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Aristotle's Illicit Quantifier Shift: Is He Guilty Or Innocent
Aristos Volume 1 Issue 2 Article 2 9-2015 Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent Jack Green The University of Notre Dame Australia Follow this and additional works at: https://researchonline.nd.edu.au/aristos Part of the Philosophy Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Recommended Citation Green, J. (2015). "Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent," Aristos 1(2),, 1-18. https://doi.org/10.32613/aristos/ 2015.1.2.2 Retrieved from https://researchonline.nd.edu.au/aristos/vol1/iss2/2 This Article is brought to you by ResearchOnline@ND. It has been accepted for inclusion in Aristos by an authorized administrator of ResearchOnline@ND. For more information, please contact [email protected]. Green: Aristotle's Illicit Quantifier Shift: Is He Guilty or Innocent ARISTOTLE’S ILLICIT QUANTIFIER SHIFT: IS HE GUILTY OR INNOCENT? Jack Green 1. Introduction Aristotle’s Nicomachean Ethics (from hereon NE) falters at its very beginning. That is the claim of logicians and philosophers who believe that in the first book of the NE Aristotle mistakenly moves from ‘every action and pursuit aims at some good’ to ‘there is some one good at which all actions and pursuits aim.’1 Yet not everyone is convinced of Aristotle’s seeming blunder.2 In lieu of that, this paper has two purposes. Firstly, it is an attempt to bring some clarity to that debate in the face of divergent opinions of the location of the fallacy; some proposing it lies at I.i.1094a1-3, others at I.ii.1094a18-22, making it difficult to wade through the literature. -
Two-Dimensionalism: Semantics and Metasemantics
Two-Dimensionalism: Semantics and Metasemantics YEUNG, \y,ang -C-hun ...:' . '",~ ... ~ .. A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Master of Philosophy In Philosophy The Chinese University of Hong Kong January 2010 Abstract of thesis entitled: Two-Dimensionalism: Semantics and Metasemantics Submitted by YEUNG, Wang Chun for the degree of Master of Philosophy at the Chinese University of Hong Kong in July 2009 This ,thesis investigates problems surrounding the lively debate about how Kripke's examples of necessary a posteriori truths and contingent a priori truths should be explained. Two-dimensionalism is a recent development that offers a non-reductive analysis of such truths. The semantic interpretation of two-dimensionalism, proposed by Jackson and Chalmers, has certain 'descriptive' elements, which can be articulated in terms of the following three claims: (a) names and natural kind terms are reference-fixed by some associated properties, (b) these properties are known a priori by every competent speaker, and (c) these properties reflect the cognitive significance of sentences containing such terms. In this thesis, I argue against two arguments directed at such 'descriptive' elements, namely, The Argument from Ignorance and Error ('AlE'), and The Argument from Variability ('AV'). I thereby suggest that reference-fixing properties belong to the semantics of names and natural kind terms, and not to their metasemantics. Chapter 1 is a survey of some central notions related to the debate between descriptivism and direct reference theory, e.g. sense, reference, and rigidity. Chapter 2 outlines the two-dimensional approach and introduces the va~ieties of interpretations 11 of the two-dimensional framework. -
Scope Ambiguity in Syntax and Semantics
Scope Ambiguity in Syntax and Semantics Ling324 Reading: Meaning and Grammar, pg. 142-157 Is Scope Ambiguity Semantically Real? (1) Everyone loves someone. a. Wide scope reading of universal quantifier: ∀x[person(x) →∃y[person(y) ∧ love(x,y)]] b. Wide scope reading of existential quantifier: ∃y[person(y) ∧∀x[person(x) → love(x,y)]] 1 Could one semantic representation handle both the readings? • ∃y∀x reading entails ∀x∃y reading. ∀x∃y describes a more general situation where everyone has someone who s/he loves, and ∃y∀x describes a more specific situation where everyone loves the same person. • Then, couldn’t we say that Everyone loves someone is associated with the semantic representation that describes the more general reading, and the more specific reading obtains under an appropriate context? That is, couldn’t we say that Everyone loves someone is not semantically ambiguous, and its only semantic representation is the following? ∀x[person(x) →∃y[person(y) ∧ love(x,y)]] • After all, this semantic representation reflects the syntax: In syntax, everyone c-commands someone. In semantics, everyone scopes over someone. 2 Arguments for Real Scope Ambiguity • The semantic representation with the scope of quantifiers reflecting the order in which quantifiers occur in a sentence does not always represent the most general reading. (2) a. There was a name tag near every plate. b. A guard is standing in front of every gate. c. A student guide took every visitor to two museums. • Could we stipulate that when interpreting a sentence, no matter which order the quantifiers occur, always assign wide scope to every and narrow scope to some, two, etc.? 3 Arguments for Real Scope Ambiguity (cont.) • But in a negative sentence, ¬∀x∃y reading entails ¬∃y∀x reading. -
