What is the meaning of modal logic?
A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’.
What is modal proposition in logic?
Any proposition at least one of whose constituent concepts is a modal concept is a modal proposition. All other propositions are nonmodal. Any modal proposition can be represented in our conceptual notation by a wff containing one or more modal operators, e.g., “•”, “0”, etc.
What are the axioms of modal logic?
Some characteristic axioms of modal logic are: Lp ⊃ p and L(p ⊃ q) ⊃ (Lp ⊃ Lq). The new rule of inference in this system is the rule of necessitation: if p is a theorem of the system, then so is Lp. Stronger systems of modal logic can be obtained by adding additional axioms.
What Is syntax of modal logic?
The symbols of modal logic consistute of an infinite countable set P of proposi- tional variables, logical connectives, parenthesization, and the modal operator D. The choice of logical connectives depends on the development of proposi- tional logic one wants to follow; below I choose negation and implication.
What are the types of modal logic?
Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), or temporal (“it is always the case that”) among others.
Why is modal logic important?
The reason we want to utilize modal logic is to precisify ordinary language. Ordinary language is notoriously ambiguous and the analysis of ordinary language modal operators is fraught with difficulty. By regimenting our discourse into formal (quantified) modal logic we can eliminate some of these ambiguities.
What is the modal ontological argument?
To combine these concepts, modal ontological arguments are ontological arguments that invoke possibility or necessity. These arguments define God in a way that entails that he exists necessarily if he exists at all, and the conclusion is that he does in fact exist necessarily.
Who is the father of modal logic?
Aristotle is considered the father of logic.
What was the best argument against the ontological argument?
Anselm. Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason. Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a real predicate.
Why is the ontological argument wrong?
In the end, the Ontological Argument fails as a proof for the existence of God when careful attention is paid to the cognitive terms that it employs. When the terms are disambiguated, either nothing philosophically interesting follows or nothing follows at all.
Is the ontological argument a valid argument?
This argument seems to be valid, since the truth of the premises would guarantee the truth of the conclusion. And it also seems to be sound, since, in addition, the premises seem to be true. But there is another less direct way to argue for a claim, which is sometimes called reductio ad absurdum, or just reductio.