Periodic Reporting for period 4 - TRUST (Truth and Semantics)
Periodo di rendicontazione: 2023-04-01 al 2023-09-30
In semantics one attempts to give a systematic account of the meaning of sentences in natural language. This is everything but a trivial affaire. In particular, so-called self-referential sentences offer a stumbling block for developing natural language semantics but have been largely ignored by semanticists. However, research on self-reference and self-referential sentences is abundant in philosophy and philosophical logic in form of research on the Liar paradox (This sentence is not true. True or False?) and related paradoxes. Indeed, a number of accounts for dealing with self-reference have been developed in those fields---mostly in the form of theories of truth that avoid the paradoxical consequences. Implementing theories of truth within the framework of natural language semantics therefor amounts to an important step towards a satisfactory handling of self-referential sentences within natural language semantics.
This implementation runs into major problems with respect to, e.g. the semantics for natural language conditionals, various quantifiers, belief ascriptions and, more generally so-called hyperintensional semantics. One principal focus of the research project was to develop theories of truth for these different semantics and thereby provide the groundwork for satisfactory semantics of such contexts in the presence of self-referential, liar-like sentences. A second principal focus of the project is to assume a more metasemantic perspective and reflect on the foundations of natural language semantics conceived of as truth-conditional semantics. This raises the question of whether the natural language truth predicate (‘is true’) is related to the truth predicate employed in semantics, and if so how? Answering this question is again non-trivial and requires a thorough linguistic analysis of the natural language truth predicate, an investigation of the technical prospects and limitations of a semantic framework encapsulating this idea, as well as a comparison to views that conceives of the semantic truth predicate as a merely theoretical notion.
Overall, the project can be deemed a success. In particular, with respect to the first focal point a rich toolkit for constructing natural language semantics that can adequately process various forms of self-reference. As for the second focal point, the research is arguably more open-ended. Nonetheless the project has delivered progress of our understanding of the natural language truth predicate, the properties of truth that can be consistently assumed in a formally regimented context, as well as a foray into semantics that are self-applicable and thus allow for an identification of the semantic and natural language, i.e. object-linguistic truth predicate.
The research is of a highly abstract and foundational nature, so pointing toward any immediate importance for society, which goes beyond the scientific importance of the project for understanding key philosophical notions such as truth and belief, natural language semantics, and self-reference, is a difficult task. However, handling self-reference is also one of the major challenges and stumbling blocks of the research on artificial intelligence and, albeit in a very indirect way, our research may raise awareness and improve our understanding of the challenges to come.
This implementation runs into major problems with respect to, e.g. the semantics for natural language conditionals, various quantifiers, belief ascriptions and, more generally so-called hyperintensional semantics. One principal focus of the research project was to develop theories of truth for these different semantics and thereby provide the groundwork for satisfactory semantics of such contexts in the presence of self-referential, liar-like sentences. A second principal focus of the project is to assume a more metasemantic perspective and reflect on the foundations of natural language semantics conceived of as truth-conditional semantics. This raises the question of whether the natural language truth predicate (‘is true’) is related to the truth predicate employed in semantics, and if so how? Answering this question is again non-trivial and requires a thorough linguistic analysis of the natural language truth predicate, an investigation of the technical prospects and limitations of a semantic framework encapsulating this idea, as well as a comparison to views that conceives of the semantic truth predicate as a merely theoretical notion.
Overall, the project can be deemed a success. In particular, with respect to the first focal point a rich toolkit for constructing natural language semantics that can adequately process various forms of self-reference. As for the second focal point, the research is arguably more open-ended. Nonetheless the project has delivered progress of our understanding of the natural language truth predicate, the properties of truth that can be consistently assumed in a formally regimented context, as well as a foray into semantics that are self-applicable and thus allow for an identification of the semantic and natural language, i.e. object-linguistic truth predicate.
The research is of a highly abstract and foundational nature, so pointing toward any immediate importance for society, which goes beyond the scientific importance of the project for understanding key philosophical notions such as truth and belief, natural language semantics, and self-reference, is a difficult task. However, handling self-reference is also one of the major challenges and stumbling blocks of the research on artificial intelligence and, albeit in a very indirect way, our research may raise awareness and improve our understanding of the challenges to come.
The following work was performed over the duration of the project:
Development of semantics for languages with a self-applicable truth predicate
• Semantics for propositional attitudes
• Semantics for conditionals and restricted quantifiers for languages with a self-applicable truth predicate and, more generally, a strategy for developing semantics for non-montone notions for languages with self-applicable semantic concepts.
• Self-applicable exact truthmaker semantics: a semantics that can be applied to itself
The truth predicate in natural language
• Investigation of whether the truth predicate is gradable, context-sensitive and/or ambiguous: the tentative conclusion is negative on all three scores.
