Possible world

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In philosophy and logic , the concept of the possible world is used to explain the meaning of modal statements, that is, statements that qualify their content with modal terms such as “possible” and “necessary” (see also modal logic ).

In order to be able to judge the truth of a modal statement, it is not enough to know whether the stated facts actually exist or not:

  1. It is possible that the earth is flat.
  2. It is necessary that the earth be spherical.

Knowing that the earth is actually spherical does not yet indicate whether (1) it is possible that the earth could have been another shape; or whether (2) it is necessary for the earth to be spherical, i.e. whether it could not be made otherwise.

A possible world is an idea that respects logic and how reality could be constituted - that is, a logically consistent set of ideas of the possible facts. A possibility statement is then designated as true overall if it is fulfilled in such a world (“in at least one possible world”); a necessity statement is said to be true if it is fulfilled in all such worlds ("in all possible worlds"). The modal realism , whose most representative tester in the 20th century David K. Lewis is likely to be, summarizes these possible worlds as a true idea of parallel worlds on.

Possibility, necessity and contingency

Philosophers who use the concept of the possible world distinguish the idea of ​​the actual state of things - the actual "world", often also called "actual world" or "reality" - from other ideas of how things could be. The actual or actual world is the correct idea of ​​reality (better reality ) as that is the case. The other worlds are called counterfactual possible worlds.

It is essential that the counterfactual possible worlds are ideas, for example the results of mind games, in Saul A. Kripke's words : "Possible worlds are determined and not discovered by powerful telescopes." From the point of view of logic, there are no restrictions with regard to the question of which “worlds”, d. H. which ideas may and may not be formed - as long as logic is not disregarded. The question of which ideas are actually possible is of a philosophical nature and only comes into play when one wants to apply the concept of possible worlds to extra-logical questions.

The relationship between statements and possible worlds is very close: every given statement is either true or false in every supposed possible world; from this the modal state of a proposition can be derived, understood as the two sets of possible worlds in which it is true and in which it is false. This can be used to form the following additional terms, see David Kellogg Lewis On the Plurality of Worlds (1986):

  • True , those statements that are in are true actual world (z. B. "Gerhard Schroeder was chancellor in 1998." ")
  • Statements that are false in the current world are false (e.g. "Angela Merkel became Federal Chancellor in 1998.")
  • Such statements are possible that are true in at least one possible world (e.g. "Esther Schweins became Federal Chancellor in 1998.")
  • Statements are contingent that are true in at least one possible world and false in at least one possible world (e.g. "Gerhard Schröder became Federal Chancellor in 1998").
  • Statements that are true in all possible worlds are necessary (e.g. "All circles are round.")
  • Such statements are impossible that are false in all possible worlds (e.g. "There are rectangular circles.")

The idea of ​​possible worlds is usually associated with Gottfried Wilhelm Leibniz , who understood possible worlds as ideas in the spirit of God and used the expression to mean that the world actually created should therefore represent the best of all possible worlds due to the omnipotence and omnipotence of God .

However, research has already shown traces of this idea in earlier philosophers, for example in the writings of Lucretius , Averroes or John Duns Scotus . The modern use of this term, on the other hand, was decisively shaped by Rudolf Carnap (who explicitly referred to Leibniz) and by Saul Kripke .

Formal semantics of modal logic

A systematic theory derived from the semantics of possible worlds was first developed in the 1950s by Saul Kripke and other philosophers at the time. Similar to the procedure above, the concept of the possible world was used to establish semantics for statements about possibility and necessity: A statement in 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 considered true or false if it is true or false at least in reality (the actual, actual world). also the table under “Various theories on possible worlds”. (Note that according to this definition, all necessary statements are also possible and true.)

