Science a road to wisdom by Evert W. BethReview by: H. L. BerghelThe Journal of Symbolic Logic, Vol. 40, No. 2 (Jun., 1975), pp. 255-256Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2271938 .

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255 REVIEWS

tial, meaningless, or infelicitous. Now (1) is presumed to refer to rain on Monday, and (2) is presumed to refer to rain on Monday, so (1) and (2) are presumptively contradictory.

"To relate tensed statements logically one must relate them as regards temporal reference; and to do this one must put them in a context of accompanying presumptions. This means that one must work within a discipline I have... called dialectic, rather than just within logic." Dialectic is the study of dialogue. "Descriptive dialectic is concerned with our actual linguistic conduct. Formal dialectic is concerned with systematic languages of communication having precise rules....

"We can imagine to ourselves that each participant in a dialogue carries around with him a slate on which he chalks various statements as he makes them, or as they are made to him and implicitly or explicitly agreed to by him, or as he answers questions in such a way as to imply them. Commitments can also be retracted, and the corresponding items wiped off the slate. The slate is used ... to keep a running tally of commitments." Commitments "are essentially public and are not to be confused with beliefs. The concept of commitment is an oversimplifica- tion since there are half-utterances and half-commitments; commitments apply sometimes more to meanings than words; they age and fade, may be presumptive, unclear, or differently under- stood by different participants....

..... presumptions themselves are in the nature of commitments: they appear, as it were in parentheses, beside each item in store. We can suppose the commitment slate, perhaps, divided up into different areas, each containing a group of commitments that are the result of a set of effectively contemporaneous statements... and each group augmented with the pre- sumptions concerning the timing and dating of the set." In any case, "logical relations within this model can be explicated as holding between statements that appear together on a slate; and we need not consider those that do not."

Comment. The reviewer does not understand some of the author's assertions and arguments, but he believes that the author's basic ideas concerning the role of presumptions in dialogue are worth formalizing and studying in detail. DAVID HARRAH

EVERT W. BETH. Preface. English translation of XL 256(1). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. XI-XIII.

EVERT W. BETH. Science as a cultural factor. English translation of XL 256(2). Ibid., pp. 1-10.

EVERT W. BETH. Natural science, philosophy, and persuasion. English translation of XL 256(3). Ibid., pp. 11-20.

EVERT W. BETH. Scientific philosophy: its aims and means. English translation of XL 256(4). Ibid., pp. 29-34.

EVERT W. BETH. Symbolic logic as a continuation of traditional formal logic. English translation of XL 256(5). Ibid., pp. 42-61.

EVERT W. BETH. Science a road to wisdom. English translation of XL 256(6). Ibid., pp. 69-75.

EVERT W. BETH. Modernism in science. English translation of XL 256(7). Ibid., pp. 76-85.

EVERT W. BETH. In retrospect. English translation of XL 256(8). Ibid., pp. 95-105. Science a road to wisdom is a compendium of twelve short philosophical papers which Beth

wrote during the period 1939-1964. His intention in this volume was to reproduce a "modest selection from my purely historical work ... and a survey of my ideas and my work in the field of general philosophy." While the majority of the twelve articles represents what Beth himself calls the fourth stage of his intellectual development (circa 1950-1969), the book gives the reader at least a flavor of his philosophical leanings from the beginning of the Second World War on. Regrettably, in this treatment of his general philosophy, Beth avoided any discussion of his contributions to mathematical logic for which he is so well known.

Perhaps the most informative article is the autobiographical sketch, In retrospect (1960), in which he offers a chronological perspective for the other eleven papers. Here he describes how his earlier philosophy (i.e., before 1935) was so greatly influenced by the 'Genootschap' and its leading figure, Goedewaagen; and how his disenchantment with the dogmatism at the time

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REVIEWS 256

culminated in his interest in scientific objectivity and the relevance of mathematical thought. It is this association with the 'Genootschap' and the later extrication which Beth characterizes as his first (pre-1935) and second (1935-1942) periods of intellectual development. After a brief study of law (1940-1942) interrupted his philosophy, Beth became more interested in in- tuitionism and significs, topics with which he had been acquainted since the mid-thirties, and with the history of science. Beth's interests in these areas, particularly the latter, must have been productive for he illustrates this third period (1942-1950) with examples of apparently well thought-out views ranging from the conviction that the weakening of support for the Aristotelian conception of science accounts for many of the philosophical attacks on new developments in science, to the notion that our self-knowledge fails to provide us with the degree of certainty which we normally credit to it. But these interests were to be of secondary importance after Beth met Tarski in 1950 and became convinced that there remained many problems in mathematical logic still unanswered. From that time on, his fourth period in fact, Beth remained a devotee to the philosophically significant problems of mathematical logic. In this context it is interesting to note Beth's delineation of the four distinguishable activities within mathematical logic: (a) development of systems, (b) application of systems, (c) the internal foundation of systems, and (d) the relation between the systems and thought. While Beth considers most of his work as representative of the second and third activities, his work with Piaget, Mathematical epistemology and psychology (XL 258(6, 8)), adds the fourth to his list of achievements. Beth gives the impression that the development of systems escaped his attention largely because of its non-philosophical orientation and his lack of training in formal mathematics.

In most of the remaining articles, Beth calls for philosophy to maintain a close contact with the advancements of science while at the same time preserving its autonomy. Only then, Beth claims, can philosophy serve its optimal role of advancing a rational persuasion in terms of which the products of the 'exact sciences' can be meaningfully evaluated and applied. While this position is best explained in the title article (1955), this theme is recurrent in all of the other articles concerning science and scientific philosophy as well. In addition, however, Beth takes the opportunity in three papers to remark on such divergent topics as whether abstract art was founded on the developments of abstract mathematics, whether causality plays different roles at different levels of thought, and whether it is a moral obligation for persons involved in philosophical or scientific disputes to divulge their prejudices.

While it may be safe to say that the reader of Science a road to wisdom will not want to accept Beth's views as conclusive, he will probably agree that this collection does provide significant insight into the philosophical tendencies of one of the world's renowned logicians. Of course, Beth admits that the publication of these reflections "may perhaps be justified by the circum- stance that the personal experiences to which they refer may be considered more or less typical"; but even as a collection of reflections, the book is well worth the price. H. L. BERGHEL

EVERT W. BETH. Ten geleide. Dutch original of XL 255(1). Door wetenschap tot wi/sheid, by Evert W. Beth, Van Gorcum & Comp. N.V., Assen 1964, pp. 1-3.

EVERT W. BETH. De wetenschap als cultuurfactor. Dutch original of XL 255(2). Ibid., pp. 5-15.

EVERT W. BETH. Natuurwetenschap, wijsbegeerte en levensbeschouwing. Dutch original of XL 255(3). Ibid., pp. 16-27.

EVERT W. BETH. De wetenschappelhke wijjsbegeerte: haar doelstelling en hulpmiddelen. Dutch original of XL 255(4). Ibid., pp. 37-44.

EVERT W. BETH. De logistiek als voortzetting van de traditionele formele logica. Dutch original of XL 255(5). Ibid., pp. 53-73.

EVERT W. BETH. Door wetenschap tot wischeid. Dutch original of XL 255(6). Ibid., pp. 82-89.

EVERT W. BETH. Modernisme in de wetenschap. Dutch original of XL 255(7). Ibid., pp. 90-100.

EVERT W. BETH. Een terugblik. Dutch original of XL 255(8). Ibid., pp. 111-122.

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