The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets

2020 ◽  
Author(s):  
David Ellerman
Keyword(s):  
Logical Theory ◽  
Universal Constructions

Keynes and the Ethics of Socialism

2019 ◽  
Vol 22 (2) ◽  
pp. 139-180
Author(s):  
Edward Fuller
Keyword(s):  
Social System ◽  
Ethical Theory ◽  
Private Property ◽  
Economic Thought ◽  
Logical Theory ◽  
Rule Based ◽  
Ethical Justification ◽  
General Rules

This paper examines John Maynard Keynes’s ethical theory and how it relates to his politico-economic thought. Keynes’s ethical theory represents an attack on all general rules. Since capitalism is a rule-based social system, Keynes’s ethical theory is incompatible with capitalism. And since socialism rejects the general rules of private property, the Keynesian ethical theory is consistent with socialism. The unexplored evidence presented here confirms Keynes advocated a consistent form of non-Marxist socialism from no later than 1907 until his death in 1946. However, Keynes’s ethical theory is flawed because it is based on his defective logical theory of probability. Consequently, Keynes’s ethical theory is not a viable ethical justification for socialism.

The Problem of a Logical Theory of Belief Statements

1960 ◽  
Vol 27 (1) ◽  
pp. 88-95 ◽  
Author(s):  
Nicholas Rescher
Keyword(s):  
Logical Theory ◽  
Belief Statements

A TYPE-FREE THEORY OF HALF-MONOTONE INDUCTIVE DEFINITIONS

1995 ◽  
Vol 06 (03) ◽  
pp. 203-234 ◽  
Author(s):  
YUKIYOSHI KAMEYAMA
Keyword(s):  
Type Theory ◽  
Characteristic Point ◽  
Logical Theory ◽  
Inductive Definition ◽  
Program Extraction ◽  
First Order ◽  
Inductive Definitions ◽  
Free Theory ◽  
Program Proof ◽  
Definition Of

This paper studies an extension of inductive definitions in the context of a type-free theory. It is a kind of simultaneous inductive definition of two predicates where the defining formulas are monotone with respect to the first predicate, but not monotone with respect to the second predicate. We call this inductive definition half-monotone in analogy of Allen’s term half-positive. We can regard this definition as a variant of monotone inductive definitions by introducing a refined order between tuples of predicates. We give a general theory for half-monotone inductive definitions in a type-free first-order logic. We then give a realizability interpretation to our theory, and prove its soundness by extending Tatsuta’s technique. The mechanism of half-monotone inductive definitions is shown to be useful in interpreting many theories, including the Logical Theory of Constructions, and Martin-Löf’s Type Theory. We can also formalize the provability relation “a term p is a proof of a proposition P” naturally. As an application of this formalization, several techniques of program/proof-improvement can be formalized in our theory, and we can make use of this fact to develop programs in the paradigm of Constructive Programming. A characteristic point of our approach is that we can extract an optimization program since our theory enjoys the program extraction theorem.

scholarly journals LOGIC OF RELATIVITY

2021 ◽  
pp. 42-52
Author(s):  
Ihor Ohirko ◽  
Zinovii Partyko
Keyword(s):  
Modal Logic ◽  
Symbolic Logic ◽  
Logical Theory ◽  
Relative Truth ◽  
Time Space ◽  
Different Types ◽  
Logical Method ◽  
Standard Values ◽  
The Difference ◽  
Modal Values

The problem of the truth of statements is considered. This study had the goal to develop a logical theory that would allow considering the context (the paradigm) from which would depend on the truth of the statement. For the development of such a theory, called the logic of relativity, the following methods of research are used as abstraction, analysis (traditional), synthesis, deduction, formalisation, axiomatisation, logical method. In order to develop the logic of relativity, it is expedient to use the achievements in the area of situational logic. Under the situation, it is proposed to understand two circumstances (time and space) and a condition that creates a context (paradigm) statement. Specifies the modal values that these three parameters can acquire and examines different types of situations. In order to write statements in the logic of relativity, a form of the statement of statements is proposed in the language of extended symbolic logic. For the theory of the logic of relativity, a set of four axioms is proposed and a series of laws. In particular, it is indicated that the values of the assertions in the logic of relativity are the following five estimates: truth, relative truth, relative is absurd, unclear, uncertain. Some theorems of the logic of relativity are proposed. A number of examples of texts in the natural language are given to interpret the statements of the logic of relativity. It is indicated that the proposed apparatus of the logic of relativity should be regarded as a kind of modal logic. The difference in the logic of relativity from situational logic is that it considers the factor of movement (motion) of statements in time, space and environment conditions, which was not considered by situational logic. The logic of relativity should be used wherever it is necessary to take into account the possibility of moving allegations regarding time, space and environment of conditions. One of the most important conclusions of the study is that in the logic to the standard values of truth (true, probably true, false, uncertain), it is expedient to add another value: relatively true (and accordingly: relatively false).

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