I use van Heijenoort’s published writings and manuscript materials to provide a comprehensive overview of his conception of modern logic as a first-order functional calculus and of the historical developments which led to this conception of mathematical logic, its defining characteristics, and in particular to provide an integral account, from his most important publications as well as his unpublished notes and scattered shorter historico-philosophical articles, of how and why the mathematical logic, whose he traced to Frege and the culmination of (...) its formative period in the incompleteness results of Gödel, became modern logic, as distinct from the traditional logic of Aristotle, and why and how the logistic tradition that led from Frege through Russell, rather than the algebraic tradition that led from De Morgan and Boole through Peirce and Schröder, came, in his view, to define modern logic. (shrink)

In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for (...) Logical Objects and banishes encoding formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: the theory of extensions, the theory of directions and shapes, and the theory of truth values. (shrink)

Resumen En esta nota presento la teoría unificada de las oraciones copulativas propuesta por Andrea Moro, quien sostiene que el verbo ser no es más que un soporte para la flexión verbal, independientemente de las peculiaridades gramaticales y semánticas de las oraciones adscriptivas, identificativas y existenciales en que aparece. Primero contextualizo la propuesta de Moro; después explico la manera en que Moro aclara una anomalía sintáctica que parece corroborar la supuesta polisemia del verbo ser. Por último, comento algunas omisiones de (...) relevancia filosófica en la historia del verbo ser contada por Moro.In this note I present the unified theory of copular sentences proposed by Andrea Moro, who maintains that the verb to be is nothing more than a support for verbal inflection, regardless of the grammatical and semantic peculiarities of the ascriptive, equative, and existential sentences in which it appears. First, I contextualize Moro's proposal. Then, I explain how Moro clarifies a syntactic anomaly that seems to corroborate the alleged polysemy of the verb to be. Lastly, I comment on some omissions of philosophical relevance in the history of the verb to be told by Moro. (shrink)

Hermann Grassmann's Ausdehnungslehre of 1844 and his Lehrbuch der Arithmetik of 1861 are landmark works in mathematics; the former not only developed new mathematical fields but also both contributed to the setting of modern standards of rigor. Their very modernity, however, may obscure features of Grassmann's view of the foundations of mathematics that were not adopted since. Grassmann gave a key role to the learning of mathematics that affected his method of presentation, including his emphasis on making initial assumptions explicit. (...) In order to better understand this less well-known aspect of his work it will help to examine why some commentators have overlooked his theme of unifying logic, pedagogy and foundations, while others have recognised it. (shrink)

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...) objects. (shrink)

Choices confront us with questions. How we act depends on our answers to those questions. So the way our beliefs guide our choices is not just a function of their informational content, but also depends systematically on the questions those beliefs address. This paper gives a precise account of the interplay between choices, questions and beliefs, and harnesses this account to obtain a principled approach to the problem of deduction. The result is a novel theory of belief-guided action that explains (...) and predicts the decisions of agents who, like ourselves, fail to be logically omniscient: that is, of agents whose beliefs may not be deductively closed, or even consistent. (Winner of the 2021 Isaac Levi Prize.). (shrink)

HorstenLeon* * _ The Metaphysics and Mathematics of Ordinary Objects. _Cambridge University Press, 2019. Pp. xviii + 231. ISBN: 978-1-107-03941-4 ; 978-1-10860177-1. doi: 10.1017/9781139600293.

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

The problem of identity is central to epistemic transference. However, relative identity appears to be the only way to work out an epistemic useful notion of identity. Relative identity, on its part, is either parasitic on strict identity or not identity at all. If, on the contrary, we ought for a strict concept of identity capable of satisfying its requirements, we end up with a tautologic and epistemic worthless category. The paper provides an answer to this problem, which, while working (...) with a strict notion, shows how it might still serve epistemic purposes. In doing so, it shows how a formal reconstruction of our objectual world and the identities we refer to poses a workable model upon which our messy epistemic one acquires stability. The paper focuses primarily on the Geach-Quine discussion on identity. (shrink)

This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...) J. Brouwer and D. Hilbert (1899). Part 2 is mainly devoted to Hilbert’s proof theory of the 1920s (1922–1931). I begin with an account of his early attempt to prove directly, and thus not by reduction or by constructing a model, the consistency of (a fragment of) arithmetic. In subsequent sections, I give a kind of overview of Hilbert’s metamathematics of the 1920s and try to shed light on a number of difficulties to which it gives rise. One serious difficulty that I discuss is the fact, widely ignored in the pertinent literature on Hilbert’s programme, that his language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Along the way, I shall comment on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn, on G. Gentzen’s allegedly finitist consistency proof for Peano Arithmetic as well as his ideas on the provability and unprovability of initial cases of transfinite induction in pure number theory. Another topic I deal with is what has come to be known as partial realizations of Hilbert’s programme, chiefly advocated by S. G. Simpson. Towards the end of this essay, I take a critical look at Wittgenstein’s views about (in)consistency and consistency proofs in the period 1929–1933. I argue that both his insouciant attitude towards the emergence of a contradiction in a calculus and his outright repudiation of metamathematical consistency proofs are unwarranted. In particular, I argue that Wittgenstein falls short of making a convincing case against Hilbert’s programme. I conclude with some philosophical remarks on consistency proofs and soundness and raise a question concerning the consistency of analysis. (shrink)

