Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models (...) which satisfy them. It turns out that the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics. (shrink)

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system (...) QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

In his influential Naming and Necessity lectures, Saul Kripke made new sense of modal statements: “Kant might have been a bachelor”, “Königsberg is necessarily identical with Kaliningrad”. Many took the notions he introduced-metaphysical necessity and rigid designation -- to herald new metaphysical issues and have important consequences. In fact, the Kripkean insight is at bottom semantic, rather than metaphysical: it is part of how proper names work that they purport to refer to individuals to whom modal properties can be (...) ascribed. We can see this by reflecting on analytic truths that ground modal claims like the two examples above. (shrink)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such (...) points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements (...) about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

Quantum mechanics admits a “linguistic interpretation” if one equates preliminary any quantum state of some whether quantum entity or word, i.e. a wave function interpret-able as an element of the separable complex Hilbert space. All possible Feynman pathways can link to each other any two semantic units such as words or term in any theory. Then, the causal reasoning would correspond to the case of classical mechanics (a single trajectory, in which any next point is causally conditioned), and the probabilistic (...) reasoning, to the case of quantum mechanics (many Feynman trajectories). Frame semantics turns out to be the natural counterpart of that linguistic interpretation of quantum mechanics. (shrink)

I argue that Kripke’s construal of the distinction between speaker’s reference and semantic reference, in ‘Speaker’s reference and semantic reference’ (Kripke in Midwest Stud Philos 2:255–276, 1977), in conjunction with an intuitive view of the nature of conventions, implies a theory of semantic reference that is distinct from his causal theory. On this theory, semantic reference is conventionalized speaker’s reference. The argument concerning Kripke has two general implications. First, any theory that features a notion of speaker’s reference (...) will have great difficulty in avoiding the view that semantic reference is conventionalized speaker’s reference. Second, theories that deny that there is a viable notion of speaker’s reference, and thereby deny that semantic reference is conventionalized speaker’s reference, will face an uphill battle in meeting certain general constraints originating in the theory of conventions. (shrink)

Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite (...) model property. The method of axiomatization hinges upon the fact that a "difference" operator is definable in hyperboolean algebras, and makes use of additional non-Hilbert-style rules. Finally, we discuss a number of open questions and directions for further research. (shrink)

Book synopsis: New work on a hot topic by an outstanding team of authors At the intersection of several central areas of philosophy It is the linguistic job of singular terms to pick out the objects that we think or talk about. But what about singular terms that seem to fail to designate anything, because the objects they refer to don't exist? We can employ these terms in meaningful thought and talk, which suggests that they are succeeding in fulfilling their (...) representational task. A team of leading experts presents new essays on the much-debated problem of empty reference and thought. In the 1960s and 1970s Keith Donnellan, David Kaplan, Saul Kripke and Hilary Putnam initiated a revolution in the then standard conception of reference—a concept at the core of philosophical inquiry. The repercussions of the revolution, particularly felt in metaphysics and epistemology, were soon refined by other influential writers such as Tyler Burge, Gareth Evans, and John Perry. They argued that some linguistic and mental representations have contents individuated by what they are about—by ordinary referents of expressions such as proper names, indexicals, definite descriptions and common nouns, i.e. by planets, people or natural kinds. The view was at odds with a central philosophical presumption at that time: that cognitive and linguistic access to objective reality is indirect and accidental, mediated by general descriptive characterizations, the only constitutive semantic feature of the expressions; hence its ontological and epistemological repercussions. A turning-point in the debate about how linguistic and mental representation reach external contents concerned the nature of empty mental and linguistic representations, framed by means of the very same expressions crucially invoked in the Donnellan-Kaplan-Kripke-Putnam arguments. The papers in this volume address different aspects of reference and thought about the non-existent. (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)

In his article Evgeny Borisov offers an original solution to Kripke’s sceptical problem of meaning. Its conceptual core is the point of view of the participant of speech acts. He believes that first-person statements of speech act participants like “I know for certain that the expression ‘e’ is used by me in the meaning of m” cannot carry any epistemic fallacies. As a criticism, I propose to point out that non-factual Cartesian semantics have serious epistemic flaws that make (...) it vulnerable to sceptical attacks and accusations of petitio principii. (shrink)

