We deal with the modal logic of cluster-decomposable Kripke interpretations, present an axiomatization, and prove some additional results regarding this logic.

There are two problematic assumptions in Kripke’s semantic argument against descriptivism. Assumption 1 is that the referential relation of a name to an object is only an objective or metaphysical relation between language and the world; it has nothing to do with the understanding of the name by our linguistic community. Assumption 2 is that descriptivism has to hold that, if name a has its meaning and the meaning is given by one description or a cluster of descriptions, (...) the description should supply a set of necessary and sufficient conditions for determining what a designates; and that it is possible for us to find out such a setof conditions. Emphasizing the sociality, intentionality, conventionality and historicity of language and meaning, this paper rejects Assumption 1, and argues that Assumption 2 is an unfair interpretation of descriptivism, and it is not necessary for descriptivists to hold Assumption 2. This paper finally concludes that Kripke’s semantic argument against descriptivism fails. (shrink)

It is generally thought that Searle 's cluster theory of the sense of a proper name was soundly refuted by Kripke in Naming and Necessity. This paper challenges this widespread belief and argues that the observations made by Kripke do not show that Searle 's version of descriptivism is false. Indeed, charitably interpreted, Searle 's theory retains considerable plausibility.

In this work a calculation of the cluster decomposable formalism for relativistic scattering as developed by Lindesay, Markevich, Noyes, and Pastrana (LMNP) is made for an ultra-light quantum model. After highlighting areas of the theory vital for calculation, a description is made of the process to go from the general theory to an eigen-integral equation for bound state problems, and calculability is demonstrated. An ultra-light quantum exchange model is then developed to examine calculability.

This paper sketches a way of supplementing classical mathematics with a motivation for a Brouwerian theory of free choice sequences. The idea is that time is unending, i.e. that one can never come to an end of it, but also indeterminate, so that in a branching time model only one branch represents the ‘actual’ one. The branching can be random or subject to various restrictions imposed by the creating subject. The fact that the underlying mathematics is classical makes such perhaps (...) delicate issues as the fan theorem no longer problematic. On this model, only intuitionistic logic applies to the Brouwerian free choice sequences, and there it applies not because of any skepticism about classical mathematics, but because there is no ‘end of time’ from the standpoint of which everything about the sequences can be decided. (shrink)

Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the result.

Tensions between idealism and scientific realism have been resolved by an appeal to the theory/observation distinction. but many who support incommensurability reject the distinction in favor of a version of idealism, e.g., thomas kuhn who supports a version of relativist idealism in which the terms of a theory do refer, but only to a paradigm--relative world of entities. it is argued that the three kinds of idealism depend on a cluster theory of meaning for fixing the reference of scientific (...) terms, and that a realist interpretation of the growth of science must eschew such a theory of meaning. the kripke-putnam theory for reference fixing of theoretical terms is employed to show how one term, 'mass', is referentially invariant despite change in the theory of motion from newton to einstein. (shrink)

“Modal logic was conceived in sin: the sin of confusing use and mention.” So quips Quine. The stigma stuck with modal logic for a while. But by the mid-sixties, a whole cluster of mathematically elegant interpretations of modal logic became available. All are natural extensions of the classical Tarskian semantics of predicate logic. By the mid-seventies, Quine’s criticisms seemed obsolete. Today, we teach the model theory of modal logic as a matter of course. Quine’s “interpretive problem” is just (...) forgotten. The purpose of my dissertation is to revamp Quine’s thesis: the very foundations of modal logic—simple propositional modal logic, even before quantifiers are added—are shaky. Quine holds that the natural interpretation of the operator “necessarily” is in terms of a full-blooded metaphysical notion of real necessity. Such a notion, Quine conjectures, is committed to the “metaphysical jungle of Aristotelian essentialism”. Hence, the intended interpretation is to be rejected. Thus Quine: so much the worse for real necessity. An alternative comes to mind: a meta-level, formal rather than real, semantic interpretation of the operator of necessity. In the late forties, Carnap developed this line of interpretation which culminates in the aforementioned model theory (“Kripke’s possible world semantics”) in the sixties. On this basis a formal interpretation is introduced: it grounds necessity in the notion of model theoretic validity. As pointed by friends of the formal interpretation (Marcus, Parsons and Kaplan), no invidious essentialist claim is verified. But have Quine’s concerns been answered? Yes and no. Technical problems regarding quantification across modal operators, substitutivity, matters of scope, and the basis of cross-world identification have indeed been solved. However, no real interpretation of “necessarily” has been provided. I argue that the seeds of such an interpretation are present in Kripke’s philosophical discussion of de re necessities in Naming and Necessity. It is not model theoretic, and it does not reduce necessity to some non-modal notion, just as Quine predicted. Even more in his vein, the real interpretation is (i) metaphysically, grounded indeed in essentialist theses, and (ii) epistemologically, forced to give up Kant’s ideal that all necessities are known a priori. (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.

