In his unpublished 1979 Lectures on the Philosophy of Mind, Saul Kripke offers a knowledge argument against materialism focusing on deaf people who lack knowledge of auditory experience. Kripke's argument is a precursor of Frank Jackson's better‐known knowledge argument against materialism (1982). The paper sets out Kripke's argument, brings out its interest and philosophical importance, and explores some similarities and differences between Kripke's knowledge argument and Jackson's.

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to (...) be true in KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

Saul Kripke is one of the most important and original post-war analytic philosophers. His work has undeniably had a profound impact on the philosophy of language and the philosophy of mind. Yet his ideas are amongst the most challenging frequently encountered by students of philosophy. In this informative and accessible book, Arif Ahmed provides a clear and thorough account of Kripke's philosophy, his major works and ideas, providing an ideal guide to the important and complex thought of this (...) key philosopher. The book offers a detailed review of his two major works, Naming and Necessity and Wittgenstein on Rules and Private Language, and explores how Kripke's ideas often seem to overturn widely accepted views and even perceptions of common sense. Geared towards the specific requirements of students who need to reach a sound understanding of Kripke's thought, the book provides a cogent and reliable survey of the nature and significance of Kripke's contribution to philosophy. This is the ideal companion to the study of this most influential and challenging of philosophers. (shrink)

Recently, there has been a significant upsurge of interest in what has come to be known as the 'Adoption Problem', first developed by Saul Kripke in 1974. The problem purports to raise a difficulty for Quine’s anti-exceptionalist conception of logic. In what follows, we first offer a statement of the problem and argue that, so understood, it depends upon natural but resistible assumptions. We then use that discussion as a springboard for developing a different adoption problem, arguing that, for (...) a significant class of basic logical principles, there is indeed a difficulty in seeing how they might be ‘freely adopted,’ thereby vindicating something close to the spirit of Kripke’s original claim. This first part of our argument will enforce a significant qualification of Quine’s claim that basic logical principles can be empirically confirmed. In the concluding sections of the paper, we turn to the question, specifically, of the empirical revisability of logic, arguing that when proper attention is paid to the role of reasoning in theory revision, it does indeed emerge that anti-exceptionalism, in full generality, is untenable. (shrink)

This collection of essays, based on Saul Kripke's published and unpublished works, represents the most comprehensive analysis of his philosophy and writings available.

We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a (...) coimplication operator, similar to Curry's subtraction operator, which is resituated with Linear Logic's contensor product. And we can add contraction to get nondistributive Relevance Logic. The model rests heavily on Urquhart's representation of nondistributive lattices and also on Dunn's Gaggle Theory. Indeed, the paper may be viewed as an investigation into nondistributive Gaggle Theory restricted to binary operations. The valuations on the Kripke model are three valued: true, false, and indifferent. The lattice representation theorem of Urquhart has the nice feature of yielding Priestley's representation theorem for distributive lattices if the original lattice happens to be distributive. Hence the representation is consistent with Stone's representation of distributive and Boolean lattices, and our semantics is consistent with the Lemmon-Scott representation of modal algebras and the Routley-Meyer semantics for Relevance Logic. (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)

In?201 of Philosophical Investigations, Ludwig Wittgenstein puts forward his famous? rule - following paradox.? The paradox is how can one follow in accord with a rule? the applications of which are potentially infinite? when the instances from which one learns the rule and the instances in which one displays that one has learned the rule are only finite? How can one be certain of rule - following at all? In Wittgenstein: On Rules and Private Language, Saul Kripke concedes the (...) skeptical position that there are no facts that we follow a rule but that there are still conditions under which we are warranted in asserting of others that they are following a rule. In this paper, I explain why Kripke?s solution to the rule - following paradox fails. I then offer an alternative. (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)

Kripke in his famous book on Wittgenstein’s later philosophy argues, on behalf of Wittgenstein, that there can be no fact of the matter as to what a speaker means by her words, that is, no fact that can meet the Constitution Demand and the Normativity Demand. He particularly argues against the dispositional view, according to which meaning facts are constituted by facts about the speaker's dispositions to respond in a certain way on certain occasions. He argues that facts about (...) dispositions are finite and are incapable of constituting facts about what speakers mean by their words; they are also essentially descriptive, not prescriptive and thus, cannot meet the Normativity Demand. Hannah Ginsborg, one of the most important contemporary philosophers of language, has recently attempted to resist Kripke’s Wittgenstein’s arguments against by defending a new sort of reductive dispositionalism which can meet both demands at the same time. In this paper, I will argue that she would not be successful in her project. (shrink)

