Arguments of Interpretation and Argumentation Schemes
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“The Church-Turing “Thesis” As a Special Corollary of Gödel's
“The Church-Turing “Thesis” as a Special Corollary of Gödel’s Completeness Theorem,” in Computability: Turing, Gödel, Church, and Beyond, B. J. Copeland, C. Posy, and O. Shagrir (eds.), MIT Press (Cambridge), 2013, pp. 77-104. Saul A. Kripke This is the published version of the book chapter indicated above, which can be obtained from the publisher at https://mitpress.mit.edu/books/computability. It is reproduced here by permission of the publisher who holds the copyright. © The MIT Press The Church-Turing “ Thesis ” as a Special Corollary of G ö del ’ s 4 Completeness Theorem 1 Saul A. Kripke Traditionally, many writers, following Kleene (1952) , thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing ’ s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis — what Turing (1936) calls “ argument I ” — has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing himself in what he calls “ argument II. ” The idea is that computation is a special form of math- ematical deduction. Assuming the steps of the deduction can be stated in a first- order language, the Church-Turing thesis follows as a special case of G ö del ’ s completeness theorem (first-order algorithm theorem). I propose this idea as an alternative foundation for the Church-Turing thesis, both for human and machine computation. Clearly the relevant assumptions are justified for computations pres- ently known. -
A Compositional Analysis for Subset Comparatives∗ Helena APARICIO TERRASA–University of Chicago
A Compositional Analysis for Subset Comparatives∗ Helena APARICIO TERRASA–University of Chicago Abstract. Subset comparatives (Grant 2013) are amount comparatives in which there exists a set membership relation between the target and the standard of comparison. This paper argues that subset comparatives should be treated as regular phrasal comparatives with an added presupposi- tional component. More specifically, subset comparatives presuppose that: a) the standard has the property denoted by the target; and b) the standard has the property denoted by the matrix predi- cate. In the account developed below, the presuppositions of subset comparatives result from the compositional principles independently required to interpret those phrasal comparatives in which the standard is syntactically contained inside the target. Presuppositions are usually taken to be li- censed by certain lexical items (presupposition triggers). However, subset comparatives show that presuppositions can also arise as a result of semantic composition. This finding suggests that the grammar possesses more than one way of licensing these inferences. Further research will have to determine how productive this latter strategy is in natural languages. Keywords: Subset comparatives, presuppositions, amount comparatives, degrees. 1. Introduction Amount comparatives are usually discussed with respect to their degree or amount interpretation. This reading is exemplified in the comparative in (1), where the elements being compared are the cardinalities corresponding to the sets of books read by John and Mary respectively: (1) John read more books than Mary. |{x : books(x) ∧ John read x}| ≻ |{y : books(y) ∧ Mary read y}| In this paper, I discuss subset comparatives (Grant (to appear); Grant (2013)), a much less studied type of amount comparative illustrated in the Spanish1 example in (2):2 (2) Juan ha leído más libros que El Quijote. -
Interpretations and Mathematical Logic: a Tutorial
Interpretations and Mathematical Logic: a Tutorial Ali Enayat Dept. of Philosophy, Linguistics, and Theory of Science University of Gothenburg Olof Wijksgatan 6 PO Box 200, SE 405 30 Gothenburg, Sweden e-mail: [email protected] 1. INTRODUCTION Interpretations are about `seeing something as something else', an elusive yet intuitive notion that has been around since time immemorial. It was sys- tematized and elaborated by astrologers, mystics, and theologians, and later extensively employed and adapted by artists, poets, and scientists. At first ap- proximation, an interpretation is a structure-preserving mapping from a realm X to another realm Y , a mapping that is meant to bring hidden features of X and/or Y into view. For example, in the context of Freud's psychoanalytical theory [7], X = the realm of dreams, and Y = the realm of the unconscious; in Khayaam's quatrains [11], X = the metaphysical realm of theologians, and Y = the physical realm of human experience; and in von Neumann's foundations for Quantum Mechanics [14], X = the realm of Quantum Mechanics, and Y = the realm of Hilbert Space Theory. Turning to the domain of mathematics, familiar geometrical examples of in- terpretations include: Khayyam's interpretation of algebraic problems in terms of geometric ones (which was the remarkably innovative element in his solution of cubic equations), Descartes' reduction of Geometry to Algebra (which moved in a direction opposite to that of Khayyam's aforementioned interpretation), the Beltrami-Poincar´einterpretation of hyperbolic geometry within euclidean geom- etry [13]. Well-known examples in mathematical analysis include: Dedekind's interpretation of the linear continuum in terms of \cuts" of the rational line, Hamilton's interpertation of complex numbers as points in the Euclidean plane, and Cauchy's interpretation of real-valued integrals via complex-valued ones using the so-called contour method of integration in complex analysis. -