We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal (...) language even over the class of K4 models, a fairly standard result for which we also provide a proof. We then propose a minor extension of the language adding a sequent operator $${\natural}$$ (‘tangle’) which can be interpreted over Kripke models as well as over topological spaces. Over finite Kripke models it indicates the existence of clusters satisfying a specified set of formulas, very similar to an operator introduced by Dawar and Otto. In the extended language $${{\sf L}^+ = {\sf L}^{\square\natural}}$$ , being simulated by a point on a finite transitive Kripke model becomes definable, both over the class of (arbitrary) Kripke models and over the class of topological S4 models. As a consequence of this we obtain the result that any class of finite, transitive models over finitely many propositional variables which is closed under simulability is also definable in L + , as well as Boolean combinations of these classes. From this it follows that the μ -calculus interpreted over any such class of models is decidable. (shrink)

This paper attempts to undermine Michael McKinsey’s Important objections to Kripke’s attempts to refute cluster versions of description theories of name reference. McKinsey argues that Kripke Ignores descriptions to which a clustser theorist might appeal In constructing his counterexamples, but that these same descriptions are what guide our intuitions In evaluating the examples. I argue that the descriptions McKinsey offers are question-begging, and thus of no help to a cluster theorist. In a second brief section, I (...) offer an argument designed to show that even If McKinsey*s descriptions were legitimate, the views Kripke endorses in "Naming and Necessity" would be supported rather than vitiated. (shrink)

Kripke has taken the Gödel case as a counterexample for reference descriptivism. Machery et al. question the validity of Kripke’s case and had conducted empirical studies to show its inadequacy. Experimental data suggest intuitions on this matter vary both across and within cultures. However, there is a descriptive ambiguity, we argue, in Kripke’s Gödel case, for people associate different types of descriptions with proper names, such as the description of brute facts and the description of social facts. (...) We argue in this paper with experimental data that the descriptive ambiguity exists and affects the actual ratio of Kripkeans in reference. This result flaws Machery et al.’s interpretation on empirical research, but does not challenge their claim on cross-cultural divergence. In fact, there are more East Asian descriptivists than Machery et al. expected. (shrink)

Solovay proved the arithmetical completeness theorem for the system GL of propositional modal logic of provability. Montagna proved that this completeness does not hold for a natural extension QGL of GL to the predicate modal logic. Let Th(QGL) be the set of all theorems of QGL, Fr(QGL) be the set of all formulas valid in all transitive and conversely well-founded Kripke frames, and let PL(T) be the set of all predicate modal formulas provable in Tfor any arithmetical interpretation. Montagna’s (...) results are described as Th(QGL) ⊊ (Fr(QGL), PL(PA) ⊈ Fr(QGL), and Th(QGL) ⊊ PL(PA). In this paper, we prove the following three theorems: (1) Fr(QGL) ⊈ PL(T) for any Σ1-sound recursively enumerable extension T of I Σ1, (2) PL(T) ⊈ Fr(QGL) for any recursively enumerable S1755020312000275_inline1 A -theory T extending I Σ1, and (3) Th(QGL) ⊊ Fr(QGL) ∩ PL(T) for any recursively enumerable S1755020312000275_inline2 A -theory T extending I Σ2. To prove these theorems, we use iterated consistency assertions and nonstandard models of arithmetic, and we improve Artemov’s lemma which is used to prove Vardanyan’s theorem on the Π0 2-completeness of PL(T). (shrink)

erative clustering. First, we show formally that the common heuristic agglomerative clustering algorithms – Ward’s method, single-link, complete-link, and a variant of group-average – are each equivalent to a hierarchical model-based method. This interpretation gives a theoretical explanation of the empirical behavior of these algorithms, as well as a principled approach to resolving practical issues, such as number of clusters or the choice of method. Second, we show how a model-based viewpoint can suggest variations on these basic agglomerative algorithms. We (...) introduce adjusted complete-link, Mahalanobis-link, and line-link as variants, and demonstrate their utility. (shrink)

