The Different Approaches to Understanding Possible Worlds

2023-2 Modal Logic (Segment 3)

 

Q) Describe in some detail the different approaches to understanding possible worlds—e.g., out in Lycan’s discussion in “The Trouble with Possible Worlds”. What is the problem of how we know we are actual”? What are some main difficulties of and attempt at a combinatorial approach to possible worlds? What sense of “possible” seems more amenable to a combinatorial approach? How might a distinction between “logical” and “causal” (or even metaphysical) possibility help in answering some of the difficulties? There are differences in cases of the metaphysics: logical modality, causal modality, temporal modality, and intentionality. Is Lewis a Meinongian? What is it to be a Meinongian? Is the Russellian “robust sense of reality” just a prejudice in favor of the actual?

#1) It is highly controversial whether we can accept the notion of “possible but nonexistent beings or possible but nonactual worlds” (Lycan 1994: 3). The most classical example of this debate is how we can construe a sentence like “there is no rounded square.” What is the ontological status, if any, of such an object? As is widely known, Meinong holds that there are both non-existent possibles and impossibles (Lycan 1994: 4). According to this view, rounded squares belong to the totality of the objects of knowledge notwithstanding their nonexistence. Russell entirely despises such an idea. For him, Meinong’s supposed ‘objects’ “are apt to infringe the law of contradiction,” as a rounded square is both round and not round (Russell 1905: 483). In fact, the concept of ‘things that do not exist’ seems per se contradictory, since it amounts to saying ‘(∃x)~(∃y)(y=x)’ (Lycan 1994: 11).

To reply to this objection, one might argue that “the law of contradiction holds for existent objects only” (Maria 2022). But this appears to be merely an ad hoc argument; it requires us to discard the universal validity of a logical principle for the sake of theory maintenance. In the same vein, Russell believes that every theory without a robust sense of reality will deteriorate into meaningless exercises. He said:

The sense of reality is vital in logic, and whoever juggles with it by pretending that Hamlet has another kind of reality is doing a disservice to thought. A robust sense of reality is very necessary in framing a correct analysis of propositions about unicorns, golden mountains, round squares, and other such pseudo-objects. (Russell 1993: 170; my emphasis)

However, a Russellian objection is not conclusive. First and foremost, Meinong clearly distinguishes Sosein (so-being) from Sein (being). Rejecting the notion that ‘there is’ means the same as ‘exist,’ he argues that the latter expression is only involved in Sein (Maria 2022). Therefore, the assurance of an existing (in a Meinongian sense) rounded square lies in the Sosein of the object of the intentional act of thinking, not in its actual existence (Landini 2011: 205). Following this distinction, Lycan proposes a way to avoid the above contradiction as follows:

(∃x)ₘ~(∃y:Actual(y))(y = x) (Lycan 1994: 12)

Arguably, there is no contradiction here. The distinction between (∃x)ₘ and (∃x)ₐ appears to rehabilitate a Meinongian account. Building on this idea, contemporary Meinongians “use the quantifier ‘there is’ to range over all the objects in their ontology and use the existence predicate to pick out some portion of that domain” (Linsky and Zalta 1991: 440). Does this account also satisfy the Russellian robust sense of reality? As Linsky and Zalta point out, what satisfies Russell’s robust sense of reality in a Meinongian account is only confined to the predicate ‘exists’, which refers to the present, material, spatiotemporal objects (Linsky and Zalta 1991: 440). In other words, Russell would not allow to interpret an existence quantifier in two ways, as Meinongians do.

Thus, the Russell-Meinong debate has now shifted to the question of whether we have the right to use a Meinongian quantifier, (∃x)ₘ. And the crux of the matter lies in the fact that we must make a choice between the two. It is challenging to imagine how we can reconcile a Meinongian quantifier with a robust sense of reality; for Russell adheres to the doctrine that “there is only one world, the ‘real’ world.” (Russell 1993: 169). On the other hand, renouncing (∃x)ₘ makes a Meinongian account collapse into realism altogether.

In this regard, Lycan concludes that an incompatibility between two perspectives stems from a difference in their willingness to accept certain concepts as primitives (Lycan 1979: 285). Considering itself a better alternative, the Meinongian would argue that the Russellian robust sense of reality is merely a prejudice in favor of the actual.

But I think Russell’s criticism should not be considered a matter of taste for the following reasons. First, it seems that Russellian realism is in a better position since it does not require changing our well-established notion of an existence quantifier. On the contrary, Meinongians are burdened with providing a semantical explanation to understand their novel primitives (Lycan 1994: 13). Lycan specify this requirement as follows:

In particular, what I am implicitly demanding is a model-theoretic semantics, done entirely in terms of actual objects and their properties-for what else is there really? I am allowing the Meinongian the funny operator “(∃x)ₘ” only on the condition that it be explained to me in non-Meinongian terms. (Lycan 1994: 13)

Second, Meinongians are also burdened with explaining the predicate ‘Actual,’ even if they introduce ‘(∃x)ₘ’ as a primitive (Lycan 1994: 14). Third, it is questionable how we can properly evaluate the explanatory power of the Meinongian account. For instance, Quine famously argued that Occam’s Razor will count for noting in the framework of the Meinongian account (Lycan 1994: 7). In essence, the explanatory power of every theory has a criterion vis-à-vis reality. So, even if it doesn’t need to be robust, some sense of reality seems necessary to assure the viability of the theory.

As Modal Logic and its semantics are developed, many philosophers have constructed theories to address this problem. Lycan identifies two main approaches: Actualism and Concretism. Whereas Actualism is a ‘one-world’ construal of logical space, Concretism claims that every possible world is physical, in a sense that they are not abstract nor subsidiary (Lycan 1994: 15-16).