Recently, two new portrayals of Kripke’s Wittgenstein have emerged. Both understand KW as targeting the Tractarian picture of semantic fact as a speaker’s mental representation of the truth-conditions of the sentences he uses. According to the factualist interpretation, KW holds that meaning ascriptions are legitimate descriptions because semantic facts are not entities that explain people’s linguistic behavior. The second, Alex Miller’s non-standard non-factualist interpretation, sees KW as claiming that because no fact can explain our linguistic behavior, meaning ascriptions express (...) a speaker’s attitudes towards his interlocutors rather than stating what they mean. This paper advances the minimal factualist interpretation by elaborating two points: that Miller’s reading of the skeptical argument contradicts semantic non-factualism; and that KW’s view of meaning is based on a primitivist rendition of the skeptic’s insight that nothing justifies our use of language, which allows him to assert that semantic facts exist simply because we ordinarily say so. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees (...) are sound and complete for the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (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.

The paper discusses Saul Kripke's Normativity Argument against semantic dispositionalism: it criticizes the orthodox interpretation of the argument, defends an alternative reading and argues that, contrary to what Kripke himself seems to have been thinking, the real point of the Normativity Argument is not that meaning is normative. According to the orthodox interpretation, the argument can be summarized as follows: (1) it is constitutive of the concept of meaning that its instances imply an ought, but (2) it is (...) not constitutive of the concept of a disposition that dispositions imply an ought, hence (3) no dispositional analysis of meaning can work. According to my alternative reading, the point of the argument is another one, namely that while (1) dispositionalism is committed to the thesis that speakers have non-inferential knowledge of their unmanifested linguistic dispositions, (2) speakers, as a matter of fact, do not have such a knowledge. A point that is in principle independent from the issue of the normativity of meaning. (shrink)

My paper examines the popular idea, defended by Kripke, that meaning is an essentially normative notion. I consider four common versions of this idea and suggest that none of them can be supported, either because the alleged normativity has nothing to do with normativity or because it cannot plausibly be said that meaning is normative in the sense suggested. I argue that contrary to received opinion, we don’t need normativity to secure the possibility of meaning. I conclude by considering (...) the repercussions of rejecting semantic normativity on three central issues: justification, communication, and naturalism. (shrink)

Kripke’s main argument against descriptivism is rooted in a category error that confuses statements about the world with statements about models of the world. It is only because of the ambiguity introduced by the fact that a single sentence can frame two different propositions, one necessary and the other a posteriori, that one reaches the mistaken conclusion that there can be necessary a posteriori truths. This ambiguity from language was carried over into modal logic by Kripke. However, (...) we must consider the two different propositions (1) and (2) separately. Doing so reveals that a given proposition is either necessary and a priori or contingent and a posteriori. It cannot be both. (shrink)

According to the sceptic Saul Kripke envisages in his celebrated book on Wittgenstein on rules and private language, there are no facts about an individual that determine what she means by any given expression. If there are no such facts, the question then is, what justifies the claim that she does use expressions meaningfully? Kripke’s answer, in a nutshell, is that she by and large uses her expressions in conformity with the linguistic standards of the community she belongs (...) to. While Kripke’s sceptical problem has gripped philosophers for over three decades, few, if any, have been satisfied by his proposed solution, and many have struggled to come up with one of their own. The purpose of this paper is to show that a more satisfactory answer to Kripke’s challenge can be developed on the basis of Donald Davidson’s writings on triangulation, the idea of two individuals interacting simultaneously with each other and the world they share. It follows from the triangulation argument that the facts that can be regarded as determining meaning are irreducible. Yet, contra Kripke, they are not mysterious, for the argument does spell out what is needed for an individual’s expressions to be meaningful. (shrink)

The semantic issues that Saul Kripke addressed in Naming and Necessity overlap substantially with those that were addressed by Michel Foucault in “What Is an Author?”. The present essay examines their area of overlap, with a view to showing that each of these works affords a perspective on the other, from which facets that are usually obscure can be brought into view. It shows that Foucault needs to take some assumptions from Kripke’s theory of naming in order to (...) secure one of his arguments for treating authorial names as special. It then shows that, once it has been placed on these Kripkean foundations, Foucault’s position avoids the metaphysically peculiar commitments that are sometimes thought to be essential... (shrink)

In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a solution to (...) the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

