Possible world

In philosophy and logic, the notion of possible world is used to explain the meaning of modal statements, ie statements of the "possible" and "necessary" to qualify their content with Modalbegriffen like. ( For details, see modal logic )

In order to assess the truth of a modal statement, it is not enough to know whether the expressed facts are actually true or false:

The knowledge that the Earth is actually spherical, are still inconclusive on whether ( 1) it would be possible that the earth had a different shape; or if ( 2) it is necessary that the Earth has a spherical shape, so if they could not be of another nature.

As a possible world is called a logic -respecting idea how reality could be constructed - that is, a logically consistent set of ideas of possible issues. One possibility statement is referred to as true when they are in such a world ( " in at least one possible world " ) is actually true; a necessity statement is called true if it ( " in all possible worlds " ) is in all such worlds true. The modal realism, whose most famous member is likely to be in the 20th century David K. Lewis, summarizes these possible worlds as a true idea of ​​parallel worlds.

Possibility, necessity and contingency

Philosophers who use the notion of possible world, distinguish the idea of ​​the actual state of affairs - the actual "world" often " actual world " or "reality" called - of other ideas about how things could be. The real or actual world is the suitable understanding of reality as the former is the case. The other worlds are called counterfactual possible worlds.

It is essential that it is in the counterfactual possible worlds for ideas, for example, results of intellectual games, in the words of Saul A. Kripke: ". Possible worlds are established and not discovered by powerful telescopes " From the standpoint of logic, there are no restrictions as to the question of what, that is what ideas may "worlds" are formed and which are not - as long as the logic is not disregarded. The question of which ideas are actually possible, is philosophical in nature, and only comes into play if you want to apply the concept of possible worlds to non- logical issues.

The relationship between propositions and possible worlds is very tight: Any given statement is either true or false in every possible world adopted; it can then the modal status of a proposition derived, understood as the two sets of possible worlds in which it where it is true and false. Thus, the following additional terms can be formed:

• True are those statements that are true in the aktualen world ( for example, " German Chancellor Gerhard Schröder in 1998. " ")
• False are those statements that are wrong in the world aktualen (eg " Angela Merkel Chancellor in 1998. " )
• Are possible such statements that are true in at least one possible world (eg, " Esther pig in 1998 Chancellor. " )
• Quota are those statements that are false in at least one possible world and true in at least one possible world ( for example, " German Chancellor Gerhard Schröder in 1998 ").
• Necessary are those statements that are true in all possible worlds (such as " All circles are round. " )
• Impossible are those statements that are false in all possible worlds (eg, " There are rectangular circuits. " )

The idea of possible worlds is usually associated with Gottfried Wilhelm Leibniz in connection, the conceptual possible worlds as representations in the mind of God and the expressions to used that actually created world because of the infinite goodness and omnipotence of God, consequently, the best of all possible worlds would represent.

However, research has also been detected traces of this idea in earlier philosophers, such as in the writings of Lucretius, Averroes and John Duns Scotus. The modern use of this term, however, was critical of Rudolf Carnap ( explicitly was referring to Leibniz ) and marked by Saul Kripke.

Formal semantics of modal logic

A derived from the semantics of possible worlds systematic theory was first developed in the 1950s by Saul Kripke and other former philosophers. Similar to the above process, the concept of possible world has used to establish a semantics for statements of possibility and necessity: A statement in the modal logic is called possible if it is true in at least one possible world. A statement is considered necessary if it is true in all possible worlds; and a statement is true or false, if it at least in the real world ( the actual world aktualen ) is true or false. also the table under " Various theories of possible worlds ." (Note that according to this definition, all the necessary statements are also possible and true. )

The term " possible world semantics " is often used synonymously with " Kripke semantics "; often but is also the term " possible world semantics " to the analysis alethischer forms of logic, that is, those that deal with the truth and falsity of statements is limited. In contrast, the Kripke semantics is also ideal for logics that are not concerned with the truth as such, for example, for deontic logic that deals with the prohibitions or permissions and analyzed. Finally, the term " Kripke semantics " linguistically neutral, because he, unlike the talk of possible worlds does not have the appeal of a modal realism.