The expression “possible worlds semantics” is often used synonymously with “Kripke semantics”; however, the term “possible worlds semantics” is often applied to the analysis of alethic forms of logic, i. H. those who deal with the truth and falsehood of statements are limited. In contrast, the Kripke semantics are also suitable for logics that are not concerned with truth as such, e.g. B. for the deontic logic, which treats and analyzes prohibitions and permissions. After all, the term “Kripke semantics” is linguistically more neutral because, in contrast to the talk of possible worlds, it does not have the appeal of modal realism .

From modal logic to a philosophical tool

From this basis, the theory of possible worlds in the course of the 1960s, became a central part of many philosophical investigations, including as perhaps the best known example, the analysis of counterfactual conditionals means "closer possible worlds", as described by David Lewis and Robert Stalnaker promoted has been. Following this analysis, the truth of counterfactual statements is (d. H. Of statements that discuss what happened was , when this and that was the case would be ) by the truth of this closest possible world (or the amount of this potential closest Worlds) in which these conditions occur. A possible world W 1 is closer to another possible world W 2 with regard to R, the higher the number of identical facts with regard to R that are present in both W 1 and W 2 . The more different these facts are, the further apart the two worlds will be with regard to R. Now consider the following conditional sentence : "If Angela Merkel had not become Chancellor of the FRG in 2005 , Gerhard Schröder would have made it again." This sentence is now interpreted under the "Possible Worlds" analysis to the effect that he wanted to express the following statement : "For all possible worlds closest to our real world in the relevant considerations, the following applies: If Angela Merkel had not won the federal election of the FRG in 2005 , Gerhard Schröder would have become Federal Chancellor instead." If there is now a (in the relevant respects) closest possible world , in which Gerhard Schröder would not have become Federal Chancellor, according to the analysis, the above statement must be incorrect.

Nowadays the concept of a possible world continues to play an important role in many contemporary debates, including the zombie argument and the possibility of supervenience of physical properties in the philosophy of mind . In addition, a heated debate has broken out over the ontological status of possible worlds, driven primarily by David Lewis' assumption that talk of possible worlds can best be justified on the basis of innumerable real worlds besides our own. The decisive question is: Assuming that the modal logic works and that at least some semantics are correct for it: How can one imagine these possible worlds to which we refer in our interpretation of modal statements? - Lewis himself has argued that we then actually quantify using real, very concretely existing worlds that exist just as clearly as our own world and can only be distinguished from it by their lack of spatial, temporal and causal references to it. (In Lewis' view the only “special” property of our world is a purely relational one: we live in it. This thesis is called “the indexicality of actuality”: “actual” is then just an indexical expression such as “here” and “ now"). Other philosophers such as Robert Merrihew Adams and William Lycan then rejected Lewis' conception as an example of metaphysical extravagance. Instead, it was proposed to imagine possible worlds as maximally complete and self-consistent sets of descriptions or propositions about the world. (Lewis calls these and similar proposals, as put forward by Alvin Plantinga and Peter Forrest , "modal substitute realism"; he suggests that such theories would attempt in vain to make the maximum use of the concept of a possible world for modal logic exploit minimal use of realistic assumptions.) Saul Kripke was raised in Naming and Necessity explicitly Lewis'schen thesis and defended in return a stipulativen approach to the possible worlds as a purely formal (logical) entities and not as a real existing worlds or amount of consistent propositions can be characterized.

Various theories about possible worlds

person Name of the theory description Quote (s)
Rubio Plures mundos possibiles Possibiles sunt plures mundi specie, ac numero distincti: probatur vtrunque hoc argumento: non repugnat ex parte divinaæ omnipotentiæ, neque ex parte rei faciendæ, ergo posible est, vtroq; modo fieri plures. "Posterior vero pars argumenti pro cedit ab initio in potentia, ad infiniti mundi sunt creabile in infinitum perfectiores, cum haec potentia possit reduci ad actum, poterunt dari infiniti mundi actu creati, & actu infiniti perfectiones secundum speciem."
Leibniz Theory of the best of all possible worlds God created the best of all possible worlds . If he wants to transform a world from the possible into the real, he needs a sufficient reason , since he cannot choose arbitrarily. The only criterion that qualitatively distinguishes a world from all others is to be the best. Leibniz thus points to a necessary connection between good and bad: there is good that can only be had at the price of the existence of evil. The real world is the best and a. in the sense that the good in it could not be realized even by God with a lesser degree of evil. "We live in the best of all possible worlds"
Kripke Semantics for statements about possibility and necessity Kripke introduced semantics of the possible worlds. "It is possible" is z. B. equated with "there is a possible world in which it is the case" and "it is necessary" means "it is the case in all possible worlds". It was possible that the stick had a different length at t, that is, there is a possible world in which it had a different length.

