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)

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)

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)

Burge famously argued that one can have thoughts involving a concept C even if one’s understanding of C is incomplete. Even though this view has been extremely influential, it has also been taken by critics as less than clear. The aim of this paper is to show that the cases imagined by Burge as being ones in which incomplete understanding of concepts is involved can be made clearer given an account of direct concept ascriptions—such as “Peter has the concept of (...) arthritis”—according to which these ascriptions are to be analysed in terms of ascriptions of the knowledge of what something is. The upshot is that the cases imagined by Burge can be explained is terms of the idea of subjects knowing in part what something is. (shrink)

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)

Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.

Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

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.

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).

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 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.

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.

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’.

This article discusses the thesis that a subject can have a concept, think thoughts containing it, that she incompletely understands. The central question concerns how to construe the distinction between having a concept and understanding it. Two important versions of the thesis are distinguished: a metasemantic version and an epistemic version. According to the first, the subject may have concept C without being a fully competent user, in virtue of deference to other speakers or to the world. According to the (...) second, the subject may have a concept without being able to provide a proper explication of it. It is argued that whereas the epistemic version is plausible, the metasemantic version faces some challenges. First, it needs to be explained precisely how deference enables a speaker to have C. Second, metasemantic incomplete understanding is in tension with the idea that concepts serve to capture the subject’s cognitive perspective. (shrink)

We present an analogue of Gödel’s second incompleteness theorem for systems of second-order arithmetic. Whereas Gödel showed that sufficiently strong theories that are $\Pi ^0_1$ -sound and $\Sigma ^0_1$ -definable do not prove their own $\Pi ^0_1$ -soundness, we prove that sufficiently strong theories that are $\Pi ^1_1$ -sound and $\Sigma ^1_1$ -definable do not prove their own $\Pi ^1_1$ -soundness. Our proof does not involve the construction of a self-referential sentence but rather relies on ordinal analysis.

Full proofs of the Gödel incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of Gödel’s theorems without (...) getting mired in syntactic or computational details. One of the most important of these efforts was made by Löb [8] in connection with his analysis of sentences asserting their own provability. Löb formulated three conditions (now known as the Hilbert-Bernays-Löb derivability conditions), on the provability predicate in a formal system which are jointly sufficient to yield the Gödel’s second incompleteness theorem for it. A key role in Löb’s analysis is played by (a special case of) what later became known as the diagonalization or fixed point property of formal systems, a property which had already, in essence, been exploited by Gödel in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere’s [7] category-theoretic account of incompleteness phenomena (see also [10]). Incompleteness theorems have also been subjected to intensive investigation within the framework of modal logic (see, e.g.[4], [5]). In this formulation the modal operator takes up the role previously played by the provability predicate, and the derivability conditions on the latter are translated into algebraic conditions (the so-called GL, i.e., Gödel–Löb, conditions) on the former. My purpose here is to present a framework for incompleteness phenomena, fully compatible with intuitionistic or constructive principles, in which the idea of a coding system is retained, only in a 2 simple, but very general form, a form wholly free of syntactical notions. As codes we shall take the elements of an arbitrary given nonempty set, possibly, but not necessarily, the set of natural numbers.. (shrink)

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)

In the early seventies, several logicians developed a semantics for propositional systems of relevance logic. The essential ingredients of this semantics were a privileged point o, an ‘accessibility’ relation R and a special operator * for evaluating negation. Under the truth- conditions of the semantics, each formula A(Pl,…,Pn) could be seen as expressing a first order condition A+(pl,…,pn, o, R,*) on sets p1,…,pn and o, R, *, while each formula-scheme could be regarded as expressing the second-order condition ∀p1,…,∀pn A+(p1,…,pn, o, (...) R, *). It could then be shown that many standard systems of propositional relevance logic were complete in the sense that their theorems were just those formulas true in all models whose components o, R and * conformed to the second-order conditions expressed by the axioms of the system. (shrink)

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.

