Lecture 2:] the Research Process Scientific Reasoning and Paradigms What Is Science?
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Complexity Classifications for Propositional Abduction in Post's
Complexity Classifications for Propositional Abduction in Post’s Framework∗ Nadia Creignou1, Johannes Schmidt1, Michael Thomas2 1 LIF, UMR CNRS 6166, Aix-Marseille Universit´e 163, Avenue de Luminy, 13288 Marseille Cedex 9, France [email protected] [email protected] 2 Institut f¨ur Theoretische Informatik, Gottfried Wilhelm Leibniz Universit¨at Appelstr. 4, 30167 Hannover, Germany [email protected] Abstract. In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world’s behavior it aims at finding an explanation for some observed manifestation. In this paper we consider propositional abduction, where the knowledge base and the manifesta- tion are represented by propositional formulae. The problem of deciding p whether there exists an explanation has been shown to be Σ2 -complete in general. We focus on formulae in which the allowed connectives are taken from certain sets of Boolean functions. We consider different vari- ants of the abduction problem in restricting both the manifestations and the hypotheses. For all these variants we obtain a complexity classifica- tion for all possible sets of Boolean functions. In this way, we identify easier cases, namely NP-complete, coNP-complete and polynomial cases. Thus, we get a detailed picture of the complexity of the propositional abduction problem, hence highlighting sources of intractability. Further, we address the problem of counting the explanations and draw a com- plete picture for the counting complexity. Keywords: abduction, computational complexity, Post’s lattice, propo- sitional logic, boolean connective arXiv:1006.4923v1 [cs.CC] 25 Jun 2010 ∗ Supported by ANR Algorithms and complexity 07-BLAN-0327-04 and DFG grant VO 630/6-1. -
1.2. INDUCTIVE REASONING Much Mathematical Discovery Starts with Inductive Reasoning – the Process of Reaching General Conclus
1.2. INDUCTIVE REASONING Much mathematical discovery starts with inductive reasoning – the process of reaching general conclusions, called conjectures, through the examination of particular cases and the recognition of patterns. These conjectures are then more formally proved using deductive methods, which will be discussed in the next section. Below we look at three examples that use inductive reasoning. Number Patterns Suppose you had to predict the sixth number in the following sequence: 1, -3, 6, -10, 15, ? How would you proceed with such a question? The trick, it seems, is to discern a specific pattern in the given sequence of numbers. This kind of approach is a classic example of inductive reasoning. By identifying a rule that generates all five numbers in this sequence, your hope is to establish a pattern and be in a position to predict the sixth number with confidence. So can you do it? Try to work out this number before continuing. One fact is immediately clear: the numbers alternate sign from positive to negative. We thus expect the answer to be a negative number since it follows 15, a positive number. On closer inspection, we also realize that the difference between the magnitude (or absolute value) of successive numbers increases by 1 each time: 3 – 1 = 2 6 – 3 = 3 10 – 6 = 4 15 – 10 = 5 … We have then found the rule we sought for generating the next number in this sequence. The sixth number should be -21 since the difference between 15 and 21 is 6 and we had already determined that the answer should be negative. -
There Is No Pure Empirical Reasoning
There Is No Pure Empirical Reasoning 1. Empiricism and the Question of Empirical Reasons Empiricism may be defined as the view there is no a priori justification for any synthetic claim. Critics object that empiricism cannot account for all the kinds of knowledge we seem to possess, such as moral knowledge, metaphysical knowledge, mathematical knowledge, and modal knowledge.1 In some cases, empiricists try to account for these types of knowledge; in other cases, they shrug off the objections, happily concluding, for example, that there is no moral knowledge, or that there is no metaphysical knowledge.2 But empiricism cannot shrug off just any type of knowledge; to be minimally plausible, empiricism must, for example, at least be able to account for paradigm instances of empirical knowledge, including especially scientific knowledge. Empirical knowledge can be divided into three categories: (a) knowledge by direct observation; (b) knowledge that is deductively inferred from observations; and (c) knowledge that is non-deductively inferred from observations, including knowledge arrived at by induction and inference to the best explanation. Category (c) includes all scientific knowledge. This category is of particular import to empiricists, many of whom take scientific knowledge as a sort of paradigm for knowledge in general; indeed, this forms a central source of motivation for empiricism.3 Thus, if there is any kind of knowledge that empiricists need to be able to account for, it is knowledge of type (c). I use the term “empirical reasoning” to refer to the reasoning involved in acquiring this type of knowledge – that is, to any instance of reasoning in which (i) the premises are justified directly by observation, (ii) the reasoning is non- deductive, and (iii) the reasoning provides adequate justification for the conclusion. -
Thomas Kuhn on Paradigms
