This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

The aim of this paper is to discuss theories that attempt to single out the class of intentional states by appealing to factors that are supposedly criterial for intentional sentences. The papers starts with distinguishing two issues that arise when one thinks about intentional expressions: the Taxonomy Problem and the Fundamental Demarcation Problem. The former concerns the relation between the classes of distinct intentional verbs and distinct intentional states. The latter concerns the question about how to distinguish intentional states and (...) acts from the non-intentional ones. Next, the general desiderata for theories providing criteria for singling out the class of intentional sentences are introduced. Finally, distinct proposals for providing such criteria are analyzed. Author argues that neither is satisfactory. (shrink)

An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1. (shrink)

I defend a metalinguistic account of Mates's puzzle: sentences where synonymous expressions cannot be substituted salva veritate. If Andrea thinks that attorneys are different from lawyers, and she thinks that Fiona is the former but not the latter, we may hesitate to substitute ‘lawyer’ for ‘attorney’ in ‘Andrea believes that Fiona is an attorney’, even though ‘lawyer’ and ‘attorney’ are synonymous. I argue that these sentences report de re beliefs about linguistic expressions, thereby blocking such substitutions, and I offer a (...) compositional derivation of their meaning. (shrink)

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) the (...) contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

A detailed interpretation is provided of the ‘Gray's Elegy’ passage in Russell's ‘On Denoting’. The passage is suffciently obscure that its principal lessons have been independently rediscovered. Russell attempts to demonstrate that the thesis that definite descriptions are singular terms is untenable. The thesis demands a distinction be drawn between content and designation, but the attempt to form a proposition directly about the content (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated (...) instead of the content expressed. In light of this collapse, argues Russell, the thesis that definite descriptions are singular terms must accept that all propositions about a description's content represent it by means of a higher-level descriptive content, so that knowledge of a description's content is always ‘by description’, not ‘by acquaintance’. This, according to Russell, renders our cognitive grip on definite descriptions inexplicable. Separate responses on behalf of Fregeans and Millians are offered. (shrink)

Against standard descriptivist and referentialist semantics for fictional reports, I will defend a view according to which fictional names do not refer yet they can be distinguished from one another in virtue of their different name-using practices. The logical structures of sentences containing fictional names inherit these distinctions. Different interpretations follow.

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.

The object of the present discussion is to show that the analysis of indirect discourse obtained when the concept of assertion is construed as a relationship that obtains between the asserting person and the asserted proposition—along the familiar lines proposed by Church [3, 4]—is entirely adequate of itself to circumvent the semantical paradoxes in which indirect discourse is involved.

A new semantical antinomy, the antinomy of designation, is introduced into a metalanguage M with respect to a modal object language L. Carnap's device of restricting the principle of interchangeability for L does not suffice to prevent occurrence of this new antinomy. To achieve this result it seems most natural to replace the rules of designation for L by more complicated rules. This replacement suffices to prevent occurrence of the antinomy with respect to L. Moreover, it seems likely that analogous (...) replacement will suffice to prevent occurrence of the antinomy with respect to languages which in means of expression are richer than L. (shrink)

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)

The author defends the view that the notion of concept, if used in the logical tradition, should be explicated procedurally . He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.

According to predicativism about names, names which occur in argument positions have the same type of semantic contents as predicates. In this paper, I shall argue that these bare singular names do not have the same type of semantic contents as predicates. I will present three objections to predicativism—the modal, the epistemic, and the translation objections—and show that they succeed even against the more sophisticated versions of predicativism defended by Fara and Bach.

I argue that the principal roles standardly envisaged for abstract propositions can be discharged to the sentences themselves (and similarly for the meanings or senses of words). I discuss: (1) Cognitive Value: Hesperus-Phosphorus; (2) Indirect Sense and Propositional Attitudes; (3) the Paradox of Analysis; (4) the Picture Theory of the Tractatus; (5) Syntactical Diagrams and Meaning; (6) Quantifying-in. (7) Patterns of Use. I end with comparisons with related views of the territory.

