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)

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. (shrink)

In Transparent Intensional Logic we can recognize two distinct notions of computation that loosely correspond to term rewriting and term interpretation as known from lambda calculus. Our goal will be to further explore these two notions and examine some of their properties.

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)

According to the resemblance account of ‘what it's like’ and similar constructions, a sentence such as ‘there is something it's like to have a toothache’ means ‘there is something having a toothache resembles’. This account has proved controversial in the literature; some writers endorse it, many reject it. We show that this conflict is illusory. Drawing on the semantics of intensional transitive verbs, we show that there are two versions of the resemblance account, depending on whether ‘resembles’ is construed (...) notionally or relationally. While well-known criticisms of the resemblance account undermine its relational version, they do not touch its notional version. On the contrary, the notional version is equivalent to various accounts usually interpreted as rivals to resemblance. We end by noting that this resolution of the controversy (a) explains why ‘like’, which is a comparative, appears in a construction that concerns the properties of events and (b) removes any pressure to suppose that ‘like’ is ambiguous between a comparative and a non-comparative sense. (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)

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)

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. (shrink)

What are logical notions? According to a very popular proposal, a logical notion is something invariant under some “transformation” of objects, usually permutations or isomorphisms. The first chapter is about extending “invariance” accounts of logicality to intensional notions, by asking for invariance under arbitrary permutations of both possible worlds and objects. I discuss the results one gets in this extended theory of invariance, and how to fix many technical issues. The second chapter is about setting out a (...) better theory of logicality. I discuss the limits of invariance frameworks, and the need for a theory of logicality with a more solid philosophical ground. I believe that the concept of information can play a major role in defining what logic is and what logical notions are. I spell out this intuition, by designing a new test for logicality. A notion is logical iff it behaves in a certain way, by checking only “structural aspects of information”, and it does so under arbitrary transformations of its “informational inputs”. In the last chapter I explore some interesting features of my theory. I show how, contrary to standard invariance, in mine logical notions tend to stay persistent across different models of information. I also spell out an intermediate notion of quasi-logicality to make sense of the formality of “world-sensitive” notions: notions whose behaviour changes across worlds. I finally propose a case study: deontic modals. I discuss how one can argue for their quasi-logicality, in my framework. The dissertation is concluded with a technical appendix, in which I prove that my theory is a restriction of standard permutation invariance when we model the space of information in a certain way: as a set of complete powersets of some sets. (shrink)

There are different ways we use the expressions “extension” and “intension”. I specify in the first part of this paper two basic senses of this distinction, and try to show that the old metaphysical sense, by means of particular instance vs. universal, is more fundamental than the contemporary sense by means of substitutivity. In the second part, I argue that logic in general is essentially intensional, not only because logic is a rule-guided activity, but because even the extensional definition (...) of a logic system presupposes an intensional notion of logical consequence. DOI:10.5007/1808-1711.2010v14n1p111. (shrink)

It is not rare to find students of language interested in the many ways in which speakers talk about Fred or about the weather, assert of Fred or of the weather that he is fat or that it is fine. Many philosophers, logicians, and linguists share an interest in what words or phrases designate or describe, and what speakers refer to, mention, and say things about. But it is also notable that the Grammarian and the Philosopher, especially the Metaphysician, have (...) looked at intentionality in different ways. In this lecture I sketch the ways that the Philosophers Nelson Goodman and W.V.O Quine and by contrast the Grammarians have analyzed and used the notion of Aboutness, in Quine’s case in his famous argument against Quantifying Into intensional sentences. Goodman’s and Quine’s analyses are motivated by different intellectual goals from the Linguists’. By contrast Linguists have the notion of Topic Noun Phrase. I shall argue that the Linguists’ notion of Topic Noun Phrase offers clarification and an intellectual advance over Goodman’s and Quine’s notions, especially in the treatment of propositional attitude sentences. (shrink)

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an (...) immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives. (shrink)

This article examines Moltmann’s analysis of intensional transitive verbs , and argues that the analysis fails because the key notion it employs, ‘variable satisfier’, is inconsistent.

