FOREMOTIONS · Formal Frameworks for Modal Notions Conceived as Predicates
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2016-01-01 → 2017-12-31
- EU contribution
- €159,461
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Formal Frameworks for Modal Notions Conceived as Predicates
"The project addressed a fundamental gap in contemporary approaches to formal philosophy. Philosophy aims to provide universal theses about reality, such as ""all truths can be known"", but the way in which these claims are analyzed in contemporary philosophy is far from universal. To properly formulate them, one usually has to distinguish between a language or conceptual framework in which the thesis is formulated, the object-language, and a language in which the thesis is analyzed, the meta-language. The naive way of combining the two languages leads to paradox. The project analyzed ways to avoid paradox while restoring the intended universality. This was accomplished by mainly: (i) a careful and original analysis of the deductive properties of theories of semantic and modal notions and their different logical assumptions; (ii) a new approach to the notion of necessity that, unlike standard modal logic, is compatible with the presence of self-referential constructions in the theories; (iii) a new analysis of the notion of implicit commitment for basic mathematical theories and its relationships with semantic and modal notions. The project contributes to establish the European academic environment as the landmark for mathematically informed studies of modalities. This, combined with the use of powerful formal tools, contributes to the reconstruction of a vision of philosophy in continuity to and not in opposition with the exact sciences that represents one of the pillars of the European identity, as witnessed by great European thinkers such as Descartes and Leibniz. "
Data: CORDIS, © European Union
Project objective
Philosophy strives for a better understanding of modal notions such as necessity, possibility, truth, knowledge. Modal logic, however, the formal tool privileged by philosophers to shape their theories about intensional notions, displays severe drawbacks: its use determines an incoherent treatment of different kinds of modalities and it is expressively weak as important general claims are not fully formalizable in it. In the project I develop an alternative approach to modal notions. Instead of treating them as operators applying to formulas, I will consider them as predicates applying to terms naming formulas. The overarching aim of the proposal is to provide philosophy with an expressive and coherent framework that could represent a valid alternative to modal logic. More precisely, I will develop three research objectives corresponding to three fundamental research gaps traceable in the current literature on modal predicates: the formulation of a natural account of the bearers of modal notions, a consistent and mathematically powerful treatment of the interaction of modal predicates, a predicate approach to de re modal ascriptions that will open the way for a new approach to modal metaphysics in the predicate setting. The project will develop a unified effort to bridge mathematical logic, philosophy of mathematics and metaphysics. It will result in the establishment of leading research profile setting the agenda for a network of researchers in the flourishing area of mathematical philosophy.
Original text from CORDIS.
Participants
- LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN · PlaneggCoordinatorGermany
Links
Data: CORDIS, © European Union