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Chapter 5: Methods of Proof for Boolean Logic
Chapter 5: Methods of Proof for Boolean Logic § 5.1 Valid inference steps Conjunction elimination Sometimes called simplification. From a conjunction, infer any of the conjuncts. • From P ∧ Q, infer P (or infer Q). Conjunction introduction Sometimes called conjunction. From a pair of sentences, infer their conjunction. • From P and Q, infer P ∧ Q. § 5.2 Proof by cases This is another valid inference step (it will form the rule of disjunction elimination in our formal deductive system and in Fitch), but it is also a powerful proof strategy. In a proof by cases, one begins with a disjunction (as a premise, or as an intermediate conclusion already proved). One then shows that a certain consequence may be deduced from each of the disjuncts taken separately. One concludes that that same sentence is a consequence of the entire disjunction. • From P ∨ Q, and from the fact that S follows from P and S also follows from Q, infer S. The general proof strategy looks like this: if you have a disjunction, then you know that at least one of the disjuncts is true—you just don’t know which one. So you consider the individual “cases” (i.e., disjuncts), one at a time. You assume the first disjunct, and then derive your conclusion from it. You repeat this process for each disjunct. So it doesn’t matter which disjunct is true—you get the same conclusion in any case. Hence you may infer that it follows from the entire disjunction. In practice, this method of proof requires the use of “subproofs”—we will take these up in the next chapter when we look at formal proofs. -
In Defence of Constructive Empiricism: Metaphysics Versus Science
To appear in Journal for General Philosophy of Science (2004) In Defence of Constructive Empiricism: Metaphysics versus Science F.A. Muller Institute for the History and Philosophy of Science and Mathematics Utrecht University, P.O. Box 80.000 3508 TA Utrecht, The Netherlands E-mail: [email protected] August 2003 Summary Over the past years, in books and journals (this journal included), N. Maxwell launched a ferocious attack on B.C. van Fraassen's view of science called Con- structive Empiricism (CE). This attack has been totally ignored. Must we con- clude from this silence that no defence is possible against the attack and that a fortiori Maxwell has buried CE once and for all, or is the attack too obviously flawed as not to merit exposure? We believe that neither is the case and hope that a careful dissection of Maxwell's reasoning will make this clear. This dis- section includes an analysis of Maxwell's `aberrance-argument' (omnipresent in his many writings) for the contentious claim that science implicitly and per- manently accepts a substantial, metaphysical thesis about the universe. This claim generally has been ignored too, for more than a quarter of a century. Our con- clusions will be that, first, Maxwell's attacks on CE can be beaten off; secondly, his `aberrance-arguments' do not establish what Maxwell believes they estab- lish; but, thirdly, we can draw a number of valuable lessons from these attacks about the nature of science and of the libertarian nature of CE. Table of Contents on other side −! Contents 1 Exordium: What is Maxwell's Argument? 1 2 Does Science Implicitly Accept Metaphysics? 3 2.1 Aberrant Theories . -
A Cross-Cultural and Pragmatic Study of Felicity Conditions in the Same-Sex Marriage Discourse
Journal of Foreign Languages, Cultures and Civilizations June 2016, Vol. 4, No. 1, pp. 58-72 ISSN 2333-5882 (Print) 2333-5890 (Online) Copyright © The Author(s). All Rights Reserved. Published by American Research Institute for Policy Development DOI: 10.15640/jflcc.v4n1a7 URL: https://doi.org/10.15640/jflcc.v4n1a7 A Cross-Cultural and Pragmatic Study of Felicity Conditions in the Same-Sex Marriage Discourse Hashim Aliwy Mohammed Al-Husseini1 & Ghayth K. Shaker Al-Shaibani2 Abstract This paper investigates whether there are Felicity Conditions (FCs) for the same-sex marriage as being a contemporary practice of marriage relations in some countries. As such, the researchers adopt Austin’s (1962) Felicity Conditions (FCs) to examine if conditions of satisfaction are applicable to the same-sex marriage in Christian and Islamic cultures. The researchers focus on analysing and discussing the social, religious, and linguistic conventional procedures of the speech acts of marriage, specifically in the same-sex marriage discourse. We find out that same-sex marriage in Christianity is totally different from the traditional marriage with regard to the social, religious, and linguistic conventions. Consequently, we concluded that same-sex marriage discourse has no FCs in contrast to the traditional marriage in Christianity as well as marriage in Islam which has not changed in form and opposite sex marriage. Keyword: Felicity Conditions; homosexual relations; marriage speech acts; same-sex marriage discourse; conventional procedures 1. Introduction Trosborg (2010, p.3) stated that one can principally affirm that all pragmatic aspects, namely speech act theory and theory of politeness, may be liable to cross-cultural comparisons between two speech communities and/or two cultures. -
