on Extremism), University of Oslo.

Proof in the time of machines

We are concerned here with the nature of proof and what proof will become in this age of machines. We do so by comparing the values associated with (traditional) community based proof verification to those associated with computer proof verification. We finish by proposing ways that computer proofs might incorporate successful strategies from human experiences.

Psychoanalytic proof: Revisiting Freud’s Tally Argument

ABSTRACT This paper explores the notion of proof in clinical psychoanalysis by reconsidering an argument Freud made concerning the relation between successful psychoanalytic treatment and truth, dubbed the “Tally Argument” by the philosopher Adolf Grünbaum. I first reiterate criticisms of Grünbaum’s reconstruction of this argument, which bring out the degree to which he has misunderstood Freud. I then offer my own interpretation of the argument and the reasoning that underlies its key premise. Drawing from this discussion, I explore three forms of proof, each inspired also by analogies with other disciplines. Laurence Perrine’s “The Nature of Proof in the Interpretation of Poetry” stimulates my discussion of inferential proof, the relevant form of which involves proving an interpretation through a strong enough Inference to the Best Explanation. Mathematical proof stimulates my discussion of apodictic proof, of which psychoanalytic insight is a fitting example. Finally, holism in legal reasoning stimulates my discussion of holistic proof, which provides a reliable means by which therapeutic success can verify epistemic conclusions. These three forms of proof can play a crucial role in ascertaining psychoanalytic truth.

Formalism and Hilbert\u2019s understanding of consistency problems

Formalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism (advocated by Heine), game formalism (advocated by Thomae) and instrumental formalism (advocated by Hilbert). After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention to Hilbert’s instrumental formalism. My primary aim there will be to develop its formalist elements more fully. These are, in the main, (i) its rejection of the axiom-centric focus of traditional model-construction approaches to consistency problems, (ii) its departure from the traditional understanding of the basic nature of proof and (iii) its distinctively descriptive or observational orientation with regard to the consistency problem for arithmetic. More specifically, I will highlight what I see as the salient points of connection between Hilbert’s formalist attitude and his finitist standard for the consistency proof for arithmetic. I will also note what I see as a significant tension between Hilbert’s observational approach to the consistency problem for arithmetic and his expressed hope that his solution of that problem would dispense with certain epistemological concerns regarding arithmetic once and for all.

Platonism And Mathematical Explanations

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a nonnumerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (Rizza), the parsimony principle has been respected.Since both derivations resorting to conservative mathematics and nonnumerical best explanations also require abstract objects, concepts and principles, ontological parsimony must also be required of nominalistic accounts. One then might of course complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. However, it might prove more fruitful to leave this particular worry to one side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism.Two aspects are worthy of our attention: epistemic cost and debunking arguments. Our knowledge that good mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do play their respective theoretical role involves some question-begging assumptions regarding the nature of proofs. As for debunking, even if the face value content of either conservative or platonistic mathematical claims didn’t figure in our explanation of why we hold the mathematical beliefs that we do, we could still be justified in holding them so that the distinction between nominalistic deductions and explanations and platonistic ones turns out to be invidious with respect to the relevant propositional attitude, i.e., with respect to belief.

The Preservice Middle School Mathematics Teachers’ Opinions About the Nature of Proof

Bu çalışma ile ortaokul matematik öğretmeni adaylarının ispatın doğası hakkındaki görüşlerini ortaya çıkarmak amaçlanmıştır. Çalışmada nitel araştırma yöntemlerinden durum çalışması kullanılmıştır. Çalışma kapsamında ölçüt örnekleme yöntemi ile seçilen ve bir devlet üniversitesinin ortaokul matematik öğretmenliği programında öğrenim gören üç öğretmen adayının ispatın doğasına ilişkin görüşleri alınmıştır. Matematik öğretmen adaylarına, araştırmacılar tarafından geliştirilen ve açık uçlu sorulardan oluşan “İspatın Doğasına İlişkin Görüşme Formu” yarı yapılandırılmış görüşmeler aracılığıyla yöneltilmiştir. Görüşme verileri içerik analizi yöntemi ile analiz edilmiştir. İçerik analizi sonrasında öğretmen adaylarının ispatın doğasına ilişkin “genelleme”, “yöntem”, “doğruluğa ulaşma”, “problem çözme”, “biçime odaklanma” temaları altında tepkiler verdikleri belirlenmiştir. Çalışmada en sıklıkla ortaya çıkan tema “doğruluğa ulaşma” ; en az sıklıkla ortaya çıkan temalar ise “problem çözme” ve “biçime odaklanma” olarak belirlenmiştir. Bu çalışmada, ortaokul matematik öğretmeni adaylarının ispatın tanımını yapmada, ispatı ispat yapan şeyleri ve başarılı bir ispat için gerekli olan şeyleri belirlemede, kısacası ispatın doğasını anlamada zorluklar yaşadıkları sonucuna ulaşılmıştır.

