Some have claimed that there are laws of appearance, i.e. in principle constraints on which types of sensory experiences are possible. Within a representationalist framework, these laws amount to restrictions on what a given experience can represent. I offer an in-depth defence of one such law and explain why prevalent externalist varieties of representationalism have trouble accommodating it. In light of this, I propose a variety of representationalism on which the spatial content of experience is determined by intrinsic features of (...) conscious subjects. I conclude by considering an externalist-friendly reworking of my proposal, but suggest that the success of such a reworking is dubious. (shrink)

This paper examines a recent proposal for reviving so-called resemblance nominalism. It is argued that, although consistent, it naturally leads to trope theory upon examination for reasons having to do with the appeal of neutrality as regards certain non-trivial ontological theses.

My concern in this paper is with the intentionality of emotions. Desires and cognitions are the traditional paradigm cases of intentional attitudes, and one very direct approach to the question of the intentionality of emotions is to treat it as sui generis—as on a par with the intentionality of desires and cognitions but in no way reducible to it. A more common approach seeks to reduce the intentionality of emotions to the intentionality of familiar intentional attitudes like desires and cognitions. (...) In this paper, I argue for the sui generis approach. (shrink)

'Propositionalism' is the widely held view that all intentional mental relations-all intentional attitudes-are relations to propositions or something proposition-like. Paradigmatically, to think about the mountain is ipso facto to think that it is F, for some predicate 'F'. It seems, however, many intentional attitudes are not relations to propositions at all: Mary contemplates Jonah, adores New York, misses Athens, mourns her brother. I argue, following Brentano, Husserl, Church and Montague among others, that the way things seem is the way they (...) are, and that propositionalism must be abandoned. (shrink)

The most common account of attitude reports is the relational analysis according towhich an attitude verb taking that-clause complements expresses a two-placerelation between agents and propositions and the that-clause acts as an expressionwhose function is to provide the propositional argument. I will argue that a closerexamination of a broader range of linguistic facts raises serious problems for thisanalysis and instead favours a Russellian `multiple relations analysis' (which hasgenerally been discarded because of its apparent obvious linguistic implausibility).The resulting account can be (...) given independent philosophical motivations within anintentionalist view of truth and predication. (shrink)

We begin with a puzzle: why do some know-how attributions entail ability attributions while others do not? After rejecting the tempting response that know-how attributions are ambiguous, we argue that a satisfactory answer to the puzzle must acknowledge the connection between know-how and concept possession (specifically, reasonable conceptual mastery, or understanding). This connection appears at first to be grounded solely in the cognitive nature of certain activities. However, we show that, contra anti-intellectualists, the connection between know-how and concept possession can (...) be generalized via reflection on the cognitive nature of intentional action and the potential of certain misunderstandings to undermine know-how even when the corresponding abilities and associated propositional knowledge are in place. Such considerations make explicit the intimate relation between know-how and understanding, motivating a general intellectualist analysis of the former in terms of the latter. (shrink)

To define new property terms, we combine already familiar ones by means of certain logical operations. Given suitable constraints, these operations may presumably include the resources of first-order logic: truth-functional sentence connectives and quantification over objects. What is far less clear is whether we can also use modal operators for this purpose. This paper clarifies what is involved in this question, and argues in favor of modal property definitions.

An ontology's theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions $R_{i}$ . The power of PPL is illustrated (...) by its clarification of the self-referential nature of impredicative definitions and its distinguishing between legitimate and illegitimate forms. With a wellmotivated refinement on the axiom of comprehension, PPL is, in effect, a higher-order logic without a forced stratification of predicates into types or the use of other ad hoc restrictions. The Russell-Priest characterization of the classic self-referential paradoxes is used to show how PPL diagnosis and solves these antimonies. A direct application of PPL is made to Grelling's Paradox. Also shown is how PPL can distinguish between identity and indiscernibility. (shrink)

The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small (...) models and hence that its ontological commitments—and, therefore, those of the fundamental principle of world theory—are minimal. (shrink)

