Can truths about the natural numbers vary across possible worlds?

What is possible worlds theory?

The basis of possible worlds theory is “the set-theoretical idea that reality—the sum of the imaginable—is a universe composed of a plurality of distinct elements. This universe is hierarchically structured by the opposition of one well-designated element, to all the other members of the set” (Ryan 2005, 446).

Do merely 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.

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.

What are possible worlds in philosophy?

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 do you mean by actual world and possible world?

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.

Who came up with possible worlds?

David Lewis

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):

What is contingent truth?

A contingent truth is one that is true, but could have been false. A necessary truth is one that must be true; a contingent truth is one that is true as it happens, or as things are, but that did not have to be true.

What is modal logic in philosophy?

Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics.

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’.

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 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.