The article concerns the treatment of the so-called denoting phrases, of the forms ?every A?, ?any A?, ?an A? and ?some A?, in Russell's Principles of Mathematics. An initially attractive interpretation of what Russell's theory was has been proposed by P.T. Geach, in his Reference and Generality (1962). A different interpretation has been proposed by P. Dau (Notre Dame Journal, 1986). The article argues that neither of these is correct, because both credit Russell with a more thought-out theory (...) than he actually had. The conclusion is mainly negative: at this date Russell has no coherent theory of these phrases. An appendix notes that his understanding of the quantifiers in predicate logic is also, at this date, not entirely secure. (shrink)

Russell's new theory of denoting phrases introduced in "On Denoting" in Mind 1905 is now a paradigm of analytic philosophy. The main argument for Russell's new theory is the so-called 'Gray's Elegy' argument, which purports to show that the theory of denoting concepts promoted by Russell in the 1903 Principles of Mathematics is incoherent. The 'Gray's Elegy' argument rests on the premise that if a denoting concept occurs in a proposition, then the proposition is not about the (...) concept. I argue that the premise is false. The 'Gray's Elegy' argument does not exhaust Russell's ammunition against the theory of denoting concepts. Another reason Russell rejects the theory is, as he says, that it cannot provide an adequate account of non-uniquely denoting concepts. In the last section of the paper, I argue that even though Russell was right in thinking that the theory of denoting concepts cannot provide an adequate account of non-uniquely denoting concepts, Russell's new theory does not succeed in eliminating the occurrence of all denoting concepts, as it requires a commitment to the existence of variables that indirectly denote their values. However, the view that variables are denoting concepts is unproblematic once the 'Gray's Elegy' argument is blocked. (shrink)

In studies of Indian theories of meaning it has been standard procedure to examine their relevance to the ontological issues between Brahmin realism about universals and Buddhist nominalism. It is true that Kumārila makes efforts to secure the real existence of a generic property denoted by a word by criticizing Dignāga, who declares that the real world consists of absolutely unique individuals. The present paper, however, concentrates on the linguistic approaches Dignāga and Kumārila adopt to deny or to prove the (...) existence of universals. It turns out that in spite of adopting contrasting approaches they equally distinguish between the semantic denotation of a word and its pragmatic reference to a thing in the physical world. From a purely semantic viewpoint, Dignāga considers the exclusion of others by a word as the result of a conceptual accumulation of the sense-components accepted in the totality of worldly discourse. Among the three characteristics Dignāga held must be met by universals, Kumārila attaches special importance to their entire inherence in each individual. This is because he pragmatically pays attention to the use of a word in the discourse given in a particular context by analyzing a sentence into a topic and a comment. (shrink)

In every introductory course on logic, students learn that expressions like ‘somebody’, ‘nothing’ or ‘every woman’ are not names or referring expressions, but quantifiers, and that, owing to this,...

There are many data suggesting that we should acknowledge fictional entities in our ontological inventory, in spite of the paraphrasing strategies that Russell’s theory of descriptions can offer. Thus the realist attitude toward fictional entities of Meinongian and artifactualist accounts may seem well-motivated. Yet, these approaches infringe the Russellian “robust sense of reality.” A different realist account is proposed here, one that is compatible with the Russellian “robust sense of reality” in that it identifies fictional entities with denoting concepts, (...) understood as properties of properties. (shrink)

