This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts (...) and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures. (shrink)

This paper defends the view that perceptual ascriptions such as “Jones sees a cat” are sometimes intensional. I offer a range of examples of intensional perceptual ascriptions, respond to objections to intensional readings of perceptual ascriptions, and show how widely accepted semantic accounts of intensionality can explain the key features of intensional perceptual ascriptions.

This chapter gives a truthmaker-based account of the semantics of 'reifying' quantifiers like 'something' when they act as complements of intensional transitive verbs ('need', 'look for'). It argues that such quantifiers range over 'variable satisfiers' of the attitudinal object described by the verb (e.g. the need or the search).

The complement of intensional transitive verbs, like any nonreferential complement, can be replaced by a ‘special quantifier’ or ‘special pronoun’ such as 'something', 'the same thing', or 'what'. In this paper, I will defend the ‘Nominalization Theory’ of special quantifiers against a range of apparent counterexamples involving intensional transitive verbs.

This paper discusses the semantics of intensional transitive verbs such as 'need', 'want','recognize', 'find', and 'hire'. It proposes new linguistic criteria for intensionality and defends two semantic analyses for two different classes of intensional verbs. The paper also includes a systematic classification of intensional verbs according to the type of lexical meaning they involve.

INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, we have in mind an ...

The traditional scope theory of intensionality (STI) (see Russell 1905; Montague 1973; Ladusaw 1977; Ogihara 1992, 1996; Stowell 1993) is simple, elegant, and, for the most part, empirically adequate. However, a few quite troubling counterexamples to this theory have lead researchers to propose alternatives, such as positing null situation pronouns (Percus 2000) or actuality operators (Kamp 1971; Cresswell 1990) in the syntax of natural language. These innovative theories do correct the undergeneration of the original scope theory, but at a (...) cost: the situation pronoun and operator theories overgenerate, as argued extensively by Percus (2000) and Keshet (2008). This paper presents new data that supports the STI over other analyses, such as structures where DPs lose their de re readings in positions where syntactic movement is blocked. These data point the way to a new theory of intensionality. This new theory, called split intensionality, is a modification of the STI which aims to solve the problems raised for the original scope theory without overgenerating. The proposal calls for an additional intensional abstraction operator that creates an expression denoting an intension from an expression denoting an extension. When a DP moves to a position above this operator, it is interpreted de re; otherwise it is de dicto. The crucial part of the new proposal is that a DP may move above this operator and yet remain, for instance, below an intentional verb or inside an if-clause. Therefore, a DP within an island for syntactic movement may be de re and yet not move out of the island when the intensional abstraction operator is also within the island. (shrink)

CHAPTER 1. INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, ...

Propositionalism is the view that all intensional constructions (including nominal and clausal attitude reports) can be interpreted as relations to truth-evaluable propositional content. While propositionalism has long been silently assumed in semantics and the philosophy of language, it has only recently entered center stage in linguistic research. This article surveys the properties of intensional constructions, which require the introduction of fine-grained semantic values (intensions). It contrasts two ways of obtaining such values: through the introduction of either Russellian propositions or Frege-Church-style (...) senses. The article identifies propositionalism with a specific variant of the Russellian strategy, reviews key arguments for propositionalism, and compares familiar varieties of propositionalism on the basis of instructive examples. It closes by discussing various challenges for propositionalism and suggesting a generalization of propositionalism that meets some of these challenges. Because of the association of propositions with semantic information, the article also addresses the more general question of whether all information content (including mental and pictorial content) is propositional. (shrink)

Routledge Encyclopedia entry on Intensionality and Hyperintensionality.

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)

This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena which can be analyzed using (...) the tools of this semantic paradigm, so as to include for instance paradoxes. The volume covers topics such as the philosophical significance of different criteria of identity of proofs, and adequacy conditions for an intensional account of the notion of harmony. The author also examines the Prawitz-Tennant analysis of paradoxes by investigating on the one hand the prospects of turning it into a theory of meaning for paradoxical languages, and on the other hand two distinct kinds of phenomena, first observed by Crabbe and Ekman, showing that the Tennant-Prawitz criterion for paradoxicality overgenerates. This volume is of interest to scholars in formal and philosophical logic. (shrink)

NPs with intensional relative clauses such as 'the impact of the book John needs to write' pose a significant challenge for trope theory (the theory of particularized properties), since they seem to refer to tropes that lack an actual bearer. This paper proposes a novel semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that an alternative analysis based on the notion of an individual concept would face.

