Thoughts About Thoughts: the Structure of Fregean Propositions
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Reference and Sense
REFERENCE AND SENSE y two distinct ways of talking about the meaning of words y tlkitalking of SENSE=deali ng with relationshippggs inside language y talking of REFERENCE=dealing with reltilations hips bbtetween l. and the world y by means of reference a speaker indicates which things (including persons) are being talked about ege.g. My son is in the beech tree. II identifies persons identifies things y REFERENCE-relationship between the Enggplish expression ‘this p pgage’ and the thing you can hold between your finger and thumb (part of the world) y your left ear is the REFERENT of the phrase ‘your left ear’ while REFERENCE is the relationship between parts of a l. and things outside the l. y The same expression can be used to refer to different things- there are as many potential referents for the phrase ‘your left ear’ as there are pppeople in the world with left ears Many expressions can have VARIABLE REFERENCE y There are cases of expressions which in normal everyday conversation never refer to different things, i.e. which in most everyday situations that one can envisage have CONSTANT REFERENCE. y However, there is very little constancy of reference in l. Almost all of the fixing of reference comes from the context in which expressions are used. y Two different expressions can have the same referent class ica l example: ‘the MiMorning St’Star’ and ‘the Evening Star’ to refer to the planet Venus y SENSE of an expression is its place in a system of semantic relati onshi ps wit h other expressions in the l. -
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. -
Gottlob Frege: on Sense and Reference Professor Jeeloo Liu [Introduction]
Phil/Ling 375: Meaning and Mind [Handout #13] Gottlob Frege: On Sense and Reference Professor JeeLoo Liu [Introduction] I. Language and the World ___ How does language depict reality? Does reality have the same structure as the structure of language? For instance, the basic linguistic structure is a subject and a predicate, and the basic structure of the world is a particular and a universal (e.g. “Socrates is wise”). The subject usually is something of the world and we describe some property it has or does not have. A is F is true is A is really F, is false when A is not F. II. Different Elements of Language Singular terms: Terms that designate particular things Proper names Indexicals: now, today, here, I… Demonstratives: that, this… Pronouns (singular): he, she,… Definite descriptions (the so-and-so): Indefinite (singular) descriptions (a so-and-so) General terms: Terms that designate a kind of things or a certain property Mass nouns ___ natural kind terms (‘water,’ ‘tiger,’ ‘lemon’) ___ non-natural kind terms (‘bachelor’, ‘contract,’ ‘chair’) Adjectives (predicates): colors, shapes, etc. III. Traditional Theories of Meaning Prior to Frege [A] The Ideational Theory ___ The meaning of a linguistic expression is the speaker’s idea that is associated with the expression. [B] Mill’s Theory [the Object Theory] ___ The meaning of a singular term is the thing designated by that term; ___ the meaning of a name is just what the name stands for; the name does not have any other meaning e.g. ‘Socrates’ means Socrates e.g. ‘Dartmouth’ e.g. -
The Meaning and Significance of Dispute on Objectless Presentations
NeuroQuantology | December 2018 | Volume 16 | Issue 12 | Page 87-91| doi: 10.14704/nq.2018.16.12.1344 Seliverstov S., The Meaning and Significance of Dispute on Objectless Presentations The Meaning and Significance of Dispute on Objectless Presentations Vladimir Seliverstov* ABSTRACT This paper considers the evolution of understanding and the status of objectless presentations in the works of the three main authors of this tradition: “The Theory of Science” by B. Bolzano, “On Content and Object of Presentations” by K. Twardowski and “Intentional Objects” by E. Husserl. A critical analysis of these positions on objectless presentations is interesting, because here in one point, in one discussion, we have several very important philosophical theories that have had an impact on the philosophical debates in the twentieth century, particularly on the discussion Alexius Meinong and Bertrand Russell at the beginning of XX century. We want to show, how this Meinong’s conception has contemporary philosophy. Here author aims to show how theory of objects as such came into being and how its main ideasmade weresignificant discussed contribution and criticized into the in problemsubsequent of nonexistent philosophical objects thought. that Thisstill remainsdispute pushesone of theus tomost think debated that we in deal here with fundamental ideological differences between these conceptions. Therefore, it allowed to consider another important philosophical and methodological problem - the problem of incommunicability between logical and psychological conceptions. Key Words: Bolzano, Twardowski, Theory of Objects, Phenomenology, Objectless Presentations, Intentionality 87 DOI Number: 10.14704/nq.2018.16.12.1344 NeuroQuantology 2018; 16(12):87-91 The Problem he is often called a precursor of analytic philosophy. -
