This paper presents a precise semantics for incompletepredicates such as “ready”. Incompletepredicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incompletepredicates fail to accommodate these logical properties. The account offered here defines contexts as structures (...) containing an element called a proposition set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance. (shrink)
Elizabeth Prior claims that dispositional predicates are incomplete in the sense that they have more than one argument place. To back up this claim, she offers a number of arguments that involve such ordinary dispositional predicates as ‘fragile’, ‘soluble’, and so on. In this paper, I will first demonstrate that one of Prior’s arguments that ‘is fragile’ is an incomplete predicate is mistaken. This, however, does not immediately mean that Prior is wrong that ‘fragile’ is an (...)incomplete predicate. On the contrary, I maintain that she has offered another valid argument that does indeed establish the claim that ‘fragile’ is an incomplete predicate. I will argue further that Prior is right that ‘soluble’ is an incomplete predicate. Then does this mean that all dispositional predicates are incomplete? I don’t think so. I will suggest that there are complete dispositional predicates that have no more than one argument place. Finally, by relying on my discussion of the incompleteness of dispositional predicates, I will attempt to provide a better understanding of the context-dependence and intrinsic nature of dispositional ascriptions. (shrink)
Tyler Burge convinced us that names are predicates in at least some of their occurrences: -/- There are relatively few Alfreds in Princeton. -/- Names, when predicates, satisfy the being-called condition: schematically, a name "N" is true of a thing just in case that thing is called N. This paper defends the unified view that names are predicates in all of their occurrences. I follow Clarence Sloat, Paul Elbourne, and Ora Matushansky in saying that when a name (...) seems to occur bare in an argument position of a predicate, it is really occurring in the predicate position of a definite description with an unpronounced "the". I call these "denuded definite descriptions". There are good linguistic reasons for defending the denuded-definites view. For example, it explains why "the" cannot be dropped in a sentence like the following: -/- The ever-popular Bill will be speaking this afternoon; The taller Maria is downstairs. -/- The definite article occuring before a name doesn't get pronounced when it's right next to the name. In technical terms, it gets smushed together with it. But the smushing can't happen when another phrase intervenes. The view survives philosophical objections. Denuded definite descriptions with names are incomplete definite descriptions since most names have mutliple bearers. Incomplete definite descriptions are in general rigid, though. So the view survives Kripke's modal argument. (shrink)
The aim of this paper is (i) to defend Frege's view that the referents of predicates are certain kinds of functions, or "concepts", i.e. incomplete entities, and not their extensions (i.e. sets of objects described by those predicates); and (ii) to justify, by a natural augmentation of Frege's semantic theory with modal ingredients, Frege's position that the sameness between concepts, or property-sharing, turns only on the sameness of extensions. Several problems with the doctrine that a predicate's extension (...) is its referent are presented, including the regress argument and an argument from the modern philosophy of language related to natural kind terms. In this connection, it is also pointed out that all referential expressions are in a sense rigid. (shrink)
The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).
We discuss the challenge to truth-conditional semantics presented by apparent shifts in extension of predicates such as 'red'. We propose an explicit indexical semantics for 'red' and argue that our account is preferable to the alternatives on conceptual and empirical grounds.
Sarah Sawyer has challenged my claim that social externalism depends on the assumption that individuals have an incomplete grasp of their own concepts. Sawyer denies that Burge's later sofa thought-experiment relies on this assumption: the unifying principle behind the thought-experiments supporting social externalism, she argues, is just that referents play a role in the individuation of concepts. I argue that Sawyer fails to show that social externalism need not rely on the assumption of incomplete understanding. To establish the (...) content externalist conclusions, further considerations are required, and these do commit the externalist to the assumption of incomplete understanding. (shrink)
According to the simple proposal, a predicate is rigid iff it signifies the same property across the different possible worlds. The simple proposal has been claimed to suffer from an over-generalization problem. Assume that one can make sense of predicates signifying properties, and assume that trivialization concerns, to the effect that the notion would cover any predicate whatsoever, can be overcome. Still, the proposal would over-generalize, the worry has it, by covering predicates for artifactual, social, or evaluative properties, (...) such as 'is a knife,' 'is a bachelor,' or 'is funny.' In defense, it is argued that rigidity for predicates as characterized plays the appropriate theoretical role, and that the contention that "unnatural" properties are not to be rigidly signified is ungrounded. (shrink)
Two cases are distinguished. In one case two predicates belong to distinct languages. A straight-forward argument is presented that the predicates might be synonymous without being coextensive. In the second case the predicates belong to the same language. Here the issue is more involved, but the same conclusion is reached.
We generalize the incompleteness proof of the modal predicate logic Q-S4+ p p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.
