Gottlob Frege is not only the father of contemporary mathematical logic and the philosophy of logic, but — as advocated by others, especially M. Dummett – he is, above all, the founder of contemporary research in logic and the philosophy of language. The categories and concepts introduced by Frege were assimilated by philosophers studying language and inspired further detailed analyses. It seems impossible to overestimate the role of Frege’s theory, despite the fact that his objectives — setting a logical basis (...) for mathematics, undoing the psychologizing of logic, building a clear and accurate language for logic and science — differ from the ones set out by contemporary explorers of language. (shrink)

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing (...) semantic distinctions between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

In his Grundgesetze, §32, Frege launched the idea that the meaning of a sentence is given by its truth condition, or, in his particular version, the condition under which it will be a name of the True. This, indeed, was only one of the many roles in which truth has to serve within the Fregean system. In particular, truth is an absolute notion in the sense that bivalence holds: every Gedanke is either true or false, in complete independence of (...) any conative activity, whether by God or man. Thus various epistemological notions, such as the correctness of an assertion made, or judgement passed, are reducible to this absolute notion of truth: an assertion made through the utterance of a declarative sentence is correct when the proposition expressed by the sentence in question is true. Given this absolute status of truth it is not surprising that Frege is of the opinion that truth is a sui generis notion which has to be left unanalyzed and, indeed, which is indefinable. (shrink)

I develop a problem for the Fregean Reference Shift analysis of that-clause reference. The problem is discussed by Stephen Schiffer in his recent book The Things We Mean (2003). Either the defender of the Fregean Reference Shift analysis must count certain counterintuitive inferences as valid, or else he must reject a plausible Exportation rule. I consider several responses. I find that the best response relies on a Kaplan-inspired analysis of quantified belief reports. But I argue that this response (...) faces some serious problems. (shrink)

We study the non-Fregean propositional logic with propositional quantifiers, denoted by $\mathsf{SCI}_{\mathsf{Q}}$. We prove that $\mathsf{SCI}_{\mathsf{Q}}$ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in $\mathsf{SCI}_{\mathsf{Q}}$ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of $\mathsf{SCI}_{\mathsf{Q}}$-sentences. Finally, we present a translation of $\mathsf{SCI}_{\mathsf{Q}}$ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties (...) of $\mathsf{SCI}_{\mathsf{Q}}$. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on (...) truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further and ask about the meaning of a proof as a whole? In this paper we address this question and lay out a framework to distinguish sense and denotation of proofs. Two questions are central here. First of all, if we (...) have two different derivations, does this always lead to a difference, firstly, in sense, and secondly, in denotation? The other question is about the relation between different kinds of proof systems with respect to this distinction. Do the different forms of representing a proof necessarily correspond to a difference in how the inferential steps are given? In our framework it will be possible to identify denotation as well as sense of proofs not only within one proof system but also between different kinds of proof systems. Thus, we give an account to distinguish a mere syntactic divergence from a divergence in meaning and a divergence in meaning from a divergence of proof objects analogous to Frege’s distinction for singular terms and sentences. (shrink)

Frege's account of opacity is based on two attractive ideas: every meaningful expression has a sense (Sinn) that determines the expression's semantic value (Bedeutung); and the semantic value of a‘that’‐clause is the thought expressed by its embedded sentence. Considerations of compositionality led Frege to a more problematic view: inside ‘that’‐clauses, an expression does not have its customary Bedeutung. But contrary to initial appearances, compositionality does not entail a familiar substitutivity principle. And Fregeans can exploit this point in a way that (...) lets them reject Bedeutung‐shifting. (shrink)

The puzzle of material constitution can be expressed in at least two ways. First, how can the constituting object and the constituted object, which are materially and spatially coincident, be regarded as different objects? Second, how can the constituting object and the constituted object, which are qualitatively distinct, be regarded as identical objects? Monists argue that the constituting and constituted objects are identical since they are materially and spatially coincident and the property differences between then are simply differences in description, (...) perspective or context. In contrast, pluralists argue that the constituting and constituted objects are not identical even if they are materially and spatially coincident since they are qualitatively distinct. This paper proposes a solution to the puzzle of material constitution called ‘Fregean Monism’ (FM), and shows that it can better account for the property differences between the constituting and constituted objects without the need to regard them as two distinct objects. On the FM view, the puzzle of material constitution is partly a semantic puzzle and partly a metaphysical puzzle, and shows how a solution to the semantic part of the puzzle, based on the Fregean distinction between sense and reference, can yield a satisfactory solution to the metaphysical part of the puzzle. The key idea is that while the reference of a term picks out both the referent object and referent properties, the sense of the term determine which referent properties are picked out. (shrink)

of my axiomatic theory of abstract objects.¹ The theory asserts the ex- istence not only of ordinary properties, relations, and propositions, but also of abstract individuals and abstract properties and relations. The.

