Unpublished philosophical essays. Ed. by Francisco A. Rodríguez-Consuegra. (English) Zbl 0854.01046

Gödel, Kurt

Basel: Birkhäuser. 235 p. (1995).

In the second part of this volume F. A. Rodríguez-Consuegra presents an edition of three philosophical papers by Kurt Gödel. The first is the Gibbs lecture of 1951, entitled “Some basic theorems on the foundations of mathematics and their philosophical implications” (pp. 129-167). The two other papers are versions II and VI of Gödel’s intended (but never sent in) contribution for the Carnap volume in the Library of Living Philosophers [The philosophy of Rudolf Carnap, P. A. Schilpp (ed.), Open Court, La Salle, Ill. (1963)] with the title “Is mathematics syntax of language?” (171-222). Calling these papers “unpublished” needs some qualification. The Gibbs lecture was also published in volume III of Gödel’s Collected Works [K. Gödel, Collected Works. Ed. by Solomon Feferman. Vol. III: Unpublished essays and lectures. New York, NY: Oxford Univ. Press (1995; Zbl 0826.01038), pp. 304-323, with an introductory note by George Boolos, pp. 290-304], but in a different style of edition. The mentioned volume contains furthermore versions III and V of the paper on Carnap [ibid., pp. 334-362, with an introductory note by Warren Goldfarb, pp. 324-334]. Gödel’s papers give further evidence for his known position in the philosophy of mathematics as expressed in the Gibbs lecture: “\(\dots\) mathematical objects and facts or at least something in them exist objectively and independently of our mental acts and decisions,” defending thus a “realism” of mathematical objects (p. 136). In “Is mathematics syntax of language?” Gödel opposes two implications of neopositivistic philosophy of mathematics, namely (1) that mathematics can be replaced by syntax of language, and (2) that mathematical propositions have no content (p. 172). He holds that “\(\dots\) the scheme of the syntactical program to replace intuition by rules for the use of symbols fails because this replacing destroys any reason for expecting consistency, \(\dots\) and because for the consistency proof a mathematical intuition of the same power is necessary as for discerning the truth of the mathematical axioms” (p. 181). Part I of the volume is an extensive essay by the editor on “Kurt Gödel and the Philosophy of Mathematics” (pp. 15-106). The first section on “Realism, metamathematics, and the unpublished essays” (pp. 17-42) describes Gödel’s metamathematical results and their implications as seen by Gödel himself which led him to the realistic position. The second section on “The analytic-synthetic distinction” (pp. 43-69) is written in order to explain Gödel’s thesis that mathematical propositions are analytic (in a special sense). It is compared with different or similar opinions of Frege, Russell, Wittgenstein, Carnap, and Quine. The third section “The mathematics-physics analogy” (pp. 71-98) discusses Gödel’s main argument in favour of his realism, the analogy between deductive and empirical sciences. Again Gödel’s positions are compared with those of Russell, Hilbert, Carnap, Tarski, and Quine. Several illustrations give evidence of the editor’s successful efforts to produce readable texts from the original complex folios which contain numerous corrections, revisions, later notes and even notes to the notes. In sum the volume seems to be a perfect instrument to raise Gödel’s voice in the contemporary debate on the nature of mathematical objects still central for the philosophy of mathematics.

Reviewer: V.Peckhaus (Erlangen)

MSC:

01A75	Collected or selected works; reprintings or translations of classics
01A70	Biographies, obituaries, personalia, bibliographies

Keywords:

platonism; realism; analytic-synthetic distinction; mathematics-physics analogy; syntax

Citations:

Zbl 0826.01038