Kripke's skeptical interpretation of Wittgenstein's project in the Philosophical Investigations attributes to Wittgenstein a radical skepticism about the objectivity of rules and thus the meanings of words and the existence of language as well as a skepticism about the truth conditions underlying our alleged facts about the world. Kripke then contends that Wittgenstein solves this skeptical paradox by committing himself to what I shall call a Communitarian View of language. There are a number of difficulties with Kripke's (...) interpretation of the project of the Philosophical Investigations. These include his evaluation of the notion of the rule, his interpretation of the private language arguments, his uses of the term intention, and his truncated reading of 201. In this paper I shall address and attack this interpretation of Wittgenstein as a questionable reading of the Philosophical Investigations, and I shall suggest some alternative interpretations of Wittgenstein's views which avoid both radical skepticism and a Communitarian View of language. (shrink)

Davidson’s later philosophy of language has been inspired by Wittgenstein’s Investigations, but Davidson by no means sympathizes with the sceptical problem and solution Kripke attributes to Wittgenstein. Davidson criticizes the sceptical argument for relying on the rule-following conception of meaning, which is, for him, a highly problematic view. He also casts doubt on the plausibility of the sceptical solution as unjustifiably bringing in shared practices of a speech community. According to Davidson, it is rather success in mutual interpretation that (...) explains success in the practice of meaning something by an utterance. I will argue that Davidson’s objections to the sceptical problem and solution are misplaced as they rely on a misconstrual of Kripke’s Wittgenstein’s view. I will also argue that Davidson’s alternative solution to the sceptical problem is implausible, since it fails to block the route to the sceptical problem. I will then offer a problematic trilemma for Davidson. (shrink)

In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, while a formula ∘A means that the information (...) about A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable information for the truth and for the falsity of a given proposition. (shrink)

In medicine, some personality traits, involving specific patterns of thought, feeling, and behavior, are considered to be pathological. Personality types, characteristic of such pervasive and maladaptive traits, are known under the term “personality disorders.” However, some of these pathological traits, diagnostic of so-called Cluster B personality disorders, largely describe immoral behavior. Hence, the question arises as to how such immoral behavior could be framed also as a medical problem. Moreover, it is not immediately clear whether persons with these disorders (...) could be held responsible for their immoral actions. By drawing on virtue ethics and the concept of responsibility without blame, the article demonstrates how the problem of compatibility between medicalization, cultivation of moral character, and responsibility could be resolved. Thereby, it is suggested that Cluster B personality disorders are best understood as both a moral and medical problem. (shrink)

Kripke's Wittgenstein on Rules and Private Language has enlivened recent discussion of Wittgenstein's later philosophy. Yet it is quite possible to disengage his interpretive thesis from its supporting argumentation. Doing so leaves one with an intriguing sceptical argument which Kripke first powerfully advances, then tries to halt. But contrary to the impression his argument may leave, Kripke's solution and the position it concedes to the Sceptic are deeply allied. Here I shall demonstrate their common assumption, and on (...) that basis argue that Kripke's solution begs the Sceptic's question. Furthermore, I believe we can live with the Sceptic. The sceptical argument can be turned into a reasonable contribution to a kind of nominalism in the philosophy of meaning and truth. (shrink)