It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable divide between concept and object. These presuppositions, taken at face value, (...) reflect a significant metaphysical viewpoint, one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar “adaptations” to FOL—culminating in a standardized framework known as Common Logic —have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning upon information on the World Wide Web. (shrink)

Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed (...) some light on relevant passages of the Grundlagen. I will argue that Yourgrau does not make his case.The arguments with which we are concerned are found in the last three sections of Yourgrau's paper. A pervasive difficulty in these sections is that it is not clear exactly what Yourgrau is arguing against. The stated object of his attack is the Fregean thesis, a thesis about what numbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is that numbers number, where, roughly speaking, a number n numbers an object x just in case n can be legitimately assigned to x. The reason for this shift in emphasis appears to be rooted in a misconception. As we’ll see in more detail shortly, Yourgrau's argument against the Fregean thesis is based on an extension of a well known argument of Frege's found in §§22-3 of the Grundlagen, which Glenn Kessler has tagged the ‘relativity argument,’. According to Yourgrau, this is an argument ‘to the effect that what is literally numbered cannot simply be concrete objects’. This is incorrect. Frege himself clarifies the point of the argument in §21 with the following preface:In language, numbers (i.e., numerals] most commonly appear in adjectival form and attributive construction in the same sort of way as the words "hard" or "heavy" or "red," which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color. (shrink)

The semantical framework is fundamentally intensional: neither possible worlds nor sets as basic entities, but rather, besides individuals, propositions, properties and relations (in intension). Logical truth is defined in terms of logical form (without mentioning this notion) without employing sets of models and the concept of truth in a model. Truth itself is explicitly defined (without recursion); the truth-conditions for the logical constants of the object-language become theorems derivable from the axioms for "to intend"--the basic semantical relation.

We show how to construct certain L M, T -type interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the L T -type, truth-theoretic languages first considered by Kripke, yet each of our L M, T -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and (...) meaningfulness) of the claim that the strengthened Liar is meaningless. (shrink)

We show how to construct certain " $[Unrepresented Character]_{M,T}$ -type" interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the $[Unrepresented Character]_{T}$ -type, truth-theoretic languages first considered by. Kripke, yet each of our $[Unrepresented Character]_{M,T}$ -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and meaningfulness) (...) of the claim that the strengthened Liar is meaningless. (shrink)

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

The following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem (...) to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity. (shrink)

On the one hand, Pavel Tichý has shown in his Transparent Intensional Logic (TIL) that the best way of explicating meaning of the expressions of a natural language consists in identification of meanings with abstract procedures. TIL explicates objective abstract procedures as so-called constructions. Constructions that do not contain free variables and are in a well-defined sense ´normalized´ are called concepts in TIL. On the second hand, Kolmogorov in (Mathematische Zeitschrift 35: 58–65, 1932) formulated a theory of problems, using NL (...) expressions. He explicitly avoids presenting a definition of problems. In the present paper an attempt at such a definition (explication)—independent of but in harmony with Medvedev´s explication—is given together with the claim that every concept defines a problem. The paper treats just mathematical concepts, and so mathematical problems, and tries to show that this view makes it possible to take into account some links between conceptual systems and the ways how to replace a noneffective formulation of a problem by an effective one. To show this in concreto a wellknown Kleene’s idea from his (Introduction to metamathematics. D. van Nostrand, New York, 1952) is exemplified and explained in terms of conceptual systems so that a threatening inconsistence is avoided. (shrink)

If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended conditions.

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

Ha sido uno de los alegatos centrales de la teoría así llamada “cognitiva” de las proposiciones que su carácter representacional —y, con ello, sus condiciones de verdad— es derivativo del carácter representacional primitivo de los actos cognitivos concretos por los que un agente predica una propiedad de un objeto. Las proposiciones heredan su carácter representacional porque son ‘tipos’ de actos cognitivos particulares que poseen el ‘mismo’ contenido representacional. Se argumenta en este trabajo que esta suposición está en conflicto con el (...) hecho de que actos cognitivos concretos son instancias de ciertos tipos. Bajo la mayoría de las concepciones acerca de lo que funda el hecho de que una pluralidad de objetos comparte la ‘misma’ naturaleza —i. e., acerca de cómo son algo ‘uno’ en lo múltiple— el carácter cualitativo de un objeto está fundado en universales o en alguna otra construcción aceptable para el nominalista. (shrink)