Constraints on consistent truth predicates and natural language semantics
• Logics of truth: what unrestricted principles of reasoning with truth can be consistently assumed, i.e what is the logic of truth and is there a best or strongest logic of truth? Our research has provided sharp result to the effect that there are maximal logic of truth, as well as a philosophical interpretation of these results.
• Significant reasoning: can we reason with truth in classical logic in such a way that our reasoning is fully “significant”, i.e. is it justified from the perspective of the non-classical semantic truth theory. We develop a strategy that suggests that this may well be possible.
• Unrestricted quantification: Developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. We introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification making crucial use of Russell’s notion of range of significance.
• An investigation into metasemantics and degreed natural language semantics: what is the task and prospects of natural language semantics? Is semantics conceived of as formal modelling viable? And doesn’t work in cognitive science and psychology as well as on the paradoxes of vagueness suggest that we need to adopt a fuzzy or degreed semantics?
The results of this work have been disseminated in form of articles in leading peer-reviewed journal in general philosophy, linguistic philosophy, and mathematical and philosophical logic. In addition, the TRUST project hosted 6 workshop and conferences, and presented their work at international conferences around the world. An overview of the different research papers associated with the project as well as other project actions can be found at www.truthandsemantics.xyz.
Development of semantics for languages with a self-applicable truth predicate
• Semantics for propositional attitudes
• Semantics for conditionals and restricted quantifiers for languages with a self-applicable truth predicate and, more generally, a strategy for developing semantics for non-montone notions for languages with self-applicable semantic concepts.
• Self-applicable exact truthmaker semantics: a semantics that can be applied to itself
The truth predicate in natural language
• Investigation of whether the truth predicate is gradable, context-sensitive and/or ambiguous: the tentative conclusion is negative on all three scores.
Constraints on consistent truth predicates and natural language semantics
• Logics of truth: what unrestricted principles of reasoning with truth can be consistently assumed, i.e what is the logic of truth and is there a best or strongest logic of truth? Our research has provided sharp result to the effect that there are maximal logic of truth, as well as a philosophical interpretation of these results.
• Significant reasoning: can we reason with truth in classical logic in such a way that our reasoning is fully “significant”, i.e. is it justified from the perspective of the non-classical semantic truth theory. We develop a strategy that suggests that this may well be possible.
• Unrestricted quantification: Developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. We introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification making crucial use of Russell’s notion of range of significance.
• An investigation into metasemantics and degreed natural language semantics: what is the task and prospects of natural language semantics? Is semantics conceived of as formal modelling viable? And doesn’t work in cognitive science and psychology as well as on the paradoxes of vagueness suggest that we need to adopt a fuzzy or degreed semantics?
The results of this work have been disseminated in form of articles in leading peer-reviewed journal in general philosophy, linguistic philosophy, and mathematical and philosophical logic. In addition, the TRUST project hosted 6 workshop and conferences, and presented their work at international conferences around the world. An overview of the different research papers associated with the project as well as other project actions can be found at www.truthandsemantics.xyz.
All the principal results obtained in the project are novel and have led to progress beyond the state of the art. Amongst these results few stand out as particularly noteworthy:
• The different semantics for language with self-applicable truth have added importantly to the toolkit of researchers in both philosophy but also linguistic.
• The study of the natural language truth predicate highlighted in the previous is arguably one of the first systematic study of the truth predicate in natural language. The study will be reference point for future research for the truth predicate in natural language but also serves as an important grounding for logico-semantic discussion on the role and features of the truth predicate in natural language semantics.
• The results on logics of truth are not only novel and incisive result in mathematical logic, but the work also brings genuine conceptual innovation to the philosophical discussion.
The work conducted during the running of research project has laid the foundation for further work which is already in an advanced state. For instance, in the near future further work on the semantics of generalized quantifiers as well as on the prospects of theories of semantic truth should be completed.
• The different semantics for language with self-applicable truth have added importantly to the toolkit of researchers in both philosophy but also linguistic.
• The study of the natural language truth predicate highlighted in the previous is arguably one of the first systematic study of the truth predicate in natural language. The study will be reference point for future research for the truth predicate in natural language but also serves as an important grounding for logico-semantic discussion on the role and features of the truth predicate in natural language semantics.
• The results on logics of truth are not only novel and incisive result in mathematical logic, but the work also brings genuine conceptual innovation to the philosophical discussion.
The work conducted during the running of research project has laid the foundation for further work which is already in an advanced state. For instance, in the near future further work on the semantics of generalized quantifiers as well as on the prospects of theories of semantic truth should be completed.