This paper has completed main fields of making dialectical logic pure mathematically, it is involved both atomic proposition and 1-order predicate function for dialectical logic, and by state-dual, true-valued function vector, state-contradiction law into basic logic law. In addition, also defines true-valued function for logic operators so that more easy to represent atomic proposition. Some examples are given and shown that Boolean algebra, as a special case of dialectical logic, is how to operate hybridize-able with dialectical logic.
After introducing Millianism and touching on two problems raised by genuinely empty names for Millianism (section I), I provide a brief exposition of the Gappy Proposition View (GPV) and of how different versions of this view can reply to the problems in question (section II). In the following sections I develop my reasons against the GPV. First, I will try to argue that apparently promising arguments for the claim that gappy propositions are propositions are not successful (section III). Then, I will develop two arguments against GPs via demonstrating two odd consequences of the GPV: (a) that there can be an atomic proposition which contains other propositions that are not the semantic contents of any part of the sentence expressing that atomic proposition, and (b) that propositional structures are propositions (section IV). And finally, I will attempt to show that if any of these views can provide a successful defense of Millianism, it can do so without GPs, given some slight changes (section V). I will conclude that GPs should be avoided (section VI).
Atomic Proposition and 1-Order Predicate Function for Dialectical Logic
