This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully (...) analyzed. This second level reflects the commitments of real metaphysics. The models for these commitments assign truth conditions to natural language discourse. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

Philosophers frequently draw on natural language to motivate properties, numbers, and propositions as objects, and it is generally taken for granted that abstract objects of this sort are well-reflected in natural language and in fact that reference to them in natural language is pervasive In this paper, I will review and modify in a certain way the view I had advanced in Abstract Objects and the Semantics of Natural Language (Moltmann 2013a). This is the (...) view that natural language permits reference to abstract objects only in its periphery, not in its core. Even though reference to abstract objects of the sort of properties, propositions, and numbers is available only in the periphery of language, natural language permits reference to other sorts of abstract objects in its core, in particular abstract artifacts of various sorts. (shrink)

Platonism, considered as a philosophy of mathematics, can be formulated in two interestingly different ways. Strong platonism holds that numerals, for example, refer to certain non-physical, non-mental entities. Weak platonism holds only that numerals uniquely apply to certain non-physical, non-mental entities. (Of course, there may even be weaker views that deserve to be called ‘platonistic.’The distinction between referring to an object and uniquely applying to an object may be illustrated as follows. If there is a tallest person and I say, (...) ‘the tallest person is over seven feet tall,’ without knowing who that person is, then my use of ‘the tallest person’ uniquely applies to someone, but it does not refer to anyone. The distinction is at least as old as Russell, for we might put his views in our terms by saying that for Russell only logically proper names refer to things, while ordinary proper names and definite descriptions at best uniquely apply to things. (shrink)

This essay introduces the concept of deictic abstraction , taking as a point of departure Husserl’s prototypical but insufficient description of the act of ideation in which a shade of color comes to givenness as an ideal object, i.e., a non-individual or abstract object, on the basis of a perceived individual object. This concept comprises not only color-ideation and ideations of universalities of the sensuous sphere , but all acts founded in perceptions in which ideal objects are directly (...) referred to by means of demonstrative expressions . This allows various types of deictic ideations or abstractions, corresponding to the degree of universality and the kind of ideal object concerned, to be brought to light through the analysis of particular cases of everyday acts of deictic abstraction, including deictic abstractions of predicative universals of the lowest level of universality ; deictic abstractions of non-predicative universals, especially of universal ways of doing something ; and deictic abstractions of individual styles of doing something . Deictic abstractions not only turn out to be constitutive for the formation of perceptual concepts of the lower and lowest levels, but also prove to be foundational for all kinds of learning in which schemata of actions are acquired from a model. (shrink)

Alonzo Church has repeatedly argued that the semantic analysis of certain contexts requires reference to abstract entities of various kinds. The problem, arising from this argument for nominalists, will be examined first. Then we shall attempt to meet Church’s challenge by constructing and informally describing a semantics which was inspired by Nelson Goodman’s distinction between primary and secondary extensions. According to that semantics, no expression of the object language will make reference to any abstract or non-actual (...) entity while the system is strong enough to lend itself to semantic analysis in Church’s sense. (shrink)

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such (...) as properties, numbers, propositions, and degrees is considerably more marginal than generally held. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily (...) treated abstract objects, but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and (...) offers an account of what it is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)

Frege suggests that criteria of identity should play a central role in the explanation of reference, especially to abstract objects. This paper develops a precise model of how we can come to refer to a particular kind of abstract object, namely, abstract letter types. It is argued that the resulting abstract referents are ‘metaphysically lightweight’.