Vol. 29, No. 7, July 2020, pp. 1650–1657 DOI 10.1111/poms.13188 ISSN 1059-1478|EISSN 1937-5956|20|2907|1650 © 2020 Production and Operations Management Society Thomas Kuhn on Paradigms Gopesh Anand Department of Business Administration, Gies College of Business, University of Illinois at Urbana-Champaign, 469 Wohlers Hall, 1206 South Sixth Street, Champaign, Illinois 61820, USA, [email protected] Eric C. Larson Department of Business Administration, Gies College of Business, University of Illinois at Urbana-Champaign, 8 Wohlers Hall, 1206 S. Sixth, Champaign, Illinois 61820, USA, [email protected] Joseph T. Mahoney* Department of Business Administration, Gies College of Business, University of Illinois at Urbana-Champaign, 140C Wohlers Hall, 1206 South Sixth Street, Champaign, Illinois 61820, USA, [email protected] his study provides key arguments and contributions of Kuhn (1970) concerning paradigms, paradigm shifts, and sci- T entific revolutions. We provide interpretations of Kuhn’s (1970) key ideas and concepts, especially as they relate to business management research. We conclude by considering the practical implications of paradigms and paradigm shifts for contemporary business management researchers and suggest that ethical rules of conversation are at least as critical for the health of a scientific community as methodological rules (e.g., the rules of logical positivism) derived from the phi- losophy of science. Key words: Paradigms; paradigm shifts; scientific revolutions; normal science History: Received: February 2019; Accepted: March 2020 by Kalyan Singhal, after 3 revisions. The Structure of Scientific Revolutions the rich descriptions of the process of advancing this theory. SSR showed that science primarily advances Thomas S. -
A Philosophical Treatise on the Connection of Scientific Reasoning
mathematics Review A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic Evangelos Athanassopoulos 1 and Michael Gr. Voskoglou 2,* 1 Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece; [email protected] 2 Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece * Correspondence: [email protected] Received: 4 May 2020; Accepted: 19 May 2020; Published:1 June 2020 Abstract: The present article studies the connection of scientific reasoning with fuzzy logic. Induction and deduction are the two main types of human reasoning. Although deduction is the basis of the scientific method, almost all the scientific progress (with pure mathematics being probably the unique exception) has its roots to inductive reasoning. Fuzzy logic gives to the disdainful by the classical/bivalent logic induction its proper place and importance as a fundamental component of the scientific reasoning. The error of induction is transferred to deductive reasoning through its premises. Consequently, although deduction is always a valid process, it is not an infallible method. Thus, there is a need of quantifying the degree of truth not only of the inductive, but also of the deductive arguments. In the former case, probability and statistics and of course fuzzy logic in cases of imprecision are the tools available for this purpose. In the latter case, the Bayesian probabilities play a dominant role. As many specialists argue nowadays, the whole science could be viewed as a Bayesian process. A timely example, concerning the validity of the viruses’ tests, is presented, illustrating the importance of the Bayesian processes for scientific reasoning. -
Arguments Vs. Explanations
Arguments vs. Explanations Arguments and explanations share a lot of common features. In fact, it can be hard to tell the difference between them if you look just at the structure. Sometimes, the exact same structure can function as an argument or as an explanation depending on the context. At the same time, arguments are very different in terms of what they try to accomplish. Explaining and arguing are very different activities even though they use the same types of structures. In a similar vein, building something and taking it apart are two very different activities, but we typically use the same tools for both. Arguments and explanations both have a single sentence as their primary focus. In an argument, we call that sentence the “conclusion”, it’s what’s being argued for. In an explanation, that sentence is called the “explanandum”, it’s what’s being explained. All of the other sentences in an argument or explanation are focused on the conclusion or explanandum. In an argument, these other sentences are called “premises” and they provide basic reasons for thinking that the conclusion is true. In an explanation, these other sentences are called the “explanans” and provide information about how or why the explanandum is true. So in both cases we have a bunch of sentences all focused on one single sentence. That’s why it’s easy to confuse arguments and explanations, they have a similar structure. Premises/Explanans Conclusion/Explanandum What is an argument? An argument is an attempt to provide support for a claim. One useful way of thinking about this is that an argument is, at least potentially, something that could be used to persuade someone about the truth of the argument’s conclusion. -
Thomas Kuhn and Perspectival Realism a Thesis Presented to The