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 A holds at a world wW if and only if A holds at every world vW such that wRv. 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 -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)
The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence is false, we (...) need an independent foundation of the concept of falsity. The solution I offer is a definition of falsity in terms of the truth of a syntactic negation of the sentence. A definition of syntactic negation is proposed for English (Section 1). The considerations are applied to the analysis of definites in non-generic sentences and the analysis of generic indefinites. These two domains are investigated in breadth and some depth and the analyses compared and connected. During the discussion of non-generic predications with definite arguments and their respective negations (Section 2), a theory of predication is developed, basic to which is the distinction between integrative and summative predication. Summative predication, e.g., distributive plural, leads to contrary, all-or-no-thing, polarity contrasts due to the fundamental Presupposition of Indivisibility. Further-more, levels of predication are distinguished that are built up by various processes of constructing macropredications from lexical predicates. Given this analysis, particular (i.e., non-generic) quantification (Section 3) can be reanalyzed as an integrative, first-order form of predication that fills the truth-value gaps created by summative predication. The account comprises both nominal and adverbial quantification and relates quantification to the simpler types of predication discussed in Section 2. (shrink)
It is widely-accepted that Descartes is a substance dualist, i.e. that he holds that there are two and only two kinds of finite substance – mind and body. However, several scholars have argued that Descartes is a substance trialist, where the third kind of substance he admits is the substantial union of a mind and a body, the human being. In this paper, I argue against the trialist interpretation of Descartes. First, I show that the strongest evidence for trialism, based (...) on Descartes' discussion of so-called incomplete substances, is highly inconclusive. Second, I show that a kind of unity (‘unity of nature’), which is had by all and only substances, is not had by human beings. The fact that the proper parts of a human being, namely a mind and a body, are of different natures entails that what they compose has at most a ‘unity of composition’. And a thing cannot be a substance in virtue of having a unity of composition. Therefore, Cartesian human beings are not substances. (shrink)
This paper argues that truth values of sentences containing predicates of “personal taste” such as fun or tasty must be relativized to individuals. This relativization is of truth value only, and does not involve a relativization of semantic content: If you say roller coasters are fun, and I say they are not, I am negating the same content which you assert, and directly contradicting you. Nonetheless, both our utterances can be true (relative to their separate contexts). A formal semantic (...) theory is presented which gives this result by introducing an individual index, analogous to the world and time indices commonly used, and by treating the pragmatic context as supplying a particular value for this index. The context supplies this value in the derivation of truth values from content, not in the derivation of content from character. Predicates of personal taste therefore display a kind of contextual variation in interpretation which is unlike the familiar variation exhibited by pronouns and other indexicals. (shrink)
The most common philosophical view of existence is that existence amounts to existential quantification or is a second-order concept. A less common philosophical view is that existence is a first-order property distinguishing between nonexistent (past, possible, or merely intentional) objects and existing objects. An even less common philosophical view is that existence divides into different ‘modes of being’ for different kinds of entities. The aim of the present paper is to take a closer look at how the notion of existence (...) is in fact expressed in natural language. In natural language, it appears, existence is not so much expressed by quantification, which can be shown to be neutral as regards any distinction between existent and nonexistent objects that one might draw. Rather existence is expressed by predicates, and that is, first-order predicates, such as in English 'exist', 'occur', and 'obtain'. The semantic behavior of such existence predicates reveals a notion of existence that divides into at least three different kinds of modes being, reflecting the distinction between endurance and perdurance, as well as their space-related analogues, but also the particular mode of being of such entities as states, facts, conditions, and laws. (shrink)
This takes a closer look at the actual semantic behavior of apparent truth predicates in English and re-evaluates the way they could motivate particular philosophical views regarding the formal status of 'truth predicates' and their semantics. The paper distinguishes two types of 'truth predicates' and proposes semantic analyses that better reflect the linguistic facts. These analyses match particular independently motivated philosophical views.
Tyler Burge’s influential arguments have convinced most philosophers that a thinker can have a thought involving a particular concept without fully grasping or having mastery of that concept. In Burge’s (1979) famous example, a thinker who lacks mastery of the concept of arthritis nonetheless has thoughts involving that concept. It is generally supposed, however, that this phenomenon – incomplete understanding, for short – does not require us to reconsider in a fundamental way what it is for a thought to (...) involve a particular concept. In this paper, I argue that the real significance of incomplete understanding has not been appreciated. To the extent that theorists of content address the phenomenon of thoughts involving incompletely grasped contents at all, they tend to assume that some hand-waving about deference to other thinkers who fully grasp the relevant concepts will take care of the inconvenient cases of incomplete understanding. The main lesson of Burge’s arguments is often taken to be that the content of language and thought is socially determined. On this picture, we do not need to change our basic view about what it is to have a concept; we just need to recognize that some thinkers can manage to have a concept by piggybacking on others. In contrast, on the view I defend, taking incomplete understanding seriously forces us to rethink some of our most basic assumptions about the nature of mental content. Deference is a red herring. The role of society in determining the content of thought is not the main lesson, but at most a useful clue as to the nature of mental and linguistic content. (shrink)
Predicates of taste, such as ?fun? and ?tasty?, have received considerable attention in recent debates between contextualists and relativists, with considerations involving disagreement playing a central role. Considerations involving disagreement have been taken to present a problem for contextualist treatments of predicates of taste. My goal is to argue that considerations involving disagreement do not undermine contextualism. To the extent that relativism was supposed to be motivated by contextualists being unable to deal with disagreement, this motivation is lacking. (...) The argument against contextualism rests on a too simple and narrow conception of disagreement that turns out to be problematic once we consider a wider range of cases. If we reject the assumptions about disagreement that the argument rests on, it no longer poses a threat to contextualism. (shrink)
In this paper, I use an example from the history of philosophy to show how independently defining each side of a pair of contrary predicates is apt to lead to contradiction. In the Euthyphro, piety is defined as that which is loved by some of the gods while impiety is defined as that which is hated by some of the gods. Socrates points out that since the gods harbor contrary sentiments, some things are both pious and impious. But “pious” (...) and “impious” are contrary predicates; they cannot simultaneously characterize the same thing. Euthyphro changes his definition, but the problem of recognizing emotional ambivalence is only side-stepped. I go on to show how contemporary philosophers run into a similar problem. According to Prinz, something is good if and only if we harbor positive sentiments towards it and bad if and only if we harbor negative sentiments towards it. Thus, if we are ambivalent towards something (if we harbor both positive and negative sentiments towards it), then it is both good and bad. Like “pious” and “impious”, “good” and “bad” are contraries. Next, according to the fitting-attitude theory first elaborated by Brentano and favored by contemporary meta-ethicists like Blackburn, Brandt, Ewing, Garcia, Gibbard, McDowell, and Wiggins, something is good if and only if it is a fitting (appropriate) object of approbation, and something is bad if and only if it is a fitting (appropriate) object of disapprobation. I argue that moral ambivalence is sometimes appropriate, i.e., that the correct response to some things is to both love and hate them. Hence, according to the fitting-attitudes theory, some things are both good and bad. I conclude by discussing a variety of ways in which the problem of ambivalence may be solved, suggesting that attitudes of approbation and disapprobation be further individuated by the reasons for them. (shrink)
