# In modal logic, why not ‘possibly p’ → ‘not necessarily p’?

## What is possible modal proposition?

In classical modal logic, a proposition is said to be. possible if it is not necessarily false (regardless of whether it is actually true or actually false); necessary if it is not possibly false (i.e. true and necessarily true);

## What is possibility and necessity?

Possibility and necessity are related. Something is possible if its failing to occur is not necessary; if something is necessary, its failure to occur is not possible.

## What’s the point 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 logic with example?

Even in modal logic, one may wish to restrict the range of possible worlds which are relevant in determining whether ◻A is true at a given world. For example, I might say that it is necessary for me to pay my bills, even though I know full well that there is a possible world where I fail to pay them.

## Are there possible worlds?

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.

## What is possible world theory?

Definition. A possible world is a complete way things might be. Possible worlds are alternative worlds one of which is the actual world. Philosophers use the notion of a possible world to define and discuss ideas such as possibility or necessity.

## 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.

## What Is syntax of modal logic?

Modal logics: syntax

variables. ¬, ∧, ∨

## How do you read modal logic?

The box means what just means it is necessary that or necessarily the diamond means it is possible that or just possibly.

## Is modal logic first order?

First-order modal logics are modal logics in which the underlying propositional logic is replaced by a first-order predicate logic. They pose some of the most difficult mathematical challenges.

## What are modal statements?

Modal statements tell us something about what could be or must be the case. Such claims can come in many forms. Consider: No one can be both a bachelor and married. (‘Bachelor’ means ‘unmarried man’.)

## How does possible worlds semantics define a necessary proposition?

Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: “2 + 2 = 4”; “all bachelors are unmarried”).

## How do you know if something is logically possible?

Logical possibility is usually considered the broadest sort of possibility; a proposition is said to be logically possible if there is no logical contradiction involved in its being true.

## What is Lewis argument for the existence of possible worlds?

86) Lewis’s argument here is: The actual world is not a set of sentences. The actual world is a possible world. All possible worlds are the same kind of thing: one of them is a set of sentences iff they all are a set of sentences.

## Are there infinite possible worlds?

To have infinitely many possible worlds would require infinitely many sets of consistent propositions. Infinitely many sets of consistent propositions would require infinitely many propositions.

## How many worlds are there in Earth?

Scientists have just started to publish their findings from the data obtained from the Kepler telescope’s many observations. According to one recently-released study, some scientists now believe that there could be as many as 40 billion planets like Earth in the Milky Way galaxy.

## Who came up with possible worlds?

2.1.

The originator and, by far, the best known proponent of concretism is David Lewis. For Lewis and, as noted, concretists generally, the actual world is the concrete physical universe as it is, stretched out in space-time. As he rather poetically expresses it (1986, 1):