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any of (...) the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

We investigate synonymy in the strong sense of content identity. This notion is central in the philosophy of language and in applications of logic. We motivate, uniformly axiomatize, and characterize several “benchmark” notions of synonymy in the messy class of all possible notions of synonymy. This class is divided by two intuitive principles that are governed by a no-go result. We use the notion of a scenario to get a logic of synonymy which is the canonical representative of one division. (...) In the other division, the so-called conceptivist logics, we find, e.g., the well-known system of analytic containment. We axiomatize four logics of synonymy extending AC, relate them semantically and proof-theoretically to SF, and characterize them in terms of weak/strong subject matter preservation and weak/strong logical equivalence. This yields ways out of the no-go result and novel arguments—independent of a particular semantic framework—for each notion of synonymy discussed. This points to pluralism about meaning and a certain non-compositionality of truth in logic programs and neural networks. And it unveils an impossibility for synonymy: if it is to preserve subject matter, then either conjunction and disjunction lose an essential property or a very weak absorption law is violated. (shrink)

Though largely unnoticed, in “Two Dogmas” Quine himself invokes a distinction: a distinction between logical and analytic truths. Unlike analytic statements equating ‘bachelor’ with ‘unmarried man’, strictly logical tautologies relating two word-tokens of the same word-type, e.g., ‘bachelor’ and ‘bachelor’ are true merely in virtue of basic phonological form, putatively an exclusively non-semantic function of perceptual categorization or brute stimulus behavior. Yet natural language phonemic categorization is not entirely free of interpretive semantic considerations. “Phonemic reductionism” in both its linguistic and (...) behavioral, Newbury Park, CA, Sage Publications, 164–167) guise is false. The semantic basis of phonological equivalence, however, has repercussions vis-à-vis Quine’s critique of analyticity. A consistent rejection of meaning-based equivalencies eliminates not only analyticity, but imposes a form of phonological eliminativism too. Phonological eliminativism is the reductio result of applying Quinean meaning skepticism to the phonological typing of natural language. But unlike analyticity, phonology is presumably not subject to philosophical dismissal. The semantic basis of natural language phonology serves to neutralize Quine’s argument against analyticity: without the semantics of meaning, more than just synonymy is lost; basic phonology must also be forfeited. Let’s begin with the fact that even Quine has to admit that it is possible for two tokens of the same orthographic type to be synonymous, for that much is presupposed by his own account of logical truth. Paul Boghossian. (shrink)

Though largely unnoticed, in "Two Dogmas" Quine himself invokes a distinction: a distinction between logical and analytic truths. Unlike analytic statements equating 'bachelor' with 'unmarried man', strictly logical tautologies relating two word-tokens of the same word-type, e.g., 'bachelor' and 'bachelor' are true merely in virtue of basic phonological form, putatively an exclusively non-semantic function of perceptual categorization or brute stimulus behavior. Yet natural language phonemic categorization is not entirely free of interpretive semantic considerations. "Phonemic reductionism" in both its linguistic and (...) behavioral, Newbury Park, CA, Sage Publications, 164-167) guise is false. The semantic basis of phonological equivalence, however, has repercussions vis-à-vis Quine's critique of analyticity. A consistent rejection of meaning-based equivalencies eliminates not only analyticity, but imposes a form of phonological eliminativism too. Phonological eliminativism is the reductio result of applying Quinean meaning skepticism to the phonological typing of natural language. But unlike analyticity, phonology is presumably not subject to philosophical dismissal. The semantic basis of natural language phonology serves to neutralize Quine's argument against analyticity: without the semantics of meaning, more than just synonymy is lost; basic phonology must also be forfeited. (shrink)

Within AI and the cognitively related disciplines, there exist a multiplicity of uses of belief. On the face of it, these differing uses reflect differing views about the nature of an objective phenomenon called belief. In this paper I distinguish six distinct ways in which belief is used in AI. I shall argue that not all these uses reflect a difference of opinion about an objective feature of reality. Rather, in some cases, the differing uses reflect differing concerns with special (...) AI applications. In other cases, however, genuine differences exist about the nature of what we pre-theoretically call belief. To an extent the multiplicity of opinions about, and uses of belief, echoes the discrepant motivations of AI researchers. The relevance of this discussion for cognitive scientists and philosophers arises from the fact that (a) many regard theoretical research within AI as a branch of cognitive science, and (b) even if theoretical AI is not cognitive science, trends within AI influence theories developed within cognitive science. It should be beneficial, therefore, to unravel the distinct uses and motivations surrounding belief, in order to discover which usages merely reflect differing pragmatic concerns, and which usages genuinely reflect divergent views about reality. (shrink)

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for nested intensional model) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, (...) NIM provides agents with a conceptual map, interrelating the concepts of knowledge, belief, truth, and a number of cognate concepts, such as infers, retracts, and questions. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, -FOL (presented herein). -FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, -FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of -FOL and NIM to interagent reasoning are described and the soundness and completeness of -FOL are established herein. (shrink)