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambigu-ity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argu-ment’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

Theoria, EarlyView. -/- In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid Linnebo's conclusion by rejecting his claim that certain abstraction principles are sufficient for reference (RBA). Section (...) 1 of the paper explains Linnebo's argument for RBA. It offers a reading of Linnebo's work upon which he has two arguments for RBA: one deductive and one abductive, and argues that whilst the deductive argument is unsound the abductive one is prima facie plausible. The nominalist must therefore find a way to respond to the abductive argument. Section 2 outlines just such a response, by offering an alternative explanation of the cases Linnebo wishes to argue from. Most interestingly, it shows that abstraction in Linnebo's most difficult case (the “reference to ordinary bodies” case) can be achieved using mereological means, rather than relying on RBA. (shrink)

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambi-guity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argument’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with (...) tools for dispelling the threat of a version of referential indeterminacy, according to which nothing in our use of a singular term, even when it is guided by an associated criterion of identity, could determine which particular object it refers to. I end by examining the bearing of the indeterminacy challenge to Linnebo's treatment of Frege's Caesar Problem: in the absence of an argument against the indeterminacy of reference, it is unclear how numerical expressions could qualify as genuine singular terms. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument (...) strongly motivates nominalism, it also undermines certain nominalist theories. (shrink)

A realist view of numbers often rests on the following thesis: statements like ‘The number of moons of Jupiter is four’ are identity statements in which the copula is flanked by singular terms whose semantic function consists in referring to a number (henceforth: Identity). On the basis of Identity the realists argue that the assertive use of such statements commits us to numbers. Recently, some anti-realists have disputed this argument. According to them, Identity is false, and, thus, we may deny (...) that the relevant statements commit us to numbers. The present paper argues that the correct linguistic analysis of the relevant number statements supports the anti-realist view that Identity is false. However, as will further be shown, pace the anti-realist, this analysis does not establish that such statements do not commit us to numbers after all. (shrink)

Many languages offer a surprisingly complex range of options for referring to entities using expressions whose main descriptive content is contributed by an adjective, such as Dutch de blinde ‘the blind,’ het besprokene, ‘the discussed,’ or het ongewone van het niet roken ‘the strange about not smoking.’ In this paper, we present a case study of the syntax and compositional semantics of three such constructions in Dutch, one of which we argue has not previously been identified in the literature. The (...) data and the analysis will shed light on our understanding of how reference using adjectives differs from that using nouns in languages that have the two categories, as well as on the differences between reference to entities via their properties vs. reference to properties themselves. Finally, we briefly discuss related work and indicate directions for future study of the typological variation found in this rich and highly understudied corner of natural language. (shrink)

In its approach to fiction and fictional discourse, pretense theory focuses on the behaviors that we engage in once we pretend that something is true. These may include pretending to name, pretending to refer, pretending to admire, and various other kinds of make-believe. Ordinary discourse about fictions is analyzed as a kind of institutionalized manner of speaking. Pretense, make-believe, and manners of speaking are all accepted as complex patterns of behavior that prove to be systematic in various ways. In this (...) paper, I attempt to show: (1) that this systematicity is captured in the basic distinctions and representations that are central to the formal theory of abstract objects, and (2) that this formal theory need not be interpreted platonistically, but may instead have an interpretation on which the `objects' of the theory are things that pretense theorists already accept, namely, complex patterns of linguistic behavior. The surprising conclusion, then, is that a certain Wittgensteinian approach to meaning (e.g., the meaning of a term like `Holmes' is constituted by its pattern of use) bears an interesting relationship to a formal metaphysical theory and the semantic analyses of discourse constructed in terms of that theory---the former offers a naturalized interpretation of the latter, yet the latter makes the former more precise. (shrink)

