Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom scheme of (...) Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. (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)

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 I show that we have strong empirical and theoretical reasons to treat the verbs we use in our semantic theorizing—particularly ‘refers to ’, ‘applies to ’, and ‘is true of ’—as intensional transitive verbs. Stating our semantic theories with intensional vocabulary allows us to partially reconcile two competing approaches to the nature and subject-matter of semantics: the Chomskian approach, on which semantics is non-relational, internalistic, and concerns the psychology of language users, and the Lewisian approach, on (...) which semantics is fully relational, specifies truth-conditions, and has metaphysical implications. ITVs have two readings: an intensional, de dicto reading, and a relational, de re reading. A semantic theory stated with the de dicto readings of our semantic verbs captures the core insights of the Chomskian approach to semantics, in part because it allows us to assign extremely fine-grained semantic values to expressions, even when those expressions are empty. On the other hand, the de re reading yields a theory that is fully relational, and issues in truth-conditions. The resulting theories are related—and compatible—in that they are expressed by two different readings of the very same semantic vocabulary, and plausibly, the distinction between these two readings is one of scope. (shrink)

We enrich intuitionistic logic with a lax modal operator ○ and define a corresponding intensional enrichment of Kripke models M = (W, ⊑, V) by a function T giving an effort measure T(w, u) ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathbb{N}} \cup$$ \end{document} {∞} for each ⊑-related pair (w, u). We show that ○ embodies the abstraction involved in passing from “ϕ true up to bounded effort” to “ϕ true outright”. We then introduce (...) a refined notion of intensional validityM |= p : ϕ and present a corresponding intensional calculus iLC-h which gives a natural extension by lax modality of the well-known G: odel/dummett logic LC of (finite) linear Kripke models. Our main results are that for finite linear intensional models L the intensional theory iTh(L) = {p : ϕ | L |= p : ϕ} characterises L and that iLC-h generates complete information about iTh(L).Our paper thus shows that the quantitative intensional information contained in the effort measure T can be abstracted away by the use of ○ and completely recovered by a suitable semantic interpretation of proofs. (shrink)

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 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. /// Mis comentadores señalan aspectos en los que la propuesta de Reference without Referents es incompleta: no ofrecía una explicación de cómo oraciones construidas con verbos intensionales pueden ser verdaderas cuando una de las expresiones referenciales no refiere; y dio una explicación incompleta, y quizás engañosa, de cómo entender ciertos usos serios de nombres de ficción como en "Anna Karenina es más inteligente que Emma Bovary" y "Anna Karenina no existe". En esta respuesta indico cómo quiero ahora subsanar estas deficiencias. La verdad de las oraciones construidas con verbos intensionales puede explicarse en términos de la verdad de oraciones que no son problemáticas para la explicación de Reference without Referents, por ejemplo, oraciones dominadas por operadores que expresan actitudes proposicionales. Una reflexión sobre cómo podemos aceptar temporalmente compromisos que de hecho no compartimos conduce a una explicación más matizada de los usos serios de los nombres de ficción, algunos de los cuales manifiestan precisamente esa aceptación temporal. (shrink)

Saul Kripke’s theory of truth suffers from expressive limitations – in particular, there are no extensional operators within that framework that allow one to characterize those sentences that fail to receive a truth value within the framework. Especially worrisome is the fact that there is no operator that outputs true on exactly the paradoxical sentences. In this paper I extend Kripke’s approach via the addition of extensional operators, which allows us to characterize many (but not all) such sentences, including (...) the paradoxical ones. (shrink)

This paper proposes interpretations of the vexed notions of intensionality and intentionality and then investigates their resulting interrelations.The notion of intentionality comes from Brentano, in connection with his view that it can help us understand the mental. Setting aside Husserl’s basic definition of intentionality as not quite in line with Brentano’s explanatory purpose, this paper proposes that intentionality be defined in terms of inexistence and indeterminacy.It results that Brentano’s thesis (that all and only mental phenomena are intentional) will not (...) be strictly true. However, intentional descriptions will always be intensional, though not all intensional descriptions will be intentional. (shrink)

The purpose of this article is to provide a non‐contradictory interpretation of sentences such as “Smith's murderer might not have murdered Smith”. An anti‐actualist, two‐dimensional framework including partial functions provides the basis for my solution. I argue for two claims. The modal profile of the proposition expressed by “The F might not have been an F” is complex: at any world where there is a unique F the proposition is true; at any world without a unique F the proposition (...) has no truth‐value; hence, at no world is it false. It remains an open semantic and epistemological question which of the first two kinds of world the actual world is. The semantic method should be based on explicit intensionalization in lieu of actualism. Actualism accords a privileged role to the actual world. Explicit intensionalization places all possible worlds, including the actual one, on an equal footing. Syntactically, a lambda‐bound world variable replaces the actual‐world constant or operator, while the other world variable is existentially bound. (shrink)

