Lewis 2 Definitions of T-terms

Similar documents
Part 1: You are given the following system of two equations: x + 2y = 16 3x 4y = 2

Lecture 33 Carnap on Theory and Observation

Marc Lange -- IRIS. European Journal of Philosophy and Public Debate

Superposition - World of Color and Hardness

Lecture 12: Arguments for the absolutist and relationist views of space

1.4 Mathematical Equivalence

Elementary Linear Algebra, Second Edition, by Spence, Insel, and Friedberg. ISBN Pearson Education, Inc., Upper Saddle River, NJ.

CH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction

Solving with Absolute Value

Chapter 1 Review of Equations and Inequalities

Bar-Hillel and Carnap s Account of Semantic Information

Kripke s Theory of Truth (for the strong Kleene scheme)

PHIL12A Section answers, 14 February 2011

240 Metaphysics. Frege s Puzzle. Chapter 26

PROOF-THEORETIC REDUCTION AS A PHILOSOPHER S TOOL

Mathematics 114L Spring 2018 D.A. Martin. Mathematical Logic

Introducing Proof 1. hsn.uk.net. Contents

- 1.2 Implication P. Danziger. Implication

Presuppositions (introductory comments)

Properties of Sequences

Math 54 Homework 3 Solutions 9/

Syllogistic Logic and its Extensions

Carrying On with Infinite Decimals

INTENSIONS MARCUS KRACHT

Correlation. We don't consider one variable independent and the other dependent. Does x go up as y goes up? Does x go down as y goes up?

Arguments and Proofs. 1. A set of sentences (the premises) 2. A sentence (the conclusion)

The Converse of Deducibility: C.I. Lewis and the Origin of Modern AAL/ALC Modal 2011 Logic 1 / 26

One sided tests. An example of a two sided alternative is what we ve been using for our two sample tests:

Williamson s Modal Logic as Metaphysics

1 Limits and continuity

Today. Reading Quiz Lecture/Discussion Physics: The fundamental science Debrief activity from yesterday

Since the two-sided limits exist, so do all one-sided limits. In particular:

CS1800: Strong Induction. Professor Kevin Gold

Logic and Mathematics:

Fitting a Straight Line to Data

Searle: Proper Names and Intentionality

8. TRANSFORMING TOOL #1 (the Addition Property of Equality)

A Little History Incompleteness The First Theorem The Second Theorem Implications. Gödel s Theorem. Anders O.F. Hendrickson

Why Care About Counterfactual Support? The Cognitive Uses of Causal Order Lecture 2

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology

Math 115 Spring 11 Written Homework 10 Solutions

Propositional Logic Review

INTRODUCTION TO LOGIC 1 Sets, Relations, and Arguments. Why logic? Arguments

[Refer Slide Time: 00:45]

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield

Math 144 Summer 2012 (UCR) Pro-Notes June 24, / 15

8. Reductio ad absurdum

Temporal Extension. 1. Time as Quantity

The trick is to multiply the numerator and denominator of the big fraction by the least common denominator of every little fraction.

Boolean circuits. Lecture Definitions

FIRST PUBLIC EXAMINATION. Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY LONG VACATION 2014

Solving Equations. Lesson Fifteen. Aims. Context. The aim of this lesson is to enable you to: solve linear equations

WHAT THIS BOOK IS ABOUT

Basics of Proofs. 1 The Basics. 2 Proof Strategies. 2.1 Understand What s Going On

Wittgenstein on The Standard Metre

2 Analogies between addition and multiplication

3 The language of proof

CS 453 Operating Systems. Lecture 7 : Deadlock

Popper s Measure of Corroboration and P h b

Why maximize entropy?

6.045: Automata, Computability, and Complexity Or, Great Ideas in Theoretical Computer Science Spring, Class 8 Nancy Lynch

Lecture 18 Newton on Scientific Method

V. Graph Sketching and Max-Min Problems

SEMANTICS OF POSSESSIVE DETERMINERS STANLEY PETERS DAG WESTERSTÅHL

Commentary. Regression toward the mean: a fresh look at an old story

Proof Techniques (Review of Math 271)

Notes: Pythagorean Triples

Astronomy H161 An Introduction to Solar System Astronomy Winter Quarter 2009 Prof. Gaudi Homework #4. Due Monday, February 9 in class

Seminaar Abstrakte Wiskunde Seminar in Abstract Mathematics Lecture notes in progress (27 March 2010)

PHILOSOPHICAL STUDIES

Algebra Exam. Solutions and Grading Guide

Joint, Conditional, & Marginal Probabilities

PAC Learning. prof. dr Arno Siebes. Algorithmic Data Analysis Group Department of Information and Computing Sciences Universiteit Utrecht

Conceptual Explanations: Radicals

Automated Solution of the Riddle of Dracula and Other Puzzles

1 Multiple Choice. PHIL110 Philosophy of Science. Exam May 10, Basic Concepts. 1.2 Inductivism. Name:

30. TRANSFORMING TOOL #1 (the Addition Property of Equality)

1 Propositional Logic

Yablo s Paradox and the Omitting Types Theorem for Propositional Languages

CHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC

Hypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n =

The Pragmatics of Scientific Laws

Natural Sciences 3: Physics: Light and the Physical Bases of Explanation

Russell s logicism. Jeff Speaks. September 26, 2007

Copy anything you do not already have memorized into your notes.