Famously, Saul Kripke proposes that there are contingent a priori truths, and has offered a number of examples to illustrate his claim. The most well-known example involves the standard meter bar in Paris. Purportedly, a certain agent knows a priori that the bar is one meter long. However, in response to a long-standing objection to such examples - the "existential complaint" - generally only modified examples having a conditional form are now considered candidates for the contingent a priori. Gareth (...) Evans argues that these conditionals must be understood free-logically, and on this basis argues against Keith Donnellan's analysis of the contingent a priori. I show Evans' argument mistaken. I also take issue with the existential complaint, and suggest a way of understanding Kripke's original examples that is not subject to it. My approach focuses the debate in its right place, and allows us to take Kripke's original examples seriously. (shrink)

Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, _Naming and Necessity_, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection _Philosophical Troubles_. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained (...) guide to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. _Kripke_ will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers. (shrink)

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, (...) where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms using ∧, ∨, ∀, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model-consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (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)

In ‘Kripke on epistemic and metaphysical possibility: two routes to the necessary a posteriori’, Scott Soames identifies two arguments for the existence of necessary a posteriori truths in Naming and Necessity . He argues that Kripke's second argument relies on either of two principles, each of which leads to contradiction. He also claims that it has led to ‘two-dimensionalist’ approaches to the necessary a posteriori which are fundamentally at odds with the insights about meaning and modality expressed in (...) NN. I argue that the alleged second argument is not in NN. I identify the mistakes that lead to Soames' misinterpretation. (shrink)

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countable linear Kripke frames with constant domains: We obtain a complete characterisation of (...) axiomatisability of logics based on countable linear Kripke frames with constant domains. Furthermore, we obtain that the total number of logics defined by countable linear Kripke frames on constant domains is countable. (shrink)

This paper argues that most of the alleged straight solutions to the sceptical paradox which Kripke ascribed to Wittgenstein can be regarded as the first horn of a dilemma whose second horn is the paradox itself. The dilemma is proved to be a by‐product of a foundationalist assumption on the notion of justification, as applied to linguistic behaviour. It is maintained that the assumption is unnecessary and that the dilemma is therefore spurious. To this end, an alternative conception of (...) the justification of linguistic behaviour is outlined, a conception that vindicates some of the insights behind Kripke's Wittgenstein's sceptical solution of the paradox. This alternative conception is defended against two objections (both familiar from McDowell's works): (1) that it would imply that for the linguistic community there is no authority, no standard to meet and, therefore, no possibility of error and (2) that it would lead to a kind of idealism. (shrink)

Kripke's lectures, published as Wittgenstein on Rules and Private Language , posed a sceptical problem about following a rule, which he cautiously attributed to Wittgenstein. He briefly noticed an analogy between his new kind of scepticism and Goodman's riddle of induction. ‘Grue’, he said, could be used to formulate a question not about induction but about meaning: the problem would not be Goodman's about induction—‘Why not predict that grass, which has been grue in the past, will be grue in (...) the future?’—but Wittgenstein's about meaning: ‘Who is to say that in the past I did not mean grue by “green”, so that now I should call the sky, not the grass, “green”?’. (shrink)

Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. (...) WHAT IS A MODEL THEORY? Traditionally, a statement is regarded as logically valid if it is an instance of a logically valid form, where a form is regarded as logically valid if every instance is true. In modern logic, forms are represented by formulas involving letters and special symbols, and logicians seek therefore to define a notion of model and a notion of a formula’s truth in a model in such a way that every instance of a form will be true if and only if a formula representing that form is true in every model. Thus the unsurveyably vast range of instances can be replaced for purposes of logical evaluation by the range of models, which may be more tractable theoretically and perhaps practically. Consideration of the familiar case of classical sentential logic should make these ideas clear. Here a formula, say (p & q) ∨ ¬p ∨ ¬q, will be valid if for all statements P.. (shrink)

This paper has two purposes: the first is to critically examine Kripke’s well-known arguments against Descriptivism and suggest that they are not as decisive as many have thought; the second is to argue that proper names do encode descriptive information of various kinds, that such information may be truth-conditionally significant, and hence that a name’s truth-conditional contribution is not limited to its referent.

