Summary
This webpage chapter, 'Metaphysics', by Francesco Berto and Mark Jago, explores the philosophical underpinnings of possible and impossible worlds. It delves into fundamental questions regarding the nature of these worlds: their realism, existence, genuineness, and whether possible and impossible worlds should be treated similarly. Various metaphysical approaches, including genuine realism (Lewisian, Yagisawaian, McDanielian), ersatz realism, hybrid views, abstract object theory (Zalta), primitivism, and fictionalism, are critically examined for their strengths and weaknesses, particularly in accommodating impossible worlds.
Key Insights
The metaphysics of worlds hinges on four core questions: realism, existence, genuineness, and parity between possible and impossible worlds.
The chapter frames the discussion around four central questions: (REALISM) Should we be realist or anti-realist about non-actual worlds? This asks if we should quantify over them in serious metaphysical discourse. (EXISTENCE) Do non-actual worlds exist, or are they non-existent entities? This follows from realism, questioning their ontological status. (GENUINENESS) Are non-actual worlds genuine worlds or ersatz entities? This probes whether they are metaphysically on par with our own world. (PARITY) Should we give the same answer to these questions for both possible and impossible worlds? This question is specific to theorists of impossible worlds, exploring if they require unique metaphysical treatment. Realism and existence may overlap depending on the view of existence, with Quinean views linking quantification to existence, while others separate them.
Genuine realism posits that worlds are real entities like our own, representing possibilities by having them as parts, but faces challenges with impossible worlds due to the 'exportation' principle.
Genuine realism asserts that non-actual worlds exist and are very much like our own, often described as 'concrete' entities. They represent possibilities by having them as parts; for example, a world representing a talking wombat has a real talking wombat as a part. However, this 'genuine' aspect creates problems for impossible worlds. If a world represents an impossibility, like a round square, by having a round square as a part, then that round square must exist in reality, leading to a contradiction. This is known as the 'exportation' principle, where what is represented at a genuine world is claimed to exist simpliciter. This principle makes genuine impossible worlds problematic, as it implies the existence of contradictions. Lewisian realism, Yagisawaian realism (using 'modal stages'), and McDanielian realism (with 'modal realism with overlap') are discussed as variations of genuine realism, each facing or attempting to resolve the exportation problem for impossible worlds.
Ersatz approaches view worlds as representations (like stories or abstract objects) that represent possibilities and impossibilities without necessarily realizing them, avoiding the exportation problem and aligning with actualism.
Ersatz worlds, in contrast to genuine worlds, represent things without having them as actual parts. They are analogous to stories that describe events without those events necessarily occurring. This approach avoids the problematic 'exportation' principle, meaning that an ersatz impossible world can consistently represent contradictions (e.g., 'that A and not-A') without implying the actual existence of such contradictions. Ersatzists typically view worlds as abstract entities like maximal properties, sets of sentences, or propositions. This perspective is compatible with actualism, the view that only what actually exists does exist. The challenge for ersatzism lies in precisely explaining how these ersatz worlds represent. Various models like 'state of affairs', 'property', 'combinatorial', 'map', 'propositional', 'linguistic', and 'primitive' representations are considered, with a full discussion deferred to a later chapter.
Sections
2.1 Ways of Thinking about Worlds
The metaphysics of worlds is explored through four core questions about their nature and treatment.
The chapter introduces four central questions to guide the discussion on the metaphysics of possible and impossible worlds: (REALISM) Should we be realist or anti-realist about non-actual worlds? This concerns whether we should quantify over them in serious metaphysical discourse. (EXISTENCE) Do non-actual worlds exist, or are they non-existent entities? This question follows from realism, asking about their ontological status. (GENUINENESS) Are non-actual worlds genuine worlds or ersatz entities? This investigates their metaphysical standing compared to our own world. (PARITY) Should we give the same answer to these questions for both possible and impossible worlds? This question is specific to theorists of impossible worlds, examining if they require distinct metaphysical treatment.
Realism and existence can be distinct, especially if existence is not solely defined by quantification.
The first two questions, REALISM and EXISTENCE, are related but can differ. REALISM asks if we should commit to non-actual worlds in our most serious metaphysical talk, specifically if we should quantify over them. If the answer is yes, EXISTENCE asks whether these worlds exist or are non-existent entities. While Quine and many others equate quantification with commitment to existence, some argue that existence is a real property that things either have or lack, which allows for realism without automatic commitment to the existence of the quantified entities. The chapter uses 'anti-realism' in the sense of renouncing ontological commitment through quantification.