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

In lieu of an abstract, here is a brief excerpt of the content:Theory of types and theory of knowledge by Bernd Frohmann Dieter Wurtz. Das Verhaltnis von Beobachtungs- und theoretischer Sprache in der Erkenntnistheorie Bertrand Russells. (Europaische Hochschulschriften, Reihe 20, Bd. 53.) Frankfurt am Main, Bern and Cirencester, U.K.: Peter D. Lang, 1980.Pp. iv, 110. Sfr25. THE SUBJECT OF Dieter Wurtz's short monograph on Russell's theory of knowledge is the significance of the theory of types for (...) the distinction between theoretical and observation language in Russell's epistemology. According to Wurtz, the theory of types is central to Russell's epistemology because it forms an essential part of the logical apparatus required to construct the external world from sense-data. An unexpected result of this interpretation is that for Russell, all concepts become theoretical entities. The relation between observation language and theoretical language reduces to the relation between a concept belonging to any arbitrarily selected logical order and its extension. Since the concept is an abstract class of entities and may not be defined by or reduced to its extension, it is theoretical with respect to its extension. This result is a consequence of what Wurtz sees as Russell's confused exposition of the distinction between extension and intension. Russell's attempt to reduce theoretical expressions to perceptual expressions by means of his theory of denoting phrases fails, according to Wurtz, because the denoting phrases employed to translate theory into observation contain an irreducibly theoretical element in the concept of "the only x...". Wurtz illustrates his thesis with the simple example of the relation "to the right of" holding between two objects in the visual field. His example contains the details of his argument that the construction of physical objects involves irreducibly theoretical entities. Wurtz concludes by arguing that any adequate construction of the external world requires hypotheses as instruments for verification, and that such hypotheses provide further examples of theoretical entities that cannot be reduced to their extension. Since the language of "common sense" includes concepts, logical principles, and hypotheses, it therefore contains irreducibly theoretical elements that transcend experience. Wurtz's critical exposition is based mainly on Russell's own writings, containing almost no references to the secondary literature on his epis183 184 Russell winter 1983-84 temology. Some references are made to Hempel and Carnap in the course ofmaking the relevant comparisons between Russell's and their views on hypotheses and the logical construction of the world. Many positions taken in this very short book could benefit from more extended argument, but the work as a whole has the virtue of staying close throughout to its main theme. Russell scholarship would benefit from any further investigations that might be provoked by Wurtz's study of the relation between Russell's logic and his epistemology. The Bertrand Russell Editorial Project McMaster University... (shrink)

Even with Kientpointer's and Walton's valuable work, we do not yet have a complete theory of argument schemes. A complete theory of argument schemes should contain at least the following: its theoretical motivation, the denotation of "argument" or "ar gumentation" used in the theory, an analysis of the concept of an argument scheme, a theory of classification of argument schemes, a solution to the problem of identifying which scheme is correct, and an account of the (...) grounds of the normativity or normat ive argument schemes. The paper will supply these elements, worked out as fully as space permits. (shrink)

There is an inconsistency among claims made (or apparently made) in separate articles by Alonzo Church concerning Frege's distinction between sense and denotation taken together with plausible assertions by Frege concerning his notion of ungerade Sinn-i.e., the sense that an expression allegedly takes on in positions in which it has ungerade Bedeutung, denoting its own customary sense. As with any inconsistency, the difficulty can be avoided by relinquishing one of the joint assumptions from which contradiction may be derived. Yet (...) what seems the most plausible resolution, in light of Church's own arguments, involves abandoning the theory of sense and denotation, in the form in which it has been staunchly advocated by both Frege and Church. That theory has come under sustained criticism from several quarters. Whereas the present difficulty supplements the case against the theory, it is unlike more familiar criticisms, since it is not framed from the perspective of an alternative theory (or picture) but is based instead on an internal conflict, and therefore has special force. (shrink)

This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε calculi. The resulting (...) semantics provides a precise understanding of the theory of relations. (shrink)

In many papers dealing with the stylistic features of legal texts, metaphor is highlighted as a stylistic figure often used in the language of law. On a daily basis we can witness the frequent use of metaphoric collocations like soft laws, hard laws, silent partner, hedge funds, etc. In this paper, the author analyses the use of denotations for colours as constituent parts of metaphoric collocations in the language of law. The analysis is conducted by using a comparative approach to (...) examples extracted by means of computer technology from international bills and conventions available online. In the main part of the paper, examples are classified by using a colour denotation as the main criterion for the classification. After that, the examples are compared with corresponding expressions used in German and Croatian. Taking into account the main principle of the Skopos translation theory that differences between cultures strongly influence the translation process, the hypothesis of this research is that in many cases there will be no lexical equivalence between collocations with colour denotation in three languages. Due to the fact that international bills and conventions build the corpus of the research, and that the English language has become the lingua franca of international communication, it can be expected that some metaphoric terms and collocations would be literally translated from English. Conclusions drawn from the comparative analysis of legal collocations containing denotations for colours can be interesting to lawyers and LSP teachers in the field of law. In this sense, results of the research can contribute to motivational aspects of teaching Legal English and Legal German. (shrink)