Either in Plain Text Format As Am Attached PDF) at the End of the Term
History of Analytic Philosophy410 — Syllabus Lecturer: SidneyFelder,e-mail: [email protected] Rutgers The State University of NewJersey, Spring 2021 “Office Hours” (i.e., individual discussions): By Appointment Formanyreasons, there is no uncontroversial general characterization of the range of work that tends to be classified under the heading “Analytic Philosophy”. For our purposes, an analytic philosopher is anyone whose work is conducted in awareness of the fundamental importance, for every variety of foundational and philosophical inquiry,ofobtaining a proper understanding of what properties of thought, perception, language, and the world, and what properties of their relationship, makepossible the meaningful ascription of truth, fal- sity,and referential significance of anykind to such things as thoughts, beliefs, sentences, propositions, and judgments. This course covers the early history of analytic philosophy, concentrating largely on writings of Gottlob Frege, Bertrand Russell, G.E. Moore, and Ludwig Wittgenstein, whose work secured recognition of the necessity as well as the great difficulty of this kind of inquiry. Weeks 1, 2, 3, 4 Transition from idealism, naturalism, and Kantianism Russell Our Knowledgeofthe External World (1914) Chapter I, Current Tendencies; Chapter II, Logic As the Essence of Philosophy Frege The Foundations of Arithmetic (1884) , Introduction and sections 1-28. Moore Principia Ethica (1903) , Chapters I, II, III (36-44) ,VI(110-121) Russell The Principles of Mathematics (1903) , Chapters I, III (Sections 37-38, 43-45) ,IV, V(56-60, 63-65) ,VI(66-74) , VIII (86-87, 93) ,IX, X, XVI, XXVI, XXVII (217-219) ,XLII, XLIII (337-341) ,LI Weeks 5, 6, 7, 8, 9, 10 Construction of a Language for Mathematics. -
Tractatus Logico-Philosophicus</Em>
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 8-6-2008 Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus Thomas J. Brommage Jr. University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Brommage, Thomas J. Jr., "Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus" (2008). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/149 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus by Thomas J. Brommage, Jr. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Co-Major Professor: Kwasi Wiredu, B.Phil. Co-Major Professor: Stephen P. Turner, Ph.D. Charles B. Guignon, Ph.D. Richard N. Manning, J. D., Ph.D. Joanne B. Waugh, Ph.D. Date of Approval: August 6, 2008 Keywords: Wittgenstein, Tractatus Logico-Philosophicus, logical empiricism, resolute reading, metaphysics © Copyright 2008 , Thomas J. Brommage, Jr. Acknowledgments There are many people whom have helped me along the way. My most prominent debts include Ray Langely, Billy Joe Lucas, and Mary T. Clark, who trained me in philosophy at Manhattanville College; and also to Joanne Waugh, Stephen Turner, Kwasi Wiredu and Cahrles Guignon, all of whom have nurtured my love for the philosophy of language. -
Epistemic Two-Dimensionalism and the Epistemic Argument
Epistemic two-dimensionalism and the epistemic argument Jeff Speaks November 12, 2008 Abstract. One of Kripke's fundamental objections to descriptivism was that the theory misclassifies certain a posteriori propositions expressed by sentences involving names as a priori. Though nowadays very few philosophers would endorse a descriptivism of the sort that Kripke criticized, many find two- dimensional semantics attractive as a kind of successor theory. Because two- dimensionalism needn't be a form of descriptivism, it is not open to the epis- temic argument as formulated by Kripke; but the most promising versions of two-dimensionalism are open to a close relative of that argument. One of Kripke's most powerful objections to the descriptivist theory of names he considered in Naming & Necessity was that the theory misclassifies the propositions expressed by certain sentences as a priori. For example, Kripke