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## Aproximate World Population

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# Fictionalism

Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the world should not be construed as such, but should instead be understood as cases of "make believe", of pretending to treat something as literally true (a "useful fiction"). Two important strands of fictionalism are modal fictionalism developed by Gideon Rosen, which states that possible worlds, regardless of whether they exist or not, may be a part of a useful discourse, and mathematical fictionalism advocated by Hartry Field, which states that talk of numbers and other mathematical objects is nothing more than a convenience for doing science. Also in meta-ethics, there is an equivalent position called moral fictionalism (championed by Richard Joyce). Many modern versions of fictionalism are influenced by the work of Kendall Walton in aesthetics.
Fictionalism consists in at least the following three theses:
1. Claims made within the domain of discourse are taken to be truth-apt; that is, true or false
2. The domain of discourse is to be interpreted at face value—not reduced to meaning something else
3. The aim of discourse in any given domain is not truth, but some other virtue(s) (e.g., simplicity, explanatory scope).

# Modal fictionalism

Modal fictionalism is a term used in philosophy, and more specifically in the metaphysics of modality, to describe the position that holds that modality can be analysed in terms of a fiction about possible worlds. The theory comes in two versions: Strong and Timid. Both positions were first exposed by Gideon Rosen starting from 1990.[1]

## Strong fictionalism about possible worlds

According to strong fictionalism about possible worlds (another name for strong modal fictionalism), the following bi-conditionals are necessary and specify the truth-conditions for certain cases of modal claims:
1. It is possible that P iff the translation of P into the language of a fiction F (containing possible worlds) holds according to F.
2. It is necessary that P iff the translation of P into the language of a fiction F (containing possible worlds) always holds.
Recent supporters of this view added further specifications of these bi-conditionals to counter certain objections. In the case of claims of possibility, the revised bi-conditional is thus spelled out: (1.1) it is possible that P iff At this universe, presently, the translation of P into the language of a fiction F holds according to F.[2]

## Timid fictionalism about possible worlds

According to a timid version of fictionalism about possible worlds, our possible worlds can be properly understood as involving reference to a fiction, but the aforementioned bi-conditionals should not be taken as an analysis of certain cases of modality.

## Objections and criticisms

This objection can be spelled out in at least two ways: artificiality as contingency or artificiality as lack of accessibility.[4]
• Hale dilemma[5]
• Incompleteness
• Fictional fetishism

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# Impossible world

In philosophical logic, the concept of an impossible world (sometimes non-normal world) is used to model certain phenomena that cannot be adequately handled using ordinary possible worlds. An impossible world, w, is the same sort of thing as a possible world (whatever that may be), except that it is in some sense "impossible." Depending on the context, this may mean that some contradictions are true at w, that the normal laws of logic or of metaphysics fail to hold at w, or both.

## Applications

### Non-normal modal logics

Non-normal worlds were introduced by Saul Kripke in 1965 as a purely technical device to provide semantics for modal logics weaker than the system K— in particular, modal logics that reject the rule of necessitation:
${\displaystyle \vdash A\Rightarrow \ \vdash \Box A}$.
Such logics are typically referred to as "non-normal." Under the standard interpretation of modal vocabulary in Kripke semantics, we have ${\displaystyle \vdash A}$ if and only if in each model, ${\displaystyle A}$ holds in all worlds. To construct a model in which ${\displaystyle A}$ holds in all worlds but ${\displaystyle \Box A}$ does not, we need either to interpret ${\displaystyle \Box }$ in a non-standard manner (that is, we do not just consider the truth of ${\displaystyle A}$ in every accessible world), or we reinterpret the condition for being valid. This latter choice is what Kripke does. We single out a class of worlds as normal, and we take validity to be truth in every normal world in a model. in this way we may construct a model in which ${\displaystyle A}$ is true in every normal world, but in which ${\displaystyle \Box A}$ is not. We need only ensure that this world (at which ${\displaystyle \Box A}$ fails) have an accessible world which is not normal. Here, ${\displaystyle A}$ can fail, and hence, at our original world, ${\displaystyle \Box A}$ fails to be necessary, despite being a truth of the logic.
These non-normal worlds are impossible in the sense that they are not constrained by what is true according to the logic. From the fact that ${\displaystyle \vdash A}$, it does not follow that ${\displaystyle A}$ holds in a non-normal world.
For more discussion of the interpretation of the language of modal logic in models with worlds, see the entries on modal logic and on Kripke semantics.