This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , (...) and the boys , are all of semantic type e and denote individual-like objects, called shadows — conjunctive , disjunctive , or negative shadows, such as John-and-Mary, John-or-Mary, and not-(John-and-Mary). There is no essential difference between quantification and denotation: quantification is nothing but denotation of shadows. Individuals and shadows constitute a Boolean structure. Formal language LSD (Language for Shadows with Distributivity), which takes compound terms to denote shadows, is investigated. Expansions and enrichments of LSD are also considered toward the end of the paper. (shrink)

Predicates such as tall or to know Latin, which intuitively denote permanent properties, are called individual-level predicates. Many peculiar properties of this class of predicates have been noted in the literature. One such property is that we cannot say #John is sometimes tall. Here is a way to account for this property: this sentence sounds odd because it triggers the scalar implicature that the alternative John is always tall is false, which cannot be, given that, if John is sometimes tall, (...) then he always is. This intuition faces two challenges. First: this scalar implicature has a weird nature, since it must be surprisingly robust (otherwise, it could be cancelled and the sentence rescued) and furthermore blind to the common knowledge that tallness is a permanent property (since this piece of common knowledge makes the two alternatives equivalent). Second: it is not clear how this intuition could be extended to other, more complicated properties of individual-level predicates. The goal of this paper is to defend the idea of an implicature-based theory of individual-level predicates by facing these two challenges. In the first part of the paper, I try to make sense of the weird nature of these special mismatching implicatures within the recent grammatical framework for scalar implicatures of Chierchia (Structures and beyond, 2004) and Fox (2007). In the second part of the paper, I show how this implicature-based line of reasoning can be extended to more complicated properties of individual-level predicates, such as restrictions on the interpretation of their bare plural subjects, noted in Carlson (Reference to kinds in English. Doctoral dissertation, University of Massachusetts at Amherst, 1977), Milsark (Linguistic Analysis 3.1: 1–29, 1977), and Fox (Natural Language Semantics 3: 283–341, 1995); restrictions on German word order, noted in Diesing (Indefinites, 1992); and restrictions on Q-adverbs, noted in Kratzer (The Generic Book, ed. Carlson and Pelletier, 125–175, 1995). (shrink)

The issue on which I intend to focus is whether there is anything else, anything more than ontological economy, which, in Russell's mature account of the constituents of propositions, is gained by his rejection of denoting concepts. I will argue that in order to answer this question, it is necessary to appreciate that by the time of "On Denoting," Russell was not merely advancing a claim of philosophical logic or a theory of the logical form of the descriptive phrases (...) of English. (edited). (shrink)

This article intends to critically envisage limits and values of philosophy of art of Arthur Danto and to point out the main problems of the theory of supstitutional representation, when placed within wider theoretical frame of traditional aesthetics, such as the notion of meaning in the philosophy of art of Arthur Danto. The article focuses on the notions of exteral and interal representation and denotation of non-existent and existent entities substituted by representation. This article intends to question the (...) validity of Danto?s position. Ovaj tekst pokusava da kriticki sagleda domete i vrednosti filozofije umetnosti Artura Dantoa i da istakne osnovne probleme sa kojima supstituciona teorija reprezentacije mora da se suoci, kada se ona zastupa u sirem teorijskom okviru tradicionalne estetike, kakav je pojam znacenja u filozofiji umetnosti Artura Dantoa. Posebnu paznju tekst usmerava na pojmove eksteralne i interalne reprezentacije i denotacije nepostojecih i postojecih entiteta, koji se reprezentacijom supstituiraju. Autor nastoji pokazati da je stav koji Danto zastupa apsurdan. (shrink)

Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. (...) The purpose of this paper is first to clarify this question by examining the conceptions of (I) the function served by NPT in science, and (II) the requirements of an objective theory of statistics upon which attacks on NPT's objectivity are based. Our grounds for rejecting these conceptions suggest altered conceptions of (I) and (II) that might avoid such attacks. Second, we propose a reformulation of NPT, denoted by NPT*, based on these altered conceptions, and argue that it provides an objective theory of statistics. The crux of our argument is that by being able to objectively control error frequencies NPT* is able to objectively evaluate what has or has not been learned from the result of a statistical test. (shrink)

The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in (...) work of Sauer [Coloring subgraphs of the Rado graph, Combinatorica26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica26(2) (2006) 183–205], the Ramsey theory of H3 had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin.2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math.185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph G, there is a finite number T(G) such that for any coloring of all copies of G in H3 into finitely many colors, there is a subgraph of H3 which is again universal homogeneous triangle-free in which the coloring takes no more than T(G) colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code H3 and the development of their Ramsey theory. (shrink)