This article is a critical review of Cocchiarella’s theory of reference. In conceptual realism, there are two central distinctions regarding reference: first, between active and deactivated use of referential expressions, and, second, between using referential expressions with and without existential presupposition. Cocchiarella’s normative restrictions on the existential presuppositions of reference lead to postulating two fundamentally different kinds of objects in conceptual realism: realia or concrete objects, on the one hand, and abstract intensional objects (...) or nonexistents, on the other. According to Cocchiarella, nonexistents can be referred to only without existential presuppositions. However, referring to nonexistents with existential presuppositions is an ordinary human practice. To account for this fact, Cocchiarella’s normative theory of reference should be supplemented by a descriptive account of referring. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.2 (2000) 175-188 [Access article in PDF] Scope Note 38 Bioethics Resources on the Web * Once described as an "enormous used book store with volumes stacked on shelves and tables and overflowing onto the floor" (Pool, Robert. 1994. Turning an Info-Glut into a Library. Science 266 (7 October): 20-22, p. 20), Internet resources now receive numerous levels of organization, from basic directory (...) listings to elaborate "links" (cross-references to other Internet documents) that flash and glow in the dark. In many ways, the Internet functions as a direct extension of the traditional library. Following linked references across various sites is an electronic version of browsing library stacks, and the serendipitous discoveries made while "surfing the Net" recall the wonders of physically going "book-to-book." Although many of the Internet's best aspects augment library strengths by eliminating physical distance from sources, Net resources pose unique problems for researchers. It is not always clear who is responsible for the content of Web documents, when the document was produced, or how often (if ever) it is updated. Internet resource tools, then, must enable researchers to identify appropriate resources and to evaluate what they find when they get there. Web Research as Taking "Snapshots" Given the Internet's visual nature and fluid content, the process of conducting research on the Web has been likened to taking an informal picture of information on a specific date at a particular time. This metaphor also conveys the "zoom-in" aspect of searching through Web pages by going from general to specific categories. In the first section of this Scope Note, National Reference Center for Bioethics Literature (NRCBL) staff present a snapshot of bioethics resources taken during the spring months of 2000. Entries are divided into the categories of directories, electronic journals, full-text documents, news/current awareness, and teaching resources. In the two subsequent sections, this series of categories is repeated for entries on a specific topic within bioethics-genetics-and again for general search and evaluation tools. Where a Web site may contain pages applicable [End Page 175] to more than one category, multiple entries are made for that site with appropriate information for each category.Much as telecommunication advances have strengthened the relationship of patients and providers as partners, the dynamic nature of the Internet acknowledges that the researcher functions as a librarian whenever accessing the Web. It is our hope that BIOETHICSLINE and the other NRCBL databases not only will enable researchers to search the Web more efficiently, but also will help them to evaluate what they find when they get there. Bioethicsline on the Web: An International Plan in Progress Once only available through libraries, the U.S. National Library of Medicine (NLM), the funding agency for the ongoing development of the BIOETHICS LINE® database from the Kennedy Institute, has provided free Web access to that database of 63,000 citations since September 1998 through Internet Grateful Med. Plans are now underway to eliminate such specialty databases and incorporate all citations into PubMed (for journal articles) or LOCATORplus (for book-like materials and chapters in books). Both of these databases are likewise available at no cost on the Web. In the transition to PubMed and LOCATORplus some features of BIOETHICSLINE that presently are available may be lost. Researchers are encouraged to contact the National Reference Center for Bioethics Literature with search requests or for search strategy assistance with either the current or the future system ([email protected]).The inclusion of bioethics citations in PubMed and LOCATORplus will have several advantages. First, unique keywords from the Bioethics Thesaurus will be considered for inclusion in Medical Subject Headings (MeSH), the indexing vocabulary for PubMed and LOCATORplus, thereby enhancing retrieval of relevant clinical literature by offering more precise terminology covering ethical issues. Second, it will be easier to identify foreign-language materials, which are not currently included in the scope of BIOETHICSLINE. Third, the updating schedule will become more frequent. On the other hand, there may be some loss of searching precision because certain specialized features... (shrink)

The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards (...) objects, whereas nominalists such as Field have asserted that these apparent ontological commitments should not be taken at face value. In this article I argue for an intermediate position which upholds the legitimacy of ascribing a reference to abstract singular terms in an attenuated sense relative to the more robust ascription of reference applicable to names denoting concrete entities. In so doing I seek to clear up some confusions regarding the ramifications of such a thin notion of reference for ontological claims about mathematical objects. (shrink)

One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented (...) meaning-contents. These meaning-contents serve as the ‘thin’ referents of abstract singular terms, but are ultimately founded in prior acts of meaning-constitution. (shrink)