Saul Kripke, in his celebrated book Wittgenstein on Rules and Private Language (1982), offers a novel reading of Ludwig Wittgenstein’s main remarks in his later works, especially in Philosophical Investigations (1953) and, to some extent, in Remarks on the Foundations of Mathematics (1956). Kripke presents Wittgenstein as proposing a skeptical argument against a certain conception of meaning and linguistic understanding, as well as a skeptical solution to such a problem. Many philosophers have called this interpretation of Wittgenstein (...) class='Hi'>Kripke’s Wittgenstein or Kripkenstein because, as Kripke himself emphasizes, it is “Wittgenstein’s argument as it struck Kripke, as it presented a problem for him” (Kripke 1982, 5) and “probably many of my formulations and re-castings of the argument are done in a way Wittgenstein would not himself approve” (Kripke 1982, 5). Such an interpretation has been the subject of tremendous discussions since its publication, and this has formed a huge literature on the topic of meaning skepticism in general and Wittgenstein’s later view in particular. -/- According to the skeptical argument that Kripke extracts from Wittgenstein’s later remarks on meaning and rule-following, there is no fact about a speaker’s behavioral, mental or social life that can metaphysically determine, or constitute, what she means by her words and also fix a determinate connection between those meanings and the correctness of her use of these words. Such a skeptical conclusion has a disastrous consequence for the classical realist view of meaning: if we insist on the idea that meaning is essentially a factual matter, we face the bizarre conclusion that there is thereby “no such thing as meaning anything by any word” (Kripke 1982, 55). -/- According to the skeptical solution that Kripke attributes to Wittgenstein, such a radical conclusion is intolerable because we certainly do very often mean certain things by our words. The skeptical solution begins by rejecting the view that results in such a paradoxical conclusion, that is, the classical realist conception of meaning. The skeptical solution offers then a new picture of the practice of meaning-attribution, according to which we can legitimately assert that a speaker means something specific by her words if we, as members of a speech-community, can observe, in enough cases, that her use agrees with ours. We can judge, for instance, that she means by “green” what we mean by this word, namely, green, if we observe that her use of “green” agrees with our way of using it. Attributing meanings to others’ words, therefore, brings in the notion of a speech-community, whose members are uniform in their responses. As a result, there can be no private language. -/- This article begins by introducing Kripke’s Wittgenstein’s skeptical problem presented in Chapter 2 of Kripke’s book. It then explicates Kripke’s Wittgenstein’s skeptical solution to the skeptical problem, which is offered in Chapter 3 of the book. The article ends by reviewing some of the most important responses to the skeptical problem and the skeptical solution. (shrink)

Saul Kripke is one of the most original and creative philosophers writing today. His work has had a tremendous impact on the direction that philosophy has taken in the last thirty years and continues to dominate some of its most fundamental aspects. Given Kripke's importance it is perhaps surprising that there is no introduction to his philosophy available to the general student. This book fills that gap. As much of Kripke's work is highly technical, the book's central (...) aim is to provide clear exposition of Kripke's ideas in a form that is understandable to a beginning readership as well as a commentary on them that more advanced students will find useful. The book begins with a discussion of Kripke's early work on modal logic, which provides the foundation for many of his later philosophical contributions, before examining in detail Kripke's central ideas and arguments contained in Naming and Necessity. In further chapters, Kripke's work on semantic paradoxes and his theory of truth are outlined as well as his controversial interpretation of Wittgenstein's famous private language argument. Kripke's ideas are situated alongside those of his precursors and some of the most important and interesting responses to them are explored. The reader is thus able to appreciate the path-breaking nature of Kripke's contributions, how they have challenged fundamentally traditional interpretations, and how they have sparked some of the most important philosophical debates of recent years. (shrink)

