Towards a Logic of Justified Belief

1. Mark GivensDr. Franz-Peter GriesmaierDepartment of Philosophy Towards a Logic of Justified Belief PROPOSED RESEARCH PROJECT Introduction This study is aimed at examining a justification operator in doxastic logic. Our formulation of the axioms governing this operator assign a deontic element to justification, which is a philosophically unusual treatment of justification. From this study we hope to contribute to a philosophically robust notion of the justification of belief. • Objective of the Study • What justification does for the benefit of knowledge has been understood since Plato, but how it does that is less clear. The current logics which have attempted to make sense of justification have succeeded only by limiting their notion of justification to that exemplified by mathematical proof. We believe that a proper analysis of justification must be less constrained. This is attested by the fact that justification in the provability sense is indefeasible; that is, it is the never case that new evidence can defeat old evidence for a proof. This indefeasibility is rarely assured of beliefs. • Basic Terminology and Definitions • Epistemic sophistication – the level of experience an agent possesses in dealing with epistemic defeaters. • Epistemic stringency – the level of constraints imposed upon an agent, in accordance with her level of spistemic sophistication. • Epistemic defeaters – tokens of evidence which cause a person to revise their beliefs. These come in two kinds: • Undercutting defeaters – defeaters which indirectly show a given proposition P not to be true (i.e., of the form ((Q→¬P)∧Q)). • Rebutting defeaters – defeaters which contradict a given proposition P, thus disproving directly (i.e, of the form ¬P). • Methods – Basic Explanation • Like most philosophical explorations, this study is heavily centered on two major processes: investigation and consideration of current theories. Logical languages lend themselves to rather simple theoretical exercises; investigating the philosophical ramifications of a logic of this kind simply involves analyzing the results that can be proved from it. The most rigorous work in this study, then, is to be found in interpreting the current epistemological theories, evaluating their viability and soundness, and rendering them in formal language. • A Little Background • Doxastic logic is a branch of modal logic which interprets the possibility and necessary operators, respectively, as “an agent S believes that P” and “it is consistent with S’s beliefs that P”. It was largely developed by JaakoHintikka in his 1962 book “Knowledge and Belief”. Hintikka designed doxastic logic with the hope of being able to derive meaningful results about the dynamics of belief by crafting a set of axioms which captured philosophically grounded intuitions about belief. • How Is This Study Helpful? • Justification, outside of provability logics, has not been incorporated in any meaningful way into doxastic logic. This is partly because this study, unlike other doxastic logics, is more concerned with the formation of beliefs than the properties of existing beliefs. Although this logic is merely a module in a larger epistemological theory, it is our hope to make substantial contributions to the dialogue concerning the dynamics of belief as it is treated in doxastic logic in general. • Acknowledgements • This project would not have been possible without the gracious help of the McNair Scholars Program. The authors of this project thank the McNair Program graciously for their generosity of time and resources. • Methods – Discipline-Specific • Through the consultation of philosophical sources which treat justification in both theoretical and less technical settings, we devise axioms which capture the proper notion of justification. We formulate axioms in accordance with ascending levels of epistemic sophistication. We hope that, through the combined treatment of these concepts in our axioms, we can obtain a quantifiable insight into the dynamic nature of the constraints imposed on cognitive agents.