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**On the universe of thought. An intellectual history of logic.
(Vom Universum des Denkens. Eine Geistesgeschichte der Logik.)**
*(German)*
Zbl 1508.03007

Berlin: Springer (ISBN 978-3-662-65312-8/hbk; 978-3-662-65313-5/ebook). vii, 118 p. (2022).

The author presents in this small book in a popular way a survey of the history of logic from its ancient beginnings to recent times. The book is organized in eight sections according to basic concepts, but the presentation is largely chronological using canonical historical examples. Chapter 1 “On judgments” (pp. 1–13) discusses the Aristotelian theory of general and particular judgments (standard forms). Chapter 2 “On propositions” (pp.15–30) deals with Stoic modifications of the Aristotelian theory, logial connectives for the construction of complex propositions, the theory of conditionals, truth values, and inferences including syllogisms. Chapter 3 on “Belief and knowledge” (pp.31–42) treats topics from medieval times like the role of logic in education (collegium logicum), sophismata, paradoxes (insolubilia), and medieval textbooks, e.g., by William of Sherwood, Peter of Spain, and William of Ockham, and finally the influence of logic on the sciences of early modern times. Chapter 4 “On subject and predicate” (pp.43–55) is devoted to G.Frege’s predicate logic, his semantics as represented in his distinction between sense and reference for propositions and concepts, and finally B.Russell’s theory of definite descriptions. In Chapter 5 “On obligations, being and ought” (pp.57–71), the author deals with modalities, modal logic, A. Prior’s temporal modalities, and G. H. von Wright’s deontic logic. In Chapter 6 “On knowledge” (pp.73–85), inductive logic and the theory of probability is discussed. Chapter 7 “On mathematics” (pp.87–102) deals with mathematical logic starting with G. W. Leibniz’s ideas of calculi, then hinting at G.Boole’s algebra of logic, Frege’s Begriffsschrift, D.Hilbert’s proof theory, and G. Peano’s axiomatization of arithmetic. The final chapter “On truth” (pp.103–114) presents A.Tarski’s semantical theory of truth and J.{Ł}ukasiewiz’s three-value logic. The book closes with ideas on the diversity of logical systems and their evaluation, also in respect to their relation to reality. With this marvelous booklet, the author succeeds in drawing a vivid picture of the scope and efficiency of logical systems through the centuries, despite its sketchy character.

Reviewer: Volker Peckhaus (Paderborn)

### MSC:

03-03 | History of mathematical logic and foundations |

00A09 | Popularization of mathematics |

00-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general |

00A30 | Philosophy of mathematics |

01A05 | General histories, source books |

03A05 | Philosophical and critical aspects of logic and foundations |