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**Leibniz and modern science.
(Leibniz und die moderne Naturwissenschaft.)**
*(German)*
Zbl 1435.01004

Wissenschaft und Philosophie. Berlin: Springer (ISBN 978-3-662-59235-9/pbk; 978-3-662-59236-6/ebook). x, 185 p. (2019).

The author relates Leibniz’s philosophical (scientific) system to modern science. The remarkable coherence of Leibniz’s system is based on a few fundamental principles, combining, as the author writes, “in a grand manner logic, rational reasoning, mathematics, physics, philosophy and theology to each other” (p.VI). The author attempts to reconstruct Leibniz’s system and to position Leibnizian ideas in today’s scientific discourses.

In the first three sections the author determines Leibniz’s system based on the general principles law of identity (law of excluded contradiction), law of sufficient reason and the principle of continuity. He hints at the significance of Leibniz’s monadology, his mature metaphysical system, and his universal characteristics. A specific feature of Leibniz’s thinking can be seen in his attempts to present a coherent systematic unification of a highly complex set of elements. This programme is set into the context of 17th and 18th century philosophy and science (Sect. 2). The author sees in Leibniz’s system the result of thinking in structures, distinguished from a thinking in concepts like in classical philosophy, and a thinking in models as it can be found in physics (pp.22–3). Sect. 3 deals with matter and Leibniz’s focus on monads which constitute matter, but are themselves not material, an idea which is today relevant in high energy physics. Elements of modern physics can be found in Leibniz’s dynamics (Sect. 5), and his conceptions of space and geometry (Sect. 6). They are also relevant for the modern debate of the continuum in physics and mathematics (Sect. 7). Leibniz’s logic (Sect. 8) is connected to syllogism including graphical decision methods, algebraic methods, predicate logic, logic of relations and possible worlds semantics. The author sees modern structural reasoning at work (Sect. 9). It is supported by Leibniz’s use of symbolism where a symbol gets an operational meaning dependant of the purpose it should serve (p.73). The long section about the relation between entities and the relationality of space (Sect. 10, pp.76–111) provides a survey on the mathematical foundations of relativity theory. The author denies the assumption that Leibniz might be regarded as precursor or prophet of Einstein’s theory (p.78), in particular due to his incompatible ideas of compossibility and causal determinism. Nevertheless, the author shows that some of the problems debated by Leibniz and his contemporaries are still prevailing and that Leibniz came closer to modern conceptions than, e.g., R.Descartes or I.Newton. Sect. 11 on possible worlds relates Leibniz’s concept of the best of all possible worlds to modern multiverse speculations in cosmology and quantum theory. In the section on causality (Sect. 12) the distinction between effective and final causes is discussed, together with the related concepts of necessity and contingency. This section leads over to biology (Sect. 13) with a discussion of the directions of time in physics and biology. Leibniz’s concept of monad is related to biological concepts such as gene, cell, and the balancing effects in the development of species. The author shows that Leibniz anticipated some ideas of biological system theory. Time is taken up in Sect. 14. Periodic, entropic and evolutionary time is distinguished. The final chapter (Sect. 15) deals with consciousness and cognition in epistemology and today’s theory of cognition.

The author evaluates in this section that some of Leibniz’s insights, although time dependent, are relevant even today and that reconsidering them could help to get rid of some of the mischief discussed in the philosophy of mind and the theory of consciousness today (pp.156–7). The author of this inspiring book summarizes: Even in domains where Leibniz’s answers cannot be accepted any more, the questions he posed remain up-to-date. In most cases we have no better answers today, and the questions remain open. The way Leibniz treated these questions leads to deep insights, remaining valid in today’s discussions (p.161).

In the first three sections the author determines Leibniz’s system based on the general principles law of identity (law of excluded contradiction), law of sufficient reason and the principle of continuity. He hints at the significance of Leibniz’s monadology, his mature metaphysical system, and his universal characteristics. A specific feature of Leibniz’s thinking can be seen in his attempts to present a coherent systematic unification of a highly complex set of elements. This programme is set into the context of 17th and 18th century philosophy and science (Sect. 2). The author sees in Leibniz’s system the result of thinking in structures, distinguished from a thinking in concepts like in classical philosophy, and a thinking in models as it can be found in physics (pp.22–3). Sect. 3 deals with matter and Leibniz’s focus on monads which constitute matter, but are themselves not material, an idea which is today relevant in high energy physics. Elements of modern physics can be found in Leibniz’s dynamics (Sect. 5), and his conceptions of space and geometry (Sect. 6). They are also relevant for the modern debate of the continuum in physics and mathematics (Sect. 7). Leibniz’s logic (Sect. 8) is connected to syllogism including graphical decision methods, algebraic methods, predicate logic, logic of relations and possible worlds semantics. The author sees modern structural reasoning at work (Sect. 9). It is supported by Leibniz’s use of symbolism where a symbol gets an operational meaning dependant of the purpose it should serve (p.73). The long section about the relation between entities and the relationality of space (Sect. 10, pp.76–111) provides a survey on the mathematical foundations of relativity theory. The author denies the assumption that Leibniz might be regarded as precursor or prophet of Einstein’s theory (p.78), in particular due to his incompatible ideas of compossibility and causal determinism. Nevertheless, the author shows that some of the problems debated by Leibniz and his contemporaries are still prevailing and that Leibniz came closer to modern conceptions than, e.g., R.Descartes or I.Newton. Sect. 11 on possible worlds relates Leibniz’s concept of the best of all possible worlds to modern multiverse speculations in cosmology and quantum theory. In the section on causality (Sect. 12) the distinction between effective and final causes is discussed, together with the related concepts of necessity and contingency. This section leads over to biology (Sect. 13) with a discussion of the directions of time in physics and biology. Leibniz’s concept of monad is related to biological concepts such as gene, cell, and the balancing effects in the development of species. The author shows that Leibniz anticipated some ideas of biological system theory. Time is taken up in Sect. 14. Periodic, entropic and evolutionary time is distinguished. The final chapter (Sect. 15) deals with consciousness and cognition in epistemology and today’s theory of cognition.

The author evaluates in this section that some of Leibniz’s insights, although time dependent, are relevant even today and that reconsidering them could help to get rid of some of the mischief discussed in the philosophy of mind and the theory of consciousness today (pp.156–7). The author of this inspiring book summarizes: Even in domains where Leibniz’s answers cannot be accepted any more, the questions he posed remain up-to-date. In most cases we have no better answers today, and the questions remain open. The way Leibniz treated these questions leads to deep insights, remaining valid in today’s discussions (p.161).

Reviewer: Volker Peckhaus (Paderborn)

### MSC:

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |

01A50 | History of mathematics in the 18th century |

00A30 | Philosophy of mathematics |

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

03A10 | Logic in the philosophy of science |

83-03 | History of relativity and gravitational theory |

92-03 | History of biology |