The paper investigates the strength of the Anti-Foundation Axiom, AFA, on the basis of Kripke-Platek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength.

Kripke's objections to descriptivism may be modified to apply to Scott Soames's pragmatic account from his book Beyond Rigidity. Further, intuitions about argument-validity threaten any theory in the vicinity of Soames's.

Saul Kripke’s discussion of the necessary aposteriori in Naming and Necessity and “Identity and Necessity” -- in which he lays the foundation for distinguishing epistemic from metaphysical possibility, and explaining the relationship between the two – is, in my opinion, one of the outstanding achievements of twentieth century philosophy.1 My aim in this essay is to extract the enduring lessons of his discussion, and disentangle them from certain difficulties which, alas, can also be found there. I will argue that (...) there are, in fact, two Kripkean routes to the necessary aposteriori – one correct and philosophically far-reaching, the other incorrect and philosophically misleading. (shrink)

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.

Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem (...) for complete lattices. A Rasiowa/Sikorski style semantic tableau system is also presented with the property that if all branches of a tableau are closed, then the formula in question is a theorem of Gelfand Logic. An open branch in a completed tableaux guarantees the existence of an Kripke model in which the formula is not valid; hence it is not a theorem of Gelfand Logic. (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)

Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, Naming and Necessity, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained (...) guide to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. Kripke will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers. (shrink)

This paper deals with one kind of Kripke-style semantics, which we shall call algebraic Kripke-style semantics, for relevance logics. We first recall the logic R of relevant implication and some closely related systems, their corresponding algebraic structures, and algebraic completeness results. We provide simpler algebraic completeness proofs. We then introduce various types of algebraic Kripke-style semantics for these systems and connect them with algebraic semantics.

Saul Kripke, in a series of classic writings of the 1960s and 1970s, changed the face of metaphysics and philosophy of language. Christopher Hughes offers a careful exposition and critical analysis of Kripke's central ideas about names, necessity, and identity. He clears up some common misunderstandings of Kripke's views on rigid designation, causality and reference, and the necessary a posteriori and contingent a priori. Through his engagement with Kripke's ideas Hughes makes a significant contribution to ongoing (...) debates on, inter alia, the semantics of natural kind terms, the nature of natural kinds, the essentiality of origin and constitution, the relative merits of 'identitarian' and counterpart-theoretic accounts of modality, and the identity or otherwise of mental types and tokens with physical types and tokens. No specialist knowledge in either the philosophy of language or metaphysics is presupposed; Hughes's book will be valuable for anyone working on the ideas which Kripke made famous in the philosophy world. (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)

Saul Kripke has proposed an argument to show that there is a serious problem with many computational accounts of physical systems and with functionalist theories in the philosophy of mind. The problem with computational accounts is roughly that they provide no noncircular way to maintain that any particular function with an infinite domain is realized by any physical system, and functionalism has the similar problem because of the character of the functional systems that are supposed to be realized by (...) organisms. This paper shows that the standard account of what it is for a physical system to compute a function can avoid Kripke's criticisms without being reduced to circularity; a very minor and natural elaboration of the standard account suffices to save both functionalist theories and computational accounts generally. (shrink)

Kripke presented one of the most inuential modal arguments against psycho-physical identities. His argument as exemplified by the identity of pain and its respective neural correlates will be analysed in detail. It shall be argued that his reasoning relies on an implausible conception of introspection implying an implausible conception of mental phenomena such as pain. His account does not consider possible interaction of pain and attention as well as the interaction of pain with other psychological factors. Theoretical and empirical (...) evidences for a diferent account of pain, which represent a challenge for Kripke's argument, will be discussed. (shrink)

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there (...) are important many-valued logics like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. (...) The proof is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. (shrink)

An introduction to Kripke’s semantics for propositional and quantified modal logic (with special reference to its historical development from the original 1959 version to the extended versions of 1963 and 1965) and to his theory of truth.