Frege introduced the distinction between sense and reference to account for the information conveyed by identity statements. We can put the point like this: if the meaning of a term is exhausted by what it stands for, then how can 'a =a' and 'a =b' differ in meaning? Yet it seems they do, for someone who understands all the terms involved would not necessarily judge that a =b even though they judged that a =a. It seems that 'a =b' just (...) says something more than the trivial ’a = a' - it seems to contain more information, in some sense of 'information'. So either we have to add something to explain this extra information, or sever the very plausible links between meaning and understanding. This is what some writers have called 'Frege's Puzzle' It is undeniable that there is a phenomenon here to be explained, and it was Frege's insight to see the need for its explanation. But how should we explain it? Frege's idea was to add another semantic notion - Sinn, or Sense -— to account for the information conveyed. Sense is part of the meaning of an expression: it is the 'cognitive value' of the expression, or that ’wherein the mode of presentation is contained' (Frege 1957 p.57). Sense has a role to play in systematically determining the meanings of complex expressions, and ultimately in fixing the contents of judgements. It is the senses of whole sentences — Gedanken or Thoughts - which are candidates for truth and falsehood, and which are thus the objects of our propositional attitudes. Of course, introducing the notion of sense in this way does not, by itself, tell us what sense is. It only imposes a condition on a theory of meaning (and ultimately) belief: that it must account for distinctions in cognitive value or 'mode of presentation' (this is not a trivial thesis —- some philosophers today would deny that an explanation of Frege's Puzzle must occur within semantics or the theory of meaning: see Salmon 1985). In this paper I want to explore one way of meeting this condition for the theory of names in natural language, by examining Kripke's well-known 'Puzzle about Belief' (Kripke 1979).. (shrink)

I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or obvious (...) revenge. (shrink)

Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People can fail to infer as required due to lack of logical acumen, intoxication, confusion, deviant theories, neural malfunctioning, and so on. I present a theory stating possession conditions of concepts that are counterfactuals, rather than (...) disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by suitably undemanding requirements (unlike that of giving the sum of any two numbers) and by setting the following two preconditions upon someone’s making the inference: that she considers the inference and has no motivating reason against it. The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during the relevant interval. I argue that this accommodates some important intuitions about concept possession, in particular, the intuition that concept possession is vague along a certain dimension. (shrink)

Semantic originalism is a theory of constitutional meaning that aims to disentangle the semantic, legal, and normative strands of debates in constitutional theory about the role of original meaning in constitutional interpretation and construction. This theory affirms four theses: (1) the fixation thesis, (2) the clause meaning thesis, (3) the contribution thesis, and (4) the fidelity thesis. -/- The fixation thesis claims that the semantic content of each constitutional provision is fixed at the time the provision is framed and ratified: (...) subsequent changes in linguistic practice cannot change the semantic content of an utterance. -/- The clause meaning thesis claims that the semantic content is given by the conventional semantic meaning (or original public meaning) of the text with four modifications. The first modification is provided by the publicly available context of constitutional utterance: words and phrases that might be ambiguous in isolation can become clear in light of those circumstances of framing and ratification that could be expected to known to interpreters of the Constitution across time. The second modification is provided by the idea of the division of linguistic labor: some constitutional provisions, such as the natural born citizen clause may be terms of art, the meaning of which are fixed by the usages of experts. The third modification is provided by the idea of constitutional implicature: the constitution may mean things it does not explicitly say. The fourth modification is provided by the idea of constitutional stipulations: the constitution brings into being new terms such as House of Representatives and the meaning of these terms is stipulated by the Constitution itself. -/- The contribution thesis asserts that the semantic content of the Constitution contributes to the law: the most plausible version of the contribution thesis is modest, claiming that the semantic content of the Constitution provides rules of constitutional law, subject to various qualifications. Our constitutional practice provides strong evidence for the modest version of the contribution thesis. -/- The fidelity thesis asserts that we have good reasons to affirm fidelity to constitutional law: virtuous citizens and officials are disposed to act in accord with the Constitution; right acting citizens and officials obey the constitution in normal circumstances; constitutional conformity produces good consequences. Our public political culture affirms the great value of the rule of law. -/- We can summarize semantic originalism as a slogan: The original public meaning of the constitution is the law and for that reason it should be respected and obeyed. The slogan recapitulates each of the claims made by semantic originalism, but it is potentially misleading because it does not clearly distinguish between the semantic claims made by the fixation and clause meaning theses, the legal claim made by the contribution thesis, and the normative claim made by the fidelity thesis. -/- Part I introduces the four theses. Part II is entitled An Opinionated History of Constitutional Originalism, and it provides the context for all that follows. Part III is entitled Semantic Originalism: A Theory of Constitutional Meaning, and it lays out the case for original public meaning as the best nonnormative theory of constitutional content. Part IV is entitled The Normative Implications of Semantic Originalism, and it articulates a variety of normative arguments for originalism. Part V is entitled Conclusion: Semantic Originalism and Living Constitutionalism, and it explores the broad implications of semantic originalism for living constitutionalism and the future of constitutional theory. (shrink)