In a 2005 paper Ólafur Páll Jónsson presents a puzzle that turns on intentional identity and definite descriptions. He considers eight solutions and rejects them all, thus leaving the puzzle unsolved. In this paper I put forward a solution. The puzzle is this. Little Lotta wants most of all a bicycle for her birthday, but she gets none. Distracted by the gifts she does receive, she at first does not think about the bike. But when seeing her tricycle, she is (...) reminded of the bike. The question is how we are to analyse these two occurrences of ‘the bike’ in the absence of a unique bike that Lotta wants. So the semantics of ‘the bike’ needs to be spelt out, and it must be made explicit what the complements of Lotta’s attitudes are. My analysis shows that the attributer’s usage of ‘the bike’ blurs the distinction between a second-order and a first-order intension (a property concept and a property, respectively). My solution can be summed up in this two-premise argument. (a) In the state-of-affairs S, the property of being a bike is the extension of the property concept the property such that Lotta wants an instance of it more than any other; (b) in S, Lotta does not think about/is reminded of the property that she wants an instance of more than any other; (c) therefore, in S Lotta does not think about/is reminded of the property of being a bike. This solution requires looking beyond the confines of denotational semantics, which all of Jónsson’s eight solution candidates belong to. (shrink)

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

In the semantic literature, there is a class of examples involving anaphora in intensional contexts, i.e. under the scope of modal operators or propositional attitude predicates, which display anaphoric relations that appear at first glance to violate otherwise well-supported generalizations about operator scope and anaphoric potential. In Section 1,I will illustrate this phenomenon, which, for reasons that should become clear below, I call modal subordination; I will develop a general schema for its identification, and show how it poses problems (...) for most theories of scope and anaphoric relations. In Section 2, I will review the main approaches which have been considered in attempting to account for modal subordination and argue that only an approach involving accommodation can account for the full range of examples. The notion of accommodation is due to Lewis, who defines it as follows: If at time t something is said that requires presupposition P to be acceptable, and if P is not presupposed just before t, then - ceteris paribus and within certain limits - presupposition P comes into existence at t.(Lewis 1979: 340) The interesting question, of course, is what the limits on accommodation might be. I believe that the proper account of modal subordination has something to say about this. I will argue this briefly in section 3, where I draw some conclusions and also sketch some ... (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 aims of this paper are to survey, explicate, compare, contrast, and critically evaluate a number of (mainly recent and technical) contributions (Kanger, Porn and Áqvist) to the logic of action locutions in connection with their treatment of the concept of an agent's bringing about a state of affairs. The discussion is primarily concerned with practical applications of these formalisms for the action theorist. It is suggested that these systems are best understood as capturing a strategic sense of bringing-about, and (...) not a notion of actual bringing-about, which is merely presupposed by them. It is argued that the developments surveyed open up a new 'intensional' style of action theory, contrasted with the 'extensional' approach of Davidson. Yet because of the treatment of conditionals, they fail to capture a basic notion of 'bringing about' important for action theory. It is concluded that a study of the behavior of 'bringing-about' over non-standard conditionals would be a useful next step for intensional action logic. (shrink)

After the publication of Marshall’s theorem (2009), it has been widely accepted that the intrinsic/extrinsic distinction cannot be analyzed in broadly logical terms, but instead requires appealing to more robust metaphysical notions like grounding, naturalness or duplication. However, in this article I will defend that this is not so. Instead of showing the limitations of Marshall’s undoubtedly impressive result, I will present here a broadly logical definition of the intrinsic/extrinsic distinction, and show that it is extensional adequate regardless of (...) our preferred conception of property identity. (shrink)