Central to any form of Deflationism concerning truth (hereafter ‘DT’) is the claim that truth has no substantial theoretical role to play. For this reason, DT faces the following immediate challenge: if truth can play no substantial theoretical role then how can we model various prevalent kinds of indeterminacy—such as the indeterminacy exhibited by vague predicates, future contingents, liar sentences, truth-teller sentences, incomplete stipulations, cases of presupposition failure, and such-like? It is too hasty to assume that these phenomena (...) are all to be modelled via some epistemic conception of indeterminacy whereby indeterminacy is just some special species of ignorance which arises because of our limited powers of discrimination. Some non-epistemic model is called for—at least for certain species of indeterminacy. On what is perhaps the most enduring and popular non-epistemic model, indeterminacy gives rise to truth-value gaps. But is DT compatible with the possibility of truth-value gaps? Compatibilism says Yes; Incompatibilism says No. The broad goal of this paper is to defend a form of Incompatibilism. If DT is to make sense of various kinds of indeterminacy then truth-value gaps cannot be invoked to do so. The particular goals of this paper are: (i) To set forth a new form of Compatibilism which can address an argument against truth-value gaps given by Williamson (1994, pp. 187-192). (ii) To offer a new argument against truth-value gaps using principles entailed by DT, thereby undermining Compatibilism. (shrink)
The most common philosophical view about the notion of existence is that it is a second-order property or existential quantification. A less common view is that existence is a (first-order) property of 'existent' as opposed to 'nonexistent' (past or merely intentional) objects. An even less common view is that existence divides into different 'modes of being' for different sorts of entities. In this paper I will take a closer look at the semantic behavior of existence predicates in natural language, (...) such as exist, occur, and obtain, arguing that existence predicates in natural language support the two less common philosophical views. I will develop explicit analyses of existence predicates in their time-relative and space-relative uses which will explain why they apply to some kinds of entities, but not others. (shrink)
Predicates of personal taste (fun, tasty) and epistemic modals (might, must) share a similar analytical difficulty in determining whose taste or knowledge is being expressed. Accordingly, they have parallel behavior in attitude reports and in a certain kind of disagreement. On the other hand, they differ in how freely they can be linked to a contextually salient individual, with epistemic modals being much more restricted in this respect. I propose an account of both classes using Lasersohn’s (Linguistics and Philosophy (...) 28: 643–686, 2005) “judge” parameter, at the same time arguing for crucial changes to Lasersohn’s view in order to allow the extension to epistemic modals and address empirical problems faced by his account. (shrink)
Frege held that singular terms can refer only to objects, not to concepts. I argue that the counter-intuitive consequences of this claim ('the concept paradox') arise from Frege's mirroring principle that an incomplete expression can only express an incomplete sense and stand for an incomplete reference. This is not, as is sometimes thought, merely because predicates and singular terms cannot be intersubstituted salva veritate ( congruitate ). The concept paradox, properly understood, poses therefore a different, harder, (...) challenge. An investigation of the foundations of the mirroring principle also sheds light on the role which language plays in Frege's epistemology of logic. (shrink)
The article discusses an idea of how to extend the notion of rigidity to predicates, namely the idea that predicates stand in a certain systematic semantic relation to properties, such that this relation may hold rigidly or nonrigidly. The relation (which I call signification) can be characterised by recourse to canonical property designators which are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification (...) divides into rigid and non-rigid cases will then depend uponwhether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be nonrigid, canonical designators such as having the colour of ripe tomatoes which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented. (shrink)
It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit (...) Fine calls penumbral connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (shrink)
Critics and champions alike have fussed and fretted for well over fifty years about whether Russell’s treatment is compatible with certain alleged acceptable uses of incomplete definite descriptions,[2] where a description (the F( is incomplete just in case more than one object satisfies its nominal F, as in (1).
Standard attempts to defend Russell's Theory of Descriptions against the problem posed by incomplete descriptions, are discussed and dismissed as inadequate. It is then suggested that one such attempt, one which exploits the notion of a contextually delimited domain of quantification, may be applicable to incomplete quantifier expressions which are typically treated as quantificational: expressions of the form AllF's, NoF's, SomeF's, Exactly eightF's, etc. In this way, one is able to retain the plausible claim that such expressions ought (...) to receive their usual quantificational analyses. The conclusion tentatively drawn is that perhaps definite descriptions arenot amenable to a (Russellian) quantificational analysis. (shrink)
The history of the idea of predicate is the history of its emancipation. The lesson of this paper is that there are two more steps to take. The first is to recognize that predicates need not have a fixed degree, the second that they can combine with plural terms. We begin by articulating the notion of a multigrade predicate: one that takes variably many arguments. We counter objections to the very idea posed by Peirce, Dummett's Frege, and Strawson. We (...) show that the arguments of a multigrade predicate must be grouped into places, with perhaps several arguments occupying positions at a place. Variability may relate to places or positions. Russell's multiple judgement predicate turns out to be just one example of a family—‘is necessarily true of’, ‘is said of’, ‘is instantiated by’ and so on—of predicates with variably many places. Our main concern, however, is lists. Any adequate account of lists must include plural as well as singular terms. On one account, lists are mere strings of separate arguments, which occupy variably many positions within a place of a multigrade predicate. A quite different account takes the list itself to be a compound plural term. We compare these rival conceptions, and reach some surprising conclusions. As a coda, we deploy the conceptual apparatus developed in the paper to assess Morton's pioneer system of multigrade logic. (shrink)
In reply to Geach's objection against expressivism, some have claimed that there is a plurality of truth predicates. I raise a difficulty for this claim: valid inferences can involve sentences assessable by any truth predicate, corresponding to 'lightweight' truth as well as to 'heavyweight' truth. To account for this, some unique truth predicate must apply to all sentences that can appear in inferences. Mixed inferences remind us of a central platitude about truth: truth is what is preserved in valid (...) inferences. The question is why we should postulate truth predicates that do not satisfy this platitude. (shrink)
In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versions of the (...) unificationist “explicit” approach given by Buchanan and Ostertag. I then show that this proposal seems unable to treat the normal uses of misdescriptions. I then accept the challenge of treating misdescriptions as a key to solving the problem of context dependent descriptions. In 3. I briefly discuss Michael Devitt’s and Joseph Almog’s treatments of referential descriptions, showing that they find it difficult to explain misdescriptions. In 4. I suggest an alternative approach to DD as contextuals, under a normative epistemic stance. Definite descriptions express (i) what a speaker should have in mind in using certain words in a certain context and (ii) what a normal speaker is justified in saying in a context, given a common basic knowledge of the lexicon. In 5. I define a procedure running on contextual parameters (partiality, perspective and approximation) as a means of representing the role of pragmatics as a filter for semantic interpretation. In 6. I defend my procedural approach against possible objections concerning the problem of the boundaries between semantics and pragmatics, relying on the distinction between semantics and theory of meaning. (shrink)
We argue that the epistemic theory of vagueness cannot adequately justify its key tenet-that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson’s promising attempt to explicate our understanding of vague language on the model of a certain sort of “inexact knowledge” is at best incomplete, since certain forms of vagueness do not fit Williamson’s (...) model, and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by physics need not be-and is not commonly-interpreted as epistemic. Thus, there are aspects of contemporary science that do not accord well with the epistemicist outlook. (shrink)