It is argued that the slingshot argument does not soundly challenge the truth-maker correspondence theory of truth, by which at least some distinct true propositions are expected to have distinct truth- makers. Objections are presented to possible exact interpretations of the essential slingshot assumption, in which no fully acceptable reconstruction is discovered. A streamlined version of the slingshot is evaluated, in which explicit contradiction results, on the assumption that identity and nonidentity contexts are purely extensional relations, effectively establishing the (...) intensionality of identity. (shrink)

We expand on the fixed point semantic approach of Kripke via the addition of two unary intensional operators: a paradoxicality operator Π where Π(Φ) is true at a fixed point if and only if Φ is paradoxical (i.e., if and only if Φ receives the third, non-classical value on all fixed points that extend the current fixed point), and an unbounded truth operator Υ⊤ where Υ⊤(Φ) is true at a fixed point if and only if any fixed point (...) extending the current fixed point can be extended to one on which Φ receives the value true. We prove a generalized version of Kripke’s fixed point theorem guaranteeing the existence of models of this new language, as well as an expressive completeness result. We conclude with an exploration of the significant improvements in expressive power that result from the addition of these new operators, and we precisely identify what still cannot be said on this intensional extension of the Kripkean framework. (shrink)

Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is (...) both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. -/- Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. -/- I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. -/- Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false. (shrink)

We enrich intuitionistic logic with a lax modal operator and define a corresponding intensional enrichment of Kripke models M = (W, , V) by a function T giving an effort measure T(w, u) {} for each -related pair (w, u). We show that embodies the abstraction involved in passing from true up to bounded effort to true outright. We then introduce a refined notion of intensional validity M |= p : and present a corresponding intensional calculus iLC-h which (...) gives a natural extension by lax modality of the well-known G: odel/Dummett logic LC of (finite) linear Kripke models. Our main results are that for finite linear intensional models L the intensional theory iTh(L) = {p : | L |= p : } characterises L and that iLC-h generates complete information about iTh(L).Our paper thus shows that the quantitative intensional information contained in the effort measure T can be abstracted away by the use of and completely recovered by a suitable semantic interpretation of proofs. (shrink)

This paper proposes interpretations of the vexed notions of intensionality and intentionality and then investigates their resulting interrelations.The notion of intentionality comes from Brentano, in connection with his view that it can help us understand the mental. Setting aside Husserl’s basic definition of intentionality as not quite in line with Brentano’s explanatory purpose, this paper proposes that intentionality be defined in terms of inexistence and indeterminacy.It results that Brentano’s thesis (that all and only mental phenomena are intentional) will not (...) be strictly true. However, intentional descriptions will always be intensional, though not all intensional descriptions will be intentional. (shrink)

In the article, I discuss some ideas of the type theoretical grammar of Aarne Ranta and the analysis of the problem of Quine (Ralph and Ortcutt), which Oleg Domanov implemented by means of this theory. There are more similarities than differences in TT grammar with well-known ideas, including “fine grinding” of meanings, counterparts, procedural understanding of – intensions. The main problem, which, in my opinion, exists in the TT grammar, consists in understanding how another agent’s epistemic attitudes can be justified (...) for me. Ranta proceeds from the metaphor of the agent as a calculator, which for the general case is unacceptable. I believe that the interpretation of the epistemic attitudes of another agent must be externalistic, that is, referring not to the agent’s worlds, but to his actions in the actual world: “agent X believes that A” is true when the interpreter sees the behavior of the agent in situations that the interpreter would consider adequate for himself if he believed A and would be “in place” of X. To formalize here, it would take complicated tools which are used for describing actions. I’ve come to the conclusion that an understanding of the type in TT grammar makes it intensional in some extended sense, since the working with the naming relation is already an element of a specific pragmatics. (shrink)

According to the standard view, alethic (or modal) statements are intensional in that the Principle of Substitution (PS) fails for them -- e.g. substituting 'nine' in "Necessarily, nine is composite" with the co-referring 'the number of planets' turns this statement from true to false. It is argued in the paper that we could avoid ascribing intensionality to alethic statements altogether by separating between singular and functional uses of definite descriptions: on the singular use the description given above amounts (...) to 'the actual number of planets', which is salva veritate substitutable to 'nine' in all alethic statements; on the functional use, in turn, that description is really a function from possible worlds to numbers, and thus the Principle of Substitution is not violated in this case either, since such a function cannot be held to be co-referential with 'nine'. (shrink)

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and (...) models are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?