This thesis is an attempt to investigate the relation between the views of Wittgenstein as presented by Kripke and Donald Davidson on meaning and linguistic understanding. Kripke’s Wittgenstein, via his sceptical argument, argues that there is no fact about which rule a speaker is following in using a linguistic expression. Now, if one urges that meaning something by a word is essentially a matter of following one rule rather than another, the sceptical argument leads to the radical sceptical (...) conclusion that there is no such thing as meaning anything by any word. According to the solution Kripke’s Wittgenstein proposes, we must instead concentrate on the ordinary practice of meaning-attribution, that is, on the conditions under which we can justifiably ascribe meaning to each other and the utility such a practice has in our life. Davidson has also argued that following rules is neither necessary nor sufficient for explaining success in the practice of meaning something by an utterance. According to his alternative view of meaning, a speaker’s success in this practice is fundamentally a matter of his utterance being successfully interpreted by an interpreter in the way the speaker intended. On the basis of these remarks, Davidson raises objections to Kripke’s Wittgenstein’s sceptical argument and solution. In this thesis, I will argue that Davidson has failed to fully grasp the essentially sceptical nature of the argument and solution proposed by Kripke’s Wittgenstein. I will argue that as a result of this Davidson’s objections and his alternative solution to Kripke’s Wittgenstein’s sceptical argument are mistaken. These criticisms are pursued via an investigation of Davidson’s problematic reading of Quine’s sceptical arguments for the thesis of the indeterminacy of translation. Having criticized Davidson’s actual response to Kripke’s Wittgenstein, I will claim that Davidson’s best option for resisting the sceptical problem is to adopt a form of non-reductionism about meaning. Claudine Verheggen’s recent claim that Davidson’s use of the notion of triangulation will help to establish non-reductionism will be argued to be a failure. I will urge that the main obstacle in defending a non-reductionist view is the problem of accounting for the nature of self-knowledge of meaning and understanding. After discussing Davidson’s account of self-knowledge and Crispin Wright’s objection to this account, I will argue that, although Wright’s objection is ultimately unsuccessful, Davidson’s account fails for other reasons. Finally, I tentatively suggest that the resources for an alternative response to the sceptical problem can possibly be extracted from Davidson’s account of intending, which has some features suggestive of a judgement-dependent account of meaning and intention. (shrink)

Although Kripke’s skepticism leads to the conclusion that meaning does not exist, his argument relies upon the supposition that more than one interpretation of words is consistent with linguistic evidence. Relying solely on metaphors, he assumes that there is a multiplicity of possible interpretations without providing any strict proof. In his book The Taming of the True, Neil Tennant pointed out that there are serious obstacles to this thesis and concluded that the skeptic’s nonstandard interpretations are “will (...) o’ wisps.” In this paper, contra Tennant, I demonstrate how to construct alternative interpretations of the language of algebra. These constructed interpretations avoid Tennant’s objections and are shown to be interdefinable with the standard interpretation. Kripke’s skepticism is, as it were, an incarnate demon. In contrast, it is currently uncertain whether the same technique is generally applicable to the construction of an alternative interpretation of natural language. However, the reinterpretation of those aspects of natural language that directly relate to numbers seems to be a promising candidate for the development of nonstandard interpretations of natural language. (shrink)

Noah Rosenberg et al.'s 2002 article “Genetic Structure of Human Populations” reported that multivariate genomic analysis of a large cell line panel yielded reproducible groupings (clusters) suggestive of individuals' geographical origins. The paper has been repeatedly cited as evidence that traditional notions of race have a biological basis, a claim its authors do not make. Critics of this misinterpretation have often suggested that it follows from interpreters' personal biases skewing the reception of an objective piece of scientific writing. I contend, (...) however, that the article itself to some degree facilitates this misrepresentation. I analyze in detail several verbal and visual features of the original article that may predispose aspects of its racial interpretation; and, tracing the arguments of one philosopher and one popular science writer, I show how these features are absorbed, transformed into arguments for a biological basis of race, and re-attributed to the original. The essay demonstrates how even slight ambiguities can enable the misappropriation of scientific writing, unintentionally undermining the authors' stated circumspection on the relationship between cluster and race. (shrink)

The homeostatic property cluster theory is widely influential for its ability to account for many natural-kind terms in the life sciences. However, the notion of homeostatic mechanism has never been fully explicated. In 2009, Carl Craver interpreted the notion in the sense articulated in discussions on mechanistic explanation and pointed out that the HPC account equipped with such notion invites interest-relativity. In this paper, we analyze two recent refinements on HPC: one that avoids any reference to the causes of (...) the clustering of properties and one that replaces homeostatic mechanisms with causal networks represented by causal graphs. We argue that the former is too slender to account for some inductive inference in science and the latter, thicker account invites interest-relativity, as the original HPC does. This suggests that human interest will be an un-eliminative part of a satisfactory account of natural kindness. We conclude by discussing the implication of interest-relativity to the naturalness, reality, or objectivity of kinds and indicating an overlooked aspect of natural kinds that requires further studies. (shrink)

Hidden cluster problems can manifest when broad ethnic categories are used as proxies for cultural traits, especially when traits are assumed to encode cultural distances between groups. We suggest a granular understanding of cultural trait distributions within and between ethnic categories is fundamental to the interpretation of heritability estimates as well as general behavioral outcomes.