Genuine worlds represent by having their represented features as parts, unlike ersatz worlds which represent in other ways.
GENUINENESS asks if worlds should be understood as metaphysically equivalent to our own world or if they have a different status. This is distinguished from 'ersatz' worlds, which are non-genuine. The key distinction is in *how* worlds represent: genuine worlds represent possibilities and impossibilities directly by having them as parts (e.g., a genuine world representing a talking wombat has a real talking wombat as a part). Ersatz worlds represent in some other way, not by instantiation as parts. PARITY is a more straightforward question about whether impossible worlds should be treated the same way as possible worlds regarding realism, existence, and genuineness, or if they need special metaphysical consideration.
Not all combinations of answers to these questions are considered or feasible.
The chapter notes that not all 16 possible combinations of answers to the four questions (REALISM, EXISTENCE, GENUINENESS, PARITY) will be explored, as some are not logically coherent or have not been discussed in philosophical literature. The focus will be on the combinations that have received the most attention.
2.2 Genuine Realism
Genuine realism treats worlds as concrete entities, representing possibilities by having them as parts.
Genuine realism posits that non-actual worlds exist and are similar to our own, often described as 'concrete' entities. For example, a possible world where a wombat talks would contain a real, flesh-and-blood talking wombat as a part. This is the 'genuine' aspect: representation occurs by having the feature as a physical part.
The 'genuine' nature of worlds refers to their representational method, not necessarily their concreteness.
While initially conceived as 'concrete', the notion of 'genuine' for worlds, especially when considering impossible worlds, shifts to how they represent. A genuine world represents that an _F_ exists by having an actual _F_ as a constituent part. This applies to both possible and impossible worlds. For instance, a genuine world representing the impossibility that 3,456 is the largest natural number would have 3,456 as a part (though it's an abstract entity). Worlds that do not represent in this 'by having as a part' manner are considered 'ersatz' worlds.
Lewisian realism views worlds as maximal spatiotemporal sums of concrete entities, where 'actual' is indexical.
Lewisian realism posits that possible worlds are maximal mereological sums of concrete, spatiotemporally connected entities. Each world is a distinct spacetime whole. The term 'actual' is treated as an indexical, similar to 'here' or 'now', referring to the world of the speaker. This means that from the perspective of any world, its inhabitants are actual, and inhabitants of other worlds are non-actual 'possibilia'. This offers a reductive, non-modal account of possibility by defining it as unrestricted quantification over these worlds.
Extending Lewisian realism to impossible worlds faces the 'exportation' problem, leading to contradictions.
The 'exportation' principle states that if world _w_ represents something as being _F_, then something is _F_ (simpliciter). For Lewisian worlds, this means that if a world contains a talking wombat as a part, then a talking wombat exists in reality. This works for mere possibilities (exporting them might result in a large but consistent ontology). However, for impossible worlds, it leads to contradiction. If a genuine impossible world represents a round square, then a round square must exist in reality, which is a contradiction. Lewis himself, therefore, had no use for genuine impossible worlds.
Yagisawaian realism uses 'modal stages' to represent properties at worlds, attempting to resolve the exportation issue.
Yagisawa proposes an account where entities have properties at a world 'w' by having 'modal stages' at 'w' with those properties. For example, Lenny is portly at world 'w' due to having a portly-w-stage. This is analogous to four-dimensionalist views of time. The challenge remains whether this avoids contradiction when dealing with impossible stages (e.g., a portly-and-not-portly stage). Yagisawa suggests using distinct 'modal tenses' (actuality, mere-possibility, impossibility, and modal space at large) to avoid exporting contradictions simpliciter, though the effectiveness of this distinction, particularly for the 'modal space at large' tense, is debated.
McDanielian realism avoids exportation by treating properties as relative to worlds, but struggles with impossible worlds and identity.
McDanielian realism, or 'modal realism with overlap', suggests that entities have properties relative to specific worlds, rather than intrinsically. For instance, Lenny is 'portly-at-world-w' and 'not-portly-at-world-w1'. These are relational properties that do not conflict. This blocks the direct exportation of contradictory properties. However, extending this to impossible worlds poses problems. For example, if Iggy Pop is a singer but James Newell Osterberg isn't (an impossibility because they are the same person), McDaniel's view implies Iggy Pop and Osterberg are not identical simpliciter because they have different relations to world 'w', which contradicts their identity.