pointed out that the proposition expressed by a sentence of the form [1] If n exists, then n is F . will be, in the standard case, a posteriori. But according to the simplest version of descriptivism, the propositions expressed by sentences of the form of [1] just are the propositions expressed by the corresponding instances of [2] If the F exists, then the F is F . which seem clearly to be a priori truths. But even if many were convinced that Kripke's arguments discredited the descrip- tivist theories he considered, many were not satisfied by the Millian alternative to descriptivism. Many such philosophers take it to be a constraint on a theory of names that it capture the perceived explanatory advantages of descriptivism | including its account of the problems of empty names and of apparent substitution failures of coreferential names in attitude ascriptions | while avoiding Kripke's arguments against classical descriptivism. -
Reasoning with Ambiguity
Noname manuscript No. (will be inserted by the editor) Reasoning with Ambiguity Christian Wurm the date of receipt and acceptance should be inserted later Abstract We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it is no less ob- vious that ambiguous propositions entail other propositions (both ambiguous and unambiguous), and are entailed by other propositions. This article gives a formal analysis of the underlying mechanisms, both from an algebraic and a logical point of view. The main result can be summarized as follows: sound (and complete) reasoning with ambiguity requires a distinction between equivalence on the one and congruence on the other side: the fact that α entails β does not imply β can be substituted for α in all contexts preserving truth. With- out this distinction, we will always run into paradoxical results. We present the (cut-free) sequent calculus ALcf , which we conjecture implements sound and complete propositional reasoning with ambiguity, and provide it with a language-theoretic semantics, where letters represent unambiguous meanings and concatenation represents ambiguity. Keywords Ambiguity, reasoning, proof theory, algebra, Computational Linguistics Acknowledgements Thanks to Timm Lichte, Roland Eibers, Roussanka Loukanova and Gerhard Schurz for helpful discussions; also I want to thank two anonymous reviewers for their many excellent remarks! 1 Introduction This article gives an extensive treatment of reasoning with ambiguity, more precisely with ambiguous propositions. We approach the problem from an Universit¨atD¨usseldorf,Germany Universit¨atsstr.1 40225 D¨usseldorf Germany E-mail: [email protected] 2 Christian Wurm algebraic and a logical perspective and show some interesting surprising results on both ends, which lead up to some interesting philosophical questions, which we address in a preliminary fashion. -
A Computer-Verified Monadic Functional Implementation of the Integral
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Theoretical Computer Science 411 (2010) 3386–3402 Contents lists available at ScienceDirect Theoretical Computer Science journal homepage: www.elsevier.com/locate/tcs A computer-verified monadic functional implementation of the integral Russell O'Connor, Bas Spitters ∗ Radboud University Nijmegen, Netherlands article info a b s t r a c t Article history: We provide a computer-verified exact monadic functional implementation of the Riemann Received 10 September 2008 integral in type theory. Together with previous work by O'Connor, this may be seen as Received in revised form 13 January 2010 the beginning of the realization of Bishop's vision to use constructive mathematics as a Accepted 23 May 2010 programming language for exact analysis. Communicated by G.D. Plotkin ' 2010 Elsevier B.V. All rights reserved. Keywords: Type theory Functional programming Exact real analysis Monads 1. Introduction Integration is one of the fundamental techniques in numerical computation. However, its implementation using floating- point numbers requires continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the end-user by providing a library of exact analysis in which the computer handles the error estimates. For high assurance we use computer-verified proofs that the implementation is actually correct; see [21] for an overview. It has long been suggested that, by using constructive mathematics, exact analysis and provable correctness can be unified [7,8]. Constructive mathematics provides a high-level framework for specifying computations (Section 2.1). -
Edinburgh Research Explorer