Using and Misusing Legal Decisions: Why Antivaccine Claims About NVICP Cases Are Wrong

The question of whether vaccines cause autism has been extensively studied. Studies from different countries around the world, looking at millions of children in total, examined it and found no link. In spite of this powerful evidence, the actions of a small group of fervent believers may lead people to question the data. One tactic used to argue that vaccines cause autism is the use of compensation decisions from the National Vaccine Injury Compensation Program to claim such a link. This article demonstrates that not only does the nature of proof in the program make its decisions ill-suited to challenging the science, but the cases used do not, in their content, support that conclusions. Even the cases that most closely address the question of vaccines and autism do not show the link opponents claim exists, and many of the cases used are misrepresented and misused.

Students’ proofs of one-to-one and onto properties in introductory abstract algebra

Learning to write formal mathematical proofs presents a major challenge to undergraduates. Students who have succeeded in algorithm-intensive courses such as calculus often find the abstract logic and nonprocedural nature of proof writing to be technically difficult, ambiguous and filled with potential errors and misconceptions. This mixed-methods study examines 23 undergraduate students’ attempts to write one-to-one and onto proofs in an introductory abstract algebra course. Data collected consisted of six rounds of assessments on one-to-one and onto proofs, including homework, quizzes and exams. Using an existing framework of undergraduate proof writing, the researchers found that students’ misconceptions and errors varied substantially by student and task, with one-to-one proofs presenting unique challenges. Implications for teaching and research include emphasis on the logic of proof approaches and providing structured proof frameworks to assist undergraduates with the procedural and conceptual challenges in learning to write proofs.

The Nature of Proof in Psychiatry

The Nature of Proof in Psychiatry

60% Proof Lakatos, Proof, and Paraconsistency

Imre Lakatos’ Proofs and Refutations is a book well known to those who work in the philosophy of mathematics, though it is perhaps not widely referred to. Its general thrust is out of tenor with the foundationalist perspective that has dominated work in the philosophy of mathematics since the early years of the 20th century. It seems to us, though, that the book contains striking insights into the nature of proof, and the purpose of this paper is to explore and apply some of these.

Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.

How some college students represent their understandings of the nature of scientific theories

This study explores college students' representations about the nature of theories during their enrollment in a large astronomy course with instruction designed to address a number of nature of science issues. We focus our investigation on how nine students represent their understanding of theory, how they distinguish between scientific theories and non‐scientific theories, and how they reason about specific theories. Students' notions of theory were classified under four main categories: (1) hypothesis, (2) idea with evidence, (3) explanation, and (4) explanation based on evidence. Students' condition for deciding whether a given idea is a scientific theory or not were classified under six criteria: content domain, convention, evidence, mathematical content, methodology, and tentativeness. Students expressed slight levels of variation between their reasoning about scientific theories in general and specific theories they learned in the course. Despite increased sophistication in some students' representations, this study affirms the complex dimensions involved in teaching and assessing student understanding about theories. The implications of this study underscore the need to explicitly address the nature of proof in science and issues of tentativeness and certainty students associate with scientific theories, and provide students with more opportunities to utilize the language of science.

Peasants and Jews in Medieval Germany: Studies in Cultural, Social and Economic History (review)

244 Short Notices Parergon 21.1 (2004) other, research-oriented contributions, they reflect very well the variety and vitality of medieval studies in just one institution in the Australian higher education sector. Toby Burrows Scholars’ Centre The University of Western Australia Toch, Michael, Peasants and Jews in Medieval Germany: Studies in Cultural, Social and Economic History (Variorum Collected Studies), Aldershot, Ashgate, 2003; pp.xiv, 328; RRP £57.50; ISBN 0860788962. Michael Toch has devoted much of his scholarly life to teasing out some of the more obscure aspects of peasant history in Germany and Eastern Europe. For instance, while we know little of the language of German peasants, particularly when they are speaking to one another, he has used small but significant scenes in medieval German literature to consider what aspects of communication between lords and peasants can tell us about their social attitudes and the strategies they used at different times and in different places to maintain their particular interests. He develops some interesting ideas about the economic relationships involved that run counter to the received wisdom about the transition from direct cultivation to peasant tenure in agriculture that developed about the time of the Plague. This relates especially to the lord’s provision of the working capital for his tenants, an aspect of continental farming which did not cross the Channel and so is unfamiliar to historians of England. Agrarian credit of this and other varieties, and its organisation and importance, have been neglected. Much of his work is in such gaps, areas that have received little attention from other historians because of the difficulty and sparseness of the evidence, such as inland transport. His studies of the Jewish communities in Germany their location and function, their establishment and spread, immigration and internal growth, shows urban growth followed in the sixteenth century by rural relocation. Explanations in terms of the pull of opportunity against the push of violence, the threat of anti-Judaism and the rival interests of other power groups in the community are weighed against the evidence. He points to the form of internal migration, in extended family groups, as opposed to the movement historians are accustomed to expect of young single adults that characterises most western Short Notices 245 Parergon 21.1 (2004) internal migration. He also discusses the way in which emigration was promoted by a perceived need to protect capital from expropriation. His analysis of the size of the Jewish communities, and their stratification casts light on their cultural and intellectual development. Perhaps the most interesting article is the reassessment of Verlinden’s work that made the idea of Jewish dominance of the slave trade in the period before 1100 an orthodox historical assumption. This should be set for students as an example of the precise and careful examination of evidence and the nature of proof. Sybil M. Jack University of Sydney ...