Thomas Kuhn and Perspectival Realism A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Arts Ryan J. O'Loughlin April 2017 © 2017 Ryan J. O'Loughlin. All Rights Reserved. 2 This thesis titled Thomas Kuhn and Perspectival Realism by RYAN J. O'LOUGHLIN has been approved for the Department of Philosophy and the College of Arts and Sciences by Philip Ehrlich Professor of Philosophy Robert Frank Dean, College of Arts and Sciences 3 ABSTRACT O'LOUGHLIN, RYAN J., M.A., April 2017, Philosophy Thomas Kuhn and Perspectival Realism Director of Thesis: Philip Ehrlich In this paper I discuss Giere’s reading of Kuhn as affirming perspectival realism and I present evidence demonstrating that this reading of Kuhn is correct. I consider several scientific realist theses that Kuhn rejects and discuss whether and to what extent perspectival realism may be regarded as a scientific realist position. I suggest adding Kuhn’s account of incommensurability, understood in its later form, to Giere’s account of perspectival realism. I conclude by providing a definition of perspectival realism that incorporates Kuhn’s incommensurability thesis as well as the specific claims of scientific realism that are compatible with perspectival realism. Perspectival realism thus understood is, at most, a weak form of scientific realism. 4 TABLE OF CONTENTS Page Abstract .............................................................................................................................. -
Notes on Pragmatism and Scientific Realism Author(S): Cleo H
Notes on Pragmatism and Scientific Realism Author(s): Cleo H. Cherryholmes Source: Educational Researcher, Vol. 21, No. 6, (Aug. - Sep., 1992), pp. 13-17 Published by: American Educational Research Association Stable URL: http://www.jstor.org/stable/1176502 Accessed: 02/05/2008 14:02 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aera. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We enable the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. http://www.jstor.org Notes on Pragmatismand Scientific Realism CLEOH. CHERRYHOLMES Ernest R. House's article "Realism in plicit declarationof pragmatism. Here is his 1905 statement ProfessorResearch" (1991) is informative for the overview it of it: of scientificrealism. -
Form and Explanation
Form and Explanation Jonathan Kramnick and Anahid Nersessian What does form explain? More often than not, when it comes to liter- ary criticism, form explains everything. Where form refers “to elements of a verbal composition,” including “rhythm, meter, structure, diction, imagery,” it distinguishes ordinary from figurative utterance and thereby defines the literary per se.1 Where form refers to the disposition of those elements such that the work of which they are a part mimes a “symbolic resolution to a concrete historical situation,” it distinguishes real from vir- tual phenomena and thereby defines the task of criticism as their ongoing adjudication.2 Both forensic and exculpatory in their promise, form’s ex- planations have been applied to circumstances widely disparate in scale, character, and significance. This is nothing new, but a recent flurry of de- bates identifying new varieties of form has thrown the unruliness of its application into relief. Taken together, they suggest that to give an account of form is to contribute to the work of making sense of linguistic meaning, aesthetic production, class struggle, objecthood, crises in the humanities and of the planet, how we read, why we read, and what’s wrong with these queries of how and why. In this context, form explains what we cannot: what’s the point of us at all? Contemporary partisans of form maintain that their high opinion of its exegetical power is at once something new in the field and the field’s 1. René Wellek, “Concepts of Form and Structure in Twentieth-Century Criticism,” Concepts of Criticism (New Haven, Conn., 1963), p. -
Evaluating Empirical Research
EVALUATING EMPIRICAL RESEARCH A NTIOCH It is important to maintain an objective and respectful tone as you evaluate others’ empirical studies. Keep in mind that study limitations are often a result of the epistemological limitations of real life research situations rather than the laziness or ignorance of the researchers. It’s U NIVERSITY NIVERSITY normal and expected for empirical studies to have limitations. Having said that, it’s part of your job as a critical reader and a smart researcher to provide a fair assessment of research done on your topic. B.A. Maher’s guidelines (as cited in Cone and Foster, 2008, pp 104- V 106) are useful in thinking of others’ studies, as well as for writing up your IRTIUAL own study. Here are the recommended questions to consider as you read each section of an article. As you think of other questions that are particularly W important to your topic, add them to the list. RITING Introduction Does the introduction provide a strong rationale for why the study is C ENTER needed? Are research questions and hypotheses clearly articulated? (Note that research questions are often presented implicitly within a description of the purpose of the study.) Method Is the method described so that replication is possible without further information Participants o Are subject recruitment and selection methods described? o Were participants randomly selected? Are there any probable biases in sampling? A NTIOCH o Is the sample appropriate in terms of the population to which the researchers wished to generalize? o Are characteristics of the sample described adequately? U NIVERSITY NIVERSITY o If two or more groups are being compared, are they shown to be comparable on potentially confounding variables (e.g. -
What Is a Philosophical Analysis?