Stalnaker on Sleeping Beauty Brian Weatherson
Stalnaker on Sleeping Beauty Brian Weatherson The Sleeping Beauty puzzle provides a nice illustration of the approach to self-lo- cating belief defended by Robert Stalnaker in Our Knowledge of the Internal World (Stalnaker, 2008), as well as a test of the utility of that method. The setup of the Sleeping Beauty puzzle is by now fairly familiar. On Sunday Sleeping Beauty is told the rules of the game, and a (known to be) fair coin is flipped. On Monday, Sleeping Beauty is woken, and then put back to sleep. If, and only if, the coin landed tails, she is woken again on Tuesday after having her memory of the Monday awakening erased.1 On Wednesday she is woken again and the game ends. There are a few ques- tions we can ask about Beauty’s attitudes as the game progresses. We’d like to know what her credence that the coin landed heads should be (a) Before she goes to sleep Sunday; (b) When she wakes on Monday; (c) When she wakes on Tuesday; and (d) When she wakes on Wednesday? Standard treatments of the Sleeping Beauty puzzle ignore (d), run together (b) and (c) into one (somewhat ill-formed) question, and then divide theorists into ‘halfers’ or ‘thirders’ depending on how they answer it. Following Stalnaker, I’m going to focus on (b) here, though I’ll have a little to say about (c) and (d) as well. I’ll be following 1 orthodoxy in taking 2 to be the clear answer to (a), and in taking the correct answers to (b) and (c) to be independent of how the coin lands, though I’ll briefly question that assumption at the end. -
Semantical Paradox* Tyler Burge
4 Semantical Paradox* Tyler Burge Frege remarked that the goal of all sciences is truth, but that it falls to logic to discern the laws of truth. Perceiving that the task of determining these laws went beyond Frege’s conception of it, Tarski enlarged the jurisdiction of logic, establishing semantics as truth’s lawyer.1 At the core of Tarski’s theory of truth and validity was a diagnosis of the Liar paradox according to which natural language was hopelessly infected with contradiction. Tarski construed himself as treating the disease by replacing ordinary discourse with a sanitized, artificial construction. But those interested in natural language have been dissatisfied with this medication. The best ground for dis satisfaction is that the notion of a natural language’s harboring contradictions is based on an illegitimate assimilation of natural language to a semantical system. According to that assimilation, part of the nature of a “language” is a set of postulates that purport to be true by virtue of their meaning or are at least partially constitutive of that “language”. Tarski thought that he had identified just such postulates in natural language as spawning inconsistency. But postulates are contained in theories that are promoted by people. Natural languages per se do not postulate or Tyler Burge, “Semantical Paradox", reprinted from The Journal of Philosophy 76 (1979), 169-98. Copyright © 1979 The Journal of Philosophy. Reprinted by permission of the Editor of The Journal of Philosophy and the author. * I am grateful to Robert L. Martin for several helpful discussions; to Herbert Enderton for proving the consistency (relative to that of arithmetic) of an extension of Construction C3; to Charles Parsons for stimulating exchanges back in 1973 and 1974; and to the John Simon Guggenheim Foundation for its support. -
Performative Speech Act Verbs in Present Day English
PERFORMATIVE SPEECH ACT VERBS IN PRESENT DAY ENGLISH ELENA LÓPEZ ÁLVAREZ Universidad Complutense de Madrid RESUMEN. En esta contribución se estudian los actos performativos y su influencia en el inglés de hoy en día. A partir de las teorías de J. L. Austin, entre otros autores, se desarrolla un panorama de esta orientación de la filosofía del lenguaje de Austin. PALABRAS CLAVE. Actos performativos, enunciado performativo, inglés. ABSTRACT. This paper focuses on performative speech act verbs in present day English. Reading the theories of J. L. Austin, among others,. With the basis of authors as J. L. Austin, this paper develops a brief landscape about this orientation of Austin’s linguistic philosophy. KEY WORDS. Performative speech act verbs, performative utterance, English. 1. INTRODUCCIÓN 1.1. HISTORICAL THEORETICAL BACKGROUND 1.1.1. The beginnings: J.L. Austin The origin of performative speech acts as we know them today dates back to the William James Lectures, the linguistic-philosophical theories devised and delivered by J.L. Austin at Harvard University in 1955, and collected into a series of lectures entitled How to do things with words, posthumously published in 1962. Austin was one of the most influential philosophers of his time. In these lectures, he provided a thorough exploration of performative speech acts, which was an extremely innovative area of study in those days. In the following pages, Austin’s main ideas (together with some comments by other authors) will be presented. 1.1.1.1. Constative – performative distinction In these lectures, Austin begins by making a clear distinction between constative and performative utterances. -