Our knowledge, beliefs, doubts, etc., concern primarily logical constructions of propositions. If we assume that iterating ‘belief attitudes’ is valid, i.e., that the agent is perfectly introspective, he knows what he knows, believes, etc., then the so-called propositional attitudes are actually hyperintensional attitudes, i.e., they are relations of an agent to the construction–concept expressed by the embedded clause. Their implicit counterparts, relations of an agent to the proposition denoted by the embedded clause, are just idealised cases of an agent with (...) unlimited inferential abilities. On the other hand, our wishes, intentions, seeking, finding, etc., concern particular intensions, and the so-called notional attitudes are not hyperintensional. In the paper we formulate some criteria for notional attitudes and examine basic categories of them. In general, notional attitudes are relations-in-intension between an agent and an object to which the agent is intentionally related. Even relations of an agent to a proposition can be notional ones, in case there is no salient constructional counterpart, the attitude is not influenced by agent’s inferential abilities. Another problem we meet is the ambiguity of sentences expressing notional attitudes. These statements can often be read both in the de dicto and in the de re way. Yet, a common feature that characterizes notional attitudes is using the construction of the respective intension in the de dicto way. The respective intension is mentioned; referring on such a situation, the reporter may use any of the equivalent constructions of the intension, but not just a co-referring notion of another intension. Still, unlike the cases of relations of an agent to an individual when the respective individual office serves just as a pointer to the individual, when referring on notional attitudes the use of the respective notion of the intension is indispensable, which might perhaps justify calling such attitudes notional, though they actually are intensional. We also show that a passive form of a sentence cannot be usually read in the de dicto way. Thus a common belief at the equivalence of the active and passive form of a statement is generally not justified. (shrink)

In his paper Leblanc seeks to supplant traditional forms of semantic theory with truth-value analyses. I have tried, here, to extend the scope, if not the limits, of his results. But now, in closing, I wish to register some reservations about his notion of relevance.Leblanc eschews the customary semantic analysis of intensional languages — the so-called ‘possible worlds’ semantics — as making ‘metaphysical virtue out of logical necessity’. And so he would replace such accounts with ‘truth-value’ analyses. But, alas, (...) these theories are seen to have only limited application. Either all the atoms of a language must be evaluated by the functions in W in a truth-value ℋ 〈W, α, R〉, or the functions must be indexed. Because I share Leblanc's opinion that it ought to be that only the atoms of a theory are linguistically pertinent to it, I opt for the second alternative. Here, of course, things work out all right. But, as Leblanc notes, indexing the functions is equivalent to doing semantics in the usual way. In either case, new parameters are required for the evaluation of theories. So more than just the truth-values of a theory's atoms is relevant.My concern is with natural languages. It has long been recognized — though only more recently well articulated4 — that an adequate semantic analysis of such languages, with their indexical and intensional features, must relativize the notion of truth to various indices, viz., aspects of the contexts of utterance of sentences. It is clear that the truth-value of ‘If your feet hurt, then it may rain tomorrow’ depends on more than just the truth-values of its atoms: the speaker, hearer, place, and time of utterance of the sentence are at least to be included among the extra-linguistic features required for an evaluation of the sentence. Such indices thus provide various realizations of the notion of a possible world, and they are all relevant. (shrink)

This paper presents an elucidation of Kant’s notion of judgment, which clearly is a central challenge to the understanding of the Critic of Pure Reason, as well as of the Transcendental Idealism. In contrast to contemporary interpretation, but taking it as starting point, the following theses will be endorsed here: i) the synthesis of judgment expresses a conceptual relation understood as subordination in traditional Aristotelian logical scheme; ii) the logical form of judgment does not comprise intuitions ; iii) the relation (...) to intuition is not a judgment concern; iv) the response to the question about the ‘x’ that grounds the conceptual relation in judgments must be sought in transcendental aspects: 1) on construction in pure form of intuition, 2) in experience and 3) in the requirements to experience, respectively to mathematical, empirical, and philosophical judgments. The overall purpose is to build up an understanding of judgment that supports a latter assessment of Kant’s theoretical philosophy. (shrink)

According to the resemblance account of 'what it's like' and similar constructions, a sentence such as 'there is something it’s like to have a toothache' means 'there is something having a toothache resembles'. This account has proved controversial in the literature; some writers endorse it, many reject it. We show that this conflict is illusory. Drawing on the semantics of intensional transitive verbs, we show that there are two versions of the resemblance account, depending on whether 'resembles' is construed (...) notionally or relationally. While well-known criticisms of the resemblance account undermine its relational version, they do not touch its notional version. On the contrary, the notional version is equivalent to various accounts usually interpreted as rivals to resemblance. We end by noting that this resolution of the controversy (a) explains why 'like', which is a comparative, appears in a construction that concerns the properties of events, and (b) removes any pressure to suppose that 'like' is ambiguous between a comparative and a non-comparative sense. (shrink)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, (...) and lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

