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)

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 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 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.

There is a correlation between intensionality and syntax: intensionality manifests itself with all clausal complement constructions. For example, “Max imagined that Boris was approaching”. Although pervasive, there are apparent counterexamples. Sentences featuring intensional transitive verbs such as “Max wanted Boris” and “John imagined a unicorn”, exhibit intensionality effects but do not appear to have clausal complements. This chapter defends a view of intensional transitive constructions which is intuitive and quite familiar, but one which has also been widely (...) discounted. Specifically, the defense is of the proposal deriving from Quine and Montague that despite surface appearances, intensional transitive constructions are not transitives at all, but rather clausal complement constructions containing concealed material. (shrink)

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)

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)

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, ...

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 ...

Routledge Encyclopedia entry on Intensionality and Hyperintensionality.

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)

How can we explain the intelligence of behaviors? Radical enactivists maintain that intelligent behaviors can be explained without involving the attribution of representational contents. In this paper, I challenge this view by providing arguments showing that the intelligence of a behavior is reliant on ways of presenting the relative purpose and the environment in which that behavior is performed. This involves that a behavior is intelligent only if intesional contents are ascribed to the related agent. Importantly, this conclusion also concerns (...) basic behaviors such as those related to the perception of affordances in the environment. Accordingly, either affordance-related behaviors are not instances of intelligent behaviors and can be accounted in a contentless way or affordance-related behaviors are intelligent, but cannot be accounted without involving contents and modes of presentation. (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)

This chapter explores solutions to a somewhat underappreciated family of puzzles concerning propositional attitudes generated by intensionalism—the view that necessarily equivalent propositions are identical. After presenting the puzzles informally, the chapter introduces the apparatus of higher-order logic, which allows one to quantify into the position of any type of expression, and makes possible a formally rigorous statement of the puzzles. Many philosophers will think that it’s quite obvious how one should respond to the puzzles—namely by treating them as refutations of (...) intensionalism. But this response is arguably too quick. The chapter explores strategies for responding to the puzzles within the framework of intensionalism, laying out a taxonomy of such strategies. Certain of these strategies treat English attitude sentences as opaque and others don’t. However all of them use a transparent (i.e. non-opaque) language as the vehicle for theorizing. The focus here will be on the logical ramifications of the various strategies. (shrink)

Composition as Identity claims that a composite object is identical to its parts taken collectively. This is often understood as reducing the identity of composite objects to the identity of their parts. The author argues that Composition as Identity is not such a reduction. His central claim is that an intensional notion of composition, which is sensitive to the arrangement of the composing objects, avoids criticisms based on an extensional understanding of composition. The key is to understand composition as an (...) intensional kind of identity relation, many-one identity. Eventually, the author suggests an arrangement condition for many-one identity that allows him to distinguish between composite objects, even if they have the same parts. (shrink)

This paper investigates intensional differences between programming languages—understood as differences in how computational processes are expressed, structured, and specified rather than merely in what they compute. While such differences have been studied in classical models of computation, they remain underexplored in the context of programming languages. Yet, programming languages undeniably compute, and any account of what “computing” means must include the ways in which they do so. The paper first clarifies the extensional/intensional distinction and introduces a methodological framework to study (...) this distinction based on Carnapian explication. It then follows an idealized programming workflow, which I structure according to the Carnapian framework, to identify where and how intensional differences arise—including during problem specification, algorithm design, language choice, data representation, and physical implementation. The final part situates intensionality within the broader epistemology of programming practice, examining how it is shaped by type-theoretic assumptions, social and historical context, and the implications of bounded outcomes. Throughout, the paper examines both the “nature” (inherent features of computable functions) and “nurture” (human factors influencing programming language design and use) of intensional differences. (shrink)

Hyperintensionalists like myself hold that there are distinct but co-intensional properties. However, intensionalists object that accepting such properties violates Ockham’s Razor, the principle of parsimony that tells us that things should not be multiplied more than is necessary. After I distinguish between the qualitative parsimony and quantitative parsimony readings of Ockham’s Razor, I present two versions of this objection: the qualitative parsimony objection and the quantitative parsimony objection. I then give a reply to each version that exploits the fact that (...) intensionalists already accept that there are distinct but co-extensional properties. The upshot of this paper is that accepting co-intensional properties does not obviously violate either the qualitative parsimony or quantitative parsimony readings of Ockham’s Razor any more for the hyperintensionalist than accepting only co-extensional properties does for the intensionalist. (shrink)

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).

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)

This paper introduces a formal system in which logical inference and truth are defined not via propositional values but through structural acts of distinction. The logic models scenes, nodes, modal transitions, and recursive levels, supporting both classical and non-classical inference. We show how captures patterns such as \emph{modus ponens}, handles metaphor, and applies to cognition. A modal theory of truth is defined through stability across possible scenes. The framework addresses foundational problems in philosophy and offers applications to logic, semantics, and (...) AI. (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.