This paper aims to recover the ideas about semantics that are contained in Yāska’s _Nirukta_ (c. 6–3 century BCE), the seminal work of the Indian tradition of _nirvacana_ or etymology. It argues that, within the framework of his etymological project, Yāska developed consistent and sophisticated ideas relating to semantics—what I call his theory of meaning. It shows that this theory assumes the form of explicit and implicit reflections pertaining to the relation between three categories: denoting names (_nāman_/_nāmadheya_), denoted (...) objects (_sattva_/_artha_), and name-giving action expressed by verbal roots (_ākhyāta_). A typology of Yāska’s etymologies for what they reveal about semantics will be proposed and investigated. In doing so, attention will be paid to how Yāska’s ideas resemble and anticipate ideas concerning the difference between polysemy and homonymity, metaphoric transfer, and synecdoche. It is hoped that attending to Yāska’s thus-far largely overlooked ideas will help us better appreciate the _Nirukta_’s role in the history of early Indian engagements with semantics. (shrink)

This essay explores how Schelling’s Philosophy of Art promotes a theory of the imagination (Einbildungskraft) correlative to that reason informing his Philosophy of Identity. Against the background of Kant’s and Fichte’s transcendental-philosophical notion of the imagination, it shows how Schelling conceives the absolute identity of the ideal and the real in terms of its expression in and asthe imagination. As a name for the self-constitution of absolute identity, the term “Einbildungskraft” denotes for Schelling not merely the formative activity of (...) picturing, but instead the generative dynamic of imprinting, and this as the singular operation of unification in the sense of genuinely making the disparate—the finite and the infinite—into one. How this theory involves a view of artistic symbols as instantiating pure unity is discussed with reference to Schelling’s theory of tragedy as well as Hegel’s criticism of this conception. (shrink)

The theory of descriptions occupies a very prominent place in Russell's system of logic and indeed in his system of philosophy. Since the publication of the now classical paper “On Denoting” in Mind for 1905 the theory had been incorporated into Principia Mathematica , the first volume of which appeared in 1910. In 1918 Russell discussed descriptions in his lectures on the Philosophy of Logical Atomism, which subsequently were published in The Monist for 1919. A very lucid exposition (...) of the main tenets of the doctrine is to be found in the Introduction to Mathematical Philosophy dating from the same year. Epistemological aspects of the theory of descriptions are examined in “Knowledge by Acquaintance and Knowledge by Description“, in the Proceedings of the Aristotelian Society for 1910–11, and also in Chapter V of The Problems of Philosophy, first published in 1912. (shrink)

In recent years, many scientists and philosophers have begun to believe that a new theoretic revolution is occurring in cognitive science. The revolution is the rise of theoretical models of "4E+S" cognition. "4E" denotes "embodied", "embedded", "enacted", and "extended"; "S" denotes "situated". Differentiating from the traditional computational theory or representational theory of cognition, this branch of new cognitive scientists and philosophers have begun to claim that cognition is embodied, embedded, enacted, extended and situated. All of these five theories (...) agree that cognitive processes can proceed beyond the boundary of the brain. Thus we can synthesize them together as "transcranial cognition" or "transbrain cognition". The questions are: Are there common characteristics of these five models? Can we integrate them together with a new model of cognition? Is the "4E+S" model a real Copernicus style revolution of cognitive science? This article analyzes these questions and provides the following answers: There is a common characteristics of these cognitive theories and it is the characteristics of transcranialness, i. e. cognition or mind can exist beyond brain; We can integrate them together as transcranial cognition; The new theory of cognition or mind is a new big extended theory of traditional cognitive science. (shrink)

Algebraic theories for extensive measurement are traditionally framed in terms of a binary relation $\lesssim $ and a concatenation (x,y)→ xy. For situations in which the data is "noisy," it is proposed here to consider each expression $y\lesssim x$ as symbolizing an event in a probability space. Denoting P(x,y) the probability of such an event, two theories are discussed corresponding to the two representing relations: p(x,y)=F[m(x)-m(y)], p(x,y)=F[m(x)/m(y)] with m(xy)=m(x)+m(y). Axiomatic analyses are given, and representation theorems are proven in detail.