Radical Enactivism holds that the best explanation of basic forms of cognition is provided without involving information of any sort. According to this view, the ability to perceive visual affordances should be accounted for in terms of extensional covariations between variables spanning the agent’s body and the environment. Contrary to Radical Enactivism, I argue that the intensional properties of cognition cannot be ignored, and that the way in which an agent represents the world has consequences on the explanation of basic (...) sensorimotor abilities. To support this claim, I show that the perception of visual affordances is not segregated from higher forms of cognition; rather, it is modulated by the agent’s ability to recognize the semantic identity of the visual target. Accordingly, since the semantic recognition of an object involves a way of representing it under a certain description, it can be inferred that the perception of visual affordances cannot be accounted for without considering the intensional properties of cognition. This poses an explanatory issue for Radical Enactivism. (shrink)

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook, Cook, Schlenker, and Tourville and Cook via the addition of intensional operators such as ``is paradoxical''. In this extended framework we are able (...) to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. (shrink)

This paper aims to shed new light on certain philosophical theories of perceptual experience by examining the semantics of perceptual ascriptions such as “Jones sees an apple.” I start with the assumption, recently defended elsewhere, that perceptual ascriptions lend themselves to intensional readings. In the first part of the paper, I defend three theses regarding such readings: I) intensional readings of perceptual ascriptions ascribe phenomenal properties, II) perceptual verbs are not ambiguous between intensional and extensional readings, and III) intensional perceptual (...) ascriptions have a relational form. The second part of the paper describes the implications of I-III for theories of perceptual experience. I argue that I-III support and reconcile the three main views of perceptual experience, relationalism, disjunctivism, and representationalism. However, I-III leave open at least one important point of contention: particularism, the view that we experience external objects. I conclude by exploring the implications of accepting or denying particularism given I-III. (shrink)

NPs with intensional relative clauses such as 'the book John needs to write' pose a significant challenge for semantic theory. Such NPs act like referential terms, yet they do not stand for a particular actual object. This paper will develop a semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that a more standard analysis based on the notion of an individual concept would face. Most importantly, unlike (...) the latter, the proposed analysis can be carried over NPs such as 'the number of people that fit into the bus', which describe tropes (particularized properties). (shrink)

The purpose of this paper is to raise a new objection to externalist process reliabilism about epistemic justification. The objection is that epistemic justification is intensional—it does not permit the substitution of co-referring expressions—and reliabilism cannot accommodate that.

A verb is transitive iff it usually occurs with a direct object, and in such occurrences it is said to occur transitively . Thus ‘ate’ occurs transitively in ‘I ate the meat and left the vegetables’, but not in ‘I ate then left’ (perhaps it is not the same verb ‘left’ in these two examples, but it seems to be the same ‘ate’). A verb is intensional if the verb phrase (VP) it forms with its complement is anomalous in at (...) least one of three ways: (i) interchanging expressions in the complement referring to the same entity can change the truth-value of the sentence embedding the VP; (ii) the VP admits of a special “unspecific” reading if it contains a quantifier, or a certain type of quantifier; and (iii) the normal existential commitments of names and existential quantifiers in the complement are suspended even when the embedding sentence is negation-free. (shrink)

In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...) η-conversions) that the authors have investigated in recent work. (shrink)

Following on Westerståhl’s argument that many is not Conservative [9], I propose an intensional account of Conservativity as well as intensional versions of EXT and Isomorphism closure. I show that an intensional reading of many can easily possess all three of these, and provide a formal statement and proof that they are indeed proper intensionalizations. It is then discussed to what extent these intensionalized properties apply to various existing readings of many.