This note sketches how a theory of procedural semantics may offer a solution to the problem of the unity of the proposition. The current revival of the notion of structured meaning has made the problem of propositional unity pressing. The problem, stated in its simplest form, is how an individual a and a property F combine into the proposition P that a is an F; i.e. how two different kinds of objects combine into a third kind of object capable (...) of having properties that neither of its constituents could have. Constraints imposed on P include that P must be capable of being true/false, being known/believed to be true/false, and occurring as argument of propositional connectives, such as entailment. (shrink)

The paper concerns Grzegorczyk’s non-Fregean logics that are intended to be a formal representation of the equimeaning relation defined on descriptions. We argue that the main Grzegorczyk logics discussed in the literature are too strong and we propose a new logical system, \, which satisfies Grzegorczyk’s fundamental requirements. We present a sound and complete semantics for \ and we prove that it is decidable. Finally, we show that many non-classical logics are extensions of \, which makes it a (...) generic non-Fregean logic. (shrink)

This paper asks which free logic a Fregean should adopt. It examines options within the tradition including Carnap’s (1956) chosen object theory, Lehmann’s (1994, 2002) strict Fregean free logic, Woodruff’s (1970) strong table about Boolean operators and Bencivenga’s (1986, 1991) supervaluational semantics. It argues for a neutral free logic in view of its proximity towards explaining natural languages. However, disagreeing with Lehmann, it claims a Fregean should adopt the strong table based on Frege’s discussion on generality. (...) Supervaluation uses strong table and aims to give it a semantic justification. However, supervaluation is in turn justified by convention or mental experiments, which Lehmann argues as inadequate. The paper proposes a new justification of supervaluation based on sense and two-dimensional semantics. The resulting model, coined Supervaluational Neutral Free Logic (SNFL), resolves many conflicts between Lehmann and Bencivenga while staying close with Frege’s discussions about non-denotation. It also provides new insights into the relations among truth, logical truth, and supervaluated truth (or supertruth, for short). (shrink)

n this paper I take up these proposals, giving reasons to incorporate semantic features associated with proper names over and above their referent in any (genuine) semantic account of natural language. I also argue that my proposal is compatible with the main points made in Naming and Necessity, by contending that not Millianism but externalism was the claim most forcefully argued for in that impressive piece of work.

The truth of a statement depends on the world in two ways: what the statement says is true if the world is as the statement says it is; on the other hand, what the expressions in the statement mean depends on what the world is like (for instance, on what conventions are in place). Each of these two kinds of dependence of truth on the world corresponds to one of the dimensions on the two-dimensional semantic framework, developed in the 1970’ (...) in the work of Evans, Kaplan, Kripke and Stalnaker. The introduction provides a systematic overview of the framework, the ideas of its earlier originators, recent developments and criticism. Finally, it gives a brief overview over the contributions to the volume. (shrink)

As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called Russell-Myhill paradox that (...) threatens simple Russellian type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

The aim of this paper is (i) to defend Frege's view that the referents of predicates are certain kinds of functions, or "concepts", i.e. incomplete entities, and not their extensions (i.e. sets of objects described by those predicates); and (ii) to justify, by a natural augmentation of Frege's semantic theory with modal ingredients, Frege's position that the sameness between concepts, or property-sharing, turns only on the sameness of extensions. Several problems with the doctrine that a predicate's extension is its referent (...) are presented, including the regress argument and an argument from the modern philosophy of language related to natural kind terms. In this connection, it is also pointed out that all referential expressions are in a sense rigid. (shrink)

As Quine observed, the following sentence has a reading which, if true, would be of special interest to the authorities: Ralph believes that someone is a spy. This is the reading where the quantifier is naturally understood as taking wide scope relative to the attitude verb and as binding a variable within the scope of the attitude verb. This essay is interested in addressing the question what the semantic analysis of this kind of reading should look like from a (...) class='Hi'>Fregean perspective—a perspective according to which attitude states are generally relations to structured Fregean thoughts composed of senses. The Fregean view faces a challenge of compositionality here. This essay describes the challenge and offers a response on the Fregean's behalf. (shrink)