We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics. (shrink)

On the basis of arguments put forth by (Kripke, 1977a) and (Kripke, 1980), it is widely held that one can sometimes rationally accept propositions of the form "P and not-P" and also that there are necessary a posteriori truths. We will find that Kripke's arguments for these views appear probative only so long as one fails to distinguish between semantics and presemantics—between the literal meanings of sentences, on the one hand, and the information on the basis of which one identifies (...) those literal meanings, on the other. This same failure, it will be argued, underlies the popular thesis that intersubstituting co-referring terms sometimes turns true sentences into false ones and vice versa. Though seemingly plausible, this thesis has a number of counterintuitive consequences, among them that the occurrence of “snow” in “it is true that snow is white” doesn’t refer to snow. An understanding of the distinction between semantics and presemantics suggests a way to develop a semantic system that doesn’t have these consequences and that, moreover, reconciles our intuitions concerning cognitive content with some powerfully argued theses of contemporary philosophy of language. Some of this paper's main contentions are anticipated by Andrzej Boguslawski in his 1994 paper “Sentential Complementation and Truth.”. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)

In The Structure of Scientific Inference, Mary Hesse has argued for a realist interpretation of science. Her realism, however, is not to be understood in the context of the traditional realist/instrumentalist debate within the philosophy of science. That debate focused on the question of whether or not science did anything other than systematize the empirical data given in our experience. The traditional realist answered “yes” and most frequently described the theoretical statements of science, not only as true, but also (...) as providing descriptions of the world. The instrumentalist on the other hand answered “no” and ascribed no descriptive force to the theoretical statements of science. However, according to Hesse, neither party in the contemporary realism debate assumes the notion of an empirical given. Consequently, the present dispute must be understood as taking place on a level which is logically prior to its predecessor. (shrink)

It is commonly held, plausibly, that many true beliefs are true only contingently, that is, are actually true (or true with respect to the actual world) but would be false were the world in some relevant ways otherwise (i.e. are false with respect to some other possible worlds). However, a radically different approach, according to which no belief is contingently true, is entirely defensible. The key point in this alternative approach is that each belief concerns (...) the world in which the believer is (or would be) situated, which makes it the case that, say, the actual belief that Kofi Annan is not bald is different from the belief, in any other world, that Kofi Annan is not bald. This difference is further backed up by considerations related to disagreement between believers, and to knowledge. The most important objection to this alternative approach is that it cannot be right since it makes all true beliefs necessarily true. It will be shown, as a reply to this objection, that under this alternative approach it can still be said truly, for instance, that Annan is not bald but could have been so. (shrink)

The author examines Scheffler’s extensional alternative to the usual notion of belief and shows that it is necessarily inadequate to serve the purpose for which it was designed. This point is established by showing that Scheffler’s proposed substitute for psychologically intensional verbs like ‘believes’ can not deliver philosophers from the classical puzzles over propositional attitudes and can not be used in all cases even to provide materially equivalent extensional substitutes for ordinary belief-statements.

The author examines Scheffler’s extensional alternative to the usual notion of belief and shows that it is necessarily inadequate to serve the purpose for which it was designed. This point is established by showing that Scheffler’s proposed substitute for psychologically intensional verbs like ‘believes’ can not deliver philosophers from the classical puzzles over propositional attitudes and can not be used in all cases even to provide materially equivalent extensional substitutes for ordinary belief-statements.