This essay argues that relativist semantics provide fruitful frameworks for the study of the relationships between meaning and truth-conditions, and consequently for the analysis of the logical properties of expressions. After a discussion of the role of intensionality and indexicality within classic double-indexed semantics, I explain that the non-relativistic identification of the parameters needed for the definition of truth and for the interpretation of indexicals is grounded on considerations that are irrelevant for the assessment of the relationships between meaning (...) and truth. (shrink)

If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument exploits a self-referential function symbol where the expressed function ends up being intensional in virtue of self-reference. The prohibition on intensional functions thus entails that self-reference cannot be unconstrained, even in a language that is free of semantic terms. However, since intensional functions are already excluded in classical logic, there are no drastic revisionary implications here. Still, the argument reveals a new sort of (...) intensional context, one which does not depend on a propositional attitude verb, a modal operator, an idiom like 'so called', etc. Moreover, since classical logicians do not seem aware of the potential danger with self-reference, a word of warning is in order. (shrink)

There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.

The study of weighted structures is one of the important trends in recent computer science. The aim of the article is to provide a weighted, many-valued version of classical intensional semantics formalised in the framework of higher-order fuzzy logics. We illustrate the apparatus on several variants of fuzzy S5-style modalities. The formalism is applicable to a broad array of weighted intensional notions, including alethic, epistemic, or probabilistic modalities, generalised quantifiers, counterfactual conditionals, dynamic and non-monotonic logics, and some more.

According to a widespread view in medieval scholarship, theories of supposition are the medieval counterparts of theories of reference, and are thus essentially extensional theories. I propose an alternative interpretation: theories of supposition are theories of properties of terms, but whose aim is to allow for the interpretation of sentences. This holds especially of Ockham’s supposition theory, which is the main object of analysis in this paper. In particular, I argue for my intensional interpretation of his theory on the basis (...) of two key-phrases in his Summa Logicae: ‘denotatur’ and ‘propositio est distinguenda’. Finally, I offer a reconstruction of his theory as a set of instructions to be carried out in order to generate the possible readings of (certain) sentences. (shrink)

Paradigm intensional contexts result from the unmarked use of referential expressions as “self‐signs”, signs that refer to themselves as tokens, types, or members of Sellarsian “dot‐quoted” kinds. Self‐signing (but unquoted) linguistic expressions are more difficult to recognize than non‐linguistic self‐signs such as the color of a felt pen's casing that represents the color of ink inside. I will discuss non‐linguistic self‐signing, then examine self‐signing in quotation, in “said that …” contexts and in “believes that … ” contexts. The phenomenon of (...) intensionality may reduce to a kind of equivocation, a matter of notation rather than a necessary feature of language. (shrink)

Although a number of truth theorists have claimed that a deflationary theory of ‘is true’ needs nothing more than the uniform implication of instances of the theorem ‘the proposition that p is true if and only if p ’, reflection shows that this is inadequate. If deflationists can’t support the instances when replacing the biconditional with ‘because’, then their view is in peril. Deflationists sometimes acknowledge this by addressing, occasionally attempting to deflate, ‘because’ and ‘in virtue of’ formulas and their (...) close relatives. I examine what I take to be the most promising deflationist moves in this direction and argue that they fail. (shrink)

Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic (...) methods will also be used to establish the embedding of subintuitionistic logics into the corresponding modal logics. Finally, proof-theoretic embeddings will be interpreted as a reduction of classes of word problems. (shrink)

Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness (...) of the standard extensional semantics for mathematics. In this paper I investigate some implications of the Gödel Second Incompleteness Theorem for these positions. I argue that the realm of mathematics, proof theory in particular, has been a breeding ground for intensionality and that satisfactory intensional semantic theories are implicit in certain rigorous technical accounts. (shrink)

Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.

According to Spinoza mental events and physical events are identical. What makes Spinoza's identity theory tempting is that it solves the problem of mind body interaction rather elegantly: mental events and physical events can be causally related to each other because mental events are physical events. However, Spinoza seems to deny that there is any causal interaction between mental and physical events. My aim is to show that Spinoza's apparent denial of mind body interaction can be reconciled with the identity (...) theory. I argue that Spinoza had both an extensional and an intensional concept of cause and when Spinoza seems to deny mind body interaction he is having in mind the intensional concept of cause. This intensional concept of cause corresponds to that of causal explanation. I will argue that Spinoza anticipated Donald Davidson's view that even though mental events cannot be explained by referring to physical events and vice versa, mental and physical events are causally related to each other. (shrink)