In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, (...) one in which some complex predicates stand for properties while others do not. (shrink)
A plausible thought about vagueness is that it involves a form of semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. And where there is incomplete specification of extension there is indeterminacy—an indeterminacy between various ways that the specification of the predicate might be completed or, as some like to say, sharpened (or precisified). We shall argue that this idea is defective insofar as there are vague (...)predicates that cannot be sharpened. At least, there are predicates that are vague but that cannot be sharpened in such a way as to meet certain basic constraints that we think must be imposed on the very notion of a sharpening. (shrink)
Correspondence theories are frequently charged with being either implausible -- metaphysically troubling and overly general -- or trivial -- collapsing into deflationism's "'P' is true iff P." Philip Kitcher argues for a "modest" correspondence theory, on which reference relations are causal relations, but there is no general theory of denotation. In this paper, I start by showing that, understood this way, "modest" theories are open to charges of triviality. I then offer a refinement of modesty, and take the first steps (...) toward articulating a modest correspondence theory, giving a particular account of the relation between predicates, properties, and extensions. Finally, I argue that my account does not collapse into a deflationary one. (shrink)
In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally (...) distinguishing between natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)
0. Abstract In this paper, I argue that although the behavior of adjectives in context poses a serious challenge to the principle of compositionality of content, in the end such considerations do not defeat the principle. The first two sections are devoted to the precise statement of the challenge; the rest of the paper presents a semantic analysis of a large class of adjectives that provides a satisfactory answer to it. In section 1, I formulate the context thesis, according to (...) which the content of a complex expression depends on the context of its utterance only insofar as the contents of its constituents do. If the context thesis is false, the content of some complex expression is not compositionally determined. In section 2, using an example due to Charles Travis, I construct an objection to the context thesis based on the behavior of the adjective ‘green’. In section 3 and 4, I look at some of the difficulties surrounding the semantics of ‘good’, which provide the motivation for the thesis that most adjectives are contextually incomplete one-place predicates. In section 5, I discuss how ‘green’ and other color adjectives can be treated within such a semantic theory. Since this theory is compatible with the context thesis, the objection against the compositionality of content looses its force. (shrink)
In this paper, I argue that not only PPs and adverbs can act as predicates of the event argument of the verb, but certain NPs and certain clauses can, as well. I will give syntactic and semantic arguments that NPs that are cognate objects and clauses of (at least some) nonbridge verbs are optional predicates of the event argument of the verb. With respect to clauses, I will argue that for independent reasons the meaning of both independent and (...) embedded sentences can be construed as event-properties, namely as properties of intentional events. (shrink)
John R. Welch (2005). Gruesome Predicates. In Roberto Festa, Atocha Aliseda & Jeanne Peijnenburg (eds.), Confirmation, Empirical Progress and Truth Approximation: Essays in Debate with Theo Kuipers. Rodopi.score: 12.0
This chapter examines gruesome predicates, the most notorious of which is 'grue'. It proceeds by extending the analysis of Theo A. F. Kuipers' From Instrumentalism to Constructive Realism in three directions. It proposes an amplified typology of grue problems, first of all, and argues that one such problem is the root of the rest. Second, it suggests a solution to this root problem influenced by Kuipers' Bayesian solution to a related problem. Finally, it expands the class of gruesome (...) class='Hi'>predicates by incorporating Quine's 'undetached rabbit part', 'rabbit stage', and the like, and shows how they can be managed along the same Bayesian lines. (shrink)
The idea that temporal propositions are vague predicates is examined with attention to the nature of the objects over which the predicates range. These objects should not, it is argued, be identified once and for all with points or intervals in the real line (or any fixed linear order). Context has an important role to play not only in sidestepping the Sorites paradox (Gaifman 2002) but also in shaping temporal moments/extent (Landman 1991). The Russell-Wiener construction of time from (...) events (Kamp 1979) is related to a notion of context given by a string of observations, the vagueness in which is brought out by grounding the observations in the real line. With this notion of context, the context dependency functions in Gaifman 2002 are adapted to interpret temporal propositions. (shrink)
Indexicality is a feature of predicates and predicate components (verbs, adjectives, adverbs and the like) as well as of referring expressions. With classic referring indexicals such as 'I' or 'that' a distinctive rule takes us from token and context to some item present in the content which is the semantic correlate of the token. Predicates and predicate components may function in an analogous fashion. For example 'thus' is an indexical adverb which latches onto some manner of performance present (...) in its context. 'John sang thus', said while indicating someone singing discordantly, claims that John sang discordantly. The phenomenon of predicatival indexicality is widespread in English and is expressed in a variety of idioms. Indexical predication plays important epistemological and psychological roles and the notion may have other interesting philosophical applications. (shrink)
We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of (...)Whitehead (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)
Sober (1984) has considered the problem of determining the evidential support, in terms of likelihood, for a hypothesis that is incomplete in the sense of not providing a unique probability function over the event space in its domain. Causal hypotheses are typically like this because they do not specify the probability of their initial conditions. Sober's (1984) solution to this problem does not work, as will be shown by examining his own biological examples of common cause explanation. The proposed (...) solution will lead to the conclusion, contra Sober, that common cause hypotheses explain statistical correlations and not matchings between event tokens. (shrink)
Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of (...) counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. (shrink)
Brouwer's papers after 1945 are characterized by a technique known as the method of the creating subject. It has been supposed that the method was radically new in his work, since Brouwer seems to introduce an idealized mathematician into his mathematical practice. A newly opened source, the unpublished text of a lecture of Brouwer from 1934, fully supports the conclusions of our analysis that: - There is no idealized mathematician involved in the method;- The method was not new at all;- (...) Brouwer uses an incomplete sequence, also known as choice sequence, in this method, which is special. The method does not take its place in the standard works on choice sequences. (shrink)
Philosophers have had difficulty in explaining the difference between disjunctive and non-disjunctive predicates. Purely syntactical criteria are ineffective, and mention of resemblance begs the question. I draw the distinction by reference to relations between borderline cases. The crucial point about the disjoint predicate 'red or green', for example, is that no borderline case of 'red' is a borderline case of 'green'. Other varieties of disjunctive predicates are: inclusively disjunctive (such as 'red or hard'), disconnected (such as 'grue' on (...) the usual definitions), and skew (such as 'grue' on an emended definition). 'Green' is not a disjunctive predicate. Nelson Goodman's new riddle of induction elicits yet another response. (shrink)
Some things are left open by a work of fiction. What colour were the hero’s eyes? How many hairs are on her head? Did the hero get shot in the final scene, or did the jailor complete his journey to redemption and shoot into the air? Are the ghosts that appear real, or a delusion? Where fictions are open or incomplete in this way, we can ask what attitudes it’s appropriate (or permissible) to take to the propositions in question, (...) in engaging with the fiction. In Mimesis as Make-Believe (henceforth, MMB), Walton argues that just as truth norms belief, truth-in-fiction norms imagination. Granting that what is true-in-the-fiction should be imagined, and what is false-in-the-fiction is not to be imagined, there remains the question of what to say within the Waltonian framework about things that are neither true- nor false-in-the-fiction---the loci of incompleteness. (shrink)
Most speakers experience unclarity about the application of predicates like tall and red to liminal cases. We formulate alternative psychological hypotheses about the nature of this unclarity, and report experiments that provide a partial test of them. A psychologized version of the ‘vagueness-as-ignorance’ theory is then advanced and defended.