On the Logic of Two-Dimensional Semantics
Matrices and Modalities: On the Logic of Two-Dimensional Semantics MSc Thesis (Afstudeerscriptie) written by Peter Fritz (born March 4, 1984 in Ludwigsburg, Germany) under the supervision of Dr Paul Dekker and Prof Dr Yde Venema, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: June 29, 2011 Dr Paul Dekker Dr Emar Maier Dr Alessandra Palmigiano Prof Dr Frank Veltman Prof Dr Yde Venema Abstract Two-dimensional semantics is a theory in the philosophy of language that pro- vides an account of meaning which is sensitive to the distinction between ne- cessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two- dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. Acknowledgements I thank my supervisors Paul Dekker and Yde Venema for their help and encour- agement in preparing this thesis. -
The Ambiguous Nature of Language
International J. Soc. Sci. & Education 2017 Vol.7 Issue 4, ISSN: 2223-4934 E and 2227-393X Print The Ambiguous Nature of Language By Mohammad Awwad Applied Linguistics, English Department, Lebanese University, Beirut, LEBANON. [email protected] Abstract Linguistic ambiguity is rendered as a problematic issue since it hinders precise language processing. Ambiguity leads to a confusion of ideas in the reader’s mind when he struggles to decide on the precise meaning intended behind an utterance. In the literature relevant to the topic, no clear classification of linguistic ambiguity can be traced, for what is considered syntactic ambiguity, for some linguists, falls under pragmatic ambiguity for others; what is rendered as lexical ambiguity for some linguists is perceived as semantic ambiguity for others and still as unambiguous to few. The problematic issue, hence, can be recapitulated in the abstruseness hovering around what is linguistic ambiguity, what is not, and what comprises each type of ambiguity in language. The present study aimed at propounding lucid classification of ambiguity types according to their function in context by delving into ambiguity types which are displayed in English words, phrases, clauses, and sentences. converges in an attempt to disambiguate English language structures, and thus provide learners with a better language processing outcome and enhance teachers with a more facile and lucid teaching task. Keywords: linguistic ambiguity, language processing. 1. Introduction Ambiguity is derived from ‘ambiagotatem’ in Latin which combined ‘ambi’ and ‘ago’ each word meaning ‘around’ or ‘by’ (Atlas,1989) , and thus the concept of ambiguity is hesitation, doubt, or uncertainty and that concept associated the term ‘ambiguous’ from the first usage until the most recent linguistic definition. -
Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic
Discrete Mathematics, Chapter 1.4-1.5: Predicate Logic Richard Mayr University of Edinburgh, UK Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 1 / 23 Outline 1 Predicates 2 Quantifiers 3 Equivalences 4 Nested Quantifiers Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 2 / 23 Propositional Logic is not enough Suppose we have: “All men are mortal.” “Socrates is a man”. Does it follow that “Socrates is mortal” ? This cannot be expressed in propositional logic. We need a language to talk about objects, their properties and their relations. Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 3 / 23 Predicate Logic Extend propositional logic by the following new features. Variables: x; y; z;::: Predicates (i.e., propositional functions): P(x); Q(x); R(y); M(x; y);::: . Quantifiers: 8; 9. Propositional functions are a generalization of propositions. Can contain variables and predicates, e.g., P(x). Variables stand for (and can be replaced by) elements from their domain. Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 1.4-1.5 4 / 23 Propositional Functions Propositional functions become propositions (and thus have truth values) when all their variables are either I replaced by a value from their domain, or I bound by a quantifier P(x) denotes the value of propositional function P at x. The domain is often denoted by U (the universe). Example: Let P(x) denote “x > 5” and U be the integers. Then I P(8) is true. I P(5) is false. -
The Comparative Predictive Validity of Vague Quantifiers and Numeric