Linsky and Zalta try to explain how we can refer to mathematical objects by saying that this happens through definite descriptions which may appeal to mathematical theories. I present two issues for their account. First, there is a problem of finding appropriate pre-conditions to reference, which are currently difficult to satisfy. Second, there is a problem of ensuring the stability of the resulting reference. Slight changes in the properties ascribed to a mathematical object can result in a (...) shift of reference and this leads to various problems, e.g., it makes inferring knowledge much harder than it is. (shrink)

One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented (...) meaning-contents. These meaning-contents serve as the ‘thin’ referents of abstract singular terms, but are ultimately founded in prior acts of meaning-constitution. (shrink)

It is not a common practice to postulate meaning entities treated as objects of some kind. The paper demonstrates two ways of introducing meaning-objects in two logics of natural language, Tichy’s Transparent Intensional Logic and Zalta’s Intensional Logic of Abstract Objects. Tichy’s theory belongs to the Fregean line of thinking, with what he calls ‘constructions’ as Fregean senses, and ‘determiners’ as object-like meaning entities constructed by the senses. Zalta’s theory belongs to Meinongian logics and he postulates (...) a rich realm of abstract Meinongian objects to play the role of meanings. The paper analyses the mechanisms of reference in both conceptions and it offers a comparison of the mediating meaning-objects and the framework designed to expose this mediation in both theories. An attempt is made to expose how the treatment of the meaning entities depends upon the theory of meaning which is assumed. (shrink)

A standard understanding of abstraction principles elicits two opposite readings: Intolerant Reductionism, where abstractions are seen as reducing talk of abstract objects to talk about non-problematic domains, and Robustionism, where newly introduced terms genuinely refer to abstract objects. Against this dichotomy between such “austere” and “robust” readings, Dummett suggested ways to steer intermediate paths. We explore different options for intermediate stances, by reviewing metaontological strategies and semantic ones. Based on Dummett’s and Picardi’s understanding of the Context (...) Principle, the paper acknowledges that Frege’s Grundlagen are open to several interpretations of contextual definitions, and argues that the prospects for broadly Fregean intermediate views are all but foreclosed. (shrink)

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized language. -/- Hence I try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. -/- First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions (...) from his saturated vs. unsaturated sentence components paradigm. -/- Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. -/- Then have a comment on the just referenced label abstract objects. -/- Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. -/- Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories: and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -/- In the end I sum up what is - from my point of view - the status quo, according to my respective findings. (shrink)

Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book (...) attempts to develop the needed explanations by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. (shrink)

The use of modern medical technologies and interventions involves ethical and legal dilemmas which are yet to be solved. For the religious Jews the answer lies in Halakhah. The objective of this paper is to unscramble the difficult conundrum possessed by the halakhalic standing concerning the use of human embryonic cell for research. It also aims to take contemporary ethical issues arising from the use of technologies and medical advances made in human reproduction and study them from an abstract (...) philosophical perspective. Instead of providing any Jewish practical ruling the paper have tried to incite, stimulate and encourage philosophical thoughts about the issue through the intensive understanding of traditional Jewish thoughts. In this paper, an objective as well as a deep-rooted study has been adopted about the use of human embryos for research and the Jewish adoption of assisted reproductive technologies through the prism of the knowledge of Halakhah, Torah and Talmud. The paper finds that the embryo research sits at the crossroads of many halakhalic issues. Judaism adopts the belief that God has created man in his own image. The Jews not being dogmatic decipher “the image” of the creator as the ability to discern and reason. It follows that Judaism does not subscribe to the notion that tampering with nature is prohibited. To the Jews the mitzvah for procreation is so great that they are open to reason and adopt newer medical advancement in procreation. The Jewish laws are not only for engagement in intellectual exercise or academic pursuit but subscribe to a higher order of moral conduct. The Jewish approach is not situational but also casuistic in resolving conflicting medical issues. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing (...) begins. The main reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits ofion breaks new ground both technically and philosophically.