whole numbers that manages to assert that it itself is unprovable (from a given finite set F of axioms using formal logic). (Gödel's paper is included in the well-known anthology [1].) GF : ``GF cannot be proved from the finite set of axioms F.'' This assertion GF is therefore true if and only if it is unprovable, and the formal axiomatic system F in question either proves falsehoods (because it enables us to prove GF) or fails to prove a true (...) assertion (because it does not enable us to prove GF). If we assume that the former situation is impossible, we conclude that F is necessarily incomplete since it does not permit us to establish the true statement GF. (shrink)

This paper explores the relationships between Davidson's indeterminacy of interpretation thesis and two semantic properties of sentences that have come to be recognized recently, namely semantic incompleteness and semantic indecision.1 More specifically, I will examine what the indeterminacy thesis entails for sentences of the form 'By sentence S (or word w), agent A means that m' and 'Agent A believes that p.' My primary goal is to shed light on the indeterminacy thesis and its consequences. I will distinguish two (...) kinds of indeterminacy that have very different sources and very different consequences. But this does not purport to be an exhaustive study: there may well be other forms of indeterminacy that this .. (shrink)

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)

It is well known that Gödel’s incompleteness theorems hold for ∑1-definable theories containing Peano arithmetic. We generalize Gödel’s incompleteness theorems for arithmetically definable theories. First, we prove that every ∑n+1-definable ∑n-sound theory is incomplete. Secondly, we generalize and improve Jeroslow and Hájek’s results. That is, we prove that every consistent theory having ∏n+1set of theorems has a true but unprovable ∏nsentence. Lastly, we prove that no ∑n+1-definable ∑n-sound theory can prove its own ∑n-soundness. These three results are generalizations (...) of Rosser’s improvement of the first incompleteness theorem, Gödel’s first incompleteness theorem, and the second incompleteness theorem, respectively. (shrink)

Early in Principia Mathematica Russell presents an argument that "‘the author of Waverley’ means nothing", an argument that he calls a "definite proof". He generalizes it to claim that definite descriptions are incomplete symbols having meaning only in sentential context. This Principia "proof" went largely unnoticed until Russell reaffirmed a near-identical "proof" in his philosophical autobiography nearly 50 years later. The "proof" is important, not only because it grounds our understanding of incomplete symbols in the Principia programme, but also because (...) failure to understand it fully has been a source of much unjustified criticism of Russell to the effect that he was wedded to a naive theory of meaning and prone to carelessness and confusion in his philosophy of logic and language generally. In my paper, I (1) defend Russell’s "proof" against attacks from several sources over the last half century, (2) examine the implications of the "proof" for understanding Russell’s treatment of class symbols in Principia, and (3) see how the Principia notion of incomplete symbol was carried forward into Russell’s conception of philosophical analysis as it developed in his logical atomist period after 1910. (shrink)

This paper addresses the phenomenon of incomplete preferences in disaster risk management. If an agent finds two options to be incomparable and thus has an incomplete preference ordering, i.e., neither prefers one option over the other nor finds them equally as good, it is not possible for the agent to perform a value tradeoff, necessary for an informed decision, between these two options. In this paper we suggest a way to model incomplete preference orderings by means of probabilistic preferences, and (...) how to reveal an agent’s incomplete preference ordering within a behaviorist framework. (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.

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

Incomplete Archaeologies takes a familiar archaeological concept--assemblages--and reconsiders such groupings, collections and sets of things from the perspective of the work required to assemble them. The discussions presented here engage with the practices of collection, construction, performance and creation in the past (and present) which constitute the things and groups of things studied by archaeologists--and examine as well how these things and thing-groups are dismantled, rearranged, and even destroyed, only to be rebuilt and recreated. The ultimate aim is to reassert (...) an awareness of the incompleteness of assemblage, and thus the importance of practices of assembling (whether they seem at first creative or destructive) for understanding social life in the past as well as the present. The individual chapters represent critical engagements with this aim by archaeologists presenting a broad scope of case studies from Eurasia and the Mediterranean. Case studies include discussions of mortuary practice from numerous angles, the sociopolitics of metallurgy, human-animal relationships, landscape and memory, the assembly of political subjectivity and the curation of sovereignty. These studies emphasise the incomplete and ongoing nature of social action in the past, and stress the critical significance of a deeper understanding of formation processes as well as contextual archaeologies to practices of archaeology, museology, art history, and other related disciplines. Contributors challenge archaeologists and others to think past the objects in the assemblage to the practices of assembling, enabling us to consider not only plural modes of interacting with and perceiving things, spaces, human bodies and temporalities in the past, but also to perhaps discover alternate modes of framing these interactions and relationships in our analyses. Ultimately then, Incomplete Archaeologies takes aim at the perceived totality not only of assemblages of artefacts on shelves and desks, but also that of some of archaeology's seeming-seamless epistemological objects"--From publisher's website. (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)