c European Survey Research Association Survey Research Methods (2014) ISSN 1864-3361 Vol.8, No. 3, pp. 169-179 http://www.surveymethods.org Is Vague Valid? The Comparative Predictive Validity of Vague Quantifiers and Numeric Response Options Tarek Al Baghal Institute of Social and Economic Research, University of Essex A number of surveys, including many student surveys, rely on vague quantifiers to measure behaviors important in evaluation. The ability of vague quantifiers to provide valid information, particularly compared to other measures of behaviors, has been questioned within both survey research generally and educational research specifically. Still, there is a dearth of research on whether vague quantifiers or numeric responses perform better in regards to validity. This study examines measurement properties of frequency estimation questions through the assessment of predictive validity, which has been shown to indicate performance of competing question for- mats. Data from the National Survey of Student Engagement (NSSE), a preeminent survey of university students, is analyzed in which two psychometrically tested benchmark scales, active and collaborative learning and student-faculty interaction, are measured through both vague quantifier and numeric responses. Predictive validity is assessed through correlations and re- gression models relating both vague and numeric scales to grades in school and two education experience satisfaction measures. Results support the view that the predictive validity is higher for vague quantifier scales, and hence better measurement properties, compared to numeric responses. These results are discussed in light of other findings on measurement properties of vague quantifiers and numeric responses, suggesting that vague quantifiers may be a useful measurement tool for behavioral data, particularly when it is the relationship between variables that are of interest. -
Fuzziness-Vagueness-Generality-Ambiguity. Journal of Pragmatics (Elsevier Science B.V
Fuzziness-vagueness-generality-ambiguity. Journal of Pragmatics (Elsevier Science B.V. in New York & Amsterdam), 1998, 29 (1): pp 13-31. Fuzziness---Vagueness---Generality---Ambiguity1 Qiao Zhang Published by Journal of Pragmatics (Elsevier Science B.V. in New York & Amsterdam), 1998, 29(1): pp 13-31. Contact: Dr Grace Zhang Department of Languages and Intercultural Education Curtin University of Technology GPO Box 1987 Perth, Western Australia 6845 Australia Tel: +61 8 9266 3478 Fax: +61 8 9266 4133 Email: [email protected] Abstract In this paper, I attempt to distinguish four linguistic concepts: fuzziness, vagueness, generality and ambiguity. The distinction between the four concepts is a significant matter, both theoretically and practically. Several tests are discussed from the perspectives of semantics, syntax and pragmatics. It is my contention that fuzziness, vagueness, and generality are licensed by Grice's Co-operative Principle, i.e. they are just as important as precision in language. I conclude that generality, vagueness, and fuzziness are under-determined, and ambiguity is over-determined. Fuzziness differs from generality, vagueness, and ambiguity in that it is not simply a result of a one-to- many relationship between a general meaning and its specifications; nor a list of possible related interpretations derived from a vague expression; nor a list of unrelated meanings denoted by an ambiguous expression. Fuzziness is inherent in the sense that it has no clear-cut referential boundary, and is not resolvable with resort to context, as opposed to generality, vagueness, and ambiguity, which may be contextually eliminated. It is also concluded that fuzziness is closely involved with language users' judgments. -
Propositional Logic, Truth Tables, and Predicate Logic (Rosen, Sections 1.1, 1.2, 1.3) TOPICS
Propositional Logic, Truth Tables, and Predicate Logic (Rosen, Sections 1.1, 1.2, 1.3) TOPICS • Propositional Logic • Logical Operations • Equivalences • Predicate Logic Logic? What is logic? Logic is a truth-preserving system of inference Truth-preserving: System: a set of If the initial mechanistic statements are transformations, based true, the inferred on syntax alone statements will be true Inference: the process of deriving (inferring) new statements from old statements Proposi0onal Logic n A proposion is a statement that is either true or false n Examples: n This class is CS122 (true) n Today is Sunday (false) n It is currently raining in Singapore (???) n Every proposi0on is true or false, but its truth value (true or false) may be unknown Proposi0onal Logic (II) n A proposi0onal statement is one of: n A simple proposi0on n denoted by a capital leJer, e.g. ‘A’. n A negaon of a proposi0onal statement n e.g. ¬A : “not A” n Two proposi0onal statements joined by a connecve n e.g. A ∧ B : “A and B” n e.g. A ∨ B : “A or B” n If a connec0ve joins complex statements, parenthesis are added n e.g. A ∧ (B∨C) Truth Tables n The truth value of a compound proposi0onal statement is determined by its truth table n Truth tables define the truth value of a connec0ve for every possible truth value of its terms Logical negaon n Negaon of proposi0on A is ¬A n A: It is snowing. n ¬A: It is not snowing n A: Newton knew Einstein. n ¬A: Newton did not know Einstein. -