JEFFREY C. KING WHAT IS A PHILOSOPHICAL ANALYSIS? (Received 24 January 1996) It is common for philosophers to offer philosophical accounts or analyses, as they are sometimes called, of knowledge, autonomy, representation, (moral) goodness, reference, and even modesty.1 These philosophical analyses raise deep questions. What is it that is being analyzed (i.e. what sorts of things are the objects of analysis)? What sort of thing is the analysis itself (a proposition? sentence?)? Under what conditions is an analysis correct? How can a correct analysis be informative? How, if at all, does the production of philo- sophical analyses differ from what scientists do? The purpose of the present paper is to provide answers to these questions. The traditional answers to the ®rst and last of these questions are that concepts are the objects of philosophical analysis and that philo- sophical analyses differ from the results of scienti®c investigation in being conceptual analyses. Like many philosophers I am suspicious of the notions of concept and conceptual analysis as traditionally understood. Though the critique of these notions is beyond the scope of the present work, the answers I shall give to the questions raised above shall not invoke concepts (understood as things distinct from properties).2 I count it as a virtue of my account that it is able to provide answers to the questions raised above without an appeal to concepts. And to the extent that it has been felt that concepts are needed to answer these questions, the present account weakens the case for positing concepts. Before addressing these questions, however, we shall make the simplifying assumption that analyses are given in a ªcanonical formº. -
Internationalizing the University Curricula Through Communication
DOCUMENT RESUME ED 428 409 CS 510 027 AUTHOR Oseguera, A. Anthony Lopez TITLE Internationalizing the University Curricula through Communication: A Comparative Analysis among Nation States as Matrix for the Promulgation of Internationalism, through the Theoretical Influence of Communication Rhetors and International Educators, Viewed within the Arena of Political-Economy. PUB DATE 1998-12-00 NOTE 55p.; Paper presented at the Annual Meeting of the Speech Communication Association of Puerto Rico (18th, San Juan, Puerto Rico, December 4-5, 1998). PUB TYPE Reports Research (143) Speeches/Meeting Papers (150) EDRS PRICE MF01/PC03 Plus Postage. DESCRIPTORS *College Curriculum; *Communication (Thought Transfer); Comparative Analysis; *Educational Change; Educational Research; Foreign Countries; Global Approach; Higher Education; *International Education IDENTIFIERS *Internationalism ABSTRACT This paper surveys the current situation of internationalism among the various nation states by a comparative analysis, as matrix, to promulgate the internationalizing process, as a worthwhile goal, within and without the college and university curricula; the theoretical influence and contributions of scholars in communication, international education, and political-economy, moreover, become allies toward this endeavor. The paper calls for the promulgation of a new and more effective educational paradigm; in this respect, helping the movement toward the creation of new and better schools for the next millennium. The paper profiles "poorer nations" and "richer nations" and then views the United States, with its enormous wealth, leading technology, vast educational infrastructure, and its respect for democratic principles, as an agent with agencies that can effect positive consequences to ameliorating the status quo. The paper presents two hypotheses: the malaise of the current educational paradigm is real, and the "abertura" (opening) toward a better paradigmatic, educational pathway is advisable and feasible.