Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - TREPISTEME (Formal Truth in Epistemology)

Teaser

The project was devoted to bridging a gap in the literature between work in epistemology and work on the notion of truth. While there has been a lot of work on modelling epistemic or doxastic notions, such as knowledge or belief, and the notion of truth individually, little...

Summary

The project was devoted to bridging a gap in the literature between work in epistemology and work on the notion of truth. While there has been a lot of work on modelling epistemic or doxastic notions, such as knowledge or belief, and the notion of truth individually, little work has been conducted towards providing combined formal frameworks in which these notions are treated simultaneously. But such combined frameworks are important for adequately modelling philosophical thought, arguments and discussions. The principal objective of the project was hence to provide formal frameworks for the notion of truth and epistemic or doxastic notions, which are adequate from such an integrated perspective. The project provided (i) an analysis of the problems such a combined approach needs to overcome, (ii) an application of a combined framework to a specific philosophical problem, i.e., the question whether the mind can be mechanized and (iii) a semantic framework for truth and modal theories of knowledge and (iv) a proof-theoretic investigation into truth in hyperintensional contexts.

Work performed

The activities carried out in the project can be divided in four main themes and work pacjages. Work package 1 (Months 1-6) was devoted to understanding of the challenges posed for a combined formal treatment of truth and epistemic notions. To this end, an in depth investigation of the most prominent formal theory of truth due to Saul Kripke was carried out, as well as a systematic analysis of the work conducted to date in epistemic logic. The work on Kripke\'s theory of truth led to a novel theory of truth, which provides a promising framework for integrating epistemic notions within the truth-theoretic framework. The theory was presntedin my paper “Supervaluation-style Truth Without Supervaluations”, which is published in the Journal of Philosophical Logic. The systematic analysis of extant work in epistemic logic that also formed an important part of the first work package resulted in a survey article on epistemic logic (in German): “Epistemische Logik” in Handbuch Erkenntnistheorie edited by M. Grajner and G. Melchior, Metzler Verlag (in press).

The second work package (Months 7-12) focused on illustrating the importance of formal frameworks for truth and epistemic notions for evaluating philosophical agruments and discussions. To this end we we investigated Penrose’s so-called ‘New Argument’, which attempts to establish that the mind cannot be mechanized, i.e., that the mind is not a machine. The formulation of Penrose’s argument requires a combined framework for the epistemic notion of ‘absolute provability’ or, alternatively, ‘knowable in principle’ and the notion of truth. In this work phase one such framework was provided and Penrose’s argument was thoroughly assessed. The research resulted in two articles. In the first article entitled “Penrose’s ‘New Argument’ and Paradox” published in Truth, Existence, and Explanation – FilMat Studies in the Philosophy of Mathematics, Boston Studies in the History and Philosophy of Mathematics with Springer, it is argued that Penrose’s argument is ultimately inconclusive because the assumptions that are required for his argument lead to Liar-like paradoxes. Furthermore it is shown that there is no hope for resurrecting Penrose’s argument along the lines of his argumentative strategy. However, in the second paper “Proving that the Mind is not a Machine?” I point to a peculiar combination of philosophical views that allow for a successful argument.

In the next work package (Months 13-18) the project turned to developing semantics for epistemic languages containing the truth predicate with a special attention to the problems raised by so-called modal theories of knowledge. To this effect the main challenge consists in showing that Kripke’s theory of truth can be applied to this semantic framework. The paper “Truth and Modal Theories of Knowledge” puts forward one such framework and discusses certain limitations of the approach. The paper will appear with Routledge in the edited volume Modes of Truth, which is edited by C. Nicolai and the MSC Individual Fellow. The preparation of this edited volume is also one direct outcome of the research conducted throughout the project.

In the final work package (Months 19-24) the project focused on proof-theoretic aspects and the development of axiomatic theories of truth for epistemic and doxastic languages. Epistemic and, in particular, doxastic languages exhibit a phenomenon called hyperintensionality. In hyperintensional languages logically equivalent propositions can no longer be substituted for each other salva veritate and this phenomenon creates a major hurdle for formulating theories of truth for these languages. The reason for the hyperintensionality of epistemic and doxastic languages is often linked to the awareness of agents to logical facts. This however creates a further layer of complexity, which we decided to set aside so to first obtain a good handle of truth in hyperintensi

Final results

Summing up the research outlined above displayed a tangible advancement of the state of the art:

1. A novel theory of truth developed combines aspects of two versions of Kripke\'s theory of truth, that is, Kripke\'s theory based on the so-called strong Kleene evaluation scheme with aspect\'s of Kripke\'s theory based on the supervaluation scheme. The novel theory amounts to an important original contribution to the research on truth that will most certainly be employed in future research.

2. The research on the question of whether the mind can be mechanized firmly establishes that, at least under the most straightforward formalization, Penrose\'s argument is not successful. More importantly, the results show that Penrose\'s argument cannot be turned into a coherent argument establishing that the mind is not a machine. A further insight consists in the presentation of a precise argument for the claim that the Mind is not a Machine and the controversial combination of philosophical-logical views the argument presupposes.

3.A semantic framework for truth, knowledge and belief that can accommodate the central notions of modal theories of knowledge such as safety and sensitvity is developed. As such the semantic framework developed is the first of its kind in the literature. The results developed during the work package will be of great value for the important problem of combining Kripke’s theory of truth with a variety of different semantic frameworks employed in natural language semantics. As such the research of the work package has great influence on the research currently directed within the ERC Starting Grant TRUST, nº803684 directed by the PI the MSC Individual Fellow.

4. To our knowledge, the first ever axiomatic theory of truth for hyperintensional languages is developed. Such a theory forms a necessary prolegomenon for satisfactory formal treatments of contexts in which propositional attitudes and truth interact.

Website & more info

More info: https://sites.google.com/site/jssternjohannes/research.