We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of (...) Whitehead (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)
This article describes how historical claims frequently made in arguments about the propertization of copyright are incomplete, focusing on three examples: that intellectual property is a much older phrase than current scholarship would lead one to believe; that, regardless, copyright has been understood as property (literary, artistic, etc.) since the 18th century; that infringement of all sorts have generally been called piracy for at least that long; and that appeals to Thomas Jefferson for weaker intellectual property rights are misplaced (...) for multiple reasons. Because copyright has been viewed as property for hundreds of years, scholars who connect the increasing strength of copyright to the rise of the phrase intellectual property must make an argument completely absent from the literature - that intellectual property somehow hypnotizes in a way that literary property or plain old property did not. The paper then turns to analysis of the propertization claims themselves, showing the limits of these arguments and suggesting directions in which this scholarship might go. Finally, the paper proposes that the actual reason commentators are increasingly uncomfortable with copyright as property is the boundaries problem - the fuzziness of a copyright's borders in a world where many more people are creating and recreating expression as their vocations and avocations. As more and more of us emigrate to the realm of expression, the demands for both expressive property and expressive space put tremendous pressure on the copyright system. (shrink)
“Symmetrical predicates” have distinctive linguistic properties in many languages. But the concept of “symmetry” merits closer examination. Consider the surprising claim by the psychologist Amos Tversky (1977) that the concept ‘similar’, a standard example of a symmetrical predicate, is in fact not symmetrical. Tversky’s evidence includes the fact that experimental subjects generally rate (1a) as holding to a higher degree than (1b). (1) a. North Korea is similar to Red China. b. Red China is similar to North Korea.
Bayesian psychology, in what is perhaps its most familiar version, is incomplete: Jeffrey conditionalization is not a complete account of rational belief change. Jeffrey conditionalization is sensitive to the order in which the evidence arrives. This order effect can be so pronounced as to call for a belief adjustment that cannot be understood as an assimilation of incoming evidence by Jeffrey's rule. Hartry Field's reparameterization of Jeffrey's rule avoids the order effect but fails as an account of how new (...) evidence should be assimilated. (shrink)
The Incomplete Universe includes detailed work on the liar paradox and recent attempts at solution, Kaplan and Montague's paradox of the knower, the Godel ...
Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. (...) This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields realvalued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)
According to the simple proposal about rigidity for predicates, a predicate is rigid (roughly) if it signifies the same property across the relevant worlds. Recent critics claim that this suffers from a trivialization problem: any predicate whatsoever would turn out to be trivially rigid, according to the proposal. In this paper a corresponding "problem" for ordinary singular terms is considered. A natural solution is provided by intuitions concerning the actual truth-value of identity statements involving them. The simple proposal for (...)predicates is then defended, by exploiting corresponding intuitions concerning statements involving their nominalizations, in an analogous manner. (shrink)
PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig (...) interpolation lemma. We also consider other examples of the strong provability predicates and their applications. (shrink)
This paper examines four arguments in support of Frege's theory of incomplete entities, the heart of his semantics and ontology. Two of these arguments are based upon Frege's contributions to the foundations of mathematics. These are shown to be question-begging. Two are based upon Frege's solution to the problem of the relation of language to thought and reality. They are metaphysical in nature and they force Frege to maintain a theory of types. The latter puts his theory of (...) class='Hi'>incomplete entities in the paradoxical position of maintaining that it is no theory at all. Moreover, his metaphysics rules out well-known suggestions for avoiding this difficulty. (shrink)
A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and partial (...) in a sense analogous (though not completely identical) to the sense in which is blue is vague and partial. However, higher-order vagueness stops there. Although the anti-extension of is determinately blue differs from that of is blue, further iterations of determinately have no semantic effect. -/- The paper closes with a discussion of the need to posit sharp and precise lines dividing the range of potential application of a vague predicate into semantically distinct categories. It is argued that this is less of a problem for the present theory than for many others, because the categories into which the range is divided by the present theory -- like the category of counting as blue because the rules of the language offer speakers no discretion, as opposed to the category of counting as blue because speakers have invoked an absolute minimum of discretion in adjusting the contextually sensitive boundaries of the predicate -- are not those that the linguistic competence of ordinary speakers equips them to make highly accurate and reliable judgments about. (shrink)
A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are (...) vague predicates which cannot be sharpened in such a way as to meet certain basic constraints (of penumbral connection and public accessibility) that must be imposed on the very notion of a sharpening. (shrink)
