scholarly journals Concession and modal calculus

2019 ◽  
Vol 34 (1) ◽  
pp. 99-107
Author(s):  
Robert Martin
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Square Of Opposition ◽  
Linguistic Approach ◽  
The Universe ◽  
The Square Of Opposition

Contrary to modal logic, the linguistic approach to modality, without in any way minimizing modal relationships as such (for example by way of the “square of opposition”), tends towards a relative calculation of the knowledge and the beliefs of the speaker. In this article the (universal) modal of the universe of beliefs or of possible worlds will be updated, focusing on how the signs of concession can be interpreted, then defining the “modal calculus” (conceived as a system suitable for determining the modal content of any proposition) in order to apply it to concessive relationships.

scholarly journals Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 128
Author(s):  
Lorenz Demey
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
Kripke Models ◽  
Relational Semantics ◽  
Square Of Opposition ◽  
Neighborhood Semantics ◽  
Logical Equivalence ◽  
Different Types ◽  
Normal Modal Logics ◽  
The Square Of Opposition

Aristotelian diagrams, such as the square of opposition, are well-known in the context of normal modal logics (i.e., systems of modal logic which can be given a relational semantics in terms of Kripke models). This paper studies Aristotelian diagrams for non-normal systems of modal logic (based on neighborhood semantics, a topologically inspired generalization of relational semantics). In particular, we investigate the phenomenon of logic-sensitivity of Aristotelian diagrams. We distinguish between four different types of logic-sensitivity, viz. with respect to (i) Aristotelian families, (ii) logical equivalence of formulas, (iii) contingency of formulas, and (iv) Boolean subfamilies of a given Aristotelian family. We provide concrete examples of Aristotelian diagrams that illustrate these four types of logic-sensitivity in the realm of normal modal logic. Next, we discuss more subtle examples of Aristotelian diagrams, which are not sensitive with respect to normal modal logics, but which nevertheless turn out to be highly logic-sensitive once we turn to non-normal systems of modal logic.

The Logical Square and the Table of Oppositions

2012 ◽  
Vol 15 (1) ◽  
pp. 400-416
Author(s):  
Wolfgang Kienzler
Keyword(s):  
Reduced Form ◽  
Square Of Opposition ◽  
Logical Square ◽  
Long Time ◽  
The Square Of Opposition ◽  
The Way

The way Frege presented the Square of Opposition in a reduced form in 1879 and 1910 can be used to develop two distinct versions of the square: The traditional square that displays inferences and a “Table of Oppositions” displaying variations of negation. This Table of Oppositions can be further simplified and thus be made more symmetrical. A brief survey of versions of the square from Aristotle to the present shows how both aspects of the square have coexisted for a very long time without ever being properly distinguished.

Necessary Existence

2018 ◽  
Author(s):  
Alexander R. Pruss ◽  
Joshua L. Rasmussen
Keyword(s):  
Modal Logic ◽  
Abstract Objects ◽  
Classical Theism ◽  
Necessary Being ◽  
Necessary Existence ◽  
Concrete Entity ◽  
The Universe

A necessary being is a concrete entity that cannot fail to exist. An example of such a being might be the God of classical theism or the universe of necessitarians. Necessary Existence offers and carefully defends a number of novel arguments for the thesis that there exists at least one necessary being, while inviting the reader to a future investigation of what the neccessary being(s) is (are) like. The arguments include a defense of a classic contingency argument, a series of new modal arguments from possible causes, an argument from abstract objects, and a Gödelian argument from perfections. Furthermore, arguments against the possibility of a necessary being are critically examined. Among these arguments are old and new arguments from conceivability, a subtraction argument, problems with causation, and an argument from parsimony. Necessary Existence also includes a defense of the axioms of S5 modal logic, which is a framework for understanding several arguments for necessary existents.

The Evil That Free Will Does: Plantinga’s Dubious Defense

Metaphysica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mark Maller
Keyword(s):  
Modal Logic ◽  
Free Will ◽  
Possible Worlds ◽  
Problem Of Evil ◽  
Freedom Of Will ◽  
The Problem Of Evil ◽  
Possible Worlds Theory ◽  
Free Will Defense

Abstract Alvin Plantinga’s controversial free will defense (FWD) for the problem of evil is an important attempt to show with certainty that moral evils are compatible and justifiable with God’s omnipotence and omniscience. I agree with critics who argue that it is untenable and the FWD fails. This paper proposes new criticisms by analyzing Plantinga’s presuppositions and objectionable assumptions in God, Freedom and Evil. Notably, his limited concept of omnipotence, and possible worlds theory lack rigorous argument and are subjectively biased with irrelevant weak examples. My ontological possible worlds theory (Possible Conditional Timelines) shows that it is very likely that the omnipotent God exists of necessity in some worlds but perhaps not this one. Omnipotence is total and absolute, and should imply the freedom of will to actualize all worlds God chooses. Plantinga’s position regarding God’s omniscience of future counterfactuals is implausible based on modal logic conjecture.

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