It is necessary that the staff should have had a different length at t, that is, in all possible worlds it had a different length.

Lewis Modal realism There are possible worlds real and concrete . These are separated from one another in terms of space and time. Every world is closed in space and time. There are infinitely many worlds because there are also infinitely many possibilities. The world in which we live is the "actual" world. In “foreign”, ie not actual worlds, there are “doppelgangers” of things in the real world. The world in which possible doppelgangers of ours live is actual for them, but not for us ( indexicality of actuality ).

By looking at logical space, one can talk about all possible worlds (“ de dicto ”), but “ de re ” can never look at foreign worlds. Furthermore, possible worlds cannot be further reduced to something more elementary. They differ in content, not in type.

“When I admit realism to possible worlds, I mean it literally . Possible worlds are what they are and no other thing. When asked what kind of thing are possible worlds, I cannot give the kind of answer the questioner might expect: that is, a suggestion to reduce possible worlds to something else. At most I can ask the questioner to admit that he knows what kind of thing our actual world is, and then I can explain to him that possible worlds are more things of this kind, but which do not differ in their kind from one another, but in what content happens on them . "(translation)

“Why don't all the possibilia contain a single possible world? Or, at the other extreme, why isn't every possible neutrino a possible world in itself? [...] Nothing is so far away from us in space, or so far away from us in the future, that it would not be part of our world. " (Translation)

Stalnaker Counterfactual analysis / closer possible worlds (developed together with David Lewis) After ... "their" ... analysis, the truth becomes counterfactual . (d. h. of statements that discuss what happened would happen if this or that was the case would be ) is determined (or the amount of this closest possible worlds) by the truth of this closest possible world in which these conditions occur . A possible world W1 is closer to another possible world W2 with regard to R, the higher the number of identical facts with regard to R that are present in both W1 and W2. Depending on various circumstances this, the two worlds are farther away from each other with respect to R are. Now consider the following conditional sentence: "If Angela Merkel had not become Chancellor of the FRG in 2005, Gerhard Schröder would have made it again." This sentence is now interpreted under the "Possible Worlds" analysis to the effect that he wanted to express the following statement : "For all possible worlds closest to our real world in the relevant considerations, the following applies: If Angela Merkel had not won the Federal Parliament elections of the FRG in 2005, Gerhard Schröder would have become Chancellor instead." If there is now a (in the relevant respects) closest possible world , in which Gerhard Schröder would not have become Federal Chancellor, according to the analysis, the above statement must be incorrect. Lewis brings both common theory u. a. into this formula: “F □ → G is true in the actual world if and only if (I) any F-world in which G is valid is closer to the actual world than all F-worlds in which G is not valid, or if (II) there are no possible F-worlds. "
Hotter Means of contemplation of all possible worlds Philosophy stands for the means of contemplation of all possible worlds and outside of all: like a muse, it must constantly renounce itself in order to be philosophy. Socrates' only sentence “I know that I know nothing” would turn philosophy into a “science”, since it would be specialized in the specialist world of ignorance. "Philosophy remains indestructible in possible ignorance, but all other scientific subjects are ephemeral in their fixed knowledge. Philosophy is like the wind of possibilities in the desert of knowledge dust. The dust is blown back and forth for arguments, pros and cons and refutations of old theories ...
Bricker Allegation against Lewis' recombination principle "With the principle of recombination ..." one dismantles "... things in a" mysterious "way" [...] and put them back together again. According to Bricker, “a flying pig is not just a“ reduced ”pig with wings attached, but one that also has the corresponding DNA structures according to which the pig, it seems, can be divided and analyzed could."
Jeffrey linguistic substituteism (including Jeffrey) All substitute worlds can be described linguistically, de dicto .