This dissertation lays the foundation for a new theory of non-relational intentionality. The thesis is divided into an introduction and three main chapters, each of which serves as an essential part of an overarching argument. The argument yields, as its conclusion, a new account of how language and thought can exhibit intentionality intrinsically, so that representation can occur in the absence of some thing that is represented. The overarching argument has two components: first, that intentionality can be profi tably studied (...) through examination of the semantics of intensional transitive verbs (ITVs), and second, that providing intensional transitive verbs with a nonrelational semantics will serve to provide us with (at least the beginnings of) a non-relational theory of intentionality. This approach is a generalization of Anscombe's views on perception. Anscombe held that perceptual verbs such as "see" and "perceive" were ITVs, and that understanding the semantics of their object positions could help us to solve the problems of hallucination and illusion, and provide a theory of perception more generally. I propose to apply this strategy to intentional states and the puzzles of intentionality more generally, and so Anscombe's influence will be felt all through the dissertation. -/- In the first chapter, titled "Semantic Verbs are Intensional Transitives", I argue that semantic verbs such as "refers to", "applies to", and "is true of" have all of the features of intensional transitive verbs, and discuss the consequences of this claim for semantic theory and the philosophy of language. One theoretically enriching consequence of this view is that it allows us to perspicuously express, and partially reconcile two opposing views on the nature and subject-matter of semantics: the Chomskian view, on which semantics is an internalistic enterprise concerning speakers' psychologies, and the Lewisian view, on which semantics is a fully externalistic enterprise issuing in theorems about how the world must look for our natural language sentences to be true. Intensional Transitive Verbs have two readings: a de dicto reading and a de re reading; the de dicto reading of ITVs is plausibly a nonrelational reading, and the intensional features peculiar to this reading make it suitable for expressing a Chomskian, internalist semantic program. On the other hand, the de re reading is fully relational, and make it suitable for expressing the kinds of word-world relations essential to the Lewisian conception of semantics. And since the de dicto and de re readings are plausibly related as two distinct scopal readings of the very same semantic postulates, we can see these two conceptions of semantics as related by two scopal readings of the very same semantic postulates. -/- In chapter two, titled "Hallucination and the New Problem of Empty Names", I argue that the problem of hallucination and the problem of empty names are, at bottom, the same problem. I argue for this by reconstructing the problem of empty names in way that is novel, but implicit in much of the discussion on empty names. I then show how, once recast in this light, the two problems are structurally identical down to an extremely fine level of granularity, and also substantially overlap in terms of their content. If the problems are identical in the way I propose, then we should expect that their spaces of solutions are also identical, and there is signi cant support for this conclusion. However, there are some proposed solutions to the problem of hallucination that have been overlooked as potential solutions to the problem of empty names, and this realization opens new non-relational approaches to the problem of empty names, and to the nature of meaning more generally. -/- In chapter three, titled "Intensionality is Additional Phrasal Unity", I argue for a novel approach to the semantics of intensional contexts. At the heart of my proposal is the Quinean view that intensional contexts should, from the perspective of the semantics, be treated as units, with the material in them contributing to the formation of a single predicate. However, this proposal is subject to a number of objections, including the criticism that taken at face value, this would render intensional contexts, which seem to be fully productive, non-compositional. I begin by discussing the concept of the unity of the phrase, and pointing to various ways that phrases can gain additional unity. I then proposes that the intensionality of intensional transitive verbs is best construed as a form of semantic incorporation; ITVs, on their intensional readings, meet all of the criteria for qualifying as incorporating the nominals in their object positions. I then give a semantics for ITVs that builds on existing views of the semantics of incorporation structures, and gesture at how this can be extended to intensional clausal verbs, including the so-called propositional attitude verbs. (shrink)

The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true in (...) virtue of what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view.. (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)

I put forward a version of the Cartesian Argument from Doubt for mind–body dualism. My version utilizes de re statements, which means that it is not vulnerable to the usual charge of intensional fallacy. The key de re statement is, ‘Body is such that its existence is entailed by Mind’s believing that Body does not exist’, which is false, whereas the respective ‘Mind is such that its existence is entailed by Mind’s believing that Body does not exist’ is true.

Intensional logic (IL) and its application to natural language, which the present monograph addresses, was first developed by Richard Montague in the late 1960s (e.g., Montague 1970a, 1970b). Through the efforts of (especially) Barbara Partee (e.g., Partee 1975, 1976), and Richmond Thomason, who edited the posthumous collection of Montague’s works (Thomason 1974), this became the main framework for those who aspired to a formal semantic theory for natural language, and these included computational linguists as early as Jerry Hobbs in the (...) late 1970s (e.g., Hobbs and Rosenschein 1977). In fact, until the advent of the current interest in statistical linguistics with its own conception of what semantics is, IL, or some variant of it, was perhaps the main theory of semantics within computational linguistics generally. And within current computational semantics it still is. But over the years, philosophers, linguists, and computational linguists have noted a variety of shortcomings in Montague’s version of IL. Montague defined intensions as functions from possible worlds to extensions in that world. But this had the effect of making logically equivalent expressions have the same intension, thus leading to the problem of “logical omniscience” (believing/knowing all the logical consequences of what is believed/known). Montague had based his IL on Church’s simple theory of types (Church 1940), supplemented with intensions of each type. But this implies that each natural language item accepts only arguments of some one fixed type. However, this is not true for natural language, where conjunctions, verbs, and pretty much any functional term that accepts arguments at all can accept arguments of different types. (For example, and can accept arguments that are of the sentence type, of the verb phrase type, of the adjective type, etc.; and indeed, it can accept arguments of differing types in its different argument.. (shrink)

If there are true contradictions, where are they? In language or in the world? According to one important view, best represented by Jc Beall (2009), only the former. In this paper, we raise a problem for this view. In order to defend a “merely semantic” version of dialetheism (aka ‘glut theory’), Beall adopts transparent accounts of truth and falsity, which gives rise to “dialethic ascent” on which true contradictions are also, contradictorily, untrue contradictions. This is a consequence of (...) trying to restrict contradictions to language and keep them out of the world. However, in this paper, we show that this ascent carries over intensional contexts, so that, on this version of dialetheism, even if there are true contradictions, no one knows a true contradiction. This shows that contradictions have not been kept out of the world. We end by connecting this issue with the infamous ‘just true’ problem. (shrink)

