Professor Hannes Leitgeb is from Ludwig Maximilian University of Munich in Germany. He is an Academician of the German Academy of Natural Sciences, the member of the Academia Europaea and the International Academy of Philosophy of science. Professor Hannes Leitgeb gave two online lectures at the Wuhan University on 7^{th} of October and 14^{th} of October in 2021. The lectures are organized by the School of Philosophy at Wuhan University and live webcast is available on the online platform of XUESHUZHI. Each presentation lasts for 90 minutes with a 30-minute Q&A session. Teachers and students from the School of Philosophy at Wuhan University, as well as from home and abroad, attended the lectures via the online platform.

On the 7^{th} of October, at 3.30 pm Beijing time, Professor Hannes Leitgeb gave an online lecture titled “On merely expressive devices”. This lecture is the seventh in the series of lectures on logic and philosophy, and chaired by Professor Bo Chen (School of Philosophy at Wuhan University).

At the beginning of the lecture, Professor Hannes Leitgeb first gave a definition of “On merely expressive devices”. Merely expressive device is a linguistic part of a sentence A, such that the part plays a role in determining the proposition [A] expressed by A, without playing a role in determining the truth conditions of [A]. Professor Hannes Leitgeb then gave a paradigm case. Logical operators (e.g.disjunction) are merely expressive devices. In the report, Professor Hannes Leitgeb’s main work is to reconstruct such devices in a special kind of conceptual framework: a merely expressive device in a sentence A contributes mathematical structure by which the set [A] (of mathematical “possibilities”) expressed by A is determined. But that mathematical structure is not involved when determining whether [A] is true by comparing it to an intended interpretation (a “label”).

In the lecture, Professor Hannes Leitgeb did not give a direct definition of this conceptual framework, but first explained the idea behind it through three specific examples. These three kinds of examples are about the logical constants, stipulative definitions and analyticity, metaphysical necessity. Professor Hannes Leitgeb then summed up the similarities between the three types of examples. The frameworks are rational reconstructions of existing thought/language. First, their properties are reasonably similar to thought/language prior to reconstruction. Second, these frameworks can be used to clarify, precisify, and systematize pre-theoretic thought/language. Third, in each framework, the total underlying set of worlds is a mathematical construction and is true by math alone. Otherwise, the frameworks would not be conceptual but theories. Fourth, in each of them, the merely expressive devices are practically useful by enabling us to express propositions or making the expressing of propositions more convenient.

At the end of the lecture, Professor Hannes Leitgeb offered his own views on merely expressive devices. Mathematical symbols may themselves be viewed as merely expressive devices. Using mathematical symbols in scientific statements might merely help us express propositions about the “world”, without contributing to the truth conditions of these propositions. This would be a kind of logicism about mathematics: mathematics would merely structure “thought”, without imposing constraints on the “world”.

On the 14th of October, at 3.30 pm Beijing time, Professor Hannes Leitgeb gave an online lecture titled “Ramsification and Semantic Indeterminacy”. This lecture is the eighth in the series of lectures on logic and philosophy, and chaired by Professor Yong Cheng (School of Philosophy at Wuhan University).

Professor Hannes Leitgeb first showed that the new semantics generated by the ramsification of classical semantics can not only effectively avoid the difficulties encountered by classical semantics, but also be closer to classical semantics compared with other alternatives, such as supervaluationism. To illustrate his point, Professor Hannes Leitgeb first introduced the situation of classical semantics. Classical semantics has succeeded in reconstructing the meaning of natural language, mathematical language and scientific language, but classical semantics presupposes that there is only one definite and admissible explanation for these languages, and this presupposition conflicts with many linguistic phenomena.

Professor Hannes Leitgeb then gave us a brief introduction to classical semantics and Meta semantics, and pointed out that it is dangerous to acknowledge the central presupposition of classical semantics that there is only one permissible interpretation, because the meaning can be uncertain. To this end, Professor Hannes Leitgeb presented three examples of semantic uncertainty. The examples are as followed. Firstly, vagueness in natural language cannot be explained by classical semantics. Secondly, classical semantics cannot explain arithmetic. Thirdly, classical semantics cannot explain the conceptual progress in science.

So how can these challenges be addressed? Professor Hannes Leitgeb offered a possible solution: Ramsification. This scheme needs to discard the above-mentioned core presuppositions of classical semantics and accept the other contents of classical semantics. In order to better explain the hypothesis of Ramsey semantics, Professor Hannes Leitgeb introduced a ε operator to express the Indefinite description. If A is a formula and x is a variable, then ε x A is also a term. By using the axiom of the ε operator, Professor Hannes Leitgeb formulated the key assumption of Ramsey semantics (ADM is the set of all admissible interpretations).

1）∃F(F∈Adm)

2）I=εF(F∈Adm)

3) for all statements a in L, A is true if and only if I╞A.

Why are we doing this? Compared with supervaluationist and classical semantics, Professor Hannes Leitgeb pointed out that compared with supervaluationist, Ramsey semantics can not only be able to describe semantic uncertainty, but also better retain the many characteristics of classical semantics. Unlike supervaluationist, Ramsey semantics can retain the concept of “Truth”in classical logic. Logical consequence is still preservation of truth, and all classical rules/metarules remain logically valid even with a ‘determinately’ operator. At the same time, Ramsey semantics is less risky than classical semantics. Unlike classical semantics, Ramsey semantics does not presuppose a uniquely metasemantically determined intended interpretation. Instead, it merely presupposes that there exists a classical interpretation F that conforms to all existing metasemantic constraints and from which truth is defined by means of the classical semantic rules.

These three challenges do not pose a challenge to Ramsey semantics. With the simple help of different admissible interpretations of F, fuzzy natural language, as well as explicit mathematical and scientific language, can be easily solved. Finally, Professor Hannes Leitgeb pointed out, once again, that if we accept semantic uncertainty and expect to retain more of the characteristics of classical semantics than supervaluationist, then we should Ramsify classical semantics.

During the Q & A session, Professor Bo Chen, Professor Yong Cheng of Wuhan University, Professor Wenfang Wang of Shandong University, Associate Professor Andrea Strollo of Nanjing University, and other viewers who asked questions through the live broadcast platform exchanged views with Professor Hannes Leitgeb. The Q & A session was rich in content and lively in atmosphere. Finally, the host and participants thanked Professor Hannes Leitgeb for his two excellent lectures. According to statistics provided by XueShuZhi, until October 17th , 768 people viewed the first lecture and 564 people viewed the second lecture.

(Zhongyang Sun)