Possible worlds in logic

A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic.

Do all possible worlds exist?

Possible worlds exist – they are just as real as our world; Possible worlds are the same sort of things as our world – they differ in content, not in kind; Possible worlds cannot be reduced to something more basic – they are irreducible entities in their own right. Actuality is indexical.

Are there impossible worlds?

The worlds we are interested in are not in there. These worlds are often called logically impossible worlds, as logical laws such as the Law of Non-Contradiction or the Law of Excluded Middle are assumed to be the most general and topic-neutral: they are supposed to hold at all possible worlds.

What is metaphysically possible?

Metaphysical possibility is one way of thinking about the possibility of something being the case, a way that is often of special relevance to philosophers. If you think about it, we often use the phrase ‘x is possible’ in a variety of ways.

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Who invented possible worlds?

1The concept of possible worlds (henceforth PW), loosely inspired by Leibniz’ philosophy, was developed in the second half of the 20th century by philosophers of the analytic school (Kripke, Lewis, Hintikka [1989], Plantinga [1976], Rescher) as a means to solve problems in formal semantics.

What does it mean to be true in a possible world?

A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic.

What is a logical impossibility?

Something is logically impossible if it is contradictory, or against the laws of logic. Thus a round square is a logical impossibility, and it is logically impossible to be a tall man without being tall.

Does Leibniz believe in God?

G. W. Leibniz (1646-1716) thought the same as you: belief in God must have a rational basis, not a basis in faith alone. So he disagreed with Bayle. But this meant that Leibniz had to face the problem of natural evil head on (a task he called “theodicy”, which literal means God’s justification).

Did Leibniz believe in the Bible?

Leibniz used Christianity to back up the validity of all the premises. For the first premise, God’s existence and role as the creator of the world was proven by the Bible. The second premise is proven since “God acts always in the most perfect and most desirable manner possible”.

What does modal mean in philosophy?

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’.

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What is the modal possible?

Modal verbs express if something is certain, probable or possible. If something is possible in the future, we use ‘could’, ‘might’ or ‘may’ before the main verb to talk about it. If something is possible now or was possible in the past we add the word ‘have’ after the modal verb. This still expresses possibility.

What is modal logic with example?

For example, when A is ‘Dogs are dogs’, ◻A is true, but when A is ‘Dogs are pets’, ◻A is false.) Nevertheless, semantics for modal logics can be defined by introducing possible worlds. We will illustrate possible worlds semantics for a logic of necessity containing the symbols ∼,→, and ◻.

What does possible mean in philosophy?

In logic, possibility implies the absence of a contradiction. Such definitions as “The possible is that which either is or will be true” and “that which is not prevented by anything from happening even if it does not happen” were current in Hellenistic Greece.

What is possible existence?

Possible existence belongs to anything that does not exist through itself, and to that which depends on something other than itself for its own existence. If something is caused to exist, then its existence is not through itself.