The Common Prior Assumption (CPA) is central to the economics of information and the foundations of game theory. Recent contributions (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned its meaningfulness in situations of incomplete information where there is no ex ante stage and the primitives of the model are the individuals’ belief hierarchies. We address this conceptual issue by providing characterizations of two local versions of the CPA which are in terms of the primitives and, therefore, do (...) not involve a counterfactual and problematic ex ante stage. The characterizations involve three notions: Comprehensive Agreement, no error of beliefs and common belief in no error. Comprehensive Agreement is defined as the absence of “agreement to disagree” about any aspect of beliefs; it is a generalization of Aumann’s (1976) notion of agreement. The entire analysis is carried out locally, that is, with reference to the “true state” (which represents the actual profile of belief hierarchies) and does not rely on the Truth Axiom for individual beliefs. (shrink)
Ryle (1949, Chapter V) discusses a range of predicates which in different ways exemplify a property I shall call quasi-duality - they appear to report two actions or events in one predicate. Quasi-duality is the key property of predicates Ryle classed as achievements. Ryle's criteria for classification were not temporal or aspectual, and Vendler's subsequent adoption of the term achievement for the aktionsart of momentary events changes the term - Rylean achievements and Vendlerian achievements are in principle different (...) classes. Nevertheless, I shall argue in this paper that certain kinds of quasi-duality do have aspectual significance. This paper examines a number of quasi-dual predicates which are not generally discussed in the aktionsart literature, including break a promise, miscount, and cure the patient. Two types of quasi-dual predicates are identified and dubbed criterion predicates and causative upshot predicates. It is shown that both types of quasi-dual predicate lack process progressives, despite being durative, and it is argued that the lack of process progressives identifies these predicates as (aspectual) achievements. They are termed durative achievements to distinguish them from canonical, momentary achievements. It is argued that these predicates lack process progressives, and hence are achievements, because they express individual-level predicates on the event argument. A process progressive is stage-level for the event, and hence is incompatible with a predicate which is lexically individual-level for the event. (shrink)
IF "ALL A’S ARE B" AND "ALL A’S ARE C" ARE BOTH EQUALLY WELL SUPPORTED BY OBSERVATIONS SO FAR, YET YIELD CONFLICTING PREDICTIONS, WHICH OUGHT WE TO ADOPT? GOODMAN’S CONFLICT BETWEEN "ALL EMERALDS ARE GREEN" AND "ALL EMERALDS ARE GRUE" IS A SPECIAL CASE OF SUCH CONFLICT, WHICH MAY BE DEALT WITH BY A RULE STATING THAT WE OUGHT NOT TO PROJECT POSITIONAL IN PREFERENCE TO QUALITATIVE PREDICATES. THIS PAPER ATTEMPTS TO ELUCIDATE THE RULES GOVERNING A LARGER CLASS OF (...) SUCH CONFLICTS, IN CASES WHERE ONE PREDICATE B IS "EPISTEMOLOGICALLY PRIOR" TO ANOTHER ONE C. (shrink)
Background ideas -- Consequences -- Relations of support -- Logical consequence : the basic recipe -- Valid arguments and truth -- Language, form, and logical theories -- Language -- Atoms, connectives, and molecules -- Connectives and form -- Validity and form -- Language and formal languages -- Logical theories : rivalry -- Set-theoretic tools -- Sets -- Ordered sets : pairs and n-tuples -- Relations -- Functions -- Sets as tools -- Basic connectives -- Classical theory -- Cases : complete (...) and consistent -- Classical truth conditions -- Basic classical consequence -- Motivation : precision -- Defined connectives -- Some notable valid forms -- A paracomplete theory -- Apparent unsettledness -- Cases : incomplete -- Paracomplete truth and falsity conditions -- Paracomplete consequence -- Defined connectives -- Some notable forms -- A paraconsistent theory -- Apparent overdeterminacy -- Cases : inconsistent -- Paraconsistent truth conditions -- Paraconsistent consequence -- Defined connectives -- Some notable forms -- Innards, identity, and quantifiers -- Atomic innards -- Atomic innards : names and predicates -- Truth and falsity conditions for atomics -- Cases, domains, and interpretation functions -- Classical, paracomplete, and paraconsistent -- Identity -- Logical expressions and logical form -- Validity involving identity -- Identity : informal sketch -- Truth conditions : informal sketch -- Everything and something -- Validity involving quantifiers -- Quantifiers : an informal sketch -- Truth and falsity conditions -- Paraconsistent, paracomplete, classical -- Freedom, necessity, and beyond -- Speaking freely -- Speaking of non-existent things -- Existential import -- Freeing our terms, expanding our domains -- Truth conditions : an informal sketch -- Possibilities -- Possibility and necessity -- Towards truth and falsity conditions -- Cases and consequence -- Remark on going beyond possibility -- Glimpsing different logical roads -- Other conditionals -- Other negations -- Other alethic modalities : actuality -- Same connectives, different truth conditions -- Another road to difference : consequence. (shrink)
In "A Danger of Definition: Polar Predicates in Metaethics," Mark Alfano (2009) concludes that the response-dependence theory of Prinz and others and the fitting-attitudes theory first articulated by Brentano are false because they imply empirically false statements. He further concludes that these statements cannot be avoided by revising the definitions of the terms 'good' and 'bad' used in the two theories. I strengthen Alfano's first conclusion by arguing that the two theories are false even if they imply empirically true (...) but conceptually contingent statements, and show how, contrary to his second conclusion, the theories can avoid both empirically false and conceptually contingent implications. (shrink)
In this paper the general notion of Bourbaki structures, interpreted in terms of Suppes predicates, will be used to axiomatize a system of meta-rankings in the sense introduced by A. K. Sen. It will be argued that this axiomatization must take place in a Kantian-ruled world in order to provide a link between meta-rankings and individual actions.Dedicated to Prof. Francisco A. Doria on his 50th birthday.
Hurford argues that propositions of the form PREDICATE(x) represent conceptual structures that predate language and that can be explicated in terms of neural structure. I disagree, arguing that such predicates are descriptions of limited aspects of brain function, not available as representations in the brain to be exploited in the frog or monkey brain and turned into language in the human.
It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).