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

"If the conversation about possible worlds seems too metaphysical, we can turn our attention to novels themselves and speak of a complete and coherent novel as a possible world ."

Comparison with the many-worlds interpretation of quantum mechanics

Some interpretations of modern quantum mechanics postulate a real existence of many worlds . At least every unambiguous measurement result of a quantum mechanical process is therefore realized in one world. In addition, the interim system states can also be understood as being implemented in different worlds. If one assumes an open future, according to this interpretation, an infinite number of parallel worlds already exist in the first case. The attractiveness of these interpretations is that they give a realistic interpretation of two characteristics of quantum mechanics: firstly, the results that can only be predicted by theory with probability assessments, secondly, the superposition of system states during the course of time between measurement processes. However, this is not the only realistic interpretation of quantum mechanics, various counter-arguments are put forward against it and there are also various non-realistic interpretations (which neither assume their own ontologically real-life truth-makers for the unrealized measurement results nor for theoretical statements about superimposed states).

The ontological obligations of this interpretation of quantum mechanics are immense, but far less than those of realism with regard to possible worlds. Because the set of world states permitted by quantum mechanics is only a subset of the logically possible combinations of facts. Anyone who votes for a many-worlds interpretation of quantum mechanics is not already committed to a realism with regard to logically possible worlds. Conversely, the realist can accept the most diverse interpretations of quantum mechanics with regard to logically possible worlds. He just doesn't have to have any additional ontological reservations about improperly enriching his ontology if he accepts a many-worlds interpretation.

See also

further reading

Web links

Individual evidence

  1. Possible worlds are stipulated, not discovered by powerful telescopes. , Saul A. Kripke: Naming and Necessity . P. 267.
  2. ^ David K. Lewis: On the Plurality of Worlds. Wiley-Blackwell, 1986, ISBN 0-631-22426-2 .
  3. Anthony Rvvio Rodensis, Commentarii in libros Aristotelis Stagiritæ de caelo, et Mundo: una cum dubijs, et quaestionibus in Schola Agitari solitis. Matriti: ex Typographia Andrea Grande, 1615, 62.
  4. Rubio (Rvvio Rodensis), 1615, 66th
  5. J. Padilla Gálvez, The Best of all Possible Worlds, Cuadernos Salmantinos de Filosofía Vol. 45, 2018, 231-259.
  6. ^ Gottfried Wilhelm Leibniz : Essais de Théodicée sur la Bonté de Dieu, la Liberté de l'Homme et l'Origine du Mal , Amsterdam 1710. / Dt. Transl .: The theodicy of God's goodness, human freedom and the origin of evil , in: Philosophische Schriften, Bd. 2, Suhrkamp Vlg., Frankfurt a. M. 1996
  7. Kripke, Saul . Naming and Necessity , Harvard University Press, Cambridge, 1980.
  8. Lewis, David . (1973). Counterfactuals . Blackwell Publishers. ISBN 0-631-22425-4
  9. Lewis, David . On the Plurality of Worlds , Blackwell Publishing, Malden, 1986. (70 […] 208)
  10. Lewis, David , “Causation,” in: David Lewis, Philosophical Papers, vol. 2, New York, Oxford University Press, 1986
  11. ^ Hotler, Reinhart. David Lewis' Possible Worlds , Tectum, Marburg, 2010. (168)
  12. ^ Hotler, Reinhart. David Lewis' Possible Worlds , Tectum, Marburg, 2010. (91)
  13. Jeffrey, Richard, The Logic of Decision , University of Chicago Press, McGraw-Hill, 1965, Aug. 12