# Noonan, Harold W. Frege: a Critical Introduction.

Key Contemporary Thinkers. Cambridge: Polity Press, 2001. viii +
244 pp. Cloth, 50.00 [pounds sterling]; paper, 14.99 [pounds
sterling]--Noonan's book comprises, along with a substantial
introduction, chapters on Frege's logic, his philosophy of
arithmetic, his philosophical logic and his theory of meaning, among
them covering all his principal contributions to philosophy. The
exposition, while remaining throughout accessible to any nonspecialist
reader with a reasonable background in analytical philosophy, is
sympathetic but at the same time searching and critical, aimed both at
deepening our understanding of the reasons that led Frege to his most
important doctrines and of the connections between them, and at bringing
out clearly the difficulties to which they give rise. After a brief but
engaging account of Frege's life and career, Noonan's
introductory chapter provides a helpful sketch of the origins and
development of his leading ideas in their philosophical and mathematical
context--Kant's thesis that mathematics, while a priori, must be
synthetic and his associated insistence on the role of intuition; the
emergence of non-Euclidean geometries; and the drive for rigor and the
arithmetization of analysis by Augustine Cauchy, Karl Weierstrass, and
others--followed by a concise overview of Frege's main
contributions which serves as a useful background to their more detailed
discussion in the chapters that follow.

Chapter 2 sets out, with the aid of well-chosen examples, some of the more serious shortcomings in logic as Frege found it, brings out the underlying mathematical motivation for his Begriffsschrift, and explains in detail Frege's replacement of the traditional subject-predicate analysis of sentences by his own more powerful and flexible function-argument analysis and the development of the quantifier-variable notation--essential to his solution of the problem posed by sentences involving multiple generality and other problems besetting the traditional logic of terms--which, along with his presentation of the first formalization of (higher-order) quantification theory, constituted a massive step forward in the development of modern mathematical logic. In chapter 3, Noonan furnishes a close commentary on the argument of Frege's Grundlagen, accurately summarizing its sharp, and for the most part devastating, critique of views on the nature of number and arithmetic to which Frege was opposed, before setting forth his own analysis of the concept of number and associated defense of his thesis that the laws of arithmetic are analytic. Noonan's discussion here admirably conveys a sense of the extent to which it is--Frege's own eventual abandonment of his logicism in the face of Russell's antinomy notwithstanding--very much a live and vigorously debated question whether a modified version of Frege's position may be defensible, by assigning a leading role to Hume's principle in place of Frege's explicit definition of number in terms of extensions. While not pretending to resolve this question, Noonan clearly explains the issues on which it turns and helpfully points the reader to relevant contemporary discussion.

Chapters 4 and 5, devoted respectively to Frege's philosophical logic and theory of meaning, critically expound the central ideas developed in three articles published in the space of two years--"Function and Concept" (1891), "On Sense and Reference," and "On Concept and Object" (both 1892). In them we find, in the present reviewer's opinion, one of the clearest and most insightful introductory discussions of these key works yet published, effectively putting the reader in touch with the fundamental issues and problems in Frege's thought which still, deservedly, form the focus of the best recent work in the field. Of particular value is Noonan's careful explanation of Frege's commitment to the thesis that sentences containing empty proper names must lack truth-value, even though (according to Frege) they may nevertheless express perfectly determinate thoughts. Implausible though it is, the commitment is inevitable, Noonan argues, given Frege's functional theory of predication together with his theses that the reference of a sentence is its truth-value and that of a singular term the object it designates. It best avoided, Noonan suggests, by departing from the name/bearer relation as the prototype for the notion of reference, and allowing that empty singular terrors may have a semantic value consisting precisely in the fact that they lack a designation. This would allow such sentences to have reference even though they contain nondesignating names, and so enable one to hold that they express thoughts, but false ones. An arguably better way out, not considered by Noonan, would be to grant that sentences containing empty names need not for that reason be meaningless, but deny that they have sense in Frege's technical sense of that word, that is, deny that they express thoughts at all.

In spite of several decades of first-rate scholarship, it is open to question whether there has, prior to the appearance of this book, been a reliable introduction to his work which goes deep enough to do justice to the power and subtlety of Frege's thought while remaining accessible to beginners or nonspecialists. Noonan's book is, without qualification, the best general critical introduction to Frege's work I have read.--Bob Hale, University of Glasgow.

Chapter 2 sets out, with the aid of well-chosen examples, some of the more serious shortcomings in logic as Frege found it, brings out the underlying mathematical motivation for his Begriffsschrift, and explains in detail Frege's replacement of the traditional subject-predicate analysis of sentences by his own more powerful and flexible function-argument analysis and the development of the quantifier-variable notation--essential to his solution of the problem posed by sentences involving multiple generality and other problems besetting the traditional logic of terms--which, along with his presentation of the first formalization of (higher-order) quantification theory, constituted a massive step forward in the development of modern mathematical logic. In chapter 3, Noonan furnishes a close commentary on the argument of Frege's Grundlagen, accurately summarizing its sharp, and for the most part devastating, critique of views on the nature of number and arithmetic to which Frege was opposed, before setting forth his own analysis of the concept of number and associated defense of his thesis that the laws of arithmetic are analytic. Noonan's discussion here admirably conveys a sense of the extent to which it is--Frege's own eventual abandonment of his logicism in the face of Russell's antinomy notwithstanding--very much a live and vigorously debated question whether a modified version of Frege's position may be defensible, by assigning a leading role to Hume's principle in place of Frege's explicit definition of number in terms of extensions. While not pretending to resolve this question, Noonan clearly explains the issues on which it turns and helpfully points the reader to relevant contemporary discussion.

Chapters 4 and 5, devoted respectively to Frege's philosophical logic and theory of meaning, critically expound the central ideas developed in three articles published in the space of two years--"Function and Concept" (1891), "On Sense and Reference," and "On Concept and Object" (both 1892). In them we find, in the present reviewer's opinion, one of the clearest and most insightful introductory discussions of these key works yet published, effectively putting the reader in touch with the fundamental issues and problems in Frege's thought which still, deservedly, form the focus of the best recent work in the field. Of particular value is Noonan's careful explanation of Frege's commitment to the thesis that sentences containing empty proper names must lack truth-value, even though (according to Frege) they may nevertheless express perfectly determinate thoughts. Implausible though it is, the commitment is inevitable, Noonan argues, given Frege's functional theory of predication together with his theses that the reference of a sentence is its truth-value and that of a singular term the object it designates. It best avoided, Noonan suggests, by departing from the name/bearer relation as the prototype for the notion of reference, and allowing that empty singular terrors may have a semantic value consisting precisely in the fact that they lack a designation. This would allow such sentences to have reference even though they contain nondesignating names, and so enable one to hold that they express thoughts, but false ones. An arguably better way out, not considered by Noonan, would be to grant that sentences containing empty names need not for that reason be meaningless, but deny that they have sense in Frege's technical sense of that word, that is, deny that they express thoughts at all.

In spite of several decades of first-rate scholarship, it is open to question whether there has, prior to the appearance of this book, been a reliable introduction to his work which goes deep enough to do justice to the power and subtlety of Frege's thought while remaining accessible to beginners or nonspecialists. Noonan's book is, without qualification, the best general critical introduction to Frege's work I have read.--Bob Hale, University of Glasgow.

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Author: | Hale, Bob |
---|---|

Publication: | The Review of Metaphysics |

Article Type: | Book Review |

Date: | Sep 1, 2002 |

Words: | 828 |

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