Alfred Tarski

Tarski, Alfred - tärˈskē, 1902–, Polish-American mathematician and philosopher, Ph.D. Univ. of Warsaw, 1924. He lectured at Warsaw until 1939, emigrated to the United States, and then taught at the Univ. of California, Berkeley (1942–68). Tarski made extensive, basic contributions to the field of metamathematics, a branch of mathematical logic. His most important Read More...

10 of the Best Books and Articles on: Alfred Tarski

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1.

Undecidable Theories
by Alfred Tarski. 102 pgs.

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Title Page

Studies in Logic And The Foundations Of Mathematics

Preface

Contents

I: A General Method in Proofs Of Undecidability

II: Undecidability And Essential Undecidability In Arithmetic

III: Undecidability of The Elementary Theory of Groups

Bibliography

Index
2.

Introduction to Logic and to the Methodology of Deductive Sciences
by Alfred Tarski, Olaf Helmer-Hirschberg. 246 pgs.

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Title Page

Table of Contents

Preface

From the Preface to The Original Edition

First Part: Elements of Logic Deductive Method

I: On the Use of Variables

II: On the Sentential Calculus

• III •: On the Theory of Identity

• IV •: On the Theory of Classes

V: On the Theory of Relations

VI: On the Deductive Method

Second Part: Applications of Logic And Methodology In Constructing Mathematical Theories

VII: Construction of a Mathematical Theory: Laws of Order for Numbers

VIII: Construction of a Mathematical Theory: Laws of Addition and Subtraction

IX: Methodological Considerations On the Constructed Theory

X: Extension of the Constructed Theory Foundations of Arithmetic of Real Numbers

Suggested Readings

Index
3.

Logic, Semantics, Metamathematics: Papers from 1923 to 1938
by Alfred Tarski, J. H. Woodger. 474 pgs.

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Title Page

Translator's Preface

Author's Acknowledgements

Contents

I on the Primitive Term of Logistic

Ii Foundations of the Geometry of Solids

Iii on Some Fundamental Concepts of Metamathematics

Iv Investigations into the Sentential Calculus

Introduction

V Fundamental Concepts of the Methodology of the Deductive Sciences

Vi on Definable Sets of Real Numbers

Vii Logical Operations and Projective Sets

Viii the Concept of Truth in Formalized Languages†

Introduction

§ 6. Summary

IX: Some Observations on the Concepts of ω-Consistency and ω-Completeness†

Introductory Remarks

X Some Methodological Investigations on the Definability of Concepts†

Xi on the Foundations of Boolean Algebra

Xii Foundations of the Calculus of Systems†

Appendix

Xiii on the Limitations of the Means of Expression of Deductive Theories

Xiv on Extensions of Incomplete Systems of the Sentential Calculus†

Xv the Establishment of Scientific Semantics

Xvi on the Concept of Logical Consequence

Xvii Sentential Calculus and Topology

Abbreviations

Bibliography

Subject Index

Index of Names of Persons

Index of Symbols
4.

Meaning and Truth: Essential Readings in Modern Semantics (Part Three "On Tarski")
by Jay L. Garfield, Murray Kiteley. 638 pgs.

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Title Page

Paragon Issues in Philosophy

Contents

Acknowledgments

Preface

General Introduction

Part One: The Beginnings

Introduction

Of Names and Propositions

On Sense and Nominatum

The Semantic Conception of Truth and the Foundations of Semantics

On Denoting

Part Two: On Descriptions

Introduction

On Referring

Mr. Strawson on Referring

Meaning and Necessity

Reference and Definite Descriptions

Speaker's Reference and Semantic Reference

Presupposition and Two-Dimensional Logic

Dthat

On the Logic of Demonstratives

Part Three: On Tarski

Introduction

Donald Davidson Truth and Meaning

Tarski's Theory of Truth

Physicalism and Primitive Denotation: Field on Tarski

Part Four: Intensionality

Introduction

Quantifiers and Propositional Attitudes

On Saying That

An Overview of Montague Semantics

Subjectivity's Bailiwick: and the Person of Its Bailiff

Part Five: The Structure of Meaning

Introduction

Two Types of Quantifiers

A Logical Theory of Verb-Phrase Deletion

Structured Meanings

Structural Ambiguity

Part Six: Possible Worlds

Introduction

Propositions

Possible Worlds

Actualism and Possible Worlds

The Trouble with Possible Worlds

Part Seven: Pragmatics

Introduction

On Specificity

Metaphorese

Metaphorical Assertions

The Problem of the Essential Indexical
5.

Understanding Truth (Chap. 3 "Tarski's Definition of Truth" and Chap. 4 "The Significance of Tarski's Theory of Truth")
by Scott Soames. 268 pgs.

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Scott Soames illuminates the notion of truth and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. The main questions investigated include "Why do we need a truth predicate at all?", "What theoretical tasks does it allow us to accomplish?", and "How must we understand the content of any predicate capable of accomplishing these tasks?". The main aim of the book is to integrate and extend the most important insight on truth from a variety of sources.