The Problem of Doxastic Shift may be stated as a dilemma: on the one hand, the distribution of nominal complements of the form `the ψ that p’ strongly suggests that `that’-clauses cannot be univocally assigned propositionaldenotations; on the other hand, facts about quantification strongly suggest that `that’-clauses must be assigned univocal denotations. I argue that the Problem may be solved by defining the extension of a proposition to be a set of facts or, more generally, conditions. Given this, the logical (...) operation of descriptive predication can be introduced in a way that resolves the dilemma withoutsacrificing the singular term analysis of `that’-clauses. (shrink)

‘Drawing Metaphysical Consequences from a T-theory’. Pubblicato come quarto capitolo di Semantics, Tense, and Time: An Essay in the Metaphysics of Natural Language, Cambridge, Massachussetts, MIT Press, 1999. Per gentile concessione dell’autore e dell’editore. Traduzione italiana di Carlotta Pavese. L’idea che lo studio del linguaggio possa illuminare certe questioni metafisiche ha radici lontane nella storia della filosofia. Questa assunzione sembra già operante ai tempi del filosofo pre-soc...

‘Drawing Metaphysical Consequences from a T-theory’. Pubblicato come quarto capitolo di Semantics, Tense, and Time: An Essay in the Metaphysics of Natural Language, Cambridge, Massachussetts, MIT Press, 1999. Per gentile concessione dell’autore e dell’editore. Traduzione italiana di Carlotta Pavese. L’idea che lo studio del linguaggio possa illuminare certe questioni metafisiche ha radici lontane nella storia della filosofia. Questa assunzione sembra già operante ai tempi del filosofo pre-soc...

In this paper we investigate two purely syntactical notions ofcircularity, which we call ``self-application'''' and ``self-inclusion.'''' Alanguage containing self-application allows linguistic items to beapplied to themselves. In a language allowing for self-inclusion thereare expressions which include themselves as a proper part. We introduceaxiomatic systems of syntax which include identity criteria andexistence axioms for such expressions. The consistency of these axiomsystems will be shown by providing a variety of different models –these models being our circular languages. Finally we will show what (...) apossible semantics for these circular languages could look like. (shrink)

Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.

We critically investigate and refine Dunn's relevant predication, his formalisation of the notion of a real property. We argue that Dunn's original dialectical moves presuppose some interpretation of relevant identity, though none is given. We then re-motivate the proposal in a broader context, considering the prospects for a classical formalisation of real properties, particularly of Geach's implicit distinction between real and ''Cambridge'' properties. After arguing against these prospects, we turn to relevance logic, re-motivating relevant predication with Geach's distinction in mind. (...) Finally we draw out some consequences of Dunn's proposal for the theory of identity in relevance logic. (shrink)

Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. (...) From this observation we draw some philosophical conclusions about the possibility of a ‘correct’ analysis of structural properties. (shrink)

It is common for philosophers to offer philosophical accounts or analyses, as they are sometimes called, of knowledge, autonomy, representation, (moral) goodness, reference, and even modesty. These philosophical analyses raise deep questions.What is it that is being analyzed (i.e. what sorts of things are the objects of analysis)? What sort of thing is the analysis itself (a proposition? sentence?)? Under what conditions is an analysis correct? How can a correct analysis be informative? How, if at all, does the production of (...) philosophical analyses differ from what scientists do? The purpose of the present paper is to provide answers to these questions. (shrink)

The dominant account of propositions holds that they are structured entities that have, as constituents, the semantic values of the constituents of the sentences that express them. Since such theories hold that propositions are structured, in some sense, like the sentences that express them, they must provide an answer to what I will call Soames’ Question: “What level, or levels, of sentence structure does semantic information incorporate?”. As it turns out, answering Soames’ Question is no easy task. I argue in (...) this paper that the two most promising ways of answering it, the Logical Form Account and the LF Account, are both unsatisfactory. This result casts doubt on the very idea that propositions are structured. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