Kripke (1977) presents an argument designed to show that the considerations in Donnellan (1966) concerning attributive and referential uses of (definite) descriptions do not, by themselves, refute Russell’s (1905) unitary theory of description sentences (RTD), which takes (utterances of) them to express purely general, quantificational, propositions. Against Kripke, Marga Reimer (1998) argues that the two uses do indeed reflect a semantic ambiguity (an ambiguity at the level of literal truth conditions). She maintains a Russellian (quantificational) analysis of utterances (...) involving attributively used descriptions but attempts to defend the following two claims about utterances involving referentially used descriptions (referential utterances) (1998, p. 89). (shrink)

The Frame Problem is the problem of how one can design a machine to use information so as to behave competently, with respect to the kinds of tasks a genuinely intelligent agent can reliably, effectively perform. I will argue that the way the Frame Problem is standardly interpreted, and so the strategies considered for attempting to solve it, must be updated. We must replace overly simplistic and reductionist assumptions with more sophisticated and plausible ones. In particular, the standard (...) interpretation assumes that mental processes are identical to certain kinds of computational processes, and so solving the Frame Problem is a matter of finding a computational architecture that can effectively represent relations of semantic relevance. Instead, we must take seriously the possibility that the way in which intelligent agents use information is inherently different. Whereas intelligent agents are plausibly genuinely causally sensitive to semantic properties as such (to what they perceive, desire, believe intend, etc.), computational systems can only be causally sensitive to the formal features that represent these properties. Indeed, it is this very substitution of formal generalizations for genuinely semantic ones that is responsible for the way current AI systems are brittle, inflexible, and highly specialized. What we need is a more sophisticated way of investigating the relationship between computational information processing and genuinely semantic information use, so that these two senses of using information are not conflated, but instead the question of how they are related to one another can be studied directly. I apply the generative methodology I have developed elsewhere for cognitive science and AI research (Miracchi, 2017, 2019a) to show how the Frame Problem can be appropriately updated. (shrink)

Kripke (1977) views Donnellan's (1966) misdescription cases as cases where semantic reference and speaker's reference come apart. Such cases, however, are also cases where semantic reference conflicts with a distinct species of reference I call "public reference", i.e. the object that the cues publicly available at the time of utterance indicate is the speaker's referent of the utterance. This raises the question: do the misdescription cases trade on the distinction between semantic reference and speaker's reference, or the distinction between (...) semantic reference and public reference? I argue that Kripke's own construal in terms of semantic reference and speaker's reference is at best incomplete, and probably wrong. I also explain the general importance of the notion of 'public reference'. (shrink)

Studies of several languages, including Swahili [swa], suggest that realis (actual, realizable) and irrealis (unlikely, counterfactual) meanings vary along a scale (e.g., 0.0–1.0). T-values (True, False) and P-values (probability) account for this pattern. However, logic cannot describe or explain (a) epistemic stances toward beliefs, (b) deontic and dynamic stances toward states-of-being and actions, and (c) context-sensitivity in conditional interpretations. (a)–(b) are deictic properties (positions, distance) of ‘embodied’ Frames of Reference (FoRs)—space-time loci in which agents perceive and from which they contextually (...) act (Rohrer 2007a, b). I argue that the embodied FoR describes and explains (a)–(c) better than T-values and P-values alone. In this cognitive-functional-descriptive study, I represent these embodied FoRs using Unified Modeling Language (UML) mental spaces in analyzing Swahili conditional constructions to show how necessary, sufficient, and contributing conditions obtain on the embodied FoR networks level. (shrink)

Since Saul Kripke’s and Hilary Putnam’s groundbreaking work in the Seventies, the idea has emerged that natural kind terms are semantically special among common nouns. Stephen P. Schwartz, for example, has argued that an artifactual kind term like “pencil” functions very differently from a natural kind term like “tiger.” This, however, blatantly violates a principle that I call Semantic Uniformity. In this paper, I defend the principle. In particular, I outline a picture of how natural kind terms function based (...) on Kripke’s and Putnam’s considerations, and I use it to rebut Schwartz’s arguments, showing that if it works for natural kind terms, it can work for artifactual kind terms too, or at least that Schwartz did not provide good enough reasons to the contrary. (shrink)