Two Views of the De Re E) Scope Paradoxes: (5) John Thinks at Least Two Men in the Room Are Spies
two views of the de re e) scope paradoxes: (5) John thinks at least two men in the room are spies. (John is not thinking of them as the men in the room) PLUK, Leeds, 2014 Daniel Rothschild ([email protected]) 2 neo-Fregean orthodoxy 1 de re in attitudes Kaplan [1986], building on Quine [1956] sets the standard for accounts of the de re. Basic assumption: semantic values in attitude reports present certain problems not present for other intensional contexts (such as metaphysi- cal modals). (6) (x believes α is a drunk and α denotes y) iff (9 guise g (satisfying some conditions that could make reference to x), the g = y and x A reasonable subset of the data to be captured, for the use of a term α in believes the g is drunk.) an attitude context. Covers a), b) be modified to handle c), d) and e) a) attitude about α does not require the attitude holder to think of α under the predicative content expressed by α. So substitution of co- a) we do not require that x think about y as α. extensive terms: b) we can make the with two different guises x can think y is drunk and is not drunk. (1) John thinks the mayor/the man in the corner is tall. Kaplan puts no contextual restrictions on what guises (his `names') can be, he just quantifies over them and requires them to be vivid, be an b) double vision. at least across different conversation contexts, but per- acquaintance relation for the attitude holder of the referent. -
Mind and Language Seminar: Theories of Content
Mind and Language Seminar: Theories of Content Ned Block and David Chalmers Meetings • Main meeting: Tuesdays 4-7pm over Zoom [4-6pm in weeks without a visitor] • Student meeting: Mondays 5-6pm hybrid • Starting Feb 22 [only weeks with a visitor] • Enrolled students and NYU philosophy graduate students only. • Feb 2: Background: Theories of Content • Feb 9: Background: Causal/Teleological Theories • Feb 16: Background: Interpretivism • Feb 23: Nick Shea • March 2: Robbie Williams • March 9: Frances Egan • March 16: Adam Pautz • March 23: Veronica Gómez Sánchez • March 30: Background: Phenomenal Intentionality • April 6: Imogen Dickie • April 13: Angela Mendelovici • April 20: Background: Conceptual-Role Semantics • April 27: Christopher Peacocke • May 4: David Chalmers Assessment • Draft paper due April 19 • Term paper due May 17 Attendance Policy • Monday meetings: Enrolled students and NYU philosophy graduate students only. • Tuesday meetings: NYU and NYC Consortium students and faculty only • Very limited exceptions • Email us to sign up on email list if you haven’t already. Introductions Short History of the 20th Century • 1900-1970: Reduce philosophical questions to issues about language and meaning. • 1970s: Theories of meaning (philosophy of language as first philosophy) • 1980s: Theories of mental content (philosophy of mind as first philosophy). • 1990s: Brick wall. Theories of Content • What is content? • What is a theory of content? Content • Content (in the broadest sense?) is intentionality or aboutness • Something has content when it is about something. Contents • Content = truth-conditions • Content = satisfaction-conditions • Content = propositions • Content = objects of intentional states • Content = … What Has Content? • What sort of thing has content? What Has Content? • What sort of thing has content? • language (esp. -
Presupposition As Investigator Certainty in a Police Interrogation: the Case of Lorenzo Montoya’S False Confession
Presupposition as investigator certainty in a police interrogation: The case of Lorenzo Montoya’s false confession Author: Philip Gaines This is a postprint of an article that originally appeared in Discourse & Society on July 2018. The final version can be found at https://dx.doi.org/10.1177/0957926518754417. Gaines, Philip. "Presupposition as investigator certainty in a police interrogation: The case of Lorenzo Montoya's false confession." Discourse & Society 29, no. 4 (July 2018): 399-419. DOI:10.1177/0957926518754417. Made available through Montana State University’s ScholarWorks scholarworks.montana.edu Presupposition as investigator certainty in a police interrogation: The case of Lorenzo Montoya’s false confession Philip Gaines Montana State University, USA Abstract This article presents an analysis of the use by police investigators of presupposition-bearing questions (PBQs) in interrogation as a process for communicating certainty of guilt. Among the techniques of interrogational maximization employed by police is the communication to the suspect of the interrogators’ certainty of the suspect’s guilt. While social science research notes that such communication of certainty is given directly, for example by statements that they ‘know’ the suspect is guilty or by direct accusations such as ‘you did it’, this analysis shows that certainty of guilt can also be communicated by presuppositions embedded in interrogation questions. Discourse analysis of the complete transcript of the interrogation of a 14-year-old suspect reveals further that through the use of 177 PBQs, interrogators are able to accrue inadvertent admissions to three crucial global ‘facts’ about the suspect’s involvement in the crime – each of which is composed of multiple subsidiary ‘facts’. -