Abstract The paper is concerned with the status of vague predicates. It is argued that they are for the most part ?classifiers?, which are covertly comparatives and name not monadic properties but relations. The Sorites Paradox, it is claimed, is thus defused and a verdict theory of vague predicates is presented. Our practice in using vague words is described and it is contended that in our use of these predicates we always have a permanent possibility of independent (...) demarcation. Wittgenstein's picture of the wall and the swamp is deployed to avoid the Transition Problem and it is argued against Fregeans that we need vague language for the advancement of knowledge and understanding. (shrink)
Suppose the principles explaining how the human mind (brain) reaches logical conclusions and judgments were different from – and independent of – thoseinvolved innormatively valid reasoning. Then such principles should affect both conclusion generation and recognition that particular conclusions are or are not justified. People, however, demonstrate a discrepancy between impaired performance in generating logical conclusions as opposed to rather impressive competence in recognizing rational (versus irrational) ones. This discrepancy is hypothesized to arise from often generating an incomplete specification (...) of a logical or judgmental problem when attempting to solve it – versus a recognition of such incompleteness when it is pointed out. The basic argument is developed, with common examples, in the context of specifying or failing to specify all possible combinations in simple logical arguments and is then extended to probabilistic reasoning, where complete versus incomplete specification corresponds to attending to all or to only some components of Bayes theorem-based reasoning. (shrink)
If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for (...) an extension to be conservative. The origin of the results is algebraic logic. (shrink)
Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of 'sortal' as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates 'quantum-sortal predicates' and, instead of a process of (...) counting, to them is associated a 'criterion of cardinality'. After their general characterization, it is discussed how these predicates can be formally described. (shrink)
The paper examines the Cartesian and the Strawsonian answers to the question of why self-applied and other-applied mental predicates mean the same. While these answers relate to different, complementary aspects of this question, they seem and are usually considered as incompatible. Indeed, their apparent incompatibility constitutes a major objection to the Cartesian answer. A primary aim of the paper is to show that the Strawsonian answer does not pose a real problem to the Cartesian answer. Unlike other attempts to (...) show this, the paper does not seek to undermine the Strawsonian answer. Indeed, its second aim is to defend this answer against these other attempts. The paper’s strategy in defending the Cartesian answer is to show that the framework underlying this answer can — indeed, for internal reasons, must — accommodate the Strawsonian answer. By showing this, the paper also shows that a Cartesian framework can provide a comprehensive answer to the aforementioned question, which is its third aim. (shrink)
Within this paper we consider a model of Nash bargaining with incomplete information. In particular, we focus on fee games, which are a natural generalization of side payment games in the context of incomplete information. For a specific class of fee games we provide two axiomatic approaches in order to establish the Expected Contract Value, which is a version of the Nash bargaining solution.
Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically (...)incomplete generalized quantifiers which constitute the subject of the present paper. The only systematic study of these quantifiers from a purely logical point of view, is, to the best of my knowledge, that by van Eijck (1995). We shall take here a different approach than that of van Eijck and mention some of the abstract properties of the resulting logic. Finally we shall prove that the two approaches are interdefinable. (shrink)
The Common Prior Assumption (CPA) plays an important role in game theory and the economics of information. It is the basic assumption behind decision-theoretic justifications of equilibrium reasoning in games (Aumann, 1987, Aumann and Brandenburger, 1995) and no-trade results with asymmetric information (Milgrom and Stokey, 1982). Recently several authors (Dekel and Gul, 1997, Gul, 1996, Lipman, 1995) have questioned whether the CPA is meaningful in situations of incomplete information, where there is no ex ante stage and where the primitives (...) of the model are the individuals' beliefs about the external world (their first-order beliefs), their beliefs about the other individuals' beliefs (second-order beliefs), etc., i.e. their hierarchies of beliefs. In this context, the CPA is a mathematical property whose conceptual content is not clear. The main results of this paper (Theorems 1 and 2) provide a characterization of Harsanyi consistency in terms of properties of the belief hierarchies that are entirely unrelated to the idea of an ex ante stage. (shrink)
Attempts to give a Logic or Semantics for vague predicates and to defuse the Sorites paradoxes have been largely a failure. We point out yet another problem with these predicates which has not been remarked on before,namely that different people do and must use these predicates in individually different ways. Thus even if there were a semantics for vague predicates, people would not be able to share it. To explain the occurrence nonetheless of these troublesome (...) class='Hi'>predicates in language, we propose a different approach based on asking the question, “How do these vague predicates help people to communicate with each other?” We show that in general, even though different people assign different extensions to vague predicates, they usually benefit from receiving information framed in terms of them. (shrink)
LetEO be the elementary ontology of Leniewski formalized as in Iwanu [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function , defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that EO A iff LS (A) for each formulaA.
We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is Π 1 1 complete. Adding one unary predicate is enough to get Π 1 1 hardness, while adding more predicates (of any arity) does not make the complexity any worse.
A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of anaphoric readings of Sobel sequences and reverse Sobel sequences, and (...) proposes an explanation of the original asymmetry on its grounds. This provides an answer to the challenge for Lewis’s theory. (shrink)
We investigate the relationship between two approaches to modeling physical systems. On the first approach, simplifying assumptions are made about the level of detail we choose to represent in a computational simulation with an eye toward tractability. On the second approach simpler, analogue physical systems are considered that have more or less well-defined connections to systems of interest that are themselves too difficult to probe experimentally. Our interest here is in the connections between the artifacts of modeling that appear in (...) these two approaches. We begin by outlining an important respect in which the two are essentially dissimilar and then propose a method whereby overcoming that dissimilarity by hand results in usefully analogous behavior. We claim that progress can be made if we think of artifacts as clues to the projectible predicates proper to the models themselves. Our degree of control over the connection between interesting analogue physical systems and their targets arises from determining the projectible predicates in the analogue system through a combination of theory and experiment. To obtain a similar degree of control over the connection between large-scale, distributed simulations of complex systems and their targets we must similarly determine the projectible predicates of the simulations themselves. In general theory will be too intractable to be of use, and so we advocate an experimental program for determining these predicates. the object of the natural history which I propose is...to give light to the discovery of causes and supply a suckling philosophy with its first food . Francis Bacon, The Great Instauration. (shrink)
We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.