In this paper, I reconstruct Quine’s arguments against quantified modal logic, from the early 1940’s to the early 1960’s. Quine’s concerns were not technical. Quine was looking for a coherent interpretation of quantified-in English modal sentences. I argue that Quine’s main thesis is that the intended objectual interpretation of the quantifiers is incompatible with any semantic reading of the modal operators, for example as expressing analytic necessity, unless the entities in the domain of quantification are intensions, i.e. definitional entities. The (...) difficulty is that it makes no sense to say of an ordinary object that it bears a property necessarily or contingently when the necessity or contingency in question is analytic. However, starting in 1960, Quine claims that quantified-in modal sentences can be coherently interpreted only as essentialist predications. When we say about an object that it necessarily F ’s, we can only coherently mean that it essentially F ’s. In the paper, I argue that adequately qualified the thesis is plausible. Two important qualifications are needed. The first is the assumption that satisfaction is an irreducibly predicative notion, making any explication of satisfaction in terms of truth inadequate. The second is the ontological rejection of purely semantic, i.e. merely definitional, entities. With these qualifications in place, Quine’s rejection of the combination of objectual quantifiers and semantic modalities can be upheld. In this way, we vindicate a qualified version of Quine’s conjecture that quantified modal logic is committed to essentialism. (shrink)

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an (...) immortal gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul ] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives. (shrink)

Attempting to deflate ontological debates, the proponent of Quantifier Variance (QV) claims that there are multiple quantifier meanings of equal metaphysical merit. According to Hirsch—the main proponent of QV—metaphysical merit should be understood intensionally: two languages have equal merit if they allow us to express the same possibilities. I examine the notion of metaphysical merit and its purported link to intensionality. That link, I argue, should not be supported by adopting an intensional theory of semantic content. Rather, I give (...) a general strategy for supporting claims about metaphysical merit and examine whether that strategy can be used to link merit and intensionality. Though I don’t deliver a definitive verdict, the discussion provides a clearer framework for articulating and evaluating claims about metaphysical merit. (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)

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a constant (...) domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution. (shrink)

The paper is an addition to the intensionalist approach to decision theory, with emphasis on game theoretic modelling. Extensionality in games is an a priori requirement that players exhibit the same behavior in all algebraically equivalent games on pain of irrationality. Intensionalism denies that it is always irrational to play differently in differently represented but algebraically equivalent versions of a game. I offer a framework to integrate game non-extensionality with the more familiar idea of linguistic non-extensionality from philosophy of language, (...) followed by applications of it based on toy examples of well-known game models. I argue that the notion of what I call “Intensional Nash Equilibrium” is, in effect, very useful in understanding human decision-making. (shrink)

This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are (...) both empirical and essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. Every wooden table is necessarily wooden , one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations. (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)

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the q-consequence reflecting the idea is that its rules (...) lead from the non-rejected assumptions to the accepted conclusions.First, we focus on the syntactic features of the framework and present the q-consequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective inferential is used to characterize the approach and, possibly, the term inference operation replaces q-consequence. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g.[4], the new approach opens perspectives for further exploration. (shrink)

The paper focuses on two apparent paradoxes arising from our use of intensional verbs: first, their object can be something which does not exist, i.e. something which is nothing; second, the fact that entailment from a qualified to a non-qualified object is not guaranteed. In this paper, I suggest that the problems share a solution, insofar as they arise in connection with intensional verbs that ascribe mental states. The solution turns on (I) a properly intensional or nonrelational (...) notion of representation and (II) a notion of “putting a representation on display”. (shrink)

I am grateful to Brendan Minogue for his careful and detailed discussion of the concept of “intensional reference” as it appears in my book The Structure of Scientific Inference. He concludes that my account contains some important inconsistencies that vitiate my attempt to reconcile the idea of cumulative acquisition of scientific knowledge with radically changing theories. He rightly sees that this attempt depends crucially on the account of translatability between theories, and this in turn upon the notion of “identity (...) of intensional reference.” This means that the attempt fails if there are inconsistencies in the concept of IR. Since Minogue's careful analysis nevertheless contains some misunderstandings, I must plead guilty to a number of unclarities, but I do not believe there are basic inconsistencies. Let me try again. (shrink)