Network theory is necessary for the realization of cognitive representations and resulting empirical observations of social groups. We propose that the triadic primitives denoting individual roles are multilayer, with positive and negative relations feeding into cost–benefit calculations. Through this, we advance a computational theory that generalizes to different scales and to contexts where conflict is not present.

This paper discusses the problems of an ontological value of the variable in Russell’s philosophy. The variable is essential in Russell’s theory of denotation, which among other things, purports to prove Meinongian being outside of subsistence and existence to be logically unnecessary. I argue that neither Russell’s epistemology nor his ontology can account for the ontological value of the variable without running into qualities of Meinongian being that Russell disputed. The problem is that the variable cannot be logically (...) grounded by Russell’s theory of denotation. As such, in so far as being is concerned, Meinong and Russell’s theories are much closer than is typically thought. The arguments are supported with concerns raised by Russell, Frege, and Moore regarding the ontological value of the variable. The problem can be summarised as follows: the variable is the fundamental denoting-position of a formal theory that is meant to explain the structure of the ontological. If such a formal theory is meant to ground the ontological, then the formal must also represent the actual structure of the ontological. Yet the variable, the fundamental symbol of denotation in a theory that defines objects, is ontologically indefinable. (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)

The Pauṣkara briefly discusses the meaning-expressing nature of śabda (constituted of phonemes, varṇa) and the means to the cognition of word and sentence meaning. According to this dualistic Śaiva Tantra, meaning is denoted by nāda, a capacity of varṇas. Varṇas also are the means to the cognition of meaning through a capacity (saṃskāra) manifested in them. Although the meaning-denoting capacity is natural to varṇas, the relation of words (which are nothing but groups of varṇas) with objects is fixed by convention. (...) This article translates and analyzes the relevant passages from the sixth and eighth chapters. Certain arguments of plagiarism levelled against the eighth chapter of the Pauṣkara are examined in the concluding part of the article. (shrink)

In Section 38 of the Theory of Vision Vindicated, George Berkeley claims that he had used the method of analysis throughout the Theory of Vision. What does that mean? I first show that "analysis" denoted a fairly well-defined method in the early modern period: it was regularly described as a method of discovery. Then I show that the discussion of distance perception in the Theory of Vision exemplifies the method of analysis and may be seen as a (...) modification of a non-geometrical account of distance vision in Rene Descartes' Optics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Did Hobbes Have a Semantic Theory of Truth? WILLEM R. DEJONG 1. INTRODUCTION THE qUESTIONRAISEDin the title of this article may strike the reader as a bit anachronistic. A phrase like 'semantic theory of truth' evokes associations with rather recent developments in logic, especially the work of Alfred Tarski. Nevertheless, it is generally agreed that Hobbes made important observations of a semantical nature. Moreover, in an interesting (...) article still frequently referred to, R. M. Martin has argued that Hobbes "has in mind a clear-cut semantical concept of truth."' Examining Hobbes's semantical ideas somewhat more closely than Martin did, T6rnebohm has given a more precise characterization of Hobbes's view on truth and falsity; he speaks of Hobbes's comprehension theory of truth. ~One of the main purposes of this article is to investigate whether such a theory is correctly attributed to Hobbes. For Tarski 'true' and 'false' are predicates of (declarative) sentences) But this is not enough to speak of a semantic theory of truth: The leading idea behind Tarski's fundamental work in the field of semantics is (a restricted version of) the principle of compositionality. This principle, also known as Frege's principle, says that the semantic value of a (complex) expression is a function of the semantic values of the syntactic (and categorematic) parts it is ' R. M. Martin, "On the Semantics of Hobbes," Philosophyand PhenomenologicalResearch 14 095314): 2o5-11, esp. ~o7, 211. Cf. I. C. Hungerland and G. R. Vick, "Hobbes's Theory of Language, Speech and Reasoning," in ThomasHobbes:Computatwsire Logica--Logic, translated and commentary by A. Martinich, ed. and introduced by I. C. Hungerland and G. R. Vick (New York: 1981), 15--167, esp. 17, 121-22. 9 H. T6rnebohm, "A Study in Hobbes' Theory of Denotation and Truth," Theor~a26 (196o): 53-7o; see p. 66. 3 A. Tarski, "The Semantic Conception of Truth and the Foundations of Semantics," Philosophy and PhenomenologicalResearch4 (1944): 341-375; see p. 342. [63] 64 JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 199o composed of. Moreover, in the case of linguistic expressions which are (deciarative ) sentences this semantic value should be its truth-value. 4 As we shall see, Hobbes's theory of propositions is basically a theory of subject-predicate propositions. It is therefore reasonable to qualify his theory of truth as a semantic one only if it satisfies Frege's principle to a certain extent. Ideally, this means that the truth-value of subject-predicate propositions should be conceived as a function of the semantic interpretations of its subject and predicate. In the next three sections I will concentrate principally on the logicosyntactical aspects of language. I will then discuss successively the general structure of propositions, the various sorts of names, and the syntax of Hobbes's theory of propositions. Section 5 is devoted to Hobbes's theory of truth as interpreted by Martin and T0rnebohm. The outcome of this examination makes it necessary to break away from Martin's restricted conception of semantics. Martin, like Tarski, takes semantics as "semantics in the narrower sense," i.e., as the discipline Quine refers to as the theory of reference. 5 However, sometimes this term is used in a broader sense; the field of semantics is taken then to include the theory of meaning too. Although the wording differs frequently, the distinction between meaning and reference is almost a constant in the history of thinking about language. On the side of meaning one finds terms like connotation, intension, conception, signification and analyticity, while terms like naming, denoting, extension (and sometimes again signification) are ]inked to the notion of reference. In the Computatio sive Logica, the first part of De Corpore, containing Hobbes's most mature work on the philosophy of language, this opposition is displayed by way of a distinction between, on the one side, nominare, denotare and appellare and, on the other side, significare. Hobbes's view of the significative, as opposed to the denotative, role of linguistic expressions is treated in sections 6, 7, and 8. There it will be shown that Hobbes's radical nominalism is decisive for his doctrine of signification; moreover, this nominalism raises serious problems for the relation... (shrink)