A central part of Kripke's influential interpretation of Wittgenstein's sceptical argument about meaning is the rejection of dispositional analyses of what it is for a word to mean what it does. In this paper I show that Kripke's arguments prove too much: if they were right, they would preclude not only the idea that dispositional properties can make statements about the meanings of words true, but also the idea that dispositional properties can make true statements about paradigmatic dispositional (...) properties such as a cup's fragility or a person's bravery. However, since dispositional properties can make such statements true, Kripke-Wittgenstein's arguments against dispositionalism about meaning are mistaken. (shrink)

In Wittgenstein on Rules and Private Language, Saul Kripke rejects some of the most popular accounts of what meaning facts consist in on the grounds that they fail to accommodate the normative character of meaning. I argue that a widespread interpretation of Kripke's argument is incorrect. I contend that the argument does not rest on the contrast between descriptive and normative facts, but on the thought that speakers' uses of linguistic expressions have to be justified. I suggest that (...) the line of reasoning that I attribute to Kripke can be seen as putting pressure on the idea that predicate satisfaction is to be explained in terms of a relation between predicates and properties. (shrink)

ABSTRACT: The cluster theory of names is generally thought to have been to have been utterly discredited by the objections raised against it by Kripke in Naming and Necessity. In this paper, I develop a new version of the cluster theory in which the role played by clusters of associated descriptions is occupied by teams of cognitive relations. And I argue that these teams of relations find a home in an account of the meanings of expressions in (...) epistemic sentence frames, and in a more general theory of the reference of proper names. RÉSUMÉ: La théorie des faisceaux de noms est généralement considérée sans fondement depuis les objections soulevées par Kripke dans Naming and Necessity. Nous proposons une nouvelle version de la théorie des faisceaux dans laquelle le rôle joué par les faisceaux de descriptions associées est pris en charge par des équipes de relations cognitives. Ces équipes de relations trouvent leur place au sein de l’explication de la signification des expressions dans le cadre de phrases épistémologiques et, plus généralement, dans celui d’une théorie de la référence des noms propres. (shrink)

The received view of Kripke's Wittgenstein on Rules and Private Language is that it fails as an interpretation because, inter alia, it ignores or overlooks what Wittgenstein has to say in the second paragraph of Philosophical Investigations 201. In this paper, I demonstrate that the paragraph in question is in fact fully accommodated within Kripke's reading, and cannot therefore be reasonably utilised to object to it. -/- In part one I characterise the objection; in part two I explain (...) why it fails; in part three I suggest why commentators might have been motivated to offer it; and in part four I claim that two commentators who have offered it also imply otherwise. (shrink)

Correct interpretation of the data from integral laboratory tests, including Thrombin Generation Test, requires biochemistry-based mathematical models of blood coagulation. The purpose of this study is to describe the experimental TGT data from healthy donors and hemophilia A and B patients. We derive a simplified ODE model and apply it to analyze the TGT data from healthy donors and HA/HB patients with in vitro added tissue factor pathway inhibitor antibody. This model allows the characterization of hemophilia patients in the space (...) of three most important model parameters. The proposed approach may provide a new quantitative tool for the analysis of experimental TGT. Also, it gives a reduced model of coagulation verified against clinical data to be used in future theoretical large-scale modeling of thrombosis in flow. (shrink)

The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as (...) a specific addition to the standard Solovay construction. (shrink)

This paper examines an argument of Saul Kripke for the necessity of theoretical identification statements and defends it against a criticism of M. Perrick ("Are Kripke's Theoretical Identifications Necessary Truths?", Logique et Analyse, Volume 115, September 1986, pages 381-384). It is argued that Perrick's criticism rests on a fallacy of ambiguity. Formal modal logic is used to examine a number of plausible interpretations of Kripke's argument, and Perrick's error is shown to arise from confusion concerning the (...) scope of the modal necessity operator. (shrink)