A. Meinong’s views are usually associated with an highly inflated ontology including various kinds of nonexistent objects, incomplete and impossible ones among others. Around the turn of the century B. Russell strongly criticised this ontology accusing it of inconsistency. And perhaps because of this criticism Meinong’s views have been forgotten for a long time. Only recently some philosophers have created theories of objects which are formalisations of Meinong’s ontology or which are directly inspired by the ontology 1 . (...) However there still remains a need to discuss the problem of ways of reference to Meinongian objects regarding their specific structure of predication, and the interrelated problem of ontological commitment of those theories. Meinong’s ontological theory seems to be not so bizzare if we interpret it as a theory of possible intentional objects, i.e. possible objects of consciousness. And this interpretation perfectly agrees with phenomenological tradition from Brentano to Husserl and with the contemporary philosophy of mind. Needless to say reference is a special form of intentional relation so semantical investigations into these objects are of great relevance for general theory of intentionality. (shrink)

My belief that Socrates was wise, and your belief that Socrates was mortal can be said to have a common focus, insofar as both these thoughts are about Socrates. In Peter Geach’s terminology, the objects of our beliefs bear the feature of intentional identity, because our beliefs share the same putative target. But what if it turned out that Socrates never existed? Can a pair of thoughts share a common focus if the object both thoughts are about, does not (...) actually, really exist? Object-centric accounts of intentionality which explain the aboutness or directedness of thought in terms of the intentional object the thought in question is about, contend that thoughts which share a common focus do so in virtue of both thoughts simply being about the same intentional object. However, Alexander Sandgren contends that such theories face difficulties in explaining a puzzle of intentional identity put forward by Walter Edelberg, in which a pair of sentences seem to differ in truth value but are purportedly logically equivalent on the object-centric theory. If this is right, then it seems that any account which explains intentionality with reference to an intentional object is threatened by this result, whether this object be abstract, merely possible, Meinongian, or otherwise. In this paper, I argue that Edelberg’s Puzzle is analogous to Frege’s Puzzle and the same tools conventionally used to solve Frege’s Puzzle can be used to solve Edelberg’s Puzzle. I then propose a new object-centric solution to Edelberg’s Puzzle which takes into account modes of presentation and which is able to accommodate all the relevant linguistic data. (shrink)

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an ‘alphabet of human thought’. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract (...) class='Hi'>objects, we should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give (...) it. I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

The influence of Franz Brentano in twentieth century philosophy has been extensive. His two most famous and outstanding pupils were Alexius Meinong and Edmund Husserl. These two are closely related not only regarding their common background in the school of Brentano, but also in their common concern with problems arising from British empiricism. Such a problem is to be found in the nominalist views of Locke, Berkeley, and Hume and their concomitant theories of general ideas. While Meinong's early work continues (...) in the empiricist tradition by characterizing general ideas in terms of abstraction and not in terms of general objects as their correlates, Husserl's _Logical Investigations_ are committed to the claim that general ideas can be described only as ideas which refer to general objects. In _Meinong and Husserl onion and Universals_ the epistemological, psychological, and ontological aspects of these theories are examined and compared. Included is also a translation of _Abstraction and Comparing_ by Meinong. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give (...) it. I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

The blame for the semantic and set-theoretic paradoxes is often placed on self-reference and circularity. Some years ago, Yablo [1985; 1993] challenged this diagnosis, by producing a paradox that's liar-like but does not seem to involve circularity. But is Yablo's paradox really non-circular? In a recent paper, Beall [2001] has suggested that there are no means available to refer to Yablo's paradox without invoking descriptions, and since Priest [1997] has shown that any such description is circular, Beall concludes that (...) Yablo's paradox itself is circular. In this paper, we argue that Beall's conclusion is unwarranted, given that (1) descriptions are not the only way to refer to Yablo's paradox, and (ii) we have no reason to believe that because the description involves self-reference, the denotation of the description is also circular. As a result, for all that's been said so far, we have no reason to believe that Yablo's paradox is circular. (shrink)

