Truth, Belief and Certainty in Epistemic Logic

Standard logic tends to reduce propositions to their truth conditions. However propositions with the same truth conditions are not the contents of the same thoughts just as they are not the senses of synonymous sentences. I will first define a much finer criterion of propositional identity that takes into account predications that we make in expressing propositions. In my view, propositions have a structure of constituents. We ignore in which possible circumstances most propositions are true because we ignore real denotations of their attributes and concepts. In understanding them we just know that their truth in each circumstance is compatible with certain possible denotation assignments to their constituents and incompatible with others. So propositions have possible in addition to real truth conditions. I will explain why strictly equivalent propositions can have a different cognitive value. I will define the notion of truth according to an agent and a strong propositional implication that is known a priori. I will also formulate a logic of belief that is compatible with philosophy of mind. Human agents are minimally rather than perfectly rational in my logic. Epistemic paradoxes are solved. 1 Propositional identity and truth according to predication In philosophy, propositions are both senses of sentences with truth conditions and contents of conceptual thoughts like attitudes and illocutions. In order to take into account their double nature, I will proceed to a finer analysis in terms of predication of their logical form. Here are the basic principles of my predicative approach. 1 1.1 A finite structure of constituents In expressing propositions we predicate in a certain order a finite positive number of attributes (properties or relations) of objects to which we refer. Understanding a proposition consists mainly of understanding which attributes objects of reference must possess in order that this proposition be true. We do not directly have in mind individuals like material bodies and persons. We rather have in mind concepts of individuals and we indirectly refer to them through these concepts. So our thoughts are directed towards individuals under a concept rather than pure individuals. Concepts can be deprived of denotation. By recognizing the indispensable role of concepts in reference, logic can account for thoughts directed at inexistent objects. It can also 1 See Formal Ontology, Propositional Identity and Truth According to Predication [2003], “Propositional Identity, Truth According to Predication and Strong Implication” [2005] and “Universal Grammar and Speech Act Theory” [2001] for a more general presentation of the theory. 2 Predication as it is conceived here is independent on force and psychological mood. We make the same predication when we express a belief and a doubt that something is the case. In: Emar Maier, Corien Bary & Janneke Huitink, eds. (2005) "Proceedings of SuB9" www.ru.nl/ncs/sub9