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look like? This (...) paper makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples. (shrink)

An influential argument against the possibility of truth by linguistic convention holds that while conventions can determine which proposition a given sentence expresses, they (conventions) are powerless to make propositions true or false. This argument has been offered in the literature by Lewy, Yablo, Boghossian, Sider and others. But despite its influence and prima facie plausibility, the argument: (i) equivocates between different senses of “making true”; (ii) mistakenly assumes hyperintensional contexts are intensional; and (iii) relies upon an implausible (...) vision of the way that language works. (shrink)

Debunking arguments typically attempt to show that a set of beliefs or other intensional mental states bear no appropriate explanatory connection to the facts they purport to be about. That is, a debunking argument will attempt to show that beliefs about p are not held because of the facts about p. Such beliefs, if true, would then only be accidentally so. Thus, their causal origins constitute an undermining defeater. Debunking arguments arise in various philosophical domains, targeting beliefs about morality, (...) the existence of God, logic, and others. They have also arisen in material-object metaphysics, often aimed at debunking common-sense ontology. And while most of these arguments feature appeals to ‘biological and cultural contingencies’ that are ostensibly responsible for our beliefs about which kinds of objects exist, few of them take a serious look at what those contingencies might actually be. The purpose of this paper is twofold. First, to remedy this by providing empirical substantiation for a key premise in these debunking arguments by examining data from cognitive science, evolutionary biology, and developmental psychology that support a ‘debunking explanation’ of our common-sense beliefs and intuitions about which objects exist. Second, to argue that such data also undermines a particular kind of rationalist defense of common-sense ontology, sometimes employed as a response to the debunking threat. (shrink)

It is advisable to treat some sorts of discourse about fiction with the aid of an intensional operator "in such-And-Such fiction...." the operator may appear either explicitly or tacitly. It may be analyzed in terms of similarity of worlds, As follows: "in the fiction f, A" means that a is true in those of the worlds where f is told as known fact rather than fiction that differ least from our world, Or from the belief worlds of the community (...) in which the fiction originated. (shrink)

Much thinking about conditionals over the last twenty years has been stimulated by the so-called 'Ramsey test'. Ramsey's idea was simple, but appealing. One should believe a conditional, 'if A then B' if one would come to believe B if one were to add A to one's stock of beliefs. The Ramsey test does not justify treating conditionals with true antecedent and consequent as true, and accepting it does not require one to accept either the similarity or probability (...) theories of the conditional. It certainly does not justify denying truth-values altogether to conditionals. What it can do, is show how the truth- condition for conditionals should be articulated in an intensional logic, indeed, in one with a well-developed and well-tested semantics and proof-theory: the logic of relevant implication. The Ramsey test is nght, when rightly understood. (shrink)

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not (...) in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D.. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293-315.]. (shrink)

In Meaning and Necessity (1947/1950), Carnap advances an intensional semantic framework on which modal claims are true in virtue of semantical rules alone, and so are a priori. In 'Empiricism, Semantics, and Ontology' (1950), Carnap advances an epistemic-ontological framework on which metaphysical claims are either trivial or meaningless, since lacking any means of substantive confirmation. Carnap carried out these projects two decades before Kripke influentially argued, in Naming and Necessity (1972/1980), that some modal claims are true a posteriori. (...) How should a neo-Carnapian respond to Kripke's results? Some (notably, Chalmers and Jackson, in their 2001) have suggested that an extension of intensional semantics along lines of "epistemic two-dimensionalism" can accommodate Kripke's results while largely preserving commitment to the semantics-based a priority of modal claims. Here we consider how best to implement this suggestion, and how the resulting semantics fits with Carnap's second project. We find that the most promising (and most Carnapian!) post-Kripke version of Carnap’s semantics---abductive two-dimensionalism---presupposes an epistemology which undermines Carnap's metaphysical anti-realism. (shrink)

Hybrid metaethical theories have significant promise; they would have important upshots if they were true. But they also face severe problems. The problems are severe enough to make many philosophers doubt that they could be true. My ambition is to show that the problems are just instances of a highly general problem: a problem about what are sometimes called ‘intensional anaphora'. I'll also show that any adequate explanation of intensional anaphora immediately solves all the problems for the hybrid (...) theorist. We should regard hybrid tools as among the most legitimate tools in our toolkit—at least when we use them properly. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory (...) properties. To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