Beach's Gaelic Symphony is plausibly an abstract object that Beach created. The view that people create some abstract objects is called abstract creationism. There are abstract creationists about many kinds of objects, including musical works, fictional characters, arguments, words, internet memes, installation artworks, bitcoins, and restaurants. Alternative theories include materialism and Platonism. This paper discusses some of the most serious objections against abstract creationism. Arguably, these objections have ramifications for questions in metaphysics pertaining (...) to the abstract/concrete distinction, time, causation, vague existence, vague identity, and inadvertent creation. (shrink)

Our only channel of information about the world is the impact of external forces on our sensory surfaces. So says science itself. There is no clairvoyance. How, then, can we have parlayed this meager sensory input into a full-blown scientific theory of the world? This is itself a scientific question. The pursuit of it, with free use of scientific theory, is what I call naturalized epistemology. The Roots of Reference falls within that domain. Its more specific concern, within that (...) domain, is reference to concrete and abstract objects: what such reference consists in, and how we achieve it. (shrink)

Abstract: Hilary Putnam has reformulated his model-theoretic argument as an argument against indirect realism in the philosophy of perception. This new argument is reviewed and defended. Putnam’s new focus on philosophical theories of perception (instead of metaphysical realism) makes better sense of his previous responses to the objection from the causal theory of reference. It is argued that the model-theoretic argument can also be construed as an argument that holders of a causal theory of reference should adopt (...) direct realism in the philosophy of perception. (shrink)

This thesis provides an account of acquaintance with abstract objects. The notion of acquaintance is integral to theorising on reference and singular thought, since it is generally taken to be the relation that must exist between a subject and an object, in order for the subject to refer to, and entertain singular thoughts about the object. The most common way of understanding acquaintance is as a form of causal connection. However, this implies a problem. We seem to (...) be able to refer and have singular thoughts about abstract objects. But given that abstract objects are causally inert, this would mean that we are unable to become acquainted with them. This problem shall be the focus of this thesis. I first argue that these traditional causal interpretations of acquaintance are lacking. Instead, I show that acquaintance is dependent to some degree on factors internal to the subject, namely the skills that they possess. From doctors to sommeliers to mathematicians (and possibly even philosophers!) – these subjects seem to succeed in becoming acquainted with certain objects precisely in virtue of their respective skills. Thus, building off from Evans’ The Varieties of Reference, I present a novel account of acquaintance, which I term as Skill-based Acquaintance (SBA). On SBA, a subject is said to be acquainted with an object when they possess discriminating knowledge of that object, gained through the use of their capacities and skills. The SBA account is applied to virtual (Ch.3), fictional (Ch.4), and mathematical objects (Ch.5), as well as God (Ch.6). SBA is successful in explaining how subjects can indeed become acquainted with these problematic categories of objects - some of which are abstract – thus being able to refer and entertain singular thoughts about them. Overall, then, SBA is shown to have greater explanatory power than competing accounts and should thus be preferred. (shrink)

ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the (...) terms introduced by abstraction principles. (shrink)

According to platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how could we ever come to know of the existence of such impotent and remote objects? In Knowledge, Cause, and Abstract Objects, Colin Cheyne presents the first systematic and detailed account of this epistemological objection to the platonist doctrine that abstract objects exist and (...) can be known. Since mathematics has such a central role in the acquisition of scientific knowledge, he concentrates on mathematical platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by platonists to account for our supposed platonic knowledge. This book will be of particular interest to researchers and advanced students of epistemology and of the philosophy of mathematics and science. It will also be of interest to all philosophers with a general interest in metaphysics and ontology. (shrink)

Abstract:With his theory of descriptions Russell wanted to solve two problems concerning denotation and reference, which are formulated here as Problem I and Problem II. After presenting each problem, we describe the main points of Russell’s solution. We deal with Russell’s concepts of existence and then elaborate his presuppositions concerning the relation of denoting and referring. Next we discuss the presuppositions or principles which underlie Russell’s understanding of the objects of reference. These principles are such that (...) if the objects of reference are material objects, they are objects of classical mechanics, or very close to such an interpretation. Finally we show how these principles have to be relaxed if the objects of reference are objects of quantum mechanics or special or general relativity. (shrink)