(a) Actualism can be further categorized into three approaches: (a-1) The Paraphrastic approach, which aims to eliminate apparent reference to and ‘quantification over’ nonexistent possibles by contextual definition; (a-2) The Quantifier-Reinterpreting approach, which seeks to provide a nonstandard semantics for the Meinongian quantifier without presupposing nonactual entities; (a-3) The Ersatz approach, which attempts to find some actual entities that are isomorphic to an adequate system of possible objects and worlds. These identified actual entities serve as proxies (Ersatz) (Lycan 1994: 14-15).

(b) Concretism can also be further categorized into two approaches: (b-1) The Relentlessly Meinongian approach, which embraces the Meinongian’s two primitives; (b-2) David Lewis’ (1986) view, which also accepts nonactual entities, but rejects the Meinongian quantifier (Lycan 1994: 14-15). For the present purpose, I will discuss (a-3) and (b-2) respectively, in turn.

(a-3) Numerous candidates are available to be considered as Ersatz. Lycan proposes that there are at least six sorts of system come to mind: Linguistic entities, Propositions, Properties, Combinatorial constructs, Mental items, and Ways things might have been (Lycan 1994: 45-46). Among these, combinatorialism considers worlds “to be set-theoretic combinatorial rearrangements of the posited basic atoms of which our own world is composed” (Lycan 1994: 46). Wittgenstein encapsulates the basic idea of combinatorialism as follows:

Talking of the fact as a “complex of objects” springs from this confusion (cf. Tractatus Logico-philosophicus). Supposing we asked: “How can one imagine what does not exist?” The answer seems to be: “If we do, we imagine non-existent combinations of existing elements.” A centaur doesn't exist, but a man’s head and torso and arms and a horse’s legs do exist. “But can't we imagine an object utterly different from any one which exists?”—We should be inclined to answer: “No; the elements, individuals, must exist. If redness, roundness and sweetness did not exist, we could not imagine them.” (Wittgenstein 1969: 31)

One of the serious challenges of a combinatorial approach is associated with the concept of basic atoms. Lycan points out that “there might exist atoms that do not already exist in this world” (Lycan 1994: 49). However, if we entertain this possibility, then those atoms can never be regarded as combinatorial rearrangements. Consequently, combinatorialists should renounce either the claim that everything that does not exist is combinations of existing elements or the claim that it is possible to add fundamental atoms.

Moreover, Lycan argues that “nonatomistic worlds are also possible, such as one which consists of an undifferentiated miasma of Pure Spirit” (Lycan 1994: 50). Again, it is hard to imagine how we can consider such a world as the result of combinatorial rearrangements. Finally, the combinatorial approach is not compatible with the modal system S5. It is well-known that S5-frame is both transitive and symmetrical. Now, suppose that there are two worlds, say, A and B with an assumption that B has fewer atoms than A. For the atoms which is only contained in A is nonactual relative to B, the accessible relation between A and B is asymmetric (Lycan 1994: 50). Namely, B cannot see A while A can see B. Therefore, S5 does not hold in combinatorialism.

One viable option is to appeal to the notion of metaphysical possibility. Specifically, combinatorialists might argue that all their accounts of combination cannot be universally generalized to apply to all modalities. In this view, fundamental atoms are considered as constituents of metaphysically possible worlds. Consequently, we can assert that nonatomistic worlds are metaphysically impossible, notwithstanding that they are (logically) conceivable. Likewise, we can posit the constraint like an inclusion requirement as a metaphysical necessity.

(b-2) D. Lewis’ view is often called extreme modal realism, as he maintains that nonactual possibles and worlds exactly like our world (Lycan 1979: 287). This leads to the question of whether Lewis can be classified as a Meinongian.

Certainly, the criteria for determining who is a Meinongian are arbitrary. As mentioned earlier, Lewis cannot be labeled as a Meinongian if we consider his rejection of the Meinongian quantifier. However, Linsky and Zalta argue that Lewis’ metaphysics exhibits four Meinongian characteristics. First, his view is not compatible with a robust sense of reality (Linsky and Zalta 1991: 449). His position is at the opposite pole of the claim that “there is only one world, the ‘real’ world.” Second, like other Meinongians, he uses restricted quantification in response to the Russellian objections (Linsky and Zalta 1991: 449). Third, he also distinguishes the being from existence, as Meinong did (Linsky and Zalta 1991: 449). Finally, both Lewis and some Meinongians (such as Parsons) rejects existence-entailing (or, actuality-entailing) properties. Namely, being a person doesn’t entail the existence of a person (Linsky and Zalta 1991: 449-450).

 

References

Landini G. (2011) Russell, London and New York: Routledge.

Linsky B. & Zalta E. N (1991) “Is Lewis a Meinongian?,” Australasian Journal of Philosophy, 69 (4), pp. 438-453

Lycan, W. G. (1979) “The Trouble with Possible Worlds,” in: Michael J. Loux (ed.), The Possible and the Actual. Ithaca, NY : Cornell University Press, pp. 274-316.

Lycan, W. G. (1994) Modality and Meaning, Dordrecht: Springer.

Maria, R. (2022) “Nonexistent Objects,” The Stanford Encyclopedia of Philosophy (Winter 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/win2022/entries/nonexistent-objects/>.

Russell, B. (1905) “On Denoting,” Mind, 14, pp. 479-493.

Russell, B. (1993) Introduction to Mathematical Philosophy, New York: Dover Publications.

Wittgenstein L. (1969) The Blue and Brown Books, 2nd Ed. Oxford: Blackwell.