In this paper I propose and motivate a logic of the interdefined concepts of making true and control, understood as intensional propositional operators to be indexed to an agent. While bearing a resemblance to earlier logics in the tradition, the motivations, semantics, and object language theory differ on crucial points. Applying this logic to widespread formal theories of agency, I use it as a framework to argue against the ubiquitous assumption that the strongest actions or options available to a (...) given agent must always be pairwise incompatible. The conclusion is that this assumption conflicts with failures of higher order control of agents over their degree or precision of control, failures exhibited by such imperfect agents as ourselves. I discuss models in this setting for understanding such imperfectly self-controlling agents. In an appendix, I prove several relevant results about the logic described, including soundness and completeness both for it and for certain natural extensions. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined (...) within the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Relativism is one of the most tenacious theories about truth, with a pedigree as old as philosophy itself. Nearly as ancient is the chief criticism of relativism, namely the charge that the theory is self-refuting. This paper develops a logic of relativism that (1) illuminates the classic self-refutation charge and shows how to escape it; (2) makes rigorous the ideas of truth as relative and truth as absolute, and shows the relations between them; (3) develops an intensional logic for relativism; (...) (4) provides a framework in which relativists can consistently promote ethical, mathematical, scientific, religious, and political truths (among others) as being relative; (5) argues that the notion of incommensurability is far less troubling than is commonly thought; and (6) argues that the concept of a perspective as needed by the theory is not prey to Davidson's well-known critique of conceptual schemes. The paper will not defend relativism as the correct theory of truth, nor will it provide a fully satisfying theory about the nature of a perspective. The logic of relativism is primarily meant to provide a formal framework in which relativists can consistently develop their theories. This alone is a considerable step forward, since the debate about relativism often founders upon the rock of self-refutation. It is argued that while 'everything is relative' is inconsistent, 'everything true is relatively true' is not. The latter is all a relativist really needs. (shrink)

Model theoretic considerations purportedly show that a certain version of structural realism, one which articulates the nvtion of structure via Ramsey sentences, is in fact trivially true. In this paper we argue that the structural realist is by no means forced to Ramseyfy in the manner assumed in the formal proof. However, the structural realist's reprise is short-lived. For, as we show, there are related versions of the model theoretic argument which cannot be so easily blocked by the structural (...) realist. We examine various ways in which the structural realist may respond, and conclude that the best way of blocking the model theoretic argument involves formulating his Ramseyfied theories using intensional operators. Introduction The model theoretic arguments On Ramseyfying away predicates The model theoretic argument bites back Restricting the second order quantifiers 5.1 Naturalness 5.2 Intrinsic 5.3 Qualitative 5.4 Contingent and causal Intensional operators and relations between properties Conclusion. (shrink)

There are many kinds of negation and denial. Perhaps the most common is the Boolean negation not that applies to propositions-in-extension, i.e. truth-values. The others are, inter alia, the property of propositions of not being true which applies to propositions; the complement function which applies to sets; privation which applies to properties; negation as failure applied in logic programming; negation as argumentation ad absurdum, and many others. The goal of this paper is neither to provide a complete list, nor (...) to analyse all of them. Rather, I am going to deal with negation of propositions that come attached with a presupposition that is entailed by the positive as well as negated form of a given proposition. However, there are two kinds of negation, namely internal and external negation. I am going to prove that while the former is presupposition-preserving, the latter is presupposition-denying. This issue has much in common with the difference between topic and focus articulation within a sentence. Whereas articulating the topic of a sentence activates a presupposition, articulating the focus frequently yields merely an entailment. The main contribution of this paper is the proof that the two kinds of negation are not equivalent. While the Russellian wide-scope (external) negation gets the truthconditions of a sentence right for a subject occurring as a focus, Strawsonian narrow-scope (internal) negation is validly applicable for a subject occurring as the topic. I also deal with other kinds of presupposition triggers, in particular factive attitudes and prerequisites of a given property. My background theory is Transparent Intensional Logic (TIL). TIL is an expressive logic apt for the analysis of sentences with presuppositions, because in TIL we work with partial functions, in particular with propositions with truth-value gaps. Moreover, the procedural semantics of TIL make it possible to uncover the hidden semantic features of sentences, make them explicit and logically tractable. (shrink)

In an earlier paper, [5], I gave semantics and tableau rules for a simple firstorder intensional logic called FOIL, in which both objects and intensions are explicitly present and can be quantified over. Intensions, being non-rigid, are represented in FOIL as (partial) functions from states to objects. Scoping machinery, predicate abstraction, is present to disambiguate sentences like that asserting the necessary identity of the morning and the evening star, which is true in one sense and not true in (...) another.In this paper I address the problem of axiomatizing FOIL. I begin with an interesting sublogic with predicate abstraction and equality but no quantifiers. In [2] this sublogic was shown to be undecidable if the underlying modal logic was at least K4, though it is decidable in other cases. The axiomatization given is shown to be complete for standard logics without a symmetry condition. The general situation is not known. After this an axiomatization for the full FOIL is given, which is straightforward after one makes a change in the point of view. (shrink)