Ever since Machery et al. first decided to test whether non-philosophers assign reference in accordance with the causal-historical account, the reference of proper names has been tested by means of setups modelled on Kripke’s Gödel and Jonah cases. Over the years, the use of these setups as a means to test theories of reference has attracted much criticism. However, previous follow-up studies have supposedly accounted for these criticisms, for the most part without changing the original outcome. We conducted experiments (...) suggesting that participants’ responses in these setups never tracked what they are supposed to track. In our study, we tested the setup itself by using analogues of different setups modelled on Kripke’s Gödel and Jonah cases. Instead of proper names, our analogues featured terms for which we have independent reason to believe that the causal-historical account is not true. The analogues elicited large proportions of supposed causal-historical responses. (shrink)

Joseph Almog pointed out that Kripkean causal chains not only exist for names, but for all linguistic items (Almog 1984: 482). Based on this, he argues that the role of such chains is the presemantic one of assigning a linguistic meaning to the use of a name (1984: 484). This view is consistent with any number of theories about what such a linguistic meaning could be, and hence with very different views about the semantic reference of names. He concludes that (...) the causal theory is ‘rather trivial’ (1984: 487). In this paper I argue that Almog is correct to hold that the causal theory is trivial, but, contra Almog, argue that the triviality of the existence of causal chains is not a matter of such chains having a presemantic role in assigning linguistic meanings to utterances. Instead, such triviality is due to the fact that the causal theory reflects no more than a truism about the epistemology of convention acquisition. (shrink)

Traditional descriptivism and Kripkean causalism are standardly interpreted as rival theories on a single topic. I argue that there is no such shared topic, i.e. that there is no question that they can be interpreted as giving rival answers to. The only way to make sense of the commitment to epistemic transparency that characterizes traditional descriptivism is to interpret Russell and Frege as proposing rival accounts of how to characterize a subject’s beliefs about what names refer to. My argument relies (...) on a development of the distinction between speaker’s reference and semantic reference. (shrink)

Functionalism is often used to identify mental states with physical states. A particularly powerful case is Lewis's analytical functionalism. Kripke's view seriously challenges any such identification. The dispute between Kripke and Lewis's views boils down to whether the term ‘pain’ is rigid or nonrigid. It is a strong intuition of ours that if it feels like pain it is pain, and vice versa, so that ‘pain’ should designate, with respect to every possible world, all and only states felt (...) as pain. Hence, in order to settle the dispute, we need to check which of the two – Kripke's use of ‘pain’ as rigid, or Lewis's use of ‘pain’ as nonrigid – better meets this intuition. I show that, despite crucial differences in both their semantic and metaphysical assumptions, surprisingly, both views meet this intuition equally well. Thus it appears that this question of rigidity cannot, in principle, be solved, and so, at least with respect to this particular dispute, the jury is still out on whether mental states are identical to physical states. (shrink)

This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of Allwein (...) and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. (shrink)

In this paper, I try to outline what I take to be Naming and Necessity’s fundamental legacy to my generation and those that follow, and the new perspectives it has opened up for twenty-first century philosophy. The discussion is subdivided into three sections, concerning respectively philosophy of language, metaphysics, and metaphilosophy. The general unifying theme is that Naming and Necessity is helping philosophy to recover a Golden Age, by freeing it from the strictures coming from the empiricist and Kantian traditions (...) and reconnecting it to the world and the objects that populate it. Because of this, in the concluding paragraph I tentatively suggest that Kripke’s philosophy may be seen as a sui generis form of naturalism. (shrink)

Traditional theists are, with few exceptions, global semantic realists about the interpretation of external world statement. Realism of this kind is treated by many as a shibboleth of traditional Christianity, a sine qua non of theological orthodoxy. Yet, this love affair between theists and semantic realism is a poor match. I suggest that everyone (theist or no) has compelling evidence drawn from everyday linguistic practice to reject a realist interpretation of most external world statements. But theists have further reason to (...) forswear this view, because those who insist on global semantic realism open themselves to the charge of hubris of a theologically inappropriate kind. If the arguments in this paper are sound, then neither God nor any of us have reason to apply a realist interpretation to all or even most statements about the external world. (shrink)