Call for Manuscripts: Focus Issue on the Role of Proof throughout the Mathematics Curriculum

Proof has traditionally been the touchstone of mathematics—that which distinguishes it from theother sciences. The role and nature of proof in a Standards-based curriculum merit reexaminationin an era of reform. In 1998 a fall issue of the Mathematics Teacher will focus on the theme of proof inall aspects of secondary school mathematics. The Editorial Panel is seeking manuscripts for thisissue.

Call for Manuscripts: Focus Issue on the Role of Proof throughout the Mathematics Curriculum

Proof has traditionally been the touchstone of mathematics—that which distinguishes it from the other sciences. The role and nature of proof in a Standards-based cwTiculum merit reexamination in an era of reform. In 1998 a fall issue of the Mathematics Teacher will focus on the theme of proof in all aspects of secondary school mathematics. The Editorial Panel is seeking manuscripts for this issue.

Implicit Epistemic Aspects of Constructive Logic

In the present paper I wish to regard constructive logic as a self-contained system for the treatment of epistemological issues; the explanations of the constructivist logical notions are cast in an epistemological mold already from the outset. The discussion offered here intends to make explicit this implicit epistemic character of constructivism. Particular attention will be given to the intended interpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Lof, puts the system on par with the early efforts of Frege and Whitehead-Russell. This quite recent work, however, has proved valuable not only in the philosophy and foundations of mathematics, but has also found practical application in computer science, where the language of constructivism serves as an implementable programming language, and within the philosophy of language.\footnote{Nordstr\"{o}m et al. (1990) give an overview of the work in computer science, whereas Ranta (1995) provides an impressive constructivist alternative to Montague Grammar using the richer type structure of Martin-L\"{o}f in place of the simple classical type theory of Church.} My presentation will be carried out through a contrast with standard metamathematical work.\footnote{Troelstra and van Dalen (1988) give an encyclopedic treatment of the metamathematics of constructivism.} In the course of the development I have occasion to offer some novel considerations (in Sections~6 and 8) on the nature of proof and inference(-acts).

Call for Manuscripts: Focus Issue on the Role of Proof throughout the Mathematics Curriculum

Proof has traditionally been the touchstone of mathematics—that which distinguishes it from the other sciences. The role and nature of proof in a Standards-based curriculum merit reexamination in an era of reform. In 1998 a fall issue of the Mathematics Teacher will focus on the theme of proof in all aspects of secondary school mathematics. The Editorial Panel is seeking manuscripts for this issue.

Call for Manuscripts: Focus Issue on the Role of Proof throughout the Mathematics Curriculum

Proof has tradjtionally been the touchstone of mathematics—that which distinguishes it from the other sciences. The role and nature of proof in a Standards-based curriculum merit reexamination in an era of reform. In 1998 a fall issue of the Mathematics Teacher will focus on the theme of proof in all aspects of secondary school mathematics. The Editorial Panel is seeking manuscripts for this issue.

Call for Manuscripts: Focus Issues on the Role of Proof throughout the Mathematics Curriculum

Proof has traditionally been the touchstone of mathematics—that which distinguishes it from the other sciences. The role and nature of proof in a Standards-based curriculum merit reexamination in an era of reform. In 1998 a fall issue of the Mathematics Teacher will focus on the theme of proof in all aspects of secondary school mathematics. The Editorial Panel is seeking manuscripts for this issue.

Textual Forensics

Because textual scholarship, having no definable Fach, or subject matter, is an exemplary postmodernist antidiscipline, it can serve as a site for testing the epistemological assumptions and protocols of the current debate over the status of evidence and the nature of proof. Since text is “authority” and “original” and yet also “network” and “tissue” and since forensics encompasses both hard physical “facts” and the rhetorical formulation that gives such data interpretive meaning, a textual forensics will codify and test the interaction of the phenomenological world and the hermeneutic analysis of its evidence. With procedural and conceptual links both to scientific empiricism and to rhetorical strategies for persuasion, textual scholarship becomes a vehicle for anatomizing the postmodernist breakdown of the master narratives, including that of evidence and proof.