299 Abelson, RP, 66 Abductive Argument Argumentation Scheme For
Cambridge University Press 978-1-107-03930-8 - Methods of Argumentation Douglas Walton Index More information Index Abelson, R.P., 66 Anchored narrative, 137 , 163 Abductive argument Appeal to authority, 216–17 argumentation scheme for, 162 Appeal to expert opinion, 216 , 221 critical questions for, 162 Appeal to the people, see Fallacy of Abductive reasoning, 111 , 160 , 187–88 argument from popular opinion argumentation scheme for, 84 , 206 Araucaria, 15 , 16 , 99 critical questions for, 84 compared, 19–20 modeling with, 160–61 described, 12–13 Abortion case, 143–44 , 148 ArguMed, 16 , 17 Abstract argumentation framework, comparison, 20 35–36 Argument defi ned, 33 attack, 27 , 42 , 53 , 55 , 78 Action-based alternating transition back and forth exchange, 92 system, 156 composition, 46 , 48 , 90 ACTOS example, 1 , 20 defi nition, 48 , 88 , 89 critical questions, 15–16 defeasible, 7 , 30 , 227 , 229 , 246–47 explained, 14 open-ended, 238 Ad hominem argument, 50 , 159 , 234 evaluated, 33 defi ned, 96 identifying, 94–97 requirements of, 97 requirements for identifying, 89–90 types of, 118 Argument diagram, 72 , 255–56 , 259 Ad hominem attack, 235 composition of, 10 Ad verecundiam fallacy, 274 Argument from analogy, 42 , 114 , 139 , Affi davit example, 44–45 143 , 146 Agent argumentation scheme for, 122 , 145 described, 101 core, 126 , 130–31 , 149 desires and beliefs, 5 derived scheme, 130–31 Aiken, S., 281 simplest, 126 , 147–49 , 151–52 Airline fl ight schedule, 244 single respect scheme, 128 , 149–50 Ali, S., 104 version 1 , 141 , 142 -
Church's Thesis and the Conceptual Analysis of Computability
Church’s Thesis and the Conceptual Analysis of Computability Michael Rescorla Abstract: Church’s thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing’s work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church’s thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing’s work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we must correlate these syntactic entities with numbers. I argue that, in providing this correlation, we must demand that the correlation itself be computable. Otherwise, the Turing machine will compute uncomputable functions. But if we presuppose the intuitive notion of a computable relation between syntactic entities and numbers, then our analysis of computability is circular.1 §1. Turing machines and number-theoretic functions A Turing machine manipulates syntactic entities: strings consisting of strokes and blanks. I restrict attention to Turing machines that possess two key properties. First, the machine eventually halts when supplied with an input of finitely many adjacent strokes. Second, when the 1 I am greatly indebted to helpful feedback from two anonymous referees from this journal, as well as from: C. Anthony Anderson, Adam Elga, Kevin Falvey, Warren Goldfarb, Richard Heck, Peter Koellner, Oystein Linnebo, Charles Parsons, Gualtiero Piccinini, and Stewart Shapiro. I received extremely helpful comments when I presented earlier versions of this paper at the UCLA Philosophy of Mathematics Workshop, especially from Joseph Almog, D. -
Understanding Students' Reasoning
Understanding Students’ Reasoning: Argumentation Schemes as an Interpretation Method in Science Education Aikaterini Konstantinidou & Fabrizio Macagno Science & Education Contributions from History, Philosophy and Sociology of Science and Mathematics ISSN 0926-7220 Sci & Educ DOI 10.1007/s11191-012-9564-3 1 23 Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be self- archived in electronic repositories. If you wish to self-archive your work, please use the accepted author’s version for posting to your own website or your institution’s repository. You may further deposit the accepted author’s version on a funder’s repository at a funder’s request, provided it is not made publicly available until 12 months after publication. 1 23 Author's personal copy Sci & Educ DOI 10.1007/s11191-012-9564-3 Understanding Students’ Reasoning: Argumentation Schemes as an Interpretation Method in Science Education Aikaterini Konstantinidou • Fabrizio Macagno Ó Springer Science+Business Media Dordrecht 2012 Abstract The purpose of this paper is to investigate the argumentative structure of students’ arguments using argumentation schemes as an instrument for reconstructing the missing premises underlying their reasoning. Building on the recent literature in science education, in order for an explanation to be persuasive and achieve a conceptual change it needs to proceed from the interlocutor’s background knowledge to the analysis of the unknown or wrongly interpreted phenomena. Argumentation schemes represent the abstract forms of the most used and common forms of human reasoning, combining logical principles with semantic concepts. -
How to Build an Interpretation and Use Argument