Our aim is to illuminate the interconnected notions of meaning and truth. For this purpose, we investigate the relationship between meaning theories based on commonsensical ‘means that’ and interpretive truth theories. The latter are Tarski–Davidson-style truth theories serving as meaning theories. We consider analytically true semantic principles containing ‘means’ and ‘means that’ side to side with ‘denotes’, ‘satisfies’, and ‘true’, which constitute the extensional semantic constants of interpretive truth theories. We show that these semantic constants are definable in terms of (...) ‘means’ and ‘means that’ operators. The definitions themselves are semantic principles in the role of meaning postulates. We extend a meaning theory based on ‘means that’ by adjoining semantic principles to the axioms of the theory. Then, all axioms, hence all theorems, of a corresponding interpretive truth theory are provable in the extension of the meaning theory. Furthermore, every interpretive truth theory can be included in the extension of a corresponding meaning theory. Therefore, the extension of a meaning theory resulting from the adjunction of semantic principles constitutes a unified meaning-and-truth theory since it includes both a meaning theory and an interpretive truth theory. (shrink)

According to neo-Russellianism, in a sentence such as John believes that Mont Blanc is 4000 m high, any other proper name co-referring with Mont Blanc can be substituted for it without any change in the proposition expressed. Prima facie, our practice of translation shows that this cannot be correct. We will then show that neo-Russellians have a way out of this problem, which consists in holding that actual translations are not a matter of semantics, but also make an attempt at (...) preserving some pragmatic features of the sentences to be translated. We then turn to translations that only preserve the semantic characteristics of the sentences and we argue that, although these translations are unable to show that neo-Russellianism is incorrect, they still show that it relies on some theses that seem to have no justification, apart from saving neo-Russellianism itself. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, (...) it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

Mates’s Puzzle has flown below many philosophers’ radar, despite its relations to both Frege’s Puzzle and the Paradox of Analysis. We explain the relations amongst these puzzles on the way to arguing that Mates’s Puzzle suggests a generalization of Frege’s Puzzle, and of the sense-reference distinction itself, in the form of hierarchy of senses. We explain how Mates’s Puzzle and the hierarchy, to different degrees, illuminate each other, and how their connection is missed in the literature. However, we argue that (...) the potential of Mates’s Puzzle to illuminate the hierarchy is yet to be fully actualised. We suggest that in order to do better, we need to formulate Mates’s Puzzle as a puzzle in the philosophy of thought and not as puzzle in the philosophy of language. What is needed, to which the present paper is a precursor, is an account of the cognitive significance of higher-order senses. (shrink)

A new kind of defense of the Millian theory of names is given, which explains intuitive counter-examples as depending on pragmatic effects of the relevant sentences, by direct application of Grice’s and Sperber and Wilson’s Relevance Theory and uncontroversial assumptions. I begin by arguing that synonyms are always intersubstitutable, despite Mates’ considerations, and then apply the method to names. Then, a fairly large sample of cases concerning names are dealt with in related ways. It is argued that the method, as (...) applied to the various cases, satisfies the criterion of success: that for every sentence in context, it is a counter-example to Millianism to the extent that it has pragmatic effects (matching speakers’ intuitions). (shrink)

Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by "impossible worlds". We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the (...) same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both). (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (1) (...) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would (...) be lost. (shrink)

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the (...) propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic. (shrink)

The representation of propositional attitudes (beliefs, desires, etc.) and the analysis of natural-language, propositional-attitude reports presents difficult problems for cognitive science and artificial intelligence. In particular, various representational approaches to attitudes involve the incorrect “imputation,” to cognitive agents, of the use of artificial theory-laden notions. Interesting cases of this problem are shown to occur in several approaches to attitudes. The imputation problem is shown to arise from the way that representational approaches explicate properties and relationships, and in particular from the (...) way they explicate propositional attitudes themselves. Another factor contributing to imputation is the compositional nature of typical semantic approaches to propositional-attitude reports. Some strategies for avoiding undesirable imputation are examined. One of the main conclusions is that the importance of imputations that arise in a representation scheme depends strongly on the use to which the scheme is put -- on whether, for instance, the scheme is used as part of a formal, objective account of natural language, or is used rather as a representational tool within an agent. (shrink)

§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical (...) observations of the first importance.Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are philosophers who seriously underestimate and even consciously reject these techniques. (shrink)

In the paper, I develop what I call the “Neo-Hintikkan theory” of belief sentences. What is characteristic of this approach is that the meaning of an ascription is analyzed in terms of the believer’s “epistemic alternatives”: the set of worlds compatible with how the believer takes the world to be. The Neo-Hintikkan approach proceeds by assuming that (1) individuals in believers’ alternatives can share spatio-temporal parts with actual individuals, and (2) ascribers can refer to individuals in believer’s alternatives in virtue (...) of their perceptual or causal interaction with the spatio-temporal parts these “believed individuals” share with actual individuals. The guiding idea underlying this view is that the source of substitutivity failure in certain central cases is that believers have put the spatio-temporal parts of the objects they have encountered together in the wrong way. (shrink)