2.3 Non-existent Worlds
Some philosophers, known as Meinongians, argue that entities can have properties without existing.
This section explores realist views that treat worlds as non-existent entities, separating realism (quantifying over worlds) from existence. Meinongianism, named after Alex Meinong, posits that objects can possess properties ('Sosein') even if they lack existence ('Sein'). This allows for realism about worlds without automatically committing to their existence. The chapter argues against the necessity of 'being' being synonymous with quantification, citing linguistic examples from German and French.
Nonexistent worlds, like fictional characters, can be conceived as objects that lack existence but possess properties.
Candidates for non-existent objects include fictional characters (Sherlock Holmes), past or future entities, and merely possible objects. Parsers and Priest propose that worlds can be understood as nonexistent objects, with only the actual world possessing the feature of existence. This allows for a distinction between actuality (identified with existence) and non-actuality. The chapter addresses concerns about the identity conditions and epistemic access to nonexistents, noting similar issues with other realist accounts (abstract or Lewisian worlds). Knowledge of modal facts might be gained through stipulation and imagination, similar to fictional characters.
Genuine nonexistent worlds still face the exportation problem if they represent by having impossible entities as parts.
A significant challenge for Meinongian realism about worlds is how they represent. If a nonexistent world is 'genuine' and represents a round square by having a round square as a part, this still implies that something is both round and square, thus committing to a contradiction via the exportation principle. While Priest, a dialetheist, might accept true contradictions, this is problematic for consistent metaphysics. The notion of parthood for nonexistent entities is also discussed as potentially metaphorical, and the idea of a wholly nonexistent world having an existent part is questioned.
Nonexistent worlds may be better understood as ersatz representations rather than genuine entities.
Given the difficulties with genuine nonexistent worlds and the exportation principle, the chapter suggests that nonexistent worlds might be better conceptualized as ersatz worlds. In this view, they are introduced as representational targets or aids, rather than as entities that perform the representation by having parts. This avoids commitment to contradictory entities but requires developing an account of how these nonexistent worlds function representationally.
2.4 Ersatz Modal Realism
Ersatz worlds represent possibilities/impossibilities without actualizing them, aligning with actualism and avoiding the exportation problem.
Ersatz worlds represent 'such-and-such' without being 'such-and-such' themselves, unlike genuine worlds. They are compared to stories that convey events without those events actually happening. This approach bypasses the 'exportation' problem, allowing impossible worlds to represent inconsistencies without implying their actual existence. Ersatz modal realism is compatible with actualism, the view that only what actually exists is real. In this view, ersatz worlds and their constituents actually exist as part of our reality, much like the words forming a story exist.
Ersatz worlds are typically abstract entities, such as sets of propositions or sentences.
Ersatzists generally consider their worlds to be abstract entities. These can be maximal properties, sets of sentences, or sets of propositions. This abstract nature allows them to include both possible and impossible worlds, for instance, by forming sets of sentences that include both 'A' and 'not-A'. This directly supports a positive answer to the PARITY question, treating possible and impossible worlds similarly from an ontological perspective.
Reducing modal notions to non-modal ones remains challenging for ersatzists.
A key challenge for ersatz modal realism is providing a reduction of modal notions to purely extensional, non-modal concepts. While analyzing possibility as quantification over possible worlds (◇ A iff A is true at some world w) is standard, delimiting this quantification to *possible* ersatz worlds is difficult if worlds are constructed from abstract entities like propositions or properties. Some ersatzists accept that a complete reduction may not be feasible, while others argue that genuine realism also faces similar challenges in achieving a full modal reduction.
Different ersatz models exist, varying in how worlds represent (e.g., via states of affairs, propositions, language).
The core question for ersatzists is *how* these worlds represent. The chapter outlines various ways this can occur: (STATE) using states of affairs, (PROPERTY) using properties reality would have, (COMBINATORIAL) recombining objects and properties, (MAP) using pictorial representations, (PROPOSITIONAL) using propositions, (LINGUISTIC) using language, and (PRIMITIVE) treating representation as a basic, unanalysable feature. Each of these leads to a different version of ersatz modal realism, which will be discussed in detail in the next chapter. 'Primitive ersatzism' is considered a borderline case.