Timothy S. Brophy Professor and Director, Institutional Assessment How to Build an University of Florida Email: [email protected] Interpretation and Phone: 352‐273‐4476 Use Argument To review the concept of validity as it applies to higher education Today’s Goals Provide a framework for developing an interpretation and use argument for assessments Validity What it is, and how we examine it • Validity refers to the degree to which evidence and theory support the interpretations of the test scores for proposed uses of tests. (p. 11) defined Source: • American Educational Research Association (AERA), American Psychological Association (APA), & National Council on Measurement in Education (NCME). (2014). Standards for educational and psychological testing. Validity Washington, DC: AERA The Importance of Validity The process of validation Validity is, therefore, the most involves accumulating relevant fundamental consideration in evidence to provide a sound developing tests and scientific basis for the proposed assessments. score and assessment results interpretations. (p. 11) Source: AERA, APA, & NCME. (2014). Standards for educational and psychological testing. Washington, DC: AERA • Most often this is qualitative; colleagues are a good resource • Review the evidence How Do We • Common sources of validity evidence Examine • Test Content Validity in • Construct (the idea or theory that supports the Higher assessment) • The validity coefficient Education? Important distinction It is not the test or assessment itself that is validated, but the inferences one makes from the measure based on the context of its use. Therefore it is not appropriate to refer to the ‘validity of the test or assessment’ ‐ instead, we refer to the validity of the interpretation of the results for the test or assessment’s intended purpose. -
Interpreting Arguments
Informal Logic IX.1, Winter 1987 Interpreting Arguments JONATHAN BERG University of Haifa We often speak of "the argument in" Two notions which would merit ex a particular piece of discourse. Although tensive analysis in a broader context will such talk may not be essential to only get a bit of clarification here. By philosophy in the philosophical sense, 'claims' I mean what are variously call it is surely a practical requirement for ed 'propositions', 'statements', or 'con most work in philosophy, whether in the tents'. I remain neutral with regard to interpretation of classical texts or in the their ontological status and shall not pre discussion of contemporary work, and tend to know exactly how to individuate it arises as well in everyday contexts them, especially in relation to sentences. wherever we care about reasons given I shall assume that for every claim there in support of a claim. (I assume this is is at least one literal, declarative why developing the ability to identify sentence typically used for making that arguments in discourse is a major goal claim, and often I shall not distinguish in many courses in informal logic or between the claim, proper, and such a critical thinking-the major goal when I sentence. teach the subject.) Thus arises the ques What I mean when I say that one tion, just how do we get from text to claim follows from other claims is much argument? harder to specify than what I do not I shall propose a set of principles for mean. I certainly do not have in mind the extrication of argu ments from any mere psychological or causal con argumentative prose. -
1 Argumentation in the Framework of Deliberation
1 ARGUMENTATION IN THE FRAMEWORK OF DELIBERATION DIALOGUE Douglas Walton, Katie Atkinson, Trevor Bench-Capon, Adam Wyner and Dan Cartwright According to argumentation theory, reasoning takes place in different types of dialogue: persuasion dialogue, negotiation, deliberation, information-seeking dialogue, inquiry, and eristic dialogue. These different dialogue types may be nested within one another. Current research in artificial intelligence is building formal models corresponding to each of these types of dialogue and showing how they can be implemented in, for example, multi-agent communications systems. In this paper, we (1) clarify the distinction between deliberation dialogue and persuasion dialogue, (2) survey some recent research in artificial intelligence studying formal properties of deliberation dialogue, (3) present a model of argumentation in deliberation dialogue that has proved to be useful in electronic democracy, and (4) argue that this model provides an attractive alternative to the dominant cost-benefit model of rational argumentation traditionally accepted in economics and other fields as the basis for evaluating argumentation of the kind used in policy decision making. One of the most important lessons of argumentation theory has been that arguments need to be analyzed and evaluated not only by identifying the logical form of an argument in abstraction from its context of use, but also by paying attention to the purpose for which an argument was supposedly used in a conversational setting. In particular, as we will show in this paper, it is vitally important to distinguish between two different types of conversational frameworks called persuasion dialogue and deliberation dialogue. As we will show, logical fallacies can easily be committed in the most common kinds of everyday reasoning by failing to take this distinction into account. -
Why We Should Abandon the Semantic Subset Principle