35 Chapter CHAPTER 4: Mathematical Proof

A Guide to Proof-Writing

Algebra Year 9. Language

Theory of Computation

Direct Proofs. the product of two consecutive integers plus the larger of the two integers

Propositions. c D. Poole and A. Mackworth 2010 Artificial Intelligence, Lecture 5.1, Page 1

Tooley on backward causation

HOW TO WRITE PROOFS. Dr. Min Ru, University of Houston

Introduction to Vector Spaces Linear Algebra, Fall 2008

KB Agents and Propositional Logic

MATH240: Linear Algebra Review for exam #1 6/10/2015 Page 1

cse541 LOGIC FOR COMPUTER SCIENCE

(Refer Time Slide: 1:35)

Line Integrals and Path Independence

Reasoning: Odd one out

Transcription:

Lewis 2 Definitions of T-terms (pp. 431 438, 445 446) Patrick Maher Philosophy 471 Fall 2006

Review The Ramsey sentence of T says T is realized: x 1... x n [x 1... x n ] The Carnap sentence says if T is realized then T is true: x 1... x n [x 1... x n ] [τ 1... τ n ] According to Carnap: The Ramsey sentence contains the factual part of T. The Carnap sentence specifies the interpretation of the T -terms.

Evaluation of Carnap s proposal It is important to separate three cases. T may have precisely one realization, or no realization, or more than one realization. (p. 431) T has precisely one realization (p. 431) In case T is uniquely realized, the Carnap sentence clearly gives exactly the right specification. It says that the T -terms name the entities in the n-tuple that is the unique realization of T. The first T -term, τ 1, names the first component of the unique realization of T ; τ 2 names the second component; and so on.

T has no realization (p. 432) In case T is not realized, the Carnap sentence says nothing about the denotation of the T -terms. But this modesty seems to be uncalled for. The T -terms were introduced on the assumption that T was realized, in order to name the components of a realization of T. There is no realization of T. Therefore they should not name anything. Phlogiston presumably is a theoretical term of an unrealized theory; we say without hesitation that there is no such thing as phlogiston. What else could we possibly say? Should we say that phlogiston is something or other, but (unless phlogiston theory turns out to be true after all) we have no hope of finding out what?

T has more than one realization (p. 432) There remains the case in which T is multiply realized. In this case, the Carnap sentence tells us that the T -terms name the components of some realization or other. But it does not tell us which; and there seems no nonarbitrary way to choose one of the realizations. So either the T -terms do not name anything, or they name the components of an arbitrarily chosen one of the realizations of T... Neither [of these alternatives] does justice to our naive impression that we understand the theoretical terms of a true theory, and without making any arbitrary choice among realizations. We should not accept Carnap s treatment in this case if we can help it. Lewis goes on to argue that we should say multiply realized theories are false and their T -terms don t refer to anything.

Definition of T -terms Definition (pp. 437 438, simplified) If T has a unique realization, then τ i denotes the ith entity in that realization. If T doesn t have a unique realization, then τ i doesn t denote anything.

The sense/reference distinction (p. 435) The reference or denotation of a term is what the term names in the actual world. The sense or meaning of a term determines what the term names in every possible world. Examples (not in Lewis) Creature with a heart and creature with a kidney : Have the same reference/denotation. Have different senses/meanings. Bachelor and unmarried man : Have the same reference/denotation. Have the same sense/meaning.

The definition gives the sense of T -terms (p. 435) Different possible worlds differ in whether T has a unique realization. According to Lewis s definition: In worlds in which T does have a unique realization, τ i denotes the ith element in that realization. In worlds in which T doesn t have a unique realization, τ i doesn t denote anything. So Lewis s definition says what τ i denotes in every possible world. Hence Lewis s definition specifies the sense of T -terms. To determine the reference of T -terms, we need to know which world we are in; that requires empirical investigation.

Later revisions of T So far, we have discussed the interpretation of T -terms only at the time of their introduction, the time when the parent theory T is first proposed. It remains to ask what happens later when T is amended and extended. (p. 445) If use the current version of T (p. 445) We might say that the T -terms should always be defined using the currently accepted version of T. As T is corrected, modified, extended, or perhaps even when we accept miscellaneous hypotheses that contain T -terms but do not belong integrally to any version of T, the T -terms gradually change their meaning... But these are very peculiar changes of meaning so peculiar that this position seems to change the meaning of change the meaning of. They occur continually, unnoticed, without impeding communication.

If use the original version of T (p. 446) We might therefore prefer to say that the T -terms keep the meanings they received at their first introduction. They should still be defined using the original version of T even after it has been superseded by revised versions. This position will work only if we permit T -terms to name components of the nearest near-realization of T, even if it is not a realization of T itself. For after T has been corrected, no matter how slightly, we will believe that the original version of T is unrealized. According to this position, we may be unable to discover the meanings of theoretical terms at a given time just by looking into the minds of the most competent language-users at that time. We will need to look at the past episodes of theory-proposing in which those terms were first introduced into the language... If we were ignorant of history, we could all be ignorant or mistaken about the meanings of words in common use among us.

Neither solution is attractive (p. 446) I do not wish to decide between these alternatives. Either seems defensible at some cost. I hope the truth lies in between, but I do not know what an intermediate position would look like.

Questions 1 Does Lewis agree that the Carnap sentence of a theory T gives the meaning of its T -terms? If not, why not? 2 State Lewis s definition of the T -terms of a theory. Does this definition specify the meaning of the T -terms, or does it merely say what they designate? Justify your answer to the latter question. 3 When Lewis considers what happens when a theory T is modified, he considers two possibilities: (a) The T -terms are defined using the original version of T. (b) The T -terms are defined using the revised version of T. Explain why neither solution is attractive.