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not come (...) for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

Paul Thom's book presents Kilwardby's science of logic as a body of demonstrative knowledge about inferences and their validity, about the semantics of non-modal and modal propositions, and about the logic of genus and species. This science is thoroughly intensional. It grounds the logic of inference on "that in virtue of which" the inference holds. It bases the truth conditions of propositions on relations between conceptual entities. It explains the logic of genus and species through the notion of essence. (...) Thom interprets this science as a formal logic of intensions with its own proof theory and semantics. This comprehensive reconstruction of Kilwardby's logic shows the medieval master to be one of the most interesting logicians of the thirteenth century. (shrink)

The aim of this paper will be to show how significant the logical theories of judgement which were worked out at the end of the nineteenth century have been for the ontological thought during the twentieth century. Against the classical - Aristotelian and Scholastic - analysis of predicative judgement, Franz Brentano on one hand and Gottlob Frege on the other hand have leveled two different criticisms, which then generated two radically divergent ontological paradigms. On one side, despite Brentano’s own nominalistic (...) stands, there was a tremendous extension of the general category of “object” as well as of the notion of “being” with, as a consequence, the exceptionnally luxuriant ontologies of Brentano’s heirs. On the other side, notwithstanding Frege’s own Platonistic affinities, there was a drastic deflation of the realm of objects to the benefit of the realm of concepts taken as classifying functions, and therefore a strong nominalistic trend among Frege’s heirs. The development of quantified modal logics at the middle of twentieth century however forced contemporary ontology to reconsider this simple alternative in order to give place to some hybrid entities such as individual concepts or other kinds of “intensional objects”. (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)

This chapter contains sections titled: Enriching Extensional Logic with Intensional Notions Changing Views of Modal Logic A Précis of Basic Modal Logic The Major Applications Fine‐Structure of Expressive Power System Combination: Action and Information Back to the Heartland Conclusion.

Problems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo α- and η-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church’s conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a (...) concept and every concept can be viewed as a problem.Kolmogorov’s idea of a connection between problems and Heyting’s calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions. (shrink)

In my paper I am concerned with Peter van Inwagen's Consequence Argument. I focus on its probably best known version. In this form it crucially employs the notion of rendering a proposition false, anotion that has never been made sufficiently clear. The main aim of my paper is to shed light on thisnotion. The explications offered so far in thedebate all are based on modal concepts. Iargue that for sufficient results a ``stronger'', hyper-intensional concept is needed, namely the concept (...) expressed by the word ``because''. I show that my analysis is superior to the prior ones. On the basis of this analysis I further explain why van Inwagen''s argument fails. (shrink)

Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single (...) occurrence of a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate. (shrink)

I follow Giordani in distinguishing between a situational and informational conception of subject-matter and consider some of the different ways in which it might be explained within both an intensional and an hyperintensional account of propositional identity.