2.5 The Hybrid View
Hybrid modal realism posits that possible worlds are genuine, while impossible worlds are ersatz constructions.
Hybrid modal realism offers a middle ground, giving a negative answer to the PARITY question: possible and impossible worlds are not treated the same. It posits that possible worlds are genuine, existing Lewisian worlds (concrete, with actual inhabitants called 'possibilia'), while impossible worlds are ersatz set-theoretic constructions. These ersatz impossible worlds represent impossibilities without realizing them, thus avoiding the exportation problem. This view aligns with the idea that possibilities exist, but impossibilities do not.
This hybrid approach aims to retain benefits of genuine realism for possibilities and ersatzism for impossibilities.
The hybrid account seeks to combine the strengths of genuine realism (for possible worlds) and ersatzism (for impossible worlds). It claims to answer REALISM and EXISTENCE affirmatively for all worlds (both genuine and ersatz, all existing), but differentiates on GENUINENESS. Possible worlds represent genuinely (by realization), while impossible worlds represent ersatzly (by construction). This allows for a fully extensional ontology of genuine worlds and sets, avoiding primitive modality issues and the exportation problem.
Hybrid realism can distinguish certain impossible propositions but faces challenges with hyperintensional distinctions.
Berto's version of hybrid modal realism differentiates impossible propositions by identifying them with set-theoretic constructions from genuine worlds. For example, 'swans are black and not black' is distinct from 'John is a married bachelor'. However, it struggles with finer-grained distinctions. It cannot distinguish between propositions like 'Hesperus is the second planet from the Sun' and 'Phosphorus is the second planet from the Sun' because, necessarily, Hesperus is Phosphorus, leading to only one way to construct ersatz impossible worlds for this identity. This limits its ability to capture beliefs that distinguish these entities.
The main advantage of hybrid realism is its potential for modal reduction, but it requires accepting Lewisian ontology.
A key advantage highlighted for hybrid modal realism is its potential for a modal reduction to extensional concepts, as it quantifies over Lewisian possible worlds. However, this requires accepting Lewis's controversial ontology of infinitely many concrete universes. The chapter notes that if actualist ersatz accounts can achieve modal reduction or if reduction is deemed less important, hybrid realism loses its primary trump card. The general hybrid approach (using Lewisian possible worlds to construct ersatz impossible worlds) is presented as flexible, with different construction methods leading to varying versions of the view.
2.6 Encoding Worlds
Zalta's abstract object theory proposes worlds encode states of affairs, distinguishing 'encoding' from 'exemplifying'.
Zalta's theory of abstract objects introduces a distinction between 'exemplifying' (or possessing) a property and 'encoding' a property. Encoding is a primitive notion for abstract objects and means being partly defined by or determined by that property. Worlds are defined as maximal situations (abstract objects that encode states of affairs), distinguishing between possible worlds (which could obtain) and impossible worlds. This theory aims to capture some benefits of genuine worlds without their pitfalls.
In Zalta's view, worlds 'encode' possibilities and impossibilities, allowing them to represent contradictory states without contradiction.
According to Zalta, a world 'w' encodes the state of affairs 'that A' if 'w' is determined by it. If 'w' encodes 'being such that A', then in the 'encoding' sense of 'is', 'w' is such that A. This allows worlds to represent possibilities and impossibilities. For example, a world could encode 'being such that there is a talking wombat' without exemplifying it, meaning it doesn't have a talking wombat as a part, thereby avoiding the exportation problem. Crucially, 'is' is claimed to be ambiguous between exemplifying and encoding.
The ambiguity of 'is' and the unconstrained nature of encoding pose challenges to Zalta's theory.
A significant challenge for Zalta's theory is the proposed ambiguity of the verb 'is'. The chapter argues that ordinary inferences like 'Lenny is barking; therefore, something is barking' suggest 'is' does not generally operate with an 'encoding' reading. Furthermore, encoding appears unconstrained; an object can encode properties without a clear reason or relationship to other properties it encodes, raising questions about the theory's explanatory power and whether 'encoding' is a truly viable reading of 'is'.
Zalta's encoding view is seen as a form of primitivism, where representation facts are metaphysically basic.