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Title Page

Acknowledgments

Contents

Introduction

Part I Foundational Issues

One: Truth Bearers

Two: Forms of Truth Skepticism

Part 11 Two Theories of Truth

Three: Tarski's Definition of Truth

Four: The Significance of Tarski's Theory of Truth

Five Lessons of the Liar

Six: Truth, Paradox, and Partially Defined Predicates

Part III Extensions

Seven: Vagueness, Partiality, and the Sorites Paradox

Eight What is Truth?: The Deflationary Perspective

Index
6.

The Philosophy of Mathematics Today (Chap. 5 "Tarski's Thesis and the Ontology of Mathematics")
by Matthias Schirn. 645 pgs.

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The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright.

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Title Page

Acknowledgmetns

Contents

Notes on the Contributors

Introduction Matthias Schirn

I. Ontology, Models, and Indeterminacy

1: What Mathematical Truth Could Not Be--I

2: Is Platonism Epistemologically Bankrupt?

3: Do We Have a Determinate Conception of Finiteness and Natural Number?

4: Logical Consequence: Models and Modality Stewart Shapiro

References

Ii. Mathematics, Science, and Method

6: Naturalizing Mathematical Methodology

7: Occam's Razor and Scientific Method

8: Beyond Definitionism--But Not Too Far Beyond

9: Holistic Mathematics

Iii. Finitism and Intuitionism

10: Finitism and Intuitive Knowledge

10: Finitism and Intuitive Knowledge

Appendix

11: Hilbert's Finitism and the Notion of Infinity

12: Constructive Existence Claims Michael Detlefsen

12: Constructive Existence Claims Michael Detlefsen

5: Conclusion

Appendix: Brouwer's Rejection of Spatial Intuition

References

Iv. Frege and the Foundations of Arithmetic

13: On the Harmless Impredicativity of N= ('Hume's Principle')

13: On the Harmless Impredicativity of N= ('Hume's Principle')

14: Neo-Fregeans: In Bad Company?

15: Response to Dummett

16: Die Grundlagen Der Arithmetik, §§82-3

Appendix 1. Counterparts in Grundgesetze of Some Propositions of Die Grundlagen

Appendix 2. Interpreting Frege Arithmetic in Second-Order Arithmetic

Appendix 3. Translations into Present-Day Notation of §§115, 117, 119 and Part of §§113 of Grundgesetze

17: The Finite and the Infinite in Frege's Grundgesetze Der Arithmetik

Appendix 1. Frege's Proof of Theorem 288, and Reflections on the Least Number Principle

Appendix 2. Tree of Important Theorems in Frege's Proof of Theorem 327

V. Sets, Structure, and Abstraction

18: Zermelo's Conception of Set Theory and Reflection Principles

19: Structure and Abstraction

19: Structure and Abstraction

6: Summary

References

20: The Limits of Abstraction

Index
7.

A General Semantics Glossary, in ETC.: A Review of General Semantics
by Robert P. Pula. 12 pgs.
8.

Conceptions of Truth (Chap. 4 "In and Out of Quotation Marks")
by Wolfgang Kunne. 493 pgs.

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Conceptions of Truth

Preface

Contents

1: Some Questions About Truth

2: A Bogus Predicate?

3: Varieties of Correspondence

4: In and Out of Quotation Marks

5: Propositions, Time, and Eternity

6: Two Pleas for Modesty

7: Truth and Justifiability

Bibliography

Name Index
9.

Quine and Davidson on Language, Thought and Reality (Chap. 4 "Truth")
by Hans-Johann Glock. 311 pgs.

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W.V. Quine and Donald Davidson are among the leading thinkers of the twentieth century. Their influence on contemporary philosophy is second to none, and their impact in disciplines such as linguistics and psychology is strongly felt. Questioning some of their basic assumptions, this text includes interesting comparisons of Quine and Davidson with other philosophers, particularly Wittgenstein. The text also offers detailed accounts of central issues in contemporary analytic philosophy.

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Title Page

Contents

Acknowledgements

Abbreviations

Introduction

1: Logical Pragmatism

2: Ontology

3: Analyticity, Apriority and Necessity

4: Truth

5: Meaning and Truth

6: Radical Translation and Radical Interpretation

7: Indeterminacies

8: Meaning and Understanding

9: Thought and Language

References

Index
10.

Truth and the Absence of Fact (Chap. 1 "Tarski's Theory of Truth")
by Hartry Field. 401 pgs.

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Truth and the Absence of Fact

Contents

Notes on Original Publication

Part 1 Truth, Meaning, and Propositional Attitudes

1: Tarski's Theory of Truth

Postscript

2: Mental Representation

Postscript

3: Stalnaker on Intentionality

4: Deflationist Views of Meaning and Content

Postscript

5: Attributions of Meaning and Content

Part 2 Indeterminacy and Factual Defectiveness

6: Theory Change and the Indeterminacy of Reference

Postscript

7: Quine and the Correspondence Theory

Appendix: Indeterminacy in the Metalanguage

Postscript

8: Disquotational Truth and Factually Defective Discourse

9: Some Thoughts on Radical Indeterminacy

Postscript

10: Indeterminacy, Degree of Belief, and Excluded Middle

Postscript

Part 3 Objectivity

11: Mathematical Objectivity and Mathematical Objects

12: Which Undecidable Mathematical Sentences Have Determinate Truth Values?

Postscript

13: Apriority as an Evaluative Notion

Index

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