In this paper I argue indirectly for Frege's semantics, in particular for his conception of propositions, by reviewing some difficulties faced by one of the main contemporary alternative approaches, i.e., the direct reference theory. While Frege's semantics can yield an explanation of cognitive value and belief-preservation, the alternative approach seems to run into trouble here. I shall also briefly consider the question of whether epistemic issues should be of any concern for semantics, i.e., whether the feature mentioned (...) above should really be regarded as an advantage of Frege's theory. (shrink)

This paper is partly exegetical, partly systematic. I argue that Frege's account of what he called “colouring” contains some important insights on how communication is related to mental states such as mental images or emotions. I also show that the Fregean perspective is supported by current research in psycholinguistics and that a full understanding of some linguistic phenomena that scholars have accounted for in terms of either semantics or pragmatics need involve psycholinguistic elements.

In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...) problem''.In this paper, Frege's treatment of the problem in Grundlagen is critically assessed. In particular, I try to shed new light on it by paying special attention to the framework of his logicism in which it appears embedded. I argue, among other things, that the Caesar problem, which is supposed to stem from Frege's tentative inductive definition of the natural numbers, is only spurious, not genuine; that the genuine Caesar problem deriving from HP is a purely semantic one and that the prospects of removing it by explicitly defining cardinal numbers as objects which are not classes are presumably poor for Frege. I conclude by rejecting two closely connected theses concerning Caesar put forward by Richard Heck: (i) that Frege could not abandon Axiom V because he could not solve the Julius Caesar problem without it; (ii) that (by his own lights) his logicist programme in Grundgesetze der Arithmetik failed because he could not overcome that problem. (shrink)

This paper provides a semantics for propositional attitude ascriptions. (In this respect, the title of the paper is quite well chosen.).

There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic (...) SCI. Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

One of the most prominent myths in analytic philosophy is the so- called “Fregean Axiom”, according to which the reference of a sentence is a truth value. In contrast to this referential semantics, a use-based formal semantics will be constructed in which the logical value of a sentence is not its putative referent but the information it conveys. Let us call by “Question Answer Semantics” (thereafter: QAS) the corresponding formal semantics: a non-Fregean many-valued logic, (...) where the meaning of any sentence is an ordered n-tupled of yes-no answers to corresponding questions. A sample of philosophical problems will be approached in order to justify the relevance of QAS. These include: (1) illocutionary forces, and the logical analysis of speech-acts; (2) the variety of logical negations, and their characterization in terms of restricted ranges of logical values; (3) change in meaning, and the use of dynamic oppositions for belief sets. (shrink)

A non-Fregean framework aims to provide a formal tool for reasoning about semantic denotations of sentences and their interactions. Extending a logic to its non-Fregean version involves introducing a new connective $$\equiv $$ ≡ that allows to separate denotations of sentences from their logical values. Intuitively, $$\equiv $$ ≡ combines two sentences $$\varphi $$ φ and $$\psi $$ ψ into a true one whenever $$\varphi $$ φ and $$\psi $$ ψ have the same semantic correlates, describe the same (...) situations, or have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk’s logics (Logic of Descriptions $$\textsf{LD}$$ LD, Logic of Descriptions with Suszko’s Axioms $$\textsf{LDS}$$ LDS, Logic of Equimeaning $$\textsf{LDE}$$ LDE ) with non-Fregean versions of certain well-known paraconsistent logics (Jaśkowski’s Discussive Logic $$\textsf{D}_2$$ D 2, Logic of Paradox $$\textsf{LP}$$ LP, Logics of Formal Inconsistency $$\textsf{LFI}{1}$$ LFI 1 and $$\textsf{LFI}{2}$$ LFI 2 ). We prove that Grzegorczyk’s logics are either weaker than or incomparable to non-Fregean extensions of $$\textsf{LP}$$ LP, $$\textsf{LFI}{1}$$ LFI 1, $$\textsf{LFI}{2}$$ LFI 2. Furthermore, we show that non-Fregean extensions of $$\textsf{LP}$$ LP, $$\textsf{LFI}{1}$$ LFI 1, $$\textsf{LFI}{2}$$ LFI 2, and $$\textsf{D}_2$$ D 2 are more expressive than their original counterparts. Our results highlight that the non-Fregean connective $$\equiv $$ ≡ can serve as a tool for expressing various properties of the ontology underlying the logics under consideration. (shrink)