Nominalizations are expressions that are particularly challenging philosophically in that they help form singular terms that seem to refer to abstract or derived objects often considered controversial. The three standard views about the semantics of nominalizations are [1] that they map mere meanings onto objects, [2] that they refer to implicit arguments, and [3] that they introduce new objects, in virtue of their compositional semantics. In the second case, nominalizations do not add anything new but pick up objects that would (...) be present anyway in the semantic structure of a corresponding sentence without a nominalization. In the first and third case, nominalizations in a sense ‘create’ new objects’, enriching the ontology on the basis of the meaning of expressions. I will argue that there is a fourth kind of nominalization which requires a quite different treatment. These are nominalizations that introduce ‘new’ objects, but only partially characterize them. Such nominalizations generally refer to events or tropes. I will explore an account according on which such nominalizations refer to truth makers. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

L’insuffisance du logicisme pour la question des fondements des mathématiques nous invite à la poser sous un point de vue épistémologique, en termes de rationalité et non plus seulement de logique, et à l’étendre aux sciences formalisées portant sur la nature, comme la physique, voire à la pensée scientifique en général. On doit tenir compte, dans tous les cas, des changements qui correspondent à des constructions conceptuelles : ce sont eux qui assurent en même temps, après coup, le bien-fondé des (...) théories qui les ont préparés, en sorte que si des fondements rationnels peuvent être obtenus, ce n’est, en règle générale, que « vers l’avant ». Ces changements posent également la question de leurs conditions de possibilités. La conclusion est qu’il faut admettre, pour que ces changements, et avec eux un accroissement de la connaissance, soient possibles, des transformations corrélatives dans les formes mêmes de la rationalité, mathématique, physique et, d’une manière générale, de la rationalité scientifique. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...) from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logical-linguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomatic approaches to language syntax which take into consideration these two (...) different philosophical orientations, respectively. It also introduces certain formal-logical foundations of language semantics, discusses and develops the problem of the syntactic and semantic categorial agreement, i.e. the agreement of the syntactic category of each language expression with the ontological category assigned to the reference of this expression. The author, in particular, gives a solution to this problem for quantifiers. (shrink)

In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...) and making an estimate of future prospects. The symptom was the contradiction that had crept into naïve set theory in the form of the set that provably is and is not its own member. The diagnosis was that it is caused by Basic Law V of the Grundgesetze (Frege, In: Grundgesetze der Arithmetik: Begrifsschriftlich abgeleitet, Jena: Herman Pohle, 1893/1903. Translated into English as Basic Laws of Arithmetic, also edited by Philip A. Ebert and Marcus Rossberg, with Crispin Wright, Oxford: Oxford University Press, 2013). Triage answers the question, “How bad is it?” The answer was that the contradiction irreparably destroys the logicist project. The treatment option was nil. The disease was untreatable. In due course, the prognosis turned out to be that a scaled-down Fregean logic could have an honourable life as a theory inference for various domains of mathematical discourse, but not for domains containing the logical objects required for logicism. Since there aren’t such objects, there aren’t such domains. On the face of it, Frege’s logicist collapse is astonishing. Why wouldn’t he have repaired the fault in Law V and gone back to the business of bringing logicism to an assured realization? In the course of our reflections, we will have nice occasion to consider the good it might have done Frege to have booked some time with Aristotle had he been able to. By the time we’re finished, we’ll have cause to think that in the end the Russell might well have begged the question against Frege. (shrink)

In this paper, we trace the conceptual history of the term ?metamathematics? in the nineteenth century. It is well known that Hilbert introduced the term for his proof-theoretic enterprise in about 1922. But he was verifiably inspired by an earlier usage of the phrase in the 1870s. After outlining Hilbert's understanding of the term, we will explore the lines of inducement and elucidate the different meanings of ?metamathematics? in the final decades of the nineteenth century. Finally, we will investigate the (...) earlier occurrences and come to the conclusion that the conceptual prehistory of the Hilbertian notion of metamathematics dates back to 1870, whereas the history of the word starts in 1799 at the latest. What is this: metamathematics? It is something amazing everybody, [?] since it makes the mind dizzy and withdraws thinking its sole fulcrum.1 1 Brunner 1898, p. 832: ?Was ist das: Metamathematik? Es ist etwas, was einen Jeden in das äusserste Staunen versetzt, [?] was das Gehirn schwindlig macht und dem Denken seinen einzigen Stütz- und Angelpunkt zu entziehen droht? (shrink)

Lembecks Philosophiebegriff ist keine Zumutung Content Type Journal Article Pages 1-9 DOI 10.1007/s10743-011-9098-6 Authors Matthias Wille, Institut für Philosophie, Fakultät für Geisteswissenschaft, Universität Duisburg-Essen, Universitätsstraße 12, 45117 Essen, Germany Journal Husserl Studies Online ISSN 1572-8501 Print ISSN 0167-9848.

Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...) all. Instead, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object. (shrink)

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings (...) — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts. (shrink)

In this article I discuss the 'procedural postulationist' view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second-order quantification means that his background logic is not free (...) of ontological commitment and that his doctrine of 'creative expansion' only makes sense from a radically anti-realist perspective. (shrink)

In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work (...) in foundations, which we consider to have been greater than previously assumed. This conjecture is based on a hitherto neglected revision of Hilbert's talk "Über den Zahlbegriff". (shrink)

We tend to talk about (refer to, quantify over) parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in the inventory over and above its constituent parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled (...) the Minimalist View: An element in the field of a part-whole relation is to be included in an inventory of the world if and only if it does not overlap any distinct element that is itself included in the inventory. (shrink)

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

In The Construction of Logical Space, Agustín Rayo defends trivialism, according to which number-involving truths are trivially equivalent to other, non-number-involving truths; picturesquely, ‘I have five fingers on my hand’ and ‘the number of fingers on my hand is five’ express the same fact, but carved up in different ways. A single fact thus has multiple structures. I distinguish two ways this might go: on the deflationary picture, facts get their structures from our linguistic practices, while on an inflationary picture, (...) facts have multiple structures independently of language. I argue that Rayo’s view is best interpreted as deflationary. Thus interpreted, it blocks off an attractive solution to the old problems of intensionality. I further argue a that a semi-deflationary variant of Rayo’s view can make use of the attractive solution—but it thereby sacrifices the supposed mathematical benefits of trivialism. (shrink)

Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.

What is an object? A prior question: What is objecthood? Au fond, and to logic’s eye, object is a role to be played with respect to a thought. It is to be a countable which that thought represent as being some way for such a countable to be; what restores the business of truth-of to that of truth outright. What plays that role for some given thought is then an object with respect to that thought. Given this, there are corresponding (...) absolute notions, to be fit for this role, and to be fit only for this role. So the fundamental task here is identifying the conditions on playing this role at all. All this is a contribution, however limited, to a topic called ‘ontology’. This last word also occurs in the plural in several contexts. The end of this essay considers how these notions might relate, and what assumptions underlie what some have seen them to. (shrink)

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must be supplemented (...) by a transcendental logic that will in fact study nothing other than thought's content. Once this feature of Kant's views is brought to light, a much deeper accord emerges between the two thinkers than has hitherto been appreciated, on both the nature of the content that is at issue in logic and the sense of logic's generality and formality. (shrink)

Fictional names present unique challenges for semantic theories of proper names, challenges strong enough to warrant an account of names different from the standard treatment. The theory developed in this paper is motivated by a puzzle that depends on four assumptions: our intuitive assessment of the truth values of certain sentences, the most straightforward treatment of their syntactic structure, semantic compositionality, and metaphysical scruples strong enough to rule out fictional entities, at least. It is shown that these four assumptions, taken (...) together, are inconsistent with referentialism, the common view that names are uniformly associated with ordinary individuals as their semantic value. Instead, the view presented here interprets names as context-sensitive expressions, associated in a context of utterance with a particular act of introduction, or dubbing, which is then used to determine their semantic value. Some dubbings are referential, which associate names with ordinary individuals as their semantic values; others are fictional, which associate names, instead, with sets of properties. Since the semantic values of names can be of different sorts, the semantic rule interpreting predication must be complex as well. In the body of the paper, I show how this new treatment of names allows us to solve our original puzzle. I defend the complexity of the semantic predication rule, and address additional worries about ontological commitment. (shrink)

In this paper, we examine a specific type of Relative Clause. We look at the construction consisting of a ‘light noun’, that is, a noun with highly non-specific lexical content which does not do referential work, plus a relative clause. It has generally been assumed that the functional contribution of RCs is to narrow the set of referents of the head noun to only those for which the predicate of the RC holds true. However, the ‘Light Head RC construction’ has (...) various interactional affordances that mostly revolve around characterizing referents with discourse-relevant properties rather than establishing reference. We argue that these various functions of LHRCs revolve around participants’ orientations to categoryhood. Data are in English and Dutch. (shrink)

British Journal for the History of Philosophy, Volume 21, Issue 1, Page 189-200, January 2013.

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it is (...) of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

: I argue that a response‐dependence account of a concept can yield metaphysical results, and not merely epistemological or semantical results, which has been a prevalent view in the literature on response‐dependence. In particular, I show how one can argue for a conferralist account of a certain property by arguing that the concept of the property is response‐dependent, if certain assumptions are made.

The impartial reader notices that Frege, in Die Verneinung, treats an opposing conception of negation, but without specifically naming its proponent. In this paper, it is proven for the first time that the view in question is that of his colleague in Jena, Bruno Bauch. Besides their different views, concerning above all the status of false thoughts, there are nonetheless broader points of agreement between the ideas of Bauch and Frege. These points of agreement cast light on both thinkers as (...) representatives of a current of Neo-Kantianism, having its source in Lotze, in which Kantian and Platonic elements are fused to form a ?transcendental Platonism? (shrink)

The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succedent proposition.

A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung.