Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, (...) the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927. (shrink)

The purpose of this paper is to discuss two phenomena related to the semantics of definite descriptions: that of incomplete uses of descriptions, and that of the underdetermination of referential uses of descriptions. The Russellian theorist has a way of accounting for incomplete uses of descriptions by appealing to an account of quantifier domain restriction, such as the one proposed in Stanley and Szabó (2000a). But, I argue, the Russellian is not the only one in a position to appeal to (...) such an account of incomplete uses of descriptions. Proponents of other theories, such as the Fregean, which does not treat descriptions as quantifiers, might benefit from this account of domain restriction. In the second part of the paper I discuss referential uses of incomplete definite descriptions. Relative to such uses, Wettstein (1981) and others have argued that the Russellian theory faces a problem of underdetermination of semantic content. Neale (2004) has replied to this objection showing why it does not pose a threat to the Russellian theory. Again, I argue that not only the Russellian, but also the Fregean can subscribe to Neale’s (2004) suggestion. (shrink)

This paper shows that some classes of multimodal paraconsistent logics endowed with weak forms of negation are incompletable with respect to Kripke semantics. The reach of such incompleteness is discussed, and we argue that this shortcoming, more than just a logical predicament, may be relevant for attempts to characterize quantum logics and to handle quantum information and quantum computation.

Incomplete penetrance and variable expressivity are non‐Mendelian phenomena resulting in the lack of correlation between genotype and phenotype. Not withstanding the diversity in mechanisms, differential expression of homologous alleles within cells manifests as variations in penetrance and expressivity of mutations between individuals of the same genotype. These phenomena are seen most often in dominantly inherited diseases, implying that they are sensitive to concentration of the gene product. In this framework and the advances in understanding the role of microRNA (miRNA) in (...) fine‐tuning gene expression at translational level, we propose miRNA‐mediated regulation as a mechanism for incomplete penetrance and variable expressivity. The presence of miRNA binding sites at 3′ UTR, co‐expression of target gene–miRNA pairs for genes showing incomplete penetrance and variable expressivity derived from available data lend support to our hypothesis. Single nucleotide polymorphisms in the miRNA target site facilitate the implied differential targeting of the transcripts from homologous alleles. (shrink)

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

In this paper, an incompleteness theorem for modal extensions of relevant logics is proved. The proof uses elementary methods and builds upon the work of Fuhrmann.

How is constitutionalism possible, when people disagree on so many questions about what is good and what is right? The answer lies in two kinds of incompletely theorized agreement - both reached amidst the sharpest disagreements about the fundamental issues in social life. The first consist of agreements on abstract formulations ; these agreements are crucial to constitution-making as a social practice. The second consist of agreements on particular doctrines and practices; these agreements are crucial to life and law under (...) existing constitutions. Incompletely theorized agreements help illuminate an enduring constitutional puzzle: how members of diverse societies can work together on terms of mutual respect amidst intense disagreements about both the right and the good. Such agreements help make constitutions and constitutional law possible, even within nations whose citizens cannot concur on the most fundamental matters. (shrink)

We give some information about new proofs of the incompleteness theorems, found in 1990s. Some of them do not require the diagonal lemma as a method of construction of an independent statement.

This paper investigates, in a simple risk-sharing framework, the extent to which the incompleteness of contracts could be attributed to the complexity costs associated with the writing and the implementation of contracts. We show that, given any measure of complexity in a very general class, it is possible to find simple contracting problems such that, when complexity costs are explicitly taken into account, the contracting parties optimally choose an incomplete contract which coincides with the ‘default’ division of surplus. Optimal contracts (...) with complexity costs are constrained efficient in our model. We therefore interpret our results as saying that, in the absence of a strategic role for complexity costs, their effect is entirely determined by their size relative to the size of payoffs. (shrink)

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.

This paper is an investigation of the relationship between G\"odel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of Spector's that the relation $\{(A,B) \in \mathbb{R}^2 : \mathcal{O}^A \leq_H B\}$ is well-founded. We provide an alternative proof of this fact that uses G\"odel's second incompleteness theorem instead of the theory of admissible ordinals. We then derive a semantic version of the second incompleteness theorem, originally due to Mummert and Simpson, from this result. Finally, (...) we turn to the calculation of the ranks of reals in this well-founded relation. We prove that, for any $A\in\mathbb{R}$, if the rank of $A$ is $\alpha$, then $\omega_1^A$ is the $(1 + \alpha)^{\text{th}}$ admissible ordinal. It follows, assuming suitable large cardinal hypotheses, that, on a cone, the rank of $X$ is $\omega_1^X$. (shrink)

I discuss two competing theories of the progressive: the theory proposed in Parsons (1980, 1985, 1989, 1990) and the theory proposed in Landman (1992). These theories differ in more than one way. Landman regards the progressive as an intentional operator, while Parsons doesn't. Moreover, Landman and Parsons disagree on what uninflected predicates denote. For Landman, cross the street has in its denotation complete events of crossing the street; the aspectual contribution of English simple past (perfective aspect) is the identity function. (...) For Parsons, both complete and incomplete events of crossing the street can be in the denotation of the base VP; perfective aspect restricts its denotation to the events that culminate. I present a version of ParsonÕs theory that avoids the problems raised by Landman, in particular the problem posed for Parsons by creation verbs. The repaired version and Landman's theory still differ in the way they analyze uninflected verbs. The repaired version and Landman's theory still differ in the way they analyze uninflected predicates. I present evidence from Slavic languages that both theories are needed. Finally, I discuss some evidence that may favor one or the other approach to the semantics of the English progressive. (shrink)

A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of anaphoric readings of Sobel sequences and reverse Sobel sequences, and proposes an (...) explanation of the original asymmetry on its grounds. This provides an answer to the challenge for Lewis’s theory. (shrink)

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be (...) special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. -/- We have introduced the most fundamental conjectures in our earlier works. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before. (shrink)

Let n be a positive integer. By a $\beta_{n}-model$ we mean an $\omega-model$ which is elementary with respect to $\sigma_{n}^{1}$ formulas. We prove the following $\beta_{n}-model$ version of $G\ddot{o}del's$ Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a $\beta_{n}-model$ of S, then there exists a $\beta_{n}-model$ of S + "there is no countable $\beta_{n}-model$ of S". We also prove a $\beta_{n}-model$ version of $L\ddot{o}b's$ Theorem. As a corollary, we obtain (...) a $\beta_{n}-model$ which is not a $\beta_{n+1}-model$. (shrink)

Using video recordings of draft meetings conducted as part of an intramural basketball program as data, this conversation analytic study examines the use of an incomplete utterance in a joint evaluative activity. In particular, we focus on how the participants, volunteer coaches, who meet to draft players for their respective teams, produce a syntactically incomplete utterance as a means to critically assess a player, a non-present third party to the interaction. Analysis reveals that the participants use an incomplete utterance as (...) part of dispreferred design; it allows them to withhold articulating overt criticism of others. By trailing off where the criticism is due, the participants display reluctance to verbalize what is to be said and treat its articulation as delicate. The syntactic structure of the utterance that includes a contrastive conjunction and accompanying embodied actions such as head shakes help them convey a critical stance. We examine the use of incomplete utterances in both agreement and disagreement sequences; the recipients display their unproblematic understanding of the critical assessment and respond by providing their own assessments that either affiliate or disaffiliate with the conveyed critical stance. (shrink)

The implicit content associated with incomplete definite descriptions is contributed in the form of definite descriptions of situations. A definite description of this kind is contributed by a small structure in the syntax, which is interpreted, in general terms, as ‘the situation that bears R to s’.

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (shrink)

We define a property R(A 0 , A 1 ) in the partial order E of computably enumerable sets under inclusion, and prove that R implies that A 0 is noncomputable and incomplete. Moreover, the property is nonvacuous, and the A 0 and A 1 which we build satisfying R form a Friedberg splitting of their union A, with A 1 prompt and A promptly simple. We conclude that A 0 and A 1 lie in distinct orbits under automorphisms of (...) E, yielding a strong answer to a question previously explored by Downey, Stob, and Soare about whether halves of Friedberg splittings must lie in the same orbit. (shrink)

In spite of incomplete knowledge we are permanently forced to act in complex real-life situations. First, a modern concept of information, the non-trivial transition from information to knowledge, patterns of missing knowledge, and the concept of perspective notions are studied. The main sections review some guidelines for action under incomplete information. A modern view of the concepts of holism and wholeness reveals that (in contrast to some critics) general system theory does not require any metaphysical assumption or previously accepted worldview. (...) The concepts of holism and wholeness, as well as general system theory, are well-founded, even under strict criteria. (shrink)

The incompleteness problem for virtue ethics is inherited by a virtue-based theory of argumentation as developed by Daniel Cohen. A complete normative theory of argumentation should be able to provide reasons for why argumentative virtues such as open-mindedness are worthwhile, along with being able to resolve conflicts of such virtues. Adumbrating virtue-based argumentation theory with a pragmatic utilitarian approach constitutes a more complete theory that can account for why argumentative virtues are worthwhile.

Defense of incompletable grounding and discussion of implications for ontological economy.

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many do, some (...) do not. (shrink)

Cappelen and Lepore (2005) maintain that Incompleteness Arguments for context sensitivity are fallacious. In their view, Incompleteness Arguments are non sequitur fallacies whose conclusions are not logically related to premises. They affirm that the conclusions of Incompleteness Arguments are metaphysical claims about the existence of entities that might be constituents of propositions, while their premises concern psychological data about speakers' dispositions to truth evaluate sentences in contexts of utterance. Cappelen and Lepore reject Incompleteness Arguments because psychological data have no bearing (...) on metaphysical issues. I do not dispute Cappelen and Lepore's claim that psychological data have no relevance to metaphysics. Nonetheless, I argue that Cappelen and Lepore's criticism is vitiated by a misunderstanding of the nature of Incompleteness Arguments that makes them overlook the link between semantics and linguistic competence. I try to shed light on the real nature of Incompleteness Arguments by pointing at the failure of Cappelen and Lepore's criticism. My aim is not to defend Semantic Contextualism, but to bring to attention the link between semantics and linguistic competence that should never be overlooked in debates in the field of semantics. (shrink)

In the presence of incomplete risk attitudes, choices between noncomparable risky prospects are random. A random choice model advanced by Karni, 2021) includes the hypothesis that choices among noncomparable risky prospects are prompted by signals drawn from personal distributions. This paper introduces a scheme designed to elicit subjects’ assessments of their personal likelihoods of choices among noncomparable risky prospects and describes experiments designed to test the aforementioned hypothesis.

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

If market transactions are optimal, why do so many transactions occur within firms themselves? Ronald H. Coase explains this phenomenon by arguing that market transaction costs differ from intra-company transaction costs and that clear intra-intra-firm property rights have the effect of reducing transaction costs. But what exactly are the relevant transaction costs, and what factors determine them? Oliver Hart argues that market contracts are incomplete, and that the key to improving efficiency is putting the power to deal with these unspecified (...) circumstances into the hands of owners within the same entity.In this paper, I argued that, the development of the theory and practice of business ethics as well as China’s innovative practice in recent decades provide a new perspective, one that is especially relevant to the issues raised by Case and Hart and that bear directly on the reform of China’s state-owned enterprises. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative (...) Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

The main point of this paper has been to show that the concept of evaluative incompleteness deserves consideration. In addition, I have suggested that it is plausible to accept that certain states of affairs in fact are evaluatively incomplete. But I have not sought to prove that this is so; indeed, I do not know how such proof might be given. Just which states of affairs, if any, are evaluatively incomplete is an extremely vexed question, and it is not one (...) to which I have attempted to supply any systematic answer. My aim has been merely to point out that it is arguable that certain states of affairs are evaluatively incomplete — a fact that ought not to be overlooked due to an unquestioning acceptance of (II) and a fact which, certainly, ought not to be ruled out by fiat due to an adherence to definitions and assumptions which imply that (II) is false. (shrink)

We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.

This article draws on key models of monitoring and blockholding articulated in the incomplete contracts theory of the firm. Under incomplete contracts theory, different governance systems have incentive structures that entail different tradeoffs—tradeoffs between ownership concentration and liquidity, between monitoring and management initiative, and between private rent-seeking and activity benefiting shareholders as a group. The tradeoffs delimit opportunities for productive cross-reference. More specifically, blockholder systems, such as those in Europe, subsidize monitoring by permitting blockholders to reap private benefits of control (...) through self-dealing and insider trading. Market systems, such as those in the United States and Britain, regulate such private rent-seeking toward the end of maintaining an institutional framework that supports diffuse share ownership and liquid trading markets. It follows that a legal framework conducive to blockholding may be ill-equipped to foster dispersed equity ownership and thick trading markets and that a legal framework conducive to liquid trading markets may have properties that discourage blockholding. This gives rise to questions for law reform agendas on both sides of the Atlantic. In the United States, proponents ask for deregulation of controls on institutional investors, looking to encourage blockholding and more effective monitoring. In Europe, proponents ask for stronger securities regulation, looking to encourage deeper trading markets. This article suggests that each reform program may lead to disappointing results because neither assures conforming adjustments to the pertinent actors’ incentives. Alternatively, strict reforms that materially change prevailing incentive patterns could perversely destabilize workable arrangements without assuring the appearance of more effective alternatives. (shrink)

It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

Kripke bundle and C-set semantics are known as semantics which generalize standard Kripke semantics. In [4] and in [1, 2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics . Modal predicate logic Q-S4.1 is not Kripke bundle complete of the present paper). This is shown by using difference of Kripke bundle semantics and C-set semantics. In this paper, (...) by using the same idea we show that incompleteness results in Kripke bundle semantics which are extended versions of [2]. (shrink)

Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at least one (...) of these conditions, thus rendering IPC semantically incomplete for them. Only for Goldfarb’s [1] proof-theoretic semantics, which deviates from standard approaches, IPC turns out to be complete. Overall, these results show that basic ideas of proof-theoretic semantics for propositional logic are not captured by IPC. (shrink)

Hannah Arendt is commonly criticized for defining action as an end in itself, of horizontal power and of councils as an alternative to representative democracy that is unrealistic and unrealizable. In contrast, I show how much Arendt was concerned about the dangers of these concepts: the replacement of action by fabrication, of power by domination and violence, and the impossibility of a council democracy in the face of a highly administrative and depoliticized society. Arendt shows how these hybrid forms revealed (...) their pure forms as a hidden tradition in revolutionary situations. The supposed incompleteness and failure of a struggle for another society can therefore be understood as a recurring possibility and reality and thus as a specific condition of the political. The critique of the hybrid form also includes the critique of modern scientific thought and political thought. (shrink)

When processing of stimuli occurs without attention, phenomenal experience, as well as cognitive access, may be lost. Sensory representations are, however, constructed by neural machinery extending far beyond sensory receptors. In conditions such as cerebral achromatopsia incomplete sensory representations may still elicit phenomenal experience but these representations might be too aberrant to be integrated into the wider cognitive workspace.

This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is (...) semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979). (shrink)

This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, the (...) concern is with metaphysical and epistemological implications of these results: what such results may have to teach us about knowledge, truth, and possibility. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

By demostrating how Kapital is incomplete, The Incomplete Marx provides the basis for a re-interpretation of Marx that looks beyond the Marx of Kapital.

Russell urged that some phrases having no meaning in isolation could nonetheless, Contribute to the meaning of sentences in which they occur. In the case of definite descriptive phrases, A proof is offered. It is argued that russell's proof is valid, Contrary to some commentators. Proper understanding of the notion of "incomplete symbol" plays a key role in the assessment of the argument, As well as in full appreciation of the radical departure of russell's analysis from "surface" grammar.

We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate “heterological” is itself heterological. We show that this sentence doesn't follow from T and is equivalent to the consistency of T. Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.

Slavoj Žižek is known for quoting with the same enthusiasm the main names of Western Philosophy and the classics of pop culture, cinema, literature, and music. Therefore, in such rich theoretical framework, it is possible to glimpse a few connections that the philosopher himself has not yet developed in detail. This essay is precisely about of these connections. More specifically, this essay can be seen as an endeavor to think some of Žižek’s writings on music having as a main reference (...) the concept of ontological incompleteness. The philosopher discusses the concept of ontological incompleteness based on several areas, from sciences to movies and literature. Notwithstanding, in this specific case musical examples are left aside. Even though Žižek does not analyse music from the perspective of such concept of ontology, it is possible to argue that Žižek’s writings on music already leave some clues and examples that justify an analysis of that kind. That is the task proposed in this critical essay: to present how an approximation between his thoughts on music and on ontology is pos. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Thomas G. Pavel INCOMPLETE WORLDS, RITUAL EMOTIONS' IN recent years, the notion of "fictional world" has enjoyed a considerable rise in fortune. The expression, however, is not entirely new. To refer to the world of a literary work, of a novel or of a play, has always been a favorite way of speaking for literary critics and aestheticians. In most cases, these were informal worlds. A discussion of the (...) world of Balzac, Dostoyevsky, HenryJames, or Proust often amounts to a description of each author's preferences in die selection and rearrangement of his material. Such discussion primarily fits authors who purposefully attempt to build comprehensive representational artifacts. One speaks quite naturally about l'univers balzacien, or about the universe of Musil. But is one entitled to refer with equal ease to the world ofBenjamin Constant, meagerly perceptible in his Adolphe, a short novel built in the spirit of economy, displaying just a few characters and a minimum of worldly information? Perhaps density and comprehensiveness are not indispensable characteristics of literary worlds. Aestheticians and narratologists using the "fictional worlds" terminology seem to believe mat any kind of artistic text projects a world, be it rich or poor. Such worlds are imagined in the fashion of modern philosophy of logic as states of affairs, more or less comprehensive. Some writers believe that the states of affairs comprised in fictional worlds must be fairly sizable, since diey should include "not only what the author indicates, but also whatever is required (entailed) by that which he indicates." 1 The laws of nature which are not specifically contradicted by the text would belong to its world. Thus, a few notorious cases aside, there is no reason to doubt that every child born in fiction has been engendered by a human fadier as long as the text does not report an exception. And if it does? Then, assuming that the laws of logic still govern if not fiction itself at least our understanding of it, we may appeal to what "possible world" philosophers have called "small miracles." * Editor's note: This article, as well as the contributions by Gerald Prince, Peter van Inwagen, and Kendall Walton which follow it, grew out ofa symposium on "Styles ofFictionality," organized by Professor Pavel and held at Harvard University in 1981. The Fall, 1983 issue of PHILOSOPHY AND LITERATURE will contain additional papers presented at the symposium. 48 Thomas G. Pavel49 Imagine, for instance, the world in which Notre Dame de Paris would be covered with blue paint. While everything else would preserve the properties it possesses in the actual world, with the laws of nature and the caused chains maintained, a small local change, somewhat miraculous, would modify only the color of the venerable building. Similarly, the world of Balzac may be understood as the world of early and mid-nineteenth-century France, slightly modified by the addition of a few hundred imagined characters. That diese conform surprisingly well to the general laws of French society of the time is so much the goal of Balzac's successful project, that for the sociologically-minded reader die' actual nonexistence of Rastignac, Rubempré, Vautrin, or Birotteau may appear a mere accident. These characters, one may surmise, display every trait that actual counterparts of theirs would possess, except existence. Hence, why would Rastignac's or Vautrin's emergence in a world omerwise identical to nineteenth-century France amount to anydiing more than a "small miracle"? On the other hand, Balzac's world being blessed wim hundreds of such miracles, the very magnitude of the project vindicates the attribute of "visionary," ascribed to Balzac by Béguin, or, if metaphorically undercut, mat of"God the Father" given him by Thibaudet. For, would not such magnitude entail more than just local changes in an otherwise faithful representation of the "actual" nineteenthcentury France? Similarly, would we interpret a fictional world in which a child has been engendered not by a human father, but by a divinity, as identical in all respects to the actual world, except for the limited modification attributed to a small miracle? 2 If we grant for a moment the improbable assumption that nineteenth-century France was a given and that Balzac... (shrink)