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

Church's simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Church's system called PF in which functions may be partial. The semantics of PF, which is based on Henkin's general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for (...) partial functions corresponds closely to mathematical practice, and the formulation of PF adheres tightly to the framework of Church's system. (shrink)

In 1931–1934 Kazimierz Ajdukiewicz formulated two versions of the theory of meaning (A1 and A2). Tarski showed that A2 allows synonymous names to exist with different denotations. Tarski and Ajdukiewicz found that this feature disparages the theory. The force of Tarski’s argument rests on the assumption that none of adequate theories of meaning allow synonymous names to exist with different denotations. In the first part of this paper we present an appropriate fragment of A2 and Tarski’s argument. In (...) the second part we consider an elementary interpreted language in which individual constants occur, but not functional symbols. For such a language we define semantically a relation of synonymity for simple names and show that it fulfills syntactical conditions formulated by Ajdukiewicz in A2 and allows synonymous names to exist with different denotations. (shrink)

In this article I argue that Russell's multiple-relation theory of judgment is a continuation of the campaign against Frege and Meinong begun in “On Denoting” with the theory of descriptions. More precisely, I hold that the problem of false belief, to which the multiple-relation theory is presented as a solution, emerges quite naturally out of the problem context of “On Denoting” and threatens to give new life to the theories Russell purports to have laid to rest there, (...) and that Russell's solution to the much neglected third puzzle of “On Denoting” contains the gist of the multiple-relation theory. The failure of that theory to solve the problem of false belief thus signifies the failure of the theory of descriptions. (shrink)

The idea of ‘modal fields’ is inspired by regional and pluralistic ontologies, which were sketched and developed by Hegel, Husserl and especially Nicolai Hartmann. It suggests that the world is structured by spheres which are not reducible to each other, and that modal fields denote the scope of real possibilities inside the spheres. It is, for example, possible to distinguish between physical, biological, ecological, economic and technological possibilities/modal fields. It is also possible to define, for the purpose of scientific research, (...) very specific modal fields. For example, we can ask “What are the physiological or social possibilities of ants?”, or “What are the social and psychological possibilities of fundamental religious sects?” It is possible to apply this ontological theory to philosophy of science in order to clarify the scope and limits of causal explanations and hermeneutic understanding especially in human and environmental sciences. In general, this ontological theory serves as a fruitful basis for the kind of scientific thinking which is open to counterfactuals and possibilities and which considers deterministic causal thinking too restricted for human and environmental sciences. On the other hand, this theory avoids the individualistic and anthropocentric presuppositions of hermeneutical understanding, connecting it to the real subjective and objective possibilities in a certain historical situation. (shrink)