According to Frege a proposition—or, in his terms, a thought—is an abstract structured entity constituted by senses which satisfies, at least, the three following properties: it can be semantically assessed as true or as false, it is the object of so called propositional attitudes and it can be grasped. What Frege meant by 'grasping' is the peculiar way in which we can have epistemic access to propositions. The possibility for propositions to be grasped is put by Frege as a warrant (...) for their existence: to challenge their graspability would amount to jeopardise their ontological reality. But is it true, as Frege uncritically maintained, that the "graspability requirement" is satisfied as far as propositions (as he conceived them) are concerned? This is the topic of the present work. A negative answer to the above mentioned question has been given in recent time by the representatives of what has come to be labelled the "cognitive turn" in analytical philosophy. People such as Fodor and Johnson-Laird patently denied the possibility for propositions, conceived à la Frege, to be accessed by the grasping relation. What grounds their position is, to put it roughly, the following train of thought: in order for something to be the target of the grasping relation it must enter the mind. Nothing which is different from a mental entity can enter the mind. Therefore, what can be grasped must be mental. The upshot of this move implies, among other things, the rejection of that radical anti-psychologism which was characteristic of the forefathers of the analytical tradition. In our work we shall try to resist their conclusion by showing that it is not necessary to zero the distinction between propositions and mental entities in order to provide an adequate account of the grasping relation. What one has to give up, instead, is only Frege's late Platonism of the "third realm" which, in our view, is a wholly unnecessary and dispensable accretion of his picture. For, as we shall show, if Platonism is in place it is difficult to provide an account of the grasping relation which makes no use of the "representationalist hypothesis" — i.e. of the hypothesis that ideas mediate our access to whatever can be given to us. But representationalism, once in place, makes the theoretical role of the notion of sense dispensable or purely additional. (shrink)

In a review of Frege's Puzzle1, Graeme Forbes makes the claim that Salmon's account of belief might be seen, under certain conditions, as a mere notational variant of a neo-Fregean theory; and thus that such an account might be reduced to a neo-Fregean one simply by rewriting it in terms of Fregean terminology. With a view to supporting his claim, Forbes offers an outline of an account of belief which, according to him, would satisfy the following conditions: (...) (i) it could be directly obtained from Salmon's own analysis by means of a certain set of substitutions, which presumably would not affect the essential features of Salmon's view; (ii) it could naturally be described as Fregean, in the sense that it would preserve, (at least) the spirit of Frege's doctrines, especially his fundamental intuitions about belief. Of course, the upshot of Forbes's argument is that Salmon's theory would not, at bottom, constitute a genuine alternative to a Fregean semantics for belief ascriptions. In this paper I argue to the effect that Forbes's claim is not in general sound. It seems to me that the sort of indirect argument used by Forbes - that of trying to undermine Salmon's theory by showing that it is just a version of a neo-Fregean account - does not provide someone working within a Fregean framework with an adequate strategy to counter Salmon's neo-Russellian views. It would perhaps be better to concentrate a Fregean attack on certain apparently dubious and highly controversial theses and results which are constitutive of Salmon's view, e.g. the counterintuitive character of a substantial set of consequences which follow from his theory of belief, as well as the associated revisionist stand he is forced to take towards our current patterns of speaking about belief. (shrink)

The foregoing considerations have shown that on the Fregean model, no descriptive rendition of the meaning of a word, and no feature of the subject's psychological state, will be sufficient to answer the question of how reference takes place. Reference is determined by an independent semantical object, and the mind is limited by its perceptual access to this external semantical realm. The psychological and epistemic states of the language user will be causally influenced by this perceptual contact, and such (...) causal influences will enable the subject to evince the appropriate behavioral signs of comprehension. But the internal effects produced by the perception of meaning are not in principle sufficient to individuate their semantical causes, and hence some of the prominent criticisms of the traditional theory are simply not applicable to Frege's system. (shrink)

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom Kiφ → φ and some minimal conditions concerning common knowledge in a group. Knowledge (...) is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}. Every specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}-logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.