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception of (...) paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata. (shrink)

According to certain kinds of semantic dispositionalism, what an agent means by her words is grounded by her dispositions to complete simple tasks. This sort of position is often thought to avoid the finitude problem raised by Kripke against simpler forms of dispositionalism. The traditional objection is that, since words possess indefinite (or infinite) extensions, and our dispositions to use words are only finite, those dispositions prove inadequate to serve as ground for what we mean by our words. I (...) argue that, even if such positions (emphasizing simple tasks) avoid the traditional form of Kripke's charge, they still succumb to special cases of the finitude problem. Furthermore, I show how such positions can be augmented so as to avoid even these special cases. Doing so requires qualifying the dispositions of interest as those possessed by the abstracted version of an actual agent (in contrast to, say, an idealized version of the agent). In addition to avoiding the finitude problem in its various forms, the position that results provides new materials for appreciating the role that abstracting models can play for a dispositionalist theory of meaning. (shrink)

Dispositionalist theories of mental content have been attacked on the grounds that they are incompatible with semantic holism. In this paper, I resist important worries of this variety, raised by Paul Boghossian. I argue that his objections can be avoided by a conceptual role version of dispositionalism, where the multifarious relationships between mental contents are grounded on the relationships between their corresponding, grounding dispositions.

The influence of historical-causal theories of reference developed in the late sixties and early seventies by Donnellan, Kripke, Putnam and Devitt has been so strong that any semantic theory that has the consequence of assigning disjunctive representational content to the mental states of twins (e.g. [H2O or XYZ]) has been thereby taken to refute itself. Similarly, despite the strength of pre-theoretical intuitions that exact physical replicas like Davidson's Swampman have representational mental states, people have routinely denied that they have (...) any intentional/representational states. I want to focus on a particular brand of causal theory that is not historical, the so-called pure informational or nomic covariance theories, and examine how they propose to handle twin cases and replicas like Swampman. In particular, I will take up Fodor. (shrink)

Some years ago, Machery, Mallon, Nichols, and Stich reported the results of experiments that reveal, they claim, cross-cultural differences in speaker’s ‘intuitions’ about Kripke’s famous Gödel–Schmidt case. Several authors have suggested, however, that the question they asked their subjects is ambiguous between speaker’s reference and semantic reference. Machery and colleagues have since made a number of replies. It is argued here that these are ineffective. The larger lesson, however, concerns the role that first-order philosophy should, and more importantly should (...) not, play in the design of such experiments and in the evaluation of their results. (shrink)

We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...) appearance of critical reviews by members of the Boolean school. (shrink)

In this paper, I focus on the alleged distinction between speaker’s reference and semantic reference. I begin by discussing Saul Kripke’s notion of speaker’s reference and the theoretical roles it is supposed to play, arguing that they do not justify the claim that reference comes in two different sorts and highlighting that Kripke’s own definition makes the notion incompatible with the nowadays widely endorsed Gricean project, which aims at explaining semantic reference in terms of speaker’s reference. I then (...) examine an alternative account of speaker’s reference offered by Michael Devitt within his causal theory and express some doubts about its suitability for explaining proper name semantic reference. From all this, I conclude that there is at least some tension between Kripke’s chain of communication picture and the attempt to explain (Griceanly, so to say) semantic properties in terms of speakers’ mental states. (shrink)

Since the 1960s, Kripke has been a central figure in several fields related to mathematical logic, language philosophy, mathematical philosophy, metaphysics, epistemology and set theory. He had influential and original contributions to logic, especially modal logic, and analytical philosophy, with a semantics of modal logic involving possible worlds, now called Kripke semantics. In Naming and Necessity, Kripke proposed a causal theory of reference, according to which a name refers to an object by virtue of a (...) causal connection with the object, mediated by the communities of speakers. DOI: 10.13140/RG.2.2.26557.20964. (shrink)

In the present paper a new semantic framework for modelling the distinction between implicit and explicit belief is proposed and contrasted with the currently standard framework based on the idea that explicit belief can be construed as implicit belief accompanied by awareness. It is argued that within this new framework it is possible to get both a more intuitive interpretation of the aforementioned distinction and a straightforward solution to two critical problems to which the standard view is subjected. A system (...) of logic for belief is introduced and proved to be complete with respect to the class of all frames for implicit and explicit belief constructed in accord to the new view. (shrink)