Working with Truth

September 9, 2023 — September 10, 2023
Room 2.04, Fry Building, Bristol

The workshop is hosted by the ERC-Starting Grant ‘Truth and Semantics’ (TRUST 803684) at the University of Bristol directed by Johannes Stern. It focuses on recent work on formal theories of truth and will take place directly after the BLC Annual Meeting 2023 which also takes place at the University of Bristol.

Confirmed Speakers

  • Martin Fischer (MCMP, LMU Munich)
  • Kentaro Fujimoto (Bristol)
  • Volker Halbach (Oxford)
  • Mateusz Lelyk (Warsaw)
  • Carlo Nicolai (KCL)
  • Thomas Schindler (Amsterdam)


Day 1

  • 14.00 - 14.50: Carlo Nicolai (KCL): Internal and External Theories

  • 14.50 - 15.10: Coffee

  • 15.10 - 16.00 Thomas Schindler (Amsterdam): Levelling the playfield: classical vs non-classical theories of truth

  • 16.00 - 16.20: Coffee

  • 16.20 - 17.20: Mateusz Lelyk (Warsaw): Truth up to definability

Day 2

  • 9.30 - 10.20: Martin Fischer (LMU Munich): Significant reasoning and type-free truth

  • 10.20 - 10.40: Coffee

  • 10.40 - 11.30: Kentaro Fujimoto (Bristol): Liberal Predicativism from Semantic Perspectives

  • 11.30 - 11.40: Break.

  • 11.40 - 12.30: Volker Halbach (Oxford): Logic and Truth


Martin Fischer (LMU Munich): Significant reasoning and type-free truth

In the talk I consider different forms of reasoning for a type-free truth predicate. A reading of truth as an inferential tool suggests that significant reasoning can be adequately represented in a sequent system for partial logic, such as used for the system PKF. The question whether also in classical systems such as KF some forms of significant reasoning is adequately captured is critically discussed. Moreover, an analysis via unravelling trees is suggested that might help to interpret significant KF reasoning in a reflective extension of PKF.

The talk is based on joint work with Luca Castaldo and Johannes Stern.

Kentaro Fujimoto (Bristol): Liberal Predicativism from Semantic Perspectives

Liberal predicativism is a view about what second-order entities are, which I recently proposed originally as an interpretation of proper classes in set theory. This talk tries to give more philosophical details of the view particularly from the semantic point of view.

Volker Halbach (Oxford): Logic and Truth

I discuss the motivation for Kentaro Fujimoto’s and my theory of Classical Determinate Truth (CD). In particular, I argue that for the foundations of logic, the internal notion of truth should coincide with the external. In the case of classical logic this means that the theory of truth should be formulated in classical logic and the axiomatized notion of truth should be classical as well. Such a theory of truth has several advantages over developing semantics in either set theory or a higher-order logic.

The ‘preproof’ version of the article can be found here:

Mateusz Lelyk (Warsaw): Truth up to definability

We take a closer look at the structure consisting of all sequential theories in finite signatures ordered by a definability relation (a generalisation of relative truth definability, introduced by Kentaro Fujimoto). We show that in this structure the biconditional theories (TB, UTB) can be characterized as the least elements which have certain natural model-theoretical properties. This amounts to language-independent characterizations of these theories. Then we look at finitely axiomatized theories of truth which are below the canonical compositional truth theory CT^-. We show that this structure is a countable universal distributive lattice, i.e. each countable distributive lattice can be realised as a set of such truth theories ordered by the definability relation.

This is joint work with Bartosz Wcisło (first part) and Piotr Gruza (second part). The details of the first part are presented in Universal properties of truth (

Carlo Nicolai (KCL): Internal and External theories

In the context of Kripkean Truth, internal theories have been characterized as the simplest and most natural set of axioms and rules whose adoption would provide a subject with an understanding of truth given by fixed-point models. By contrast, external theories can be seen as the simplest and most natural axiomatic formulations of Kripke’s set-theoretic definition of fixed-points. Internal theories are typically (proof-theoretically) much weaker than external ones. Hartry Field recently investigated natural internal theories that interpret KF or its schematic extension. According to Field, this shows that the deductive gap existing between classical external theories and internal ones can be filled. By interpreting the theories in suitable external theories, I will argue that Field’s proposed vindication of nonclassical internal theories does not succeed.

Thomas Schindler (Amsterdam): The Power of Naive Truth

Timothy Williamson has argued that, based on abductive criteria, classical theories of truth are preferable to non-classical theories. One of his main considerations in favour of this claim is that logical principles are more fundamental than truth-theoretic ones. In the first part of the talk, I will present a reply to this argument. Another argument often wielded against non-classical approaches is that they are proof-theoretically much weaker than their classical counterparts. In the second part of the talk, I will present a consistent, naive theory of truth that is proof-theoretically much stronger than the usual classical theories of truth such as KF.


Participation in the workshop is free of charge, but if you wish to attend please register by sending an email with the relevant details (name, affiliation) to Johannes Stern.


For all further questions about the workshop please contact Johannes Stern.