The chapter suggests that Zalta's approach, where worlds encode properties as a primitive fact, resembles primitivism about worlds. While Zalta's theory is richer due to the encoding notion and the ambiguity of 'is', its core explanatory gap – why a world encodes what it does – is similar to straightforward primitivism. The complexity introduced by Zalta's postulates might not add significant metaphysical insight over a simpler primitivist stance.
2.7 Primitivism about Worlds
Primitivism asserts that the way worlds represent is a basic, unanalysable fact.
Primitivism about worlds holds that there is no informative answer to how or why worlds represent what they do. Facts about representation, such as 'world w represents that A', are considered primitive, foundational facts ('metaphysical bedrock'). This view often aligns with a conception of worlds as having no analysable structure, perhaps viewed as dimensionless points in modal space ('magical ersatzism').
Motivation for primitivism can stem from the difficulty of explaining representation in other accounts.
The chapter suggests that primitivism can arise if other attempts to explain how worlds represent prove unsatisfactory. If all informative proposals (like genuine or ersatz accounts) are found to have irreparable problems, primitivism emerges as the remaining option, accepting that representation is a brute fact. This is compared to Merricks's primitivism about propositions.
Primitivism faces challenges in accounting for complex representations and the relationship between worlds and propositions.
A significant issue for primitivism is explaining how worlds represent complex states of affairs, such as conjunctions. A literal primitivism denies any link between a world representing 'A and B' and its representing 'A' or 'B' individually. This conflicts with modal facts, such as conjunctions entailing their conjuncts. While a reply might be that a world represents 'A and B' because it represents both individually, this must accommodate impossible worlds where conjunctions might obtain without their conjuncts, a challenge that pure primitivism struggles to address informatively.
Formal semantics often uses worlds as primitives pragmatically, but this doesn't equate to metaphysical primitivism.
The chapter notes that in formal semantics, worlds are often treated as primitive points for the purpose of building models (e.g., assigning atomic sentences randomly to worlds). This pragmatic instrumentalism is useful for investigating logical properties but is distinct from metaphysical primitivism. Such semantic practices neither require nor imply that worlds are metaphysically primitive entities; they simply provide a functional approach without needing to resolve all metaphysical questions.
2.8 Fictionalism
Fictionalism about worlds is an anti-realist stance, viewing talk of worlds as only true 'in the fiction'.
Fictionalism offers an anti-realist perspective on worlds, asserting that claims about (and quantification over) non-actual worlds are literally false. Instead, such talk is understood as true only 'within a fiction' that is adopted because it yields useful results, particularly in the analysis of modal notions. This approach aims to gain the benefits of realism without ontological commitment to controversial entities like possible or impossible worlds.
Fictionalism uses a 'fiction' operator to allow useful claims without ontological commitment.
Drawing an analogy with moral fictionalism, where moral claims are true 'in the fiction' but not simpliciter, modal fictionalism suggests that claims about worlds are true only within a designated 'worlds fiction'. This allows proponents to engage with sophisticated theories (like Lewis's) that posit numerous worlds and entities, while maintaining that, literally speaking, only the actual world exists. The 'in the fiction' operator prevents ontological commitment to these posited entities.
Extending fictionalism to impossible worlds is straightforward if possible worlds are fictional, but the 'fiction' itself needs a grounding.
If modal fictionalism holds that possible worlds do not literally exist, its extension to impossible worlds is considered straightforward: it can be true 'in the fiction' that impossible worlds exist, without implying their actual existence. However, a challenge arises in choosing the 'right' modal fiction. Unlike mathematics, where standard mathematics provides a constraint, there isn't a single standard 'worlds-story' for impossible worlds, complicating the choice of a suitable fictional framework. The fictionalist must first resolve the problems genuine realism faces with impossible worlds before basing their fiction on them.
Fictionalism faces challenges in avoiding commitment to worlds and in accounting for semantic notions like propositions.
Fictionalism struggles to consistently avoid ontological commitment. If claims like 'it is necessary that there exist worlds' are true 'in the fiction', and those claims are about necessity, it can lead to the conclusion that worlds exist simpliciter. Furthermore, if worlds are fictional, then constructions out of worlds (like propositions, meanings, or subject matters) are also fictional. This poses a problem for theories of truth and meaning, which often rely on the existence of such entities. Fictionalists must either deny the existence of these semantic concepts or find alternative analyses, which can undermine the motivation for using worlds in the first place.
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