Bu metindeki amacım Kripke’nin kurgu çözümlemesinde özel adlar ve adımsılar arasındaki ilişkiyi ele almak. Kripke için özel adlar değişmez imleyicilerdir, yani tek bir varlığı/şeyi var olduğu tüm olanaklı dünyalarda biricik belirlerler. Adımsılar ise kurgusal söylemde ortaya çıkan kurgunun taslamasının bir parçasıdır; yani kurgu dünyadaki karakterlerin adlarıdır. Kripke’ye göre adımsılar sadece gerçek adları taklit eden fakat taklit ve benzerlik ilişkisinden öte bir ilişkileri olmayan, adlardan kategorik olarak farklı şeylerdir. Fakat Kripke için adlar ve adımsılar kategorik olarak farklı (...) olsalar da bu iki dilsel birim birbirlerini belirler gibi gözükür. Yani “Sherlock Holmes” özel adı, “Sherlock Holmes” özel adımsısı ile eşseslidir fakat bunun gerekçesi yeterince açık değildir. Bu açık olmama durumu kurgusal karakter adlandırma önermelerinin adlandırıcı açısından a priori ve olumsal mı olduğu yoksa a posteriori ve zorunlu mu olduğu sorusuyla ilişkilidir. Böylelikle bu belirleme ilişkisi ya zorunlu ya da olumsal bir ilişkidir. Ben bu belirleme ilişkisinin olumsal olduğunu savunacağım. Fakat bu belirleme ilişkisi olumsal olsa da ad ve adımsı arasında eşseslilik açısından sıkı bir ilişki olmaya devam eder. Ben bu sıkı ilişkinin genellikle kendiliğinden bir ilişki olduğunu, kurgu karakterin önce adı olabileceği gibi ilişkilendiği adımsısı da olabileceğini ve bu ayrım yeterince düşünülmediği için genellikle ad ve adımsının eşseslilik açısından çakıştığını savunacağım. Fakat ilişkilendiği adımsı ve özel adı eşsesli olmayan karakterler de olabileceğini ileri süreceğim. Son olarak ise bu dediklerimizden adımsıların geçtiği betimlemeler üretebileceğimizi ve bunlar yoluyla da kurgu varlıklara değişen imleyiciler olarak gönderimde bulunabileceğimizi savunacağım. (shrink)

A well-known polymodal provability logic inlMMLBox due to Japaridze is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic. This system plays an important role in some recent applications of provability algebras in proof theory. However, an obstacle in the study of inlMMLBox is that it is incomplete w.r.t. any class of Kripke frames. In this paper we provide a complete Kripke semantics for inlMMLBox . First, we isolate a certain (...) subsystem inlMMLBox of inlMMLBox that is sound and complete w.r.t. a nice class of finite frames. Second, appropriate models for inlMMLBox are defined as the limits of chains of finite expansions of models for inlMMLBox . The techniques involves unions of n -elementary chains and inverse limits of Kripke models. All the results are obtained by purely modal-logical methods formalizable in elementary arithmetic. (shrink)

In his 1982 book Wittgenstein On Rules and Private Language, Saul Kripke maintains that Wittgenstein´s rule following considerations land us with a skeptical argument about meaning. This essay contains a short exposition of Kripke´s argument. In addition, I hold, both on textual grounds and by an appeal to some select secondary literature, that Wittgenstein offered no such skeptical argument in the Philosophical Investigations . Although Wittgenstein certainly repudiates a view of meaning based on temporally located mental states, it (...) does not follow that there can be no meaning-grounding facts of other sorts. Although it is true that mental states, viewed atomistically, offer no sure foundation for meaning, I argue that it need not follow, pace Kripke, that no facts about an individual´s past mental life can ever make it clear that he meant ‘plus’ rather than ‘quus’ while performing any addition. For the individual´s past mental life is indeed relevant to meaning when considered in its unfolding in time. The essay further contains explorations on the very nature of the practice of following a rule and ends with a discussion of the solitary rule follower. (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)

This chapter introduces Kripke's work to advanced undergraduates, mainly focussing on his "A Puzzle About Belief" and "Wittgenstein on Rules and Private Language".

Saul Kripke’s much discussed Wittgenstein on Rules and Private Language has, I believe, been widely misinterpreted. The purpose of this note is to offer a correction. As it happens, on my reading of Kripke’s text Kripke’s Wittgenstein begins to look recognisably like Wittgenstein himself. But I shall not be concerned here with the question of whether Kripke’s Wittgenstein is Wittgenstein. My only aim is to correct the misinterpretation.

Kripke has argued that proper names, as rigid designators, cannot be equivalent in meaning to definite descriptions. in this paper, i argue that definite descriptions are sometimes used rigidly and that proper names are equivalent to definite descriptions used rigidly.