Kripke's epistemic argument against descriptivism is reconstructed as follows. Premise 1: if descriptivism is correct, then “N is the F” should be knowable a priori; Premise 2: in fact, “N is the F” is not knowable a priori; Conclusion: descriptivism is wrong. This article accepts P2 of the argument as true, but rejects P1 by arguing for the evolution of language and the growth of meaning; so it concludes that the argument fails. It also criticizes Kripke's conception of (...) “a priori,” and interprets why “N is the F” is not knowable a priori. Sometimes this article uses materials from Chinese ancient philosophers, for example, Xunzi and later Moists, to support its arguments. (shrink)

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.

A decomposition model of Net Final Values (NFV), named Systemic Value Added (SVA), is proposed for decision-making purposes, based on a systemic approach introduced in Magni [Magni, C. A. (2003), Bulletin of Economic Research 55(2), 149–176; Magni, C. A. (2004) Economic Modelling 21, 595–617]. The model translates the notion of excess profit giving formal expression to a counterfactual alternative available to the decision maker. Relations with other decomposition models are studied, among which Stewart’s [Stewart, G.B. (1991), The Quest for Value: (...) The EVA™ Management Guide, Harper Collins, Publishers Inc]. The index here introduced differs from Stewart’s Economic Value Added (EVA) in that it rests on a different interpretation of the notion of excess profit and is formally connected with the EVA model by means of a shadow project. The SVA is formally and conceptually threefold, in that it is economic, financial, accounting-flavoured. Some results are offered, providing sufficient and necessary conditions for decomposing NFV. Relations between a project’s SVA and its shadow project’s EVA are shown, all results of Pressacco and Stucchi [Pressacco, F. and Stucchi, P. (1997), Rivista di Matematica per le Scienze Economiche e Sociali 20, 165–185] are proved by making use of the systemic approach and the shadow counterparts of those results are also shown. (shrink)

In “Naming and Necessity” Saul Kripke describes some cases which, he claims, provide counterexamples both to cluster theories and, more generally, to description theories of proper names. My view of these cases is that while they do not provide counterexamples to cluster theories, they can be used to provide evidence against single-description theories. In this paper I shall defend both of the claims involved in my view.

The paper suggests a straight solution to the problem of meaning skepticism presented in Kripke’s Wittgenstein on Rules and Private Language. The solution is based on Ladov’s moderate solution to the problem. Ladov’s solution is to the effect that the total skepticism cannot be a theory because it cannot be stated without performative contradiction. This entails that only a limited skepticism is possible as a theory. I argue that the limited skepticism is compatible with the view that meaning can (...) be known provided the knowledge of meaning is construed as an internal part of a speech act, not as a result of interpretation of behavioral facts. (shrink)

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in (...) turn to the appropriate categorical models for these logics. (shrink)

Kripke’s Wittgenstein is standardly understood as a non-factualist about meaning ascription. Non-factualism about meaning ascription is the idea that sentences like “Joe means addition by ‘plus’” are not used to state facts about the world. Byrne and Kusch have argued that Kripke’s Wittgenstein is not a non-factualist about meaning ascription. They are aware that their interpretation is non-standard, but cite arguments from Boghossian and Wright to support their view. Boghossian argues that non-factualism about meaning ascription is incompatible with (...) a deflationary theory of truth. Wright argues that non-factualism about meaning ascription is incoherent. To support the standard interpretation, I’ll respond to each argument in turn. To the degree that my responses are successful, Byrne and Kusch have an unmotivated interpretation of Kripke’s Wittgenstein. Wilson provides a factualist interpretation that is not based on Boghossian and Wright’s arguments. Miller argues for a non-factualist interpretation against Wilson, but I’ll show that Miller’s interpretation faces a dilemma. Miller’s argument cannot be maintained if a coherent interpretation of the skeptical solution is to be provided. I’ll show how this dilemma can be avoided and provide an independent argument against Wilson so that a non-factualist interpretation of the skeptical solution can be maintained. (shrink)

I consider Lewis’ appeal to naturalness to solve Kripke ’s rule - following paradox. I then present a different interpretation of this paradox and offer reasons for thinking that this is what Kripke had in mind. I argue that Lewis’ proposal cannot provide a solution to this version of paradox.