We present a new logic -based approach to the reasoning about knowledge which is independent of possible worlds semantics.? k is a non- Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i??? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical (...) omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc, can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between? k and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self - referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in? k. Every specific? k - logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

Quine’s arguments in the final two sections of “Two Dogmas of Empiricism” bring semantic and epistemic concerns into spectacular collision. Many have thought that the arguments succeed in irreparably smashing a conception of a distinctively analytic and a priori philosophy to pieces. In Constructing the World, David Chalmers argues that much of this distinctively analytical and a priori conception of philosophy can be reconstructed, with Quine’s criticisms leaving little lasting damage. I agree with Chalmers that Quine’s arguments do not have (...) the lasting damage some take them to have. However, I do not think that Chalmers has succeeded in explaining why. The core of Chalmers’s error lies in the rational dispositionalism that forms the metasemantics of his Carnapian intensionalism. Responding to Quine requires recognizing conceptions of both concepts and epistemic normativity that go beyond the opposition between irrationality and conceptual change that Chalmers brings to bear on Quine. I explain this expanded conception of concepts and epistemic normativity in terms of another fundamental aim of Constructing the World, namely that of providing an account of Fregean sense, or more generally of defending what Chalmers calls epistemological semantics. (shrink)

One of the most pressing issues in contemporary semantics is whether propositions are structured entities that should be individuated in terms of their components or, contrarily, they lack structure and should be individuated in terms of their inferential relations. Another one is whether propositions should always contain all the information that is needed to deem them true or false—whether they should always be Fregean propositions. The latter debate might seem to presuppose a certain position in the former. However, (...) it is the first aim of this paper to argue that the two debates are orthogonal. Moreover, we will use Frege’s thoughts as an example of what we would contemporarily call ‘propositions’ that, though trivially Fregean, lack structure. Since it is not uncontroversial that Frege’s thoughts are unstructured, it is the second aim of this paper to show that it follows from Frege’s writings that they are. (shrink)

The nature of reference, or the relation of a word to the object to which it refers, has been perhaps the dominant concern of twentieth-century analytic philosophy. Extremely influential arguments by Gottlob Frege around the turn of the century convinced the large majority of philosophers that the meaning of a word must be distinguished from its referent, the former only providing some kind of direction for reaching the latter. In the last twenty years, this Fregean orthodoxy has been vigorously (...) challenged by those who argue that certain important kinds of words, at least, refer directly without need of an intermediate meaning or sense. The essays in this volume record how a long-term study of Frege has persuaded the author that Frege's pivotal distinction between sense and reference, and his attendant philosophical views about language and thought, are unsatisfactory. Frege's perspective, he argues, imposes a distinctive way of thinking about semantics, specifically about the centrality of cognitive significance puzzles for semantics. Freed from Frege's perspective, we will no longer find it natural to think about semantics in this way. (shrink)

During the last twenty-five years Fred Sommers has developed a series of inter-related theories of language structure, ontological structure, logical syntax, and truth. Each theory has naturally contained valuable suggestions concerning semantic issues. But Sommers has not yet offered a specifically semantic theory. I attempt here to fill that gap by sketching a theory of semantics based upon his logical theses. The theory holds that terms, as used in statement making sentences, have both denotation and signification. Terms denote objects (...) and signify properties. Terms, when quantified, refer to some or all of their denotations, and, when qualified, characterize the subjects to which they are predicated as having or lacking the properties they signify. The semantic, syntactic, and ontological theses presented in this theory are contrasted with those found in classical, scholastic, Leibnizian, Fregean, and Quinean theories. (shrink)

During the last twenty-five years Fred Sommers has developed a series of inter-related theories of language structure, ontological structure, logical syntax, and truth. Each theory has naturally contained valuable suggestions concerning semantic issues. But Sommers has not yet offered a specifically semantic theory. I attempt here to fill that gap by sketching a theory of semantics based upon his logical theses. The theory holds that terms, as used in statement making sentences, have both denotation and signification. Terms denote objects (...) and signify properties. Terms, when quantified, refer to some or all of their denotations, and, when qualified, characterize the subjects to which they are predicated as having or lacking the properties they signify. The semantic, syntactic, and ontological theses presented in this theory are contrasted with those found in classical, scholastic, Leibnizian, Fregean, and Quinean theories. (shrink)

I outline a neo-Fregean strategy in the debate on the existence of possible worlds. The criterion of identity and the criterion of application are formulated. Special attention is paid to the fact that speakers do not possess proper names for worlds. A broadly Quinean solution is proposed in response to this difficulty.

We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the (...) quantifier-free language by the new connective < that expresses reference between statements and yields a finer characterization of intensional models. Our results in the intuitionistic setting lead to a clear distinction between the notion of denotation of a sentence and the here-proposed notion of extension of a sentence (both concepts are equivalent in the classical context). We generalize the Fregean Axiom to an intuitionistic version not valid in $\in_I$. A main result of the paper is the development of several model constructions. We construct intensional models and present a method for the construction of standard models which contain specific (self-)referential propositions. (shrink)