Curry's Paradox is a serious problem for logicians who are interested in developing formal languages that are "semantically closed" (i.e. that can express their own semantics). The paradox relies on the seemingly obvious principle of contraction:
${\displaystyle (A\rightarrow (A\rightarrow B))\rightarrow (A\rightarrow B)}$.
There are ways of utilizing non-normal worlds in a semantical system that invalidate contraction. Moreover, these methods can be given a reasonable philosophical justification by construing non-normal worlds as worlds at which "the laws of logic fail."

### Counternecessary statements

A counternecessary statement is a counterfactual conditional whose antecedent is not merely false, but necessarily so (or whose consequent is necessarily true).
For the sake of argument, assume that either (or both) of the following are the case:
1. Intuitionism is false.
2. The law of excluded middle is true.
Presumably each of these statements is such that if it is true (false), then it is necessarily true (false).
Thus one (or both) of the following is being assumed:
1′. Intuitionism is false at every possible world.
2′. The law of excluded middle is true at every possible world.
Now consider the following:
3. If intuitionism is true, then the law of excluded middle holds.
This is intuitively false, as one of the fundamental tenets of intuitionism is precisely that the LEM does not hold. Suppose this statement is cashed out as:
3′. Every possible world at which intuitionism is true is a possible world at which the law of excluded middle holds true.
This holds vacuously, given either (1′) or (2′).
Now suppose impossible worlds are considered in addition to possible ones. It is compatible with (1′) that there are impossible worlds at which intuitionism is true, and with (2′) that there are impossible worlds at which the LEM is false. This yields the interpretation:
3*. Every (possible or impossible) world at which intuitionism is true is a (possible or impossible) world at which the law of excluded middle holds.
This does not seem to be the case, for intuitively there are impossible worlds at which intuitionism is true and the law of excluded middle does not hold.

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# Possible world

In philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse but has been disputed.

## Possibility, necessity, and contingency

Those theorists who use the concept of possible worlds consider the actual world in which we live to be one of the many possible worlds. For each distinct way the world could have been, there is said to be a distinct possible world. Among such theorists there is disagreement about the nature of possible worlds; their precise ontological status is disputed, and especially the difference, if any, in ontological status between the actual world and all the other possible worlds. One position on these matters is set forth in David Lewis's modal realism (see below). There is a close relation between propositions and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status of a proposition is understood in terms of the worlds in which it is true and worlds in which it is false. The following are among the assertions we may now usefully make:
• True propositions are those that are true in the actual world (for example: "Richard Nixon became president in 1969").
• False propositions are those that are false in the actual world (for example: "Ronald Reagan became president in 1969"). (Reagan did not run for president until 1976, and thus couldn't possibly have been elected.)
• Possible propositions are those that are true in at least one possible world (for example: "Hubert Humphrey became president in 1969"). (Humphrey did run for president in 1968, and thus could have been elected.) This includes propositions which are necessarily true, in the sense below.
• Impossible propositions (or necessarily false propositions) are those that are true in no possible world (for example: "Melissa and Toby are taller than each other at the same time").
• 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").[1]
• Contingent propositions are those that are true in some possible worlds and false in others (for example: "Richard Nixon became president in 1969" is contingently true and "Hubert Humphrey became president in 1969" is contingently false).
The idea of possible worlds is most commonly attributed to Gottfried Leibniz, who spoke of possible worlds as ideas in the mind of God and used the notion to argue that our actually created world must be "the best of all possible worlds". Arthur Schopenhauer argued that on the contrary our world must be the worst of all possible worlds, because if it were only a little worse it could not continue to exist.[2]
Scholars have found implicit earlier traces of the idea of possible worlds in the works of René Descartes,[3] a major influence on Leibniz, Al-Ghazali (The Incoherence of the Philosophers), Averroes (The Incoherence of the Incoherence),[4] Fakhr al-Din al-Razi (Matalib al-'Aliya)[5] and John Duns Scotus.[4]The modern philosophical use of the notion was pioneered by David Lewis and Saul Kripke.

## Formal semantics of modal logics

A semantics for modal logic was first introduced in the late-1950s work of Saul Kripke and his colleagues. A statement in modal logic that is possible is said to be true in at least one possible world; a statement that is necessary is said to be true in all possible worlds.

