Theory of science. 4 volume set. Translated from the German and edited by Paul Rusnock and Rolf George (Q2873772)

This excellent scholarly English translation comprising four volumes amounting to more than 2000 pages ranks in its significance at the same level as the landmark work it translates, \textit{B. Bolzano}'s \textit{Wissenschaftslehre}, first published in 1837 (cf. for the new edition of Vol. 1 [JFM 45.0119.09]; for second edition of Vol. 1[JFM 55.0027.01]), a pioneering work in the philosophy of science and the philosophy of mathematics. The translation follows the critical edition in Bolzano's \textit{Gesamtausgabe}, published in 12 volumes (cf. [Zbl 0549.01025; Zbl 0609.01048; Zbl 0623.01027; Zbl 0634.01011; Zbl 0645.01029; Zbl 0672.01042; Zbl 0805.01038; Zbl 0941.01308; Zbl 0959.01503; Zbl 0959.01504; Zbl 0961.01037]).NEWLINENEWLINEThe editors support the reader furthermore with a valuable apparatus facilitating access to Bolzano's text and his theory.NEWLINENEWLINEVol. 1 begins with a ``General introduction'' (pp. xvii--xxviii) providing a sketch of Bolzano's life and work and a discussion of the significance of his theory of science. The editors hint on particulars of translating Bolzano's terminology adding a list with ``Translations of key terms'' (p. xxix).NEWLINENEWLINEEach volume is provided with a separate introduction indicating significant topics dealt with in the respective volumes. The ``Introduction to volume one'' (pp. xxx--lxii) discusses essential terms and basic parts of Bolanzo's theory, among them his ``Theory of fundamentals'' developing among other things the notions of ideas and propositions in themselves. Propositions in themselves are ``propositions (both true and false) independently of human thought and even language'' (p. xxxiii). Bolzano denies, however, that they have any existence or actuality (p. xxxiv). His ``Theory of elements'' contains three parts on ideas, propositions, and inferences. The editors discuss Bolzano's notion of ideas as being parts of propositions, an opinion which radically departed from logical tradition (p. xxxviii). The editors maintain that ``Bolzano's account of ideas constitutes a quiet revolution in logic and marks the beginning of what Coffa called the semantic tradition'' (p. xli). Bolzano had an early theory of reference related to the senses of expressions, thus significantly deviating from the philosophical tradition. They discuss Bolzano's ontological views, e.g., Bolzano's notion of an object understood as something, encompassing entities of all sorts. The editors introduce Bolzano's logic of classes, classes understood as extensions of ideas.NEWLINENEWLINEThe second volume completes the theory of elements dealing with propositions and inferences. For the editors the most noteworthy parts of this volume ``are those dealing with propositional form, Bolzano's variation logic, and the theory of ground and consequences'' (p. xv). In their introduction (pp. xv--liv), the editors concentrate on these topics. Variation logic is the best-known part of Bolzano's logical work, based on his general conception of form (p. xxvii). It investigates the features of propositions and relations between the propositions if the propositions are varied. In this connection, Bolzano formulates an entire theory of relations. For the editors variation logic ``is a thing of rare beauty and represents, perhaps, the greatest advance in logical theory since antiquity'' (p. xxxix). Bolzano's account is ``actually a \textit{generalisation} of Tarski's, in that the set of variands is not fixed once and for all, but rather is itself allowed to vary'' (ibid.). The introduction closes with a description of the relation between grounds and consequences, and finally his theory of descriptions.NEWLINENEWLINEThe third volume contains Book Three ``Theory of knowledge'' and Book Four ``The art of discovery''. Again, the main points are presented and discussed in the editor's introduction (pp. xiii--xxxviii). In his theory of knowledge, Bolzano shows his (critical) closeness to Leibniz. He distinguishes different kinds of internal psychological phenomena: subjective ideas, judgements, sensations, desires (wishes) and resolutions (acts of will). He deals with knowledge, ignorance, error and related matters, furthermore qualities of knowledge as connected to certainty, possibility, and confidence in judgements. The editors judge Bolzano's presentation with its distinctions as having ``to rank as one of the most clear and precise. And once one has mastered his distinctions, the confusions present in earlier writers (as well as his own occasional slips) become as plain as day'' (p. xxvii). In his ``Art of discovery'', Bolzano has striven ``to set out in clear terms the various rules and procedures that talented thinkers have followed, for the most part without being aware of doing so'' (\S\ 322, Vol. III, p. 295). This book also contains Bolzano's ideas about the theory of signification with material today discussed in the philosophy of language. The editors particularly hint at what Bolzano calls ``testifying'', i.e., ``the attempt to communicate'' or ``to perform actions with the intention of causing someone else to form certain beliefs'' (p. xxxvi).NEWLINENEWLINEThe concluding fourth volume contains Book Five ``Theory of science proper'', understood as ``the science that teaches us how to divide the entirety of human knowledge into individual sciences and to present these sciences in well-composed treatises'' (p. xxiii). The book gives general methodological considerations on definitions, principles, proofs and classifications. The editors deal in their introduction (p. xxiii--xxxvi) extensively with Bolzano's theory of indirect proofs (pp. xxviii--xxxii).NEWLINENEWLINEIn sum: this translation, fruit of efforts which were first initiated 50 years ago, is a perfect representation of an important piece of philosophical world literature.