# Propositional Identity, Truth According to Predication and Strong Implication

With a Predicative Formulation of Modal Logic
• Daniel Vanderveken
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 2)

## Abstract

In contemporary philosophy of language, mind and action, propositions are not only Senses of sentences with truth conditions but also contents of conceptual thoughts like illocutionary acts and attitudes that human agents perform and express. It is quite clear that propositions with the same truth conditions are not the senses of the same sentences, just as they are not the contents of the same thoughts. To account for that fact, the logic of propositions according to predication advocates finer criteria of propositional identity than logical equivalence and requires of competent speakers less than perfect rationality. Unlike classical logic it analyzes the structure of constituents of propositions. The logic is predicative in the very general sense that it analyzes the type of propositions by mainly taking into consideration the acts of predication that we make in expressing and understanding them. Predicative logic distinguishes strictly equivalent propositions whose expression requires different acts of predication or whose truth conditions are understood in different ways. It also explicates a new relation of strong implication between propositions much finer than strict implication and important for the analysis of psychological and illocutionary commitments. The main purpose of this work is to present and enrich the logic of propositions according to predication by analyzing elementary propositions that predicate all kinds of attributes (extensional or not) as well as modal propositions according to which it is necessary, possible or contingent that things are so and so. I will first explain how predicative logic analyzes the structure of constituents and truth conditions of propositions expressible in the modal predicate calculus without quantifiers. The ideal object language of my logic is a natural extension of that of the minimal logic of propositions. Next I will define the structure of a model and I will formulate an axiomatic system. At the end I will enumerate important valid laws. The present work on propositional logic is part of my next book Propositions, Truth and Thought which formulates a more general logic of propositions according to predication analyzing also generalization, ramified time, historic modalities as well as action and attitudes.

## Keywords

Truth Condition Atomic Proposition Modus Ponens Elementary Proposition Strict Implication
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## Authors and Affiliations

• Daniel Vanderveken
• 1
1. 1.Université du QuébecTrois-Rivières