There seems to be a view that intuitionists not only take the Axiom of Choice (AC) to be true, but also believe it a consequence of their fundamental posits. Widespread or not, this view is largely mistaken. This article offers a brief, yet comprehensive, overview of the status of AC in various intuitionistic and constructivist systems. The survey makes it clear that the Axiom of Choice fails to be a theorem in most contexts and is even outright false in (...) some important contexts. Of the systems surveyed, only intensional type theory renders AC a theorem, but the extent of AC in that theory does not include, for instance, real analysis. Only a small amount of extensionality is required in order for the obvious proof an intuitionist might offer for AC to break down. (shrink)

In this essay, I present a new argument for the impossibility of defining truth by specifying the underlying structural property all and only true propositions have in common The set of considerations I use to support this claim take as that inspiration Alston's recent argument that it is impossible to define truth epistemically—in terms of justification or warrant According to what Alston calls the “intensional argument”, epistemic definitions are inconsistent with the T schema or the principle that it is (...) true that p if, and only if, p. Since the T-schema has great intuitive appeal, this is a powerful indictment of epistemic theories. But the basic argument that Alston employs, and the constellation of considerations which prosecute that argument, work against a much broader range of views than he considers While this implies that a traditional conceptual analysts of truth may be impossible, it opens the door to a pluralist approach to truth. (shrink)

In this essay, I present a new argument for the impossibility of defining truth by specifying the underlying structural property all and only true propositions have in common The set of considerations I use to support this claim take as that inspiration Alston's recent argument that it is impossible to define truth epistemically—in terms of justification or warrant According to what Alston calls the “intensional argument”, epistemic definitions are inconsistent with the T schema or the principle that it is (...) true that p if, and only if, p. Since the T-schema has great intuitive appeal, this is a powerful indictment of epistemic theories. But the basic argument that Alston employs, and the constellation of considerations which prosecute that argument, work against a much broader range of views than he considers While this implies that a traditional conceptual analysts of truth may be impossible, it opens the door to a pluralist approach to truth. (shrink)

Attitudinal propositionalism is the view that all mental attitude content is truth-evaluable. While attitudinal propositionalism is still silently assumed in large parts of analytic philosophy, recent work on objectual attitudes (i.e. attitudes like ‘fearing Moriarty’ and ‘imagining a unicorn’ that are reported through intensional transitive verbs with a direct object) has put attitudinal propositionalism under explanatory pressure. This paper defends propositionalism for a special subclass of objectual attitudes, viz. experiential attitudes. The latter are attitudes like seeing, remembering, and imagining whose (...) grammatical objects intuitively denote (events or) scenes. I provide a propositional analysis of experiential attitudes that preserves the merits of propositionalism. This analysis uses the possibility of representing the target-scenes of experiential attitudes by the intersection of all propositions that are true in these scenes. I show that this analysis makes available the usual (Russellian) account of intensionality and the common (Boolean) logic for entailments. (shrink)

Professor Davidson's anomalous monism has been subject to the criticism that, despite advertisements to the contrary, if it were true mental properties would be epiphenomenal. To this Davidson has replied that his critics have misunderstood his views concerning the extensional nature of causal relations and the intensional character of causal explanations. I call this his ‘extension reply’. This paper argues that there are two ways to read Davidson's ‘extension reply’; one weaker and one stronger. But the dilemma is that: (...) the weak extension reply on its own isn't sufficient to support the principle of the nomological character of causality, anything strong enough to support that principle under the weak extension reply would be strong enough to warrant the strong extension reply; but the strong extension reply threatens the very stability of anomalous monism by threatening the causal potency and reality of the mental. For these reasons, I claim that either version of the ‘extension reply’ is bad news for anomalous monism. I conclude by suggesting that a form of absolute idealism circumvents the very assumptions that generate these kinds of difficulty for committed monists. (shrink)