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of (...) logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems. (shrink)

Este trabajo explora las críticas de McDowell a la argumentación de Kripke en Wittgenstein: On Rules and Private Language y analiza su propuesta positiva, el ofrecimiento de un hecho semántico primitivo. Su idea es que el resultado escéptico alcanzado por Kripke resulta de no haber desechado la identificación entre significado e interpretación. Al contrario, el marco para dar cuenta de la noción de significado es la práctica: los hechos semánticos primitivos -elaborables a través de una semántica de condiciones (...) de verdad- son constituidos en la práctica comunitaria, y de ellos tenemos una captación individual. En mi opinión no sólo la crítica de McDowell a Kripke es errada, sino que su propuesta positiva presenta problemas fundamentales, tanto en su concepción de la normatividad como en sus aspectos epistémicos. El corolario de este trabajo será mostrar que el verdadero problema para una teoría semántica es la identificación del significado con cualquier tipo de hecho y no meramente la identificación del significado con la interpretación. This paper explores McDowell's criticisms to Kripke's argumentation in his Wittgenstein: On Rules and Private Language, and analyses his positive proposal, that is, the offering of a primitive semantic fact. His idea is that the skeptical result reached by Kripke depends on not having discarded the identification between meaning and interpretation. On the contrary, the ITamework to explain the notion of meaning is the practice: the primitive semantic facts - that may be established by truth-values semantics - are constituted by the communitarian practice, and we get an individual insight of them. In my view, not only the criticism of McDowell to Kripke is erroneous, but also his positive proposal presents fundamental problems, in his conception ofnormativity as well as in his epistemic aspects. The conclusion of this paper will be to show how the real problem for a semantic theory is the identification ofmeaning with any kind of fact and not only the identification of meaning and interpretation. (shrink)

The isolation principle rests on defining internal and external differentiation for each subset of at least two objects. Subsets with larger external than internal differentiation form isolated groups in the sense that they are internally cohesive and externally isolated. Objects that do not belong to any isolated group are termed solitary. The collection of all isolated groups and solitary objects forms a hierarchical (encaptic) structure. This ubiquitous characteristic of biological organization provides the motivation to identify universally applicable practical methods for (...) the detection of such structure, to distinguish primary types of structure, to quantify their distinctiveness, and to simplify interpretation of structural aspects. A method implementing the isolation principle (by generating all isolated groups and solitary objects) is proven to be specified by single-linkage clustering. Basically, the absence of structure can be stated if no isolated groups exist, the condition for which is provided. Structures that allow for classifications in the sense of complete partitioning into disjoint isolated groups are characterized, and measures of distinctiveness of classification are developed. Among other primary types of structure, chaining (complete nesting) and ties (isolated groups without internal structure) are considered in more detail. Some biological examples for the interpretation of structure resulting from application of the isolation principle are outlined. (shrink)

ABSTRACTThis paper discusses Claudine Verheggen's account of what she takes to be Donald Davidson's response to the sceptical paradox about rule-following and meaning developed in Saul Kripke's interpretation of Wittgenstein's ‘rule-following considerations.’ It focusses on questions about the normativity of meaning, the social character of meaning, and the role of triangulation in Davidson's account of the determination of meaning, and invites Verheggen to compare the non-reductionism she finds in Davidson with that developed in Crispin Wright's judgement-dependent account of meaning.RÉSUMÉCet (...) article examine ce que Claudine Verheggen considère comme étant la réponse de Donald Davidson au paradoxe sceptique développé dans l'interprétation qu'offre Saul Kripke des remarques de Wittgenstein sur la possibilité de suivre une règle. Je me concentre en particulier sur des questions concernant la normativité de la signification, le caractère social de la signification et le rôle que la notion de triangulation joue dans la position de Davidson sur la détermination de la signification. J'invite aussi Verheggen à comparer le non-réductionnisme davidsonien avec celui défendu par Crispin Wright dans sa conception de la signification en tant que dépendante du jugement. (shrink)

Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist quantificational (...) logic. (shrink)