Entailment, Presupposition, and Implicature in the Work of Ernest Hemingway and Tim O'brien
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1994 The tS ylistic Mechanics of Implicitness: Entailment, Presupposition, and Implicature in the Work of Ernest Hemingway and Tim O'Brien. Donna Glee Williams Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Williams, Donna Glee, "The tS ylistic Mechanics of Implicitness: Entailment, Presupposition, and Implicature in the Work of Ernest Hemingway and Tim O'Brien." (1994). LSU Historical Dissertations and Theses. 5768. https://digitalcommons.lsu.edu/gradschool_disstheses/5768 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough,m asubstandard r gins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. -
Exclamatives, Normalcy Conditions and Common Ground
Revue de Sémantique et Pragmatique 40 | 2016 Exclamation et intersubjectivité Exclamatives, Normalcy Conditions and Common Ground Franz d’Avis Electronic version URL: http://journals.openedition.org/rsp/279 DOI: 10.4000/rsp.279 ISSN: 2610-4377 Publisher Presses universitaires d'Orléans Printed version Date of publication: 1 March 2017 Number of pages: 17-34 ISSN: 1285-4093 Electronic reference Franz d’Avis, « Exclamatives, Normalcy Conditions and Common Ground », Revue de Sémantique et Pragmatique [Online], 40 | 2016, Online since 01 March 2018, connection on 10 December 2020. URL : http://journals.openedition.org/rsp/279 ; DOI : https://doi.org/10.4000/rsp.279 Revue de Sémantique et Pragmatique Revue de Sémantique et Pragmatique. 2016. Numéro 40. pp. 17-34. Exclamatives, Normalcy Conditions and Common Ground Franz d’Avis Johannes Gutenberg-Universität Mainz 1. INTRODUCTION The starting point for the search for exclamative sentence types in a lan- guage is often the description of a certain function that utterances of sentences of that type would have. One formulation could be: With the use of an excla- mative sentence, a speaker expresses that the state of affairs described by a proposition given in the sentence is not in accordance with his expectations about the world.1 Exclamative utterances may include an emotional attitude on the part of the speaker, which is often described as surprise in the literature, cf. Altmann (1987, 1993a), Michaelis/Lambrecht (1996), d’Avis (2001), Michaelis (2001), Roguska (2008) and others. Surprise is an attitude that is based on the belief that something unexpected is the case, see from a psychological point of view Reisenzein (2000). -
Felicity Conditions for Counterfactual Conditionals Containing Proper
Counterfactuals in Context: Felicity conditions for counterfactual conditionals containing proper names William Robinson A thesis Submitted in partial fulfillment of the requirements for the degree of Master of Arts University of Washington 2013 Committee: Toshiyuki Ogihara Barbara Citko Program Authorized to Offer Degree: Linguistics 2 ©Copyright 2013 William Robinson 3 University of Washington Abstract Counterfactuals in Context: Felicity conditions for counterfactual conditionals containing proper names William Robinson Chair of the Supervisory Committee: Toshiyuki Ogihara PhD Linguistics Linguistics This thesis provides felicity conditions for counterfactual conditionals containing proper names in which essential changes to an individual are counterfactually posited using contrastive focus in either the antecedent or consequent clause. The felicity conditions proposed are an adaptation of Heim’s (1992) CCP Semantics into Kratzer’s (1981) truth conditions for counterfactual conditionals in which the partition function f(w) serves as the local context of evaluation for the antecedent clause, while the set of worlds characterized by the antecedent serves as the local context for the consequent clause. In order for the felicity conditions to generate the right results, it is shown that they must be couched in a rigid designator/essentialist framework inspired by Kripke (1980). This correctly predicts that consequents containing rigid designators are infelicitous when their input context—the set of worlds accessible from the antecedent clause— does not contain a suitable referent. 4 Introduction We use counterfactual conditionals like (1a-b) to make claims about the “ways things could have been,” not about the way things actually are1 (Lewis 1973, p.84). The antecedent clause of a counterfactual conditional posits a change to the actual world from which the consequent clause would/might follow.