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 (2008), Cook (2009), Schlenker (2010), and Tourville and Cook (2016) 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)

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.

Bart Streumer employs a reductio ad absurdum to show that a hyperintensional conception of properties has a multiplication problem; roughly, this conception of properties leads to the absurd result that we can multiply distinct but co-intensional properties without end. In this paper, I will explain why Streumer’s reductio fails to convince.

This paper identifies a novel type of intensionality, arising entirely from a self-referential operation defined in purely formal terms. However, the result does not force revisions to classical logic since intensional operations are already excluded on principle. But the paper reveals an unexpected route by which intensionality can arise, showing that additional vigilance is needed to prevent such constructions.

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)

Extensional scientific realism is the view that each believable scientific theory is supported by the unique first-order evidence for it and that if we want to believe that it is true, we should rely on its unique first-order evidence. In contrast, intensional scientific realism is the view that all believable scientific theories have a common feature and that we should rely on it to determine whether a theory is believable or not. Fitzpatrick argues that extensional realism is immune, while intensional (...) realism is not, to the pessimistic induction. I reply that if extensional realism overcomes the pessimistic induction at all, that is because it implicitly relies on the theoretical resource of intensional realism. I also argue that extensional realism, by nature, cannot embed a criterion for distinguishing between believable and unbelievable theories. (shrink)

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)

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.

My commentators point to respects in which the picture provided in Reference without Referents is incomplete. The picture provided no account of how sentences constructed from intensional verbs (like “John thought about Pegasus”) can be true when one of the referring expressions fails to refer. And it gave an incomplete, and possibly misleading, account of how to understand certain serious uses of fictional names, as in “Anna Karenina is more intelligent than Emma Bovary” and “Anna Karenina does not exist”. In (...) the present response, I indicate how I would now wish to make good these deficiencies. The truth of sentences constructed from intensional verbs can be explained in terms of the truth of sentences that are unproblematic for RWR, for example, sentences dominated by operators expressing propositional attitudes. Reflection on the way in which we can temporarily accept commitments we do not in fact share leads to a more nuanced account of serious uses of fictional names, some of which manifest precisely such a temporary acceptance. (shrink)

This article deals with an alternative interpretation of syllogistics, different from the classical (extensional) one: an intensional one, in which subject and predicate are not associated with a set of individuals (the extension of the concept) but a set of attributes (the content of the concept). The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other (...) philosophical works. Currently, the intensional approach is gaining more and more popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics. The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical (non-Aristotelian logic) but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements (with absolute and ordinary negation). The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented (two particular statements are replaced by one - accidental), and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally. The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles (which occurs due to the expansion of the class of correct moods of syllogisms). (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)

Arguments challenging the existence of free will frequently share a common structure, relying on variants of a principle we call Closure, according to which having no choice about a truth is preserved under entailment. We show that, under plausible assumptions, Closure is valid if and only if the `no choice' operator is intensional. By framing the debate in terms of the intensionality of this operator, this paper illuminates previously underappreciated constraints on defenses of Closure-based arguments against the existence of (...) free will. (shrink)

Extant attempts to incorporate _intensionality_ into the grammar either systematically over-generate, or systematically under-generate. In this paper, building on Keshet (Linguist and Philos 33(4):251–283, 2011), we aim to reconcile a scopal account of _de re_ with the possibility of _de re_ readings out of scope islands. By adapting compositional techniques for dealing with exceptionally scoping indefinites (Charlow, in On the semantics of exceptional scope, PhD thesis, Rutgers University, 2014; The scope of alternatives: indefiniteness and islands. Linguist and Philos 43(4):427–472, 2020), (...) we develop an intensional grammar in which exceptional _de re_ is achieved via _cyclic scope_. World-sensitive expressions are converted into scope-takers via a constrained inventory of type-flexible operators. Type flexibility _explains_ the possibility of apparently island-violating _de re_ by predicting the possibility of cyclic scope-taking. We argue that the resulting theory—which we dub the _flexible scope theory_—is sufficiently expressive to address the under-generation issues of current accounts, while still capturing constraints on _de re_ in an explanatory fashion. (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)

Franz Brentano upheld the medieval Aristotelian doctrine of intentionality as a mark of the mental, distinguishing physical from psychological phenomena by the intentionality of the psychological and nonintentionality of the physical. But to implement, even to fully understand and appreciate Brentano’s thesis, it is necessary to know when intentionality does or does not obtain. The task of formulating satisfactory criteria of intentionality has proved elusive. The magnitude of difficulty is indicated by the number and variety of criteria proposed and defeated (...) by counter examples. Intentionality may be a primitive irreducible property incapable of reductive conceptual analysis. But nonreductive criteriological characterizations of intentionality demonstrate an equally stubborn resistance to philosophical methods. (shrink)