French materialist feminists such as Christine Delphy and Monique Wittig maintain that the social fact of women’s exploitation by men within the family pre-exists and produces gender differences as well as the perception that men and women belong to different biological sexes. They take this position to be ‘materialist’ because it puts social facts prior to ideas and beliefs and so puts the ‘material’ prior to the ‘ideal’. However, I shall claim, drawing on arguments of Sebastiano Timpanaro’s, that this is (...) an incomplete form of materialism because it neglects the shaping of social facts by their interaction with biological facts, notably the biological difference between the sexes. Wittig, though, denies that there is any ‘fact’ of biological sexual difference. Wittig claims that we only believe in and perceive two biological sexes due to the influence of gender expectations. I will try to show that Wittig’s arguments for this claim undermine themselves and actually presuppose that there are two biological sexes. I will conclude that, given that there are two biological sexes, a fully materialist form of feminism must take account of sex difference in theorising gender inequalities. (shrink)
This paper investigates, in a simple risk-sharing framework, the extent to which the incompleteness of contracts could be attributed to the complexity costs associated with the writing and the implementation of contracts. We show that, given any measure of complexity in a very general class, it is possible to find simple contracting problems such that, when complexity costs are explicitly taken into account, the contracting parties optimally choose an incomplete contract which coincides with the âdefaultâ division of surplus. Optimal (...) contracts with complexity costs are constrained efficient in our model. We therefore interpret our results as saying that, in the absence of a strategic role for complexity costs, their effect is entirely determined by their size relative to the size of payoffs. (shrink)
We study the fragment of Peano arithmetic formalizing the induction principle for the class of decidable predicates, $I\Delta_1$ . We show that $I\Delta_1$ is independent from the set of all true arithmetical $\Pi_2-sentences$ . Moreover, we establish the connections between this theory and some classes of oracle computable functions with restrictions on the allowed number of queries. We also obtain some conservation and independence results for parameter free and inference rule forms of $\Delta_1-induction$ . An open problem formulated by (...) J. Paris is whether $I\Delta_1$ proves the corresponding least element principle for decidable predicates, $L\Delta_1$ (or, equivalently. the $\Sigma_1-collection$ principle $B\Sigma_1$ ). We reduce this question to a purely computation-theoretic one. (shrink)
Robert M. Adams claims that Leibniz’s rehahilitation of the doctrine of incomplete entities is the most sustained etlort to integrate a theory of corporeal substances into the theory of simple substances. I discuss alternative interpretations of the theory of incomplete entities suggested by Marleen Rozemond and Pauline Phemister. Against Rozemond, I argue that the scholastic doctrine of incomplete entities is not dependent on a hylomorphic analysis of corporeal substances, and therefore can be adapted by Leibniz. Against Phemister, (...) I claim that Leibniz did not reduce the passivity of corporeal substances to modifications of passive aspects of simple substances. Against Adams, I argue that Leibniz’s theory of the incompleteness of the mind cannot be understood adequately without understanding the reasons for his assertion that matter is incomplete without minds. Composite substances are seen as requisites for the reality of the material world, and therefore cannot be eliminated from Leibniz’s metaphysics. (shrink)
The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley–Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (iii) (...) The class of frames for G characterizes the classically based logic T. (shrink)
This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical quantifiers. As a (...) prerequisite, much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)
Abstract The notion of necessary new terms (predicates) is proposed. It is shown that necessary new predicates in first?order logic must be directly, recursively defined. I present a first?order inductive learning algorithm that introduces new necessary predicates to model scientific revolution in which a new language is adopted. I demonstrate that my learning system can learn a genetic theory with theoretical terms which, after being induced by my system, can be interpreted as either types of genetic properties (...) (dominant or recessive) or genes, depending on the representation of the hypotheses of the same theoretical terms. (shrink)
Minimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' ϕ(P) which quarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language (...) MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)
This article presents four analyses of an interaction between the middle-Bronze Age Pharaoh Nibmuarea and the Babylonian king Kadashman-Enlil as described in the Amarna letters (Moran [1992] The Amarna Letters, The Johns Hopkins Universiy Press, Baltimore, Maryland). Intent on denying the Pharaoh his daughter in marriage, the Babylonian king was faced with the choice of sending messengers who could (''dignitaries'') or could not identify (''non-dignitaries'') his missing sister in the Pharaoh's court. Intent on marrying the king's daughter, the Pharaoh was (...) faced with the choice of showing the sister or showing someone else. Based on the assumption of complete information (game 1), the analysis revealed a dominant-strategy equilibrium: Nibmuarea shows the sister and Kadashman-Enlil sends non-dignitaries. Based on the assumption of one-sided incomplete information (Pharaoh's misperception; game 2), the analysis revealed that the Pharaoh had a dominant strategy of showing the sister irrespective of whether the king is keen or reluctant to learn about his sister's fate. Based on the assumption of one-sided incomplete information (Kadashman-Enlil's misperception; game 3), the analysis revealed that if non-dignitaries are sent, the Pharaoh prefers showing someone other than his sister. Based on the assumption of two-sided incomplete information (game 4), the Pharaoh finds it more beneficial to present the sister irrespective of whether his intentions are genuine or feigned. With incomplete information, it is difficult to judge the other's intentions; the cost of being caught cheating by not showing the sister to knowledgeable messengers was quite high. These analyses highlight the strategic uncertainty that characterized this Bronze-Age interaction. (shrink)
The predicate-argument approach, focused on perception, is compared with the ease-of-predication (or predicability) approach, focused on encyclopedic knowledge. The latter offers functional prediction and implementation in connectionist models. However, the two approaches characterise predicates in different ways. They thus resemble predicational cantilevers built out from opposite sides of cognition, with a gap that is yet to be bridged.
This paper addresses the phenomenon of incomplete preferences in disaster risk management. If an agent finds two options to be incomparable and thus has an incomplete preference ordering, i.e., neither prefers one option over the other nor finds them equally as good, it is not possible for the agent to perform a value tradeoff, necessary for an informed decision, between these two options. In this paper we suggest a way to model incomplete preference orderings by means of (...) probabilistic preferences, and how to reveal an agent’s incomplete preference ordering within a behaviorist framework. (shrink)
We relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi's type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium (BNE) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a (...) hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE. (shrink)
There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.
A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory (...) T, any expansion M + of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63), that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories. (shrink)
In spite of incomplete knowledge we are permanently forced to act in complex real-life situations. First, a modern concept of information, the non-trivial transition from information to knowledge, patterns of missing knowledge, and the concept of perspective notions are studied. The main sections review some guidelines for action under incomplete information. A modern view of the concepts of holism and wholeness reveals that (in contrast to some critics) general system theory does not require any metaphysical assumption or previously (...) accepted worldview. The concepts of holism and wholeness, as well as general system theory, are well-founded, even under strict criteria. (shrink)
Two real-valued deduction schemes are introduced, which agree on $\vdash \triangle$ but not on $\Gamma \vdash \triangle$ , where Δ and ▵ are finite sets of formulae. Using the first scheme we axiomatize real-valued equality so that it induces metrics on the domains of appropriate structures. We use the second scheme to reduce substitutivity of equals to uniform continuity, with respect to the metric equality, of interpretations of predicates in structures. This continuity extends from predicates to arbitrary formulae (...) and the appropriate models have completions resembling analytic completions of metric spaces. We provide inference rules for the two deductions and discuss definability of each of them by means of the other. (shrink)