SummaryAccording to Dummett's understanding of Frege, the sense of a denoting expression is a procedure for determining its denotation. The purpose of this article is to pursue this suggestion and develop a semi‐formal interpretation of Fregean sense for the special case of a first‐order language of arithmetic. In particular, we define the sense of each arithmetic expression to be a hypothetical process to determine the denoted number or truth value. The sense‐process is “hypothetical” in that the senses of some expressions (...) cannot be completed in a finite number of steps. The motivation for this work is to explicate an intensional notion of effectiveness in terms of the senses of function names. It is proposed, in particular, that an expression is effective if and only if its sense can be completed in a finite number of steps. It is shown that a function is computable if and only if it has an effective name.RésuméSelon la lecture que Dummet donne de Frege, le sens ?on;une expression consiste en une procédure pour déterminer sa dénotation. Le but de cet article est de développer cette suggestion par une interprétation semi‐formelle du sens frégéen dans le cas particulier ?on;un langage de premier ordre en arithmétique. En particulier, nous définissons comme sens de toute expression mathématique un procédé hypothétique pour déterminer le nombre dénoté ou la valeur de vérité. Le procédé créateur de sens est hypothetique en ce sens que les sens de certaines expressions ne peuvent pas être donnés en un nombre fini de pas. Le but de cette étude est ?on;expliciter une notion intensionnelle ?on;effectuabilite en termes de sens des noms de fonction. II est en particulier propose qu'une expression soit dite effectuable si et seulement si son sens peut être épuisé en un nombre fini de pas. On montre qu'une fonction est calculable si et seulement si elle a un nom effectuable.ZusammenfassungDummets Auffassung von Frege gemäss besteht der Sinn eines denotierenden Ausdruckes in einem Verfahren, das dessen Denotation bestimmt. Es ist der Zweck der vorliegenden Arbeit, die‐sen Vorschlag weiterzufuUhren und eine halbformale Interpretation des Fregeschen Sinnes fiir den besonderen Fall der Sprache erster Stufe der Arithmetik zu entwickeln. Es wird im besonderen der Sinn eines jeden arithmetischen Ausdruckes als hypothetisches Verfahren zur Bestimmung der denotierten Zahl oder des Wahrheitswertes definiert. Die Sinngebung ist insofern hypothe‐tisch, als der Sinn gewisser Ausdrucke nicht in einer endlichen Zahl von Schritten gegeben wer‐den kann. Das Anliegen der Arbeit grundet in der Absicht, einen intensionalen Begriff der Effek‐tivitat aufgrund des Sinnes von Funktionsnamen zu erlautern. Es wird im besonderen festgelegt, dass ein Ausdruck dann und nur dann effektiv sei, wenn sein Sinn in einer endlichen Zahl von Schritten erreicht werden kann. Es wird gezeigt, dass eine Funktion genau dann berechenbar ist, wenn sie einen effektiven Namen hat. (shrink)

La crítica contundente de Quine a las nociones intensionales, así como a todo lo superfluo para una ontología de raíz lógica de primer orden, le condujo a rechazar la validez de la noción de semejanza en el ámbito de las ciencias maduras . El artículo consiste preci-samente en responder a esta crítica desde una perspectiva no formalista en la que la ciencia no se reduce a simple teoría, sino que se comprende como un complejo interactivo de diversas prácticas . Mi (...) respuesta a Quine toma como eje fundamental el análisis de la semejanza en una ciencia madura como lo es la química, y presenta un estudio de caso en el ámbito de la química sintética. El objetivo del artí-culo es en tal sentido triple: por un lado, critico la concepción reductivis-ta quineana de la ciencia; por otro, reclamo la importancia de la semejan-za en química; y, por último, reivindico lo que denomino pragmatismo ex-perimental, un modo de análisis de la tecnociencia que tiene en cuenta la práctica real de ésta y la interacción teoría-experimento-prácticas científicas des-de una perspectiva naturalista. El título incluye el verbo “desquinear”, in-existente en español, en clara referencia a mi negativa de aceptar el análi-sis de Quine.Quine's strong criticism of intensional notions as well as of everything that is superfluous for an ontology based on first order logic led him to deny the legitimacy of the notion of similarity in the realm of the mature sciences . In this paper I try to refute Quine's view by adopting a non-formalistic perspective, i.e., a perspec-tive in which science is not simply reduced to a theory, but is rather seen as an interative complex of several different forms of scientific practices . My reply to Quine has as main pillar the analysis of the notion of similarity in a mature science like chemistry, and is based on a study of a concrete case in the realm of synthetic chemistry. The aim of this paper is, therefore, threefold: first, I shall criticize Quine's reductivism regarding science; second, I shall defend the centrality of the notion of similarity in chemistry; fi-nally, I shall defend what I call experimental pragmatism, i.e., a specific way of analysing technological sciences that takes into account both the actual scientific practice and the interaction between theory, ex-periment and practices from a naturalistic point of view. The title con-tains the verb "de-quining", which does not actually exist in Spanish, but clearly refers to my rejection of Quine's analysis. (shrink)

The theory of predication underlying assertoric syllogistic is quite extensional. Modal syllogistic is an extension of the assertoric one, dealing with a lot of intensional notions mostly borrowed from Topics and Posterior Analytics; but Aristotle’s attempt to bring together modalities and extensional form of assertoric premisses ends in failure after all, and the puzzles he faced with in building his modal syllogistic spring just from it.