In the first chapter I have introduced Carnapian intensional logic against the background of Frege's and Quine's puzzles. The main body of the dissertation consists of two parts. In the first part I discussed Carnapian modal logic and arithmetic with descriptions. In the second chapter, I have described three Carnapian theories, CCL, CFL, and CNL. All three theories have three things in common. First, they are formulated in languages containing description terms. Second, they contain a system of modal logic. Third, (...) they do not contain the unrestricted classical substitution principle, but they do contain the classical substitution principle restricted to non-modal formulas and the Carnapian substitution principle, which says that two terms can be substituted salva veritate if they are necessarily coreferential. There are two major differences between the three theories. First, CCL and CFL allow universal instantiation with description terms, whereas CNL does not. Moreover, the quantificational theory of the CCL is classical, whereas the quantificational theory of CFL is a free logic. Another difference is that CCL and CFL contain different description principles. Most importantly, the description principle of CCL ensures that even improper descriptions have a denotation, whereas the description principle of CFL does not guarantee this. CNL does not have a description principle. In the third chapter, I have studied collapse arguments for CCL, CFL, and CNL. A collapse argument is an argument for the following statement: if p is true, then it is necessarily true. A crucial role in the proofs of these collapse results was played by so-called self-predication principles, which say that under certain conditions the predicate that expresses the descriptive condition can be combined by the description term formed out of that predicate with the result being a true sentence. In this chapter I have discussed a collapse argument for the extension of CCL with a self-predication principle, I have given a collapse argument for a similarly extended CFL, and most importantly, I have given a collapse argument for the extension of CNL with a self- predication principle. Finally, I have argued that the relevant self-predication principles are unsound under a Carnapian interpretation. In the fourth chapter, I have studied the extension of Peano Arithmetic with a Carnapian modal logic C, which is a dummy letter standing for either CCL or CFL. One can prove that the principle of the necessity of identity is a theorem of CPA. This implies that one gets a collapse result for CPA. The standard principle of weak induction was crucial for the proof. One can also prove that, if one assumes a particular self-predication principle, and if one assumes the principle of strong induction or, equivalently, the least-number principle, then one gets a partial collapse of de re modal truths in de dicto modal truths. I have argued that, if the box operator is interpreted as a metaphysical necessity operator, then Platonists would not be inimical to the collapse result. But if CPA is extended with a physical theory, then there is a threat that physical truths become physical necessiti es. It was shown that, under a Carnapian interpretation, the standard principle of weak induction is unsound, and that it can be replaced by a Carnapian principle of weak induction that is sound. The problem of logical and mathematical omniscience prevents ordinary Carnapian intensional logic from being taken seriously as a logic adequate for describing the principles of demonstrability. Yet many of the proof-theoretic results of the first part carry over to the part on Carnapian epistemic arithmetic with descriptions, since proof-theoretic results are independent of the informal reading of the operators. In the fifth chapter, I looked at extensions of arithmetic with a modal logic in which the box operator is interpreted as a demonstrability operator. A first extension in that sense is Shapiro s Epistemic Arithmetic. Shapiro himself offered the problem of mathematical omniscience as a reason why it is difficult to find a model theory for EA. Horsten attempted to provide a model theory via the detour of Modal-Epistemic Arithmetic. The attention of the reader was drawn to an incoherence in the model theory of. Two alternative solutions were presented and, after a short discussion of the problem of de re demonstrability one of those alternatives was chosen. The discussion of the problem of de re demonstrability made it clear that it would be interesting to study the epistemic properties of notation systems. Horsten himself provided a framework for this, viz. Carnapian Epistemic Arithmetic, and he started a systematic study of the epistemic properties of notation systems within that framework. However, he did not provide non-trivial but adequate models. To make a start with solving the problem of finding good models for CEA, I introduced Carnapian Modal-Epistemic Arithmetic In constructing CMEA I incorporated the lesson about the principle of weak induction learnt in the fourth chapter. In the sixth chapter, I gave a critical assessment of an argument concerning the limits of de re demonstrability about the natural numbers. The conclusion of the Description Argument is that it is undemonstrable that there is a natural number that has a certain property but of which it is undemonstrable that it has that property. A crucial step in the Description Argument involved a self-predication principle. Making good use of one of the results obtained in the third chapter, I proved a collapse result for the background theory against which the Description Argument was formulated. I concluded that either the either the Description Argument is sound but its conclusion is trivial, o r the Description Argument is unsound, or it is a cheapshot. As an appendix I included an article co-authored by prof. dr. Leon Horsten and me. The topic of the article is indirectly related to some other topics investigated in my dissertation. Also, it backs up one of the addition al theses I might be asked to publicly defend during my doctoral exam. T he topic of the appendix is the set of the so-called paradoxes of strict implication. Jonathan Lowe has argued that a particular variation on C.I. Lewis notion of strict implication avoids the paradoxes of strict implication. Pace Lowe, it is argued that Lowe s notion of implication does not achieve this aim. Moreover, a general argument is offered to the effect that no other variation on Lewis notion of constantly strict implication describes the logical behaviour of natural language conditional s in a satisfactory way. (shrink)