In an attempt to accommodate natural language phenomena involving nominalization and self-application, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briefly review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version ofsubsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained (...) in the type of individuals. Russell's paradox is avoided by placing a type-constraint on lambda-abstraction, rather than by restricting comprehension. (shrink)

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional (...) logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (shrink)

Logical semantics includes once again structured meanings in its repertoire. The leading idea is that semantic and syntactic structure are more or less isomorphic. A key motive for reintroducing sensitivity to semantic structure is to obtain fine‐grained meanings, which are individuated more finely than in possible‐world semantics, namely up to necessary equivalence. Just getting the truth‐conditions right is deemed insufficient for a full semantic analysis of sentences. This paper surveys some of the most recent contributions to the program of structured (...) meaning, while providing historical background. I suggest that to make substantial advances the program needs to solve the problem of propositional unity and develop an intensional mereology of abstract objects. (shrink)

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third primitive entity. (...) Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application. (shrink)

Several intrinsic/extrinsic distinctions amongst properties, current in the literature, are discussed and contrasted. The proponents of such distinctions tend to present them as competing, but it is suggested here that at least three of the relevant distinctions (including here that between non-relational and relational properties) arise out of separate perfectly legitimate intuitive considerations: though of course different proposed explications of the informal distinctions involved in any one case may well conflict. Special attention is paid to the question of whether a (...) single notion of property is capable of supporting the various distinctions. (shrink)

A common feature of all standard theories of the laws of nature is that they are "absolutist": They take laws to be either all metaphysically necessary or all contingent. Science, however, gives us reason to think that there are laws of both kinds, suggesting that standard theories should make way for "non-absolutist" alternatives: theories which accommodate laws of both modal statuses. In this paper, we set out three explanatory challenges for any candidate non-absolutist theory and discuss the prospects of the (...) two extant candidates in light of these challenges. We then develop our own non-absolutist theory, the essentialist DTA account, which combines the nomic-necessitation or DTA account with an essentialist approach to metaphysical modality in order to meet the three explanatory challenges. Finally, we argue that the distinction between kinematical and dynamical laws found in physical theories supports both non-absolutism in general and our proposed essentialist DTA view in particular. (shrink)

Propositions, the abstract, truth-bearing contents of sentences and beliefs, continue to be the focus of healthy debates in philosophy of language and metaphysics. This article is a critical survey of work on propositions since the mid-90s, with an emphasis on newer work from the past decade. Topics to be covered include a substitution puzzle about propositional designators, two recent arguments against propositions, and two new theories about the nature of propositions.

In this paper we (i) identify the notion of ‘essentially non-conceptual content’ by critically analyzing the recent and contemporary debate about non-conceptual content, (ii) work out the basics of broadly Kantian theory of essentially non-conceptual content in relation to a corresponding theory of conceptual content, and then (iii) demonstrate one effective application of the Kantian theory of essentially non-conceptual content by using this theory to provide a ‘minimalist’ solution to the problem of perceptual self-knowledge which is raised by Strong Externalism.

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories—such as object , property , and relation —are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical (...) form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach—including Frege’s notorious paradox of the concept horse—are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments. (shrink)

If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...) sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (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 “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly (...) defining the number operator, what advantage, if any, does adopting this course possess over a direct stipulation of the Dedekind-Peano axioms? This paper attempts to answer them. In response to the first, we spell out the links between the recognition of numerical terms as vehicles of singular reference and the conception of numbers as possible objects of singular, or object-directed, thought, and the role of the acknowledgement of numbers as objects in the neo-Fregean attempt to justify the basic laws of arithmetic. In response to the second, we argue that the crucial issue concerns the capacity of either stipulation—of Hume’s Principle, or of the Dedekind-Peano axioms—to found knowledge of the principles involved, and that in this regard there are crucial differences which explain why the former stipulation can, but the latter cannot, play the required foundational role. (shrink)