## From modal logic to philosophical tool

From this groundwork, the theory of possible worlds became a central part of many philosophical developments, from the 1960s onwards – including, most famously, the analysis of counterfactual conditionals in terms of "nearby possible worlds" developed by David Lewis and Robert Stalnaker. On this analysis, when we discuss what would happen if some set of conditions were the case, the truth of our claims is determined by what is true at the nearest possible world (or the set of nearest possible worlds) where the conditions obtain. (A possible world W1 is said to be near to another possible world W2 in respect of R to the degree that the same things happen in W1 and W2 in respect of R; the more different something happens in two possible worlds in a certain respect, the "further" they are from one another in that respect.) Consider this conditional sentence: "If George W. Bush hadn't become president of the U.S. in 2001, Al Gore would have." The sentence would be taken to express a claim that could be reformulated as follows: "In all nearest worlds to our actual world (nearest in relevant respects) where George W. Bush didn't become president of the U.S. in 2001, Al Gore became president of the U.S. then instead." And on this interpretation of the sentence, if there is or are some nearest worlds to the actual world (nearest in relevant respects) where George W. Bush didn't become president but Al Gore didn't either, then the claim expressed by this counterfactual would be false.
Today, possible worlds play a central role in many debates in philosophy, including especially debates over the Zombie Argument, and physicalism and supervenience in the philosophy of mind. Many debates in the philosophy of religion have been reawakened by the use of possible worlds. Intense debate has also emerged over the ontological status of possible worlds, provoked especially by David Lewis's defense of modal realism, the doctrine that talk about "possible worlds" is best explained in terms of innumerable, really existing worlds beyond the one we live in. The fundamental question here is: given that modal logic works, and that some possible-worlds semantics for modal logic is correct, what has to be true of the world, and just what are these possible worlds that we range over in our interpretation of modal statements? Lewis argued that what we range over are real, concrete worlds that exist just as unequivocally as our actual world exists, but that are distinguished from the actual world simply by standing in no spatial, temporal, or causal relations with the actual world. (On Lewis's account, the only "special" property that the actual world has is a relational one: that we are in it. This doctrine is called "the indexicality of actuality": "actual" is a merely indexical term, like "now" and "here".) Others, such as Robert Adams and William Lycan, reject Lewis's picture as metaphysically extravagant, and suggest in its place an interpretation of possible worlds as consistent, maximally complete sets of descriptions of or propositions about the world, so that a "possible world" is conceived of as a complete description of a way the world could be – rather than a world that is that way. (Lewis describes their position, and similar positions such as those advocated by Alvin Plantinga and Peter Forrest, as "ersatz modal realism", arguing that such theories try to get the benefits of possible worlds semantics for modal logic "on the cheap", but that they ultimately fail to provide an adequate explanation.) Saul Kripke, in Naming and Necessity, took explicit issue with Lewis's use of possible worlds semantics, and defended a stipulative account of possible worlds as purely formal (logical) entities rather than either really existent worlds or as some set of propositions or descriptions.

## Possible-world theory in literary studies

Possible worlds theory in literary studies uses concepts from possible-world logic and applies them to worlds that are created by fictional texts, fictional universe. In particular, possible-world theory provides a useful vocabulary and conceptual framework with which to describe such worlds. However, a literary world is a specific type of possible world, quite distinct from the possible worlds in logic. This is because a literary text houses its own system of modality, consisting of actual worlds (actual events) and possible worlds (possible events). In fiction, the principle of simultaneity, it extends to cover the dimensional aspect, when it is contemplated that two or more physical objects, realities, perceptions and objects non-physical, can coexist in the same space-time.[vague] Thus, a literary universe is granted autonomy in much the same way as the actual universe.
Literary critics, such as Marie-Laure RyanLubomír Doležel, and Thomas Pavel, have used possible-worlds theory to address notions of literary truth, the nature of fictionality, and the relationship between fictional worlds and reality. Taxonomies of fictional possibilities have also been proposed where the likelihood of a fictional world is assessed. Possible-world theory is also used within narratology to divide a specific text into its constituent worlds, possible and actual. In this approach, the modal structure of the fictional text is analysed in relation to its narrative and thematic concerns. Rein Raud has extended this approach onto "cultural" worlds, comparing possible worlds to the particular constructions of reality of different cultures.[6] However, the metaphor of the "cultural possible worlds" relates to the framework of cultural relativism and, depending on the ontological status ascribed to possible worlds, warrants different, often controversial claims ranging from ethnocentrism to cultural imperialism.