Speech acts in Mathematics: hypothetical illocutions

• Grant number: 20/08016-7
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): June 01, 2021
• Effective date (End): May 31, 2023
• Field of knowledge: Humanities - Philosophy - Logic
• Principal researcher: Giorgio Venturi
• Grantee: Tiago Rezende de Castro Alves
• Home Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 16/25891-3 - Arbitrariness and genericity: or on how to speak of the unspeakable, AP.JP

Abstract

The main goal of the proposed research is to account for the nature of the illocutionary force corresponding to hypotheses in logic and Mathematics, as well as to explain its role in the logical structure of mathematical language. Thus, it gives way to a convergence of central ideas of two research projects: Hypotheses, leaded by Prof. Peter Schroeder-Heister (Uni-Tübingen), and Genericity and arbitrariness. Or how to speak of the unspeakable, coordinated by the supervisor - respectively: (I) to carry out a proof-theoretic (and) semantic analysis of hypotheses in formal logic; and (II) to identify and explain the illocutionary elements inherent to the structure of the languages of logic and Mathematics. The following guiding assumptions establish the motivation and the departure point of the research: (a) hypotheses are an essential part of the formal logical structure of mathematical language; (b) contemporary speech-act theory cannot account satisfactorily for the illocutionary nature of hypotheses in argumentative contexts; and (c) the formal apparatus of different hypotheses-based deductive calculi (e.g. natural deduction, sequent calculus, etc.) gives way to a proof-theoretic characterisation of the illocutionary role of hypotheses in logic and Mathematics. The main goal is thus to be pursued by means of a proof-theoretic semantical study of noteworthy formal representations of this kind of illocution against the background of contemporary speech-act theory. Indirectly, this shall also provide for the attainment of a second goal: a critical analysis of current limitations of speech-act theory, which shall improve its explanatory power over the illocutionary phenomena to be studied - both in their occurrences within formal and mathematical contexts and elsewhere. (AU)