Kim :1099–1112, 2013) defends a logicist theory of numbers. According to him, numbers are adverbial entities, similar to those denoted by “frequently” and “at 100 mph”. He even introduces new adverbs for numbers: “1-wise”, “2-wise”, and so on. For example, “Fs exist 2-wise” means that there are two Fs. Kim claims that, because we can derive Dedekind–Peano axioms from his definition of numbers as adverbial entities, it is a new form of logicism. In this paper, I will, however, argue (...) that his theory is vulnerable to an analogue of the so-called Bad Company objection to neo-Fregeanism. This means that we cannot be sure that numbers are actually given to us by Kim’s definition; for, we don’t know whether it is indeed a good definition. So, unless Kim, or somebody else, provides a demarcation criterion between good and bad adverbial definitions, Kim’s theory will remain incomplete. (shrink)

The axiom of symmetry (A ℵ 0 ) asserts that for every function F: ω 2 → ω 2 there is a pair of reals x and y in ω 2 so that y is not in the countable set $\{(F(x))_n:n coded by F(x) and x is not in the set coded by F(y). A(Γ) denotes axiom A ℵ 0 with the restriction that graph(F) belongs to the pointclass Γ. In § 2 we prove A(Σ 1 1 ). In § (...) 3 we show A(Π 1 1 ), A(Σ 1 2 ) and $^\omega 2 \nsubseteq L$ are equivalent. In § 4 several effective versions of A(REC) are examined. (shrink)

Dignāga’s theory of semantics called the “theory of apoha ” has been criticized by those who state that it may lead to a circular argument wherein “exclusion of others” is understood as mere double negation. Dignāga, however, does not intend mere double negation by anyāpoha. In his view, the word “cow” for instance, excludes those that do not have the set of features such as a dewlap, horns, and so on, by applying the semantic method called componential analysis. (...) The present paper aims to prove this by referring to the fragments quoted by Jinendrabuddhi and Siddhasenagaṇi. Dignāga logically proves that the denotation of the referent Q by the word “P” cannot be derived from the joint presence of “P” with Q. Instead, he derives it from the joint absence of “P” with the nonexistence of Q. Anyāpoha is nothing but verbal vyatireka. Componential analysis is used for describing what is to be excluded. Dignāga draws taxonomic hierarchies of words based on their customary use, and assumes componential analysis to operate in the background of the hierarchies formed in semantic fields, stating that a general term is restricted to having the same reference with one of its specific terms insofar as the former is connected with the characteristics of the latter’s referent. Moreover, he states that a proper name also denotes its referent by excluding those that do not have the cluster of a certain number of qualities. (shrink)

This paper presents an original semantic theory of proper names that aims to cover both non-empty and empty proper names. According to the theory, proper names have simple assignable hyperintensions as their content. This content provides the referent (if there is one) for which the proper name stands. The paper further describes the role of the proposed content of (empty) proper names within the compositional semantics of problematic sentences. I stress the difference between the content of a sentence (...) (i.e. its hyperintension) and the proposition (i.e. a mapping from possible worlds to truth values) denoted by that sentence. (shrink)

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this (...) paper, I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages. (shrink)

Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. (...) Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

A modified version of Normann's hierarchy of domains with totality [9] is presented and is shown to be suitable for interpretation of Martin-Löf's intuitionistic type theory. This gives an interpretation within classical set theory, which is natural in the sense that $\Sigma$ -types are interpreted as sets of pairs and $\Pi$ -types as sets of choice functions. The hierarchy admits a natural definition of the total objects in the domains, and following an idea of Berger [3] this makes (...) possible an interpretation where a type is defined to be true if its interpretation contains a total object. In particular, the empty type contains no total objects and will therefore be false (in any non-empty context). In addition, there is a natural equivalence relation on the total objects, so we derive a hierarchy of topological spaces (quotient spaces wrt. the Scott topology), and give a second interpretation using this hierarchy. (shrink)

We show that there is a computable procedure which, given an ∀∃-sentence ${\varphi}$ in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether ${\varphi}$ is true in the Medvedev degrees of ${\Pi^0_1}$ classes in Cantor space, sometimes denoted by ${\mathcal{P}_s}$.