Analyticity, Necessity and Belief Aspects of Two-Dimensional Semantics
!"# #$%"" &'( ( )#"% * +, %- ( * %. ( %/* %0 * ( +, %. % +, % %0 ( 1 2 % ( %/ %+ ( ( %/ ( %/ ( ( 1 ( ( ( % "# 344%%4 253333 #6#787 /0.' 9'# 86' 8" /0.' 9'# 86' (#"8'# Analyticity, Necessity and Belief Aspects of two-dimensional semantics Eric Johannesson c Eric Johannesson, Stockholm 2017 ISBN print 978-91-7649-776-0 ISBN PDF 978-91-7649-777-7 Printed by Universitetsservice US-AB, Stockholm 2017 Distributor: Department of Philosophy, Stockholm University Cover photo: the water at Petite Terre, Guadeloupe 2016 Contents Acknowledgments v 1 Introduction 1 2 Modal logic 7 2.1Introduction.......................... 7 2.2Basicmodallogic....................... 13 2.3Non-denotingterms..................... 21 2.4Chaptersummary...................... 23 3 Two-dimensionalism 25 3.1Introduction.......................... 25 3.2Basictemporallogic..................... 27 3.3 Adding the now operator.................. 29 3.4Addingtheactualityoperator................ 32 3.5 Descriptivism ......................... 34 3.6Theanalytic/syntheticdistinction............. 40 3.7 Descriptivist 2D-semantics .................. 42 3.8 Causal descriptivism ..................... 49 3.9Meta-semantictwo-dimensionalism............. 50 3.10Epistemictwo-dimensionalism................ 54 -
Formal Logic: Quantifiers, Predicates, and Validity
Formal Logic: Quantifiers, Predicates, and Validity CS 130 – Discrete Structures Variables and Statements • Variables: A variable is a symbol that stands for an individual in a collection or set. For example, the variable x may stand for one of the days. We may let x = Monday, x = Tuesday, etc. • We normally use letters at the end of the alphabet as variables, such as x, y, z. • A collection of objects is called the domain of objects. For the above example, the days in the week is the domain of variable x. CS 130 – Discrete Structures 55 Quantifiers • Propositional wffs have rather limited expressive power. E.g., “For every x, x > 0”. • Quantifiers: Quantifiers are phrases that refer to given quantities, such as "for some" or "for all" or "for every", indicating how many objects have a certain property. • Two kinds of quantifiers: – Universal Quantifier: represented by , “for all”, “for every”, “for each”, or “for any”. – Existential Quantifier: represented by , “for some”, “there exists”, “there is a”, or “for at least one”. CS 130 – Discrete Structures 56 Predicates • Predicate: It is the verbal statement which describes the property of a variable. Usually represented by the letter P, the notation P(x) is used to represent some unspecified property or predicate that x may have. – P(x) = x has 30 days. – P(April) = April has 30 days. – What is the truth value of (x)P(x) where x is all the months and P(x) = x has less than 32 days • Combining the quantifier and the predicate, we get a complete statement of the form (x)P(x) or (x)P(x) • The collection of objects is called the domain of interpretation, and it must contain at least one object. -
Quantifiers and Dependent Types
Quantifiers and dependent types Constructive Logic (15-317) Instructor: Giselle Reis Lecture 05 We have largely ignored the quantifiers so far. It is time to give them the proper attention, and: (1) design its rules, (2) show that they are locally sound and complete and (3) give them a computational interpretation. Quantifiers are statements about some formula parametrized by a term. Since we are working with a first-order logic, this term will have a simple type τ, different from the type o of formulas. A second-order logic allows terms to be of type τ ! ι, for simple types τ and ι, and higher-order logics allow terms to have arbitrary types. In particular, one can quantify over formulas in second- and higher-order logics, but not on first-order logics. As a consequence, the principle of induction (in its general form) can be expressed on those logics as: 8P:8n:(P (z) ^ (8x:P (x) ⊃ P (s(x))) ⊃ P (n)) But this comes with a toll, so we will restrict ourselves to first-order in this course. Also, we could have multiple types for terms (many-sorted logic), but since a logic with finitely many types can be reduced to a single-sorted logic, we work with a single type for simplicity, called τ. 1 Rules in natural deduction To design the natural deduction rules for the quantifiers, we will follow the same procedure as for the other connectives and look at their meanings. Some examples will also help on the way. Since we now have a new ele- ment in our language, namely, terms, we will have a new judgment a : τ denoting that the term a has type τ.