From modal logic to philosophical tool

From this foundation of the theory of possible worlds in the course of the 1960s, developed the analysis of counterfactual conditionals means " closer possible worlds " as they pushed to a central part of many philosophical studies, including as perhaps the best known example of David Lewis and Robert Stalnaker been. Following this analysis, the truth is of counterfactual statements (ie statements that discuss what would have happened if this or that would have been the case) by the truth of this closest possible world ( or the amount of this on closest possible worlds ) determines in which these conditions occur. In this case, with regard to a possible world W1 is R, the closer to a different possible world W2, the higher the number of the same issues with respect to R, which are present in both W1 and W2 in. The more diverse these issues, the two worlds are farther away from each other with respect to R are. Now consider the following conditional sentence: " If Angela Merkel would be 2005 not become Chancellor of the Federal Republic of Germany, it would have Gerhard Schröder done it again. " This sentence is now interpreted to the effect under the "Possible worlds " analysis that he wanted to bring the following statement expressed " For all our real world in the relevant considerations nearest possible worlds: had Angela Merkel not won the parliamentary elections of the FRG in 2005, Gerhard Schröder would instead become Chancellor. " now if it is a closest ( in the relevant respects ) possible world in which Gerhard Schröder had not become Chancellor, must, according to the analysis, the above statement be wrong.

Nowadays, the concept of a possible world plays an unabated important role in many contemporary debates, including for example the zombie argument and the possibility of supervenience of physical properties in the philosophy of mind. In addition, a fierce debate about the ontological status of possible worlds is kindled, mainly driven by David Lewis believe that talk of possible worlds can be justified on countless real existing worlds besides our own best. The crucial question is: Assuming that the modal logic works and some semantics of this are at least correct: As you can imagine these possible worlds to which we refer in our interpretation of modal statements? - Lewis himself has argued that while we actually quantify over real, concretely existing worlds that exist just as clearly as our own world and can be distinguished only by their lack of spatial, temporal and causal references to this from her. ( According to Lewis 's view, the only " special" feature of our world, a purely relational: We live in this thesis is referred to as " the indexicality of actuality '. " -Update "here is then only a indexical expression like " here " and" now "). Other philosophers such as Robert Merrihew Adams and William Lycan have then Lewis conception discarded as an example of metaphysical extravagance. Suggested, instead, to imagine possible worlds as maximal complete and self-consistent sets of descriptions or propositions about the world. ( Lewis refers to these and similar proposals, as they were also put forward by Alvin Plantinga and Peter Forrest, as " modal replacement realism", he means that such theories would try in vain to the maximum benefit of the concept of a possible world for the modal logic in minimal use of realistic assumptions exploit. ) Saul Kripke in Naming and Necessity arises explicitly Lewis'schen thesis and defended in turn to a stipulativen approach, according to which possible worlds as purely formal (logical) entities and non-existent as real worlds or quantity consistent propositions can be characterized.

Various theories of possible worlds

It was necessary that the bar to t had a different length, ie, in all possible worlds, he had a different length.

By consider the logical space, one could talk about all possible worlds ( " de dicto " ), but " de re" one could never look strange worlds. Possible worlds can also not be reduced to something more elementary. They differ in content, not in kind

"Why not include a single possible world, all the possibilia? Or, at the other extreme, why is not every possible neutrino a possible world for themselves? [ ... ] Nothing is as far away from us in space, or as far away from us in the future, it would not be part of our world. " ( Translation )

The Ersatzismus is the counter theory of modal realism. Abstract spare worlds instead of the concrete worlds of modal realism. There is only one concrete world among all.

Comparison with the many-worlds interpretation of quantum mechanics

Some interpretations of modern quantum mechanics postulate a real existence of many worlds. At least each unique Messergebenis a quantum mechanical process is thus realized in a world. In addition, the intermediate system states as in different worlds can be understood realized. If one assumes an open future, according to this interpretation, there are an infinite number of parallel worlds in the first case. The attractiveness of these interpretations is that they give a realistic interpretation for two peculiarities of quantum mechanics: first, predictable from theory only with probability scores results, secondly postulated by their superposition of system states during the time course between measurement processes. However, this is not the only realistic interpretation of quantum mechanics, against various counter-arguments are put forward alongside which exist several non- realistic interpretations (which is neither for the unrealized measurement results even for theory statements of superimposed states ever own ontologically real existing truth-makers assume ).

The ontological commitments of this interpretation of quantum mechanics are immense, but far less than those of a realism regarding possible worlds. Because the amount of authorized by quantum mechanics states of the world is only a subset of the logically possible combinations of facts. Therefore, whoever voted for a many-worlds interpretation of quantum mechanics, is not already set to a logic of realism regarding possible worlds. Also, conversely, the realist logical next possible worlds accept a wide variety of interpretations of quantum mechanics. It just needs to have no additional ontological concerns inadmissible to enrich its ontology, when he accepted a many-worlds interpretation.