LANGUAGE LEARNING AND DEVELOPMENT https://doi.org/10.1080/15475441.2018.1499517 Why We Should Abandon the Semantic Subset Principle Julien Musolinoa, Kelsey Laity d’Agostinob, and Steve Piantadosic aDepartment of Psychology and Center for Cognitive Science, Rutgers University, Piscataway, NJ, USA; bDepartment of Philosophy, Rutgers University, New Brunswick, USA; cDepartment of Brain and Cognitive Sciences, University of Rochester, Rochester, USA ABSTRACT In a recent article published in this journal, Moscati and Crain (M&C) show- case the explanatory power of a learnability constraint called the Semantic Subset Principle (SSP) (Crain et al. 1994). If correct, M&C’s argument would represent a compelling demonstration of the operation of an innate, domain specific, learning principle. However, in trying to make the case for the SSP, M&C fail to clearly define their hypothesis, omit discussion of key facts, and contradict the theory itself. Moreover, their presentation does not address the core arguments and alternatives against their account available in the literature and misrepresents the position of their critics. Once these shortcomings are understood, a very different conclusion emerges: its historical significance notwithstanding, the SSP represents a flawed and obsolete account that should be abandoned. We discuss the implications of the demise of the SSP and describe more powerful and plausible alternatives that provide a better foundation for ongoing work in language acquisition. Introduction A common assumption within generative models of language acquisition is that learners are guided by a built-in constraint called the Subset Principle (SP) (Baker, 1979; Pinker, 1979; Dell, 1981; Berwick, 1985; Manzini & Wexler, 1987; among others). -
Justification of Argumentation Schemes
Justification of Argumentation Schemes D W U W W,M 3 29, C [email protected] Received by Greg Restall Published July 8, 2005 http://www.philosophy.unimelb.edu.au/ajl/2005 c 2005 Douglas Walton Abstract: Argumentation schemes are forms of argument that capture stereotypical patterns of human reasoning, especially defeasible ones like argument from expert opinion, that have proved troublesome to view deductively or inductively. Much practical work has already been done on argumentation schemes, proving their worth in [19], but more pre- cise investigations are needed to formalize their structures. The problem posed in this paper is what form justification of a given scheme, as hav- ing a certain precise structure of inference, should take. It is argued that defeasible argumentation schemes require both a systematic and a prag- matic justification, of a kind that can only be provided by the case study method of collecting key examples of arguments of the types tradition- ally classified as fallacies, and subjecting them to comparative examina- tion and analysis. By this method, postulated structures for schemes can be formulated as hypotheses to solve three kinds of problems: (1) how to classify such arguments into different types, (2) how to identify their premises and conclusions, and (3) how to formulate the critical questions used to evaluate each type of argument. 1 On September 19, 2004, I gave a lecture on informal logic and argumentation to the graduate students of the Institute of Logic and Cognition at Sun Yat- sen University in Guangzhou, China.1 The subject of the lecture included an account of argumentation schemes representing common forms of argument that are neither deductive nor inductive. -
Applications of Argumentation Schemes Chris Reed University of Dundee
CORE Metadata, citation and similar papers at core.ac.uk Provided by Scholarship at UWindsor University of Windsor Scholarship at UWindsor OSSA Conference Archive OSSA 4 May 17th, 9:00 AM - May 19th, 5:00 PM Applications of Argumentation Schemes Chris Reed University of Dundee Doug Walton University of Winnipeg Follow this and additional works at: http://scholar.uwindsor.ca/ossaarchive Part of the Philosophy Commons Reed, Chris and Walton, Doug, "Applications of Argumentation Schemes" (2001). OSSA Conference Archive. 97. http://scholar.uwindsor.ca/ossaarchive/OSSA4/papersandcommentaries/97 This Paper is brought to you for free and open access by the Faculty of Arts, Humanities and Social Sciences at Scholarship at UWindsor. It has been accepted for inclusion in OSSA Conference Archive by an authorized conference organizer of Scholarship at UWindsor. For more information, please contact [email protected]. Title: Applications of Argumentation Schemes Authors: Chris Reed, and Doug Walton Response to this paper by: Leo Groarke © 2001 Chris Reed, and Doug Walton ABSTRACT. Argumentation schemes capture common, stereotypical patterns of reasoning which are nondeductive and nonmonotonic. As interest in understanding these schemes from a theoretical point of view grows, so too does an awareness within computational work that these schemes might yield powerful techniques in a range of domains. This paper aims to perform two functions. First, to briefly review the literature on argumentation schemes, including the key works by Hastings, Walton and Kienpointner, and to set it in a broader context, adducing concerns from deductivism and presumptive, nonmonotonic reasoning. The second is to consider the various roles argumentation schemes might play in Artificial Intelligence, and in particular to consider (i) how schemes might be characterized as planning operators in domains such as natural language generation, with operationalized schemes representing means of achieving specific (e.g.