Edinburgh Research Explorer Propositions as Types Citation for published version: Wadler, P 2015, 'Propositions as Types', Communications of the ACM, vol. 58, no. 12, pp. 75-84. https://doi.org/10.1145/2699407 Digital Object Identifier (DOI): 10.1145/2699407 Link: Link to publication record in Edinburgh Research Explorer Document Version: Peer reviewed version Published In: Communications of the ACM General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 28. Sep. 2021 Propositions as Types ∗ Philip Wadler University of Edinburgh [email protected] 1. Introduction cluding Agda, Automath, Coq, Epigram, F#,F?, Haskell, LF, ML, Powerful insights arise from linking two fields of study previously NuPRL, Scala, Singularity, and Trellys. thought separate. Examples include Descartes’s coordinates, which Propositions as Types is a notion with mystery. Why should it links geometry to algebra, Planck’s Quantum Theory, which links be the case that intuitionistic natural deduction, as developed by particles to waves, and Shannon’s Information Theory, which links Gentzen in the 1930s, and simply-typed lambda calculus, as devel- thermodynamics to communication. -
The Development of Mathematical Logic from Russell to Tarski: 1900–1935
The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu Richard Zach Calixto Badesa The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu (University of California, Berkeley) Richard Zach (University of Calgary) Calixto Badesa (Universitat de Barcelona) Final Draft—May 2004 To appear in: Leila Haaparanta, ed., The Development of Modern Logic. New York and Oxford: Oxford University Press, 2004 Contents Contents i Introduction 1 1 Itinerary I: Metatheoretical Properties of Axiomatic Systems 3 1.1 Introduction . 3 1.2 Peano’s school on the logical structure of theories . 4 1.3 Hilbert on axiomatization . 8 1.4 Completeness and categoricity in the work of Veblen and Huntington . 10 1.5 Truth in a structure . 12 2 Itinerary II: Bertrand Russell’s Mathematical Logic 15 2.1 From the Paris congress to the Principles of Mathematics 1900–1903 . 15 2.2 Russell and Poincar´e on predicativity . 19 2.3 On Denoting . 21 2.4 Russell’s ramified type theory . 22 2.5 The logic of Principia ......................... 25 2.6 Further developments . 26 3 Itinerary III: Zermelo’s Axiomatization of Set Theory and Re- lated Foundational Issues 29 3.1 The debate on the axiom of choice . 29 3.2 Zermelo’s axiomatization of set theory . 32 3.3 The discussion on the notion of “definit” . 35 3.4 Metatheoretical studies of Zermelo’s axiomatization . 38 4 Itinerary IV: The Theory of Relatives and Lowenheim’s¨ Theorem 41 4.1 Theory of relatives and model theory . 41 4.2 The logic of relatives . -
Frege's Theory of Sense
Frege’s theory of sense Jeff Speaks August 25, 2011 1. Three arguments that there must be more to meaning than reference ............................1 1.1. Frege’s puzzle about identity sentences 1.2. Understanding and knowledge of reference 1.3. Opaque contexts 2. The theoretical roles of senses .........................................................................................4 2.1. Frege’s criterion for distinctness of sense 2.2. Sense determines reference, but not the reverse 2.3. Indirect reference 2.4. Sense, force, and the theory of speech acts 3. What are senses? .............................................................................................................6 We have now seen how a theory of reference — a theory that assigns to each expression of the language a reference, which is what it contributes to determining the truth or falsity of sentences in which it occurs — might look for a fragment of English. (The fragment of English includes proper names, n-place predicates, and quantifiers.) We now turn to Frege’s reasons for thinking that a theory of reference must be supplemented with a theory of sense. 1. THREE ARGUMENTS THAT THERE MUST BE MORE TO MEANING THAN REFERENCE 1.1. Frege’s puzzle about identity sentences As Frege says at the outset of “On sense and reference,” identity “gives rise to challenging questions which are not altogether easy to answer.” The puzzle raised by identity sentences is that, if, even though “the morning star” and “the evening star” have the same reference — the planet Venus — the sentences [1] The morning star is the morning star. [2] The morning star is the evening star. seem quite different. They seem, as Frege says, to differ in “cognitive value.” [1] is trivial and a priori; whereas [2] seems a posteriori, and could express a valuable extension of knowledge — it, unlike [1], seems to express an astronomical discovery which took substantial empirical work to make.