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)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained in (...) that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

If a metaphysics identifies transcendental principles with formal principles, the inevitable result will be a reductionist collapse, that is, a theory of the nature of reality that will exclude as inessential significant differences among existing things. To avoid this result, we must take some such material differences (those, for example, that distinguish physical, biological and mental phenomena from one another) as transcendental in nature. This produces a metaphysics in which the concept of ontological emergence is central—a metaphysics that will depend (...) essentially on the material content of the natural sciences. While both Aristotle and Hegel provided such a metaphysics, they did not, I argue, accept one of its most important consequences—that it must be as incomplete as our scientific knowledge of these material differences. I examine this failure and suggest some areas in which contemporary scientific conceptions may contribute to a more contemporary metaphysics. (shrink)

The truth-table degree of the set of shortest programs remains an outstanding problem in recursion theory. We examine two related sets, the set of shortest descriptions and the set of domain-random strings, and show that the truth-table degrees of these sets depend on the underlying acceptable numbering. We achieve some additional properties for the truth-table incomplete versions of these sets, namely retraceability and approximability. We give priority-free constructions of bounded truth-table chains and bounded truth-table antichains inside the truth-table complete degree (...) by identifying an acceptable set of domain-random strings within each degree. (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)

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.

Although G¨odel proved the first incompleteness theorem by intuitionistically respectable means, G¨odel’s formula, true although undecidable,seems to offer a counter-example to the general constructivist or anti-realistclaim that truth may not transcend recognizability in principle. It is arguedhere that our understanding of the formula consists in a knowledge of itstruth-conditions, that it is true in a minimal sense and, finally, that it is recognized as such given the consistencyand ω-consistency of P. The philosophical lesson to be drawn from G¨odel’sproof is (...) that our capacities for justification in favour of minimal truth exceedwhat is strictly speaking formally provable in P by means of an algorithm. (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)

According to the displacement model of secularization, religious-theological concepts, themes, and values have been reinterpreted in non-religious contexts without fully dispensing with the religious content. Secularization is thus incomplete. The incomplete secularization argument can be used as a lens through which to read Ethan Kleinberg’s deconstructive approach to the past. In his narrative, as reconstructed here, deconstruction promises to bring us closer to a secular relationship to the past than the ontological realism Kleinberg says still dominates contemporary historical theory. By (...) contrasting Kleinberg’s analysis with Hayden White’s, whose oeuvre can be read as structured by the idea of incomplete secularization and a wish to liberate history from religious themes in order to enable a direct confrontation with meaninglessness, I argue that Kleinberg’s deconstructive approach does not fulfill its promise. Rather, it opens up a post-secular historiography in which religious themes might find a place at the very heart of historical reasoning. (shrink)

In Episode 1, we introduced the very idea of a negation-incomplete formalized theory T . We noted that if we aim to construct a theory of basic arithmetic, we’ll ideally like the theory to be able to prove all the truths expressible in the language of basic arithmetic, and hence to be negation complete. But Gödel’s First Incompleteness Theorem says, very roughly, that a nice theory T containing enough arithmetic will always be negation incomplete. Now, the Theorem comes in (...) two flavours, depending on whether we cash out the idea of being ‘nice enough’ in terms of (i) the semantic idea of T ’s being a sound theory, or (ii) the idea of odel’s own T ’s being a consistent theory which proves enough arithmetic. And we noted that G¨. (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)

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.

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.

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...) array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (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)

This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) (...) in order to obtain formal undecidability results. A generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth. (shrink)

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)