This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

Was ist eine gute Weltanschauung? Die Aufsätze behandeln einige der großen Themen der westlichen Philosophie unter neuen Gesichtspunkten, wie z. B. das Apeiron des Anaximander, das Leib-Seele-Problem bei Descartes und Wittgensteins Begriff der Sprache und Lebensform. Sie beleuchten aber auch Seitenwege wie z. B. einen Ausflug Schopenhauers, ein „Plagiat" Nietzsches und einige der Aphorismen Ludwig Hohls.

_ Source: _Volume 95, Issue 3, pp 368 - 413 Frege famously maintained that concepts are not objects. A key argument of Frege’s for this view is, in outline, as follows: if we are to account for the unity of thought, concepts must be deemed _unsaturated_; since objects are, by contrast, saturated entities, concepts cannot be objects. The author investigates what can be made of this argument and, in particular, of the unsaturated/saturated distinction it invokes. Systematically exploring a range of (...) reconstructions suggested by Frege’s writings, and drawing on contemporary work, the author illustrates that no plausible reconstruction is forthcoming. In essence, it is altogether unclear how to simultaneously substantiate, on the one hand, the claim that unsaturated entities must be recognized in order to account for unity and, on the other, the claim that unsaturatedness is incompatible with objecthood. (shrink)

In the paper, I propose a novel approach to Frege’s view on the principle of compositionality, its relation to the propositional holism and the formation of concepts. The main idea is to distinguish three stages of constructing a logically perfect language. At the first stage, only a sentence as a whole expresses a Thought. It is impossible to assign meaning to less complex units. This is the stage of an ordinary language. The second phase concerns the proper level of construction (...) of a logically perfect language. We are forced to discriminate syntactic and semantic parts of sentences to account for the inference relations. We can distinguish senses and references of parts of sentences. Furthermore, it is possible here to choose between different ways of analysing the given Thought. Finally, at the third stage, every expression of the language has an unambiguous sense and this sense determines a unique reference. The logically perfect language is ready. We may view Thoughts as composed from primitive elements. Moreover, the senses of parts of a sentence correspond to the parts of a Thought, so that the structure of the sentence serves as the image of the structure of the Thought. The principle of compositionality is met and we can discern how understanding of the infinite numbers of Thoughts is possible and how languages are learnable. The main advantage of the presented view is that it allows accommodating some aspects of Frege’s philosophy that are often seen as mutually incompatible. Furthermore, I submit extensive textual data in favour of the discussed views and conceptions. (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)

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...) is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism. (shrink)

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above (...) quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

This paper discusses three approaches to the semantics of event nominalizations and adverbial modification: the Davidsonian account, the Kimian account, and the truthmaker account. It argues that a combination of all three accounts is needed for the semantics of the full range of event, trope, and state nominalizations in English.

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (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)

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)

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)

Theorizing about something we tend to conceive of it as objective and admitting, in principle, of a clear-cut distinction between what it is in its own right and what we believe about it. Obviously this tendency gets us into trouble if we theorize about the mental, and it is the tenet of this paper that the temptation to objectify the mental is the main source of our notorious difficulties with it. Evidence is presented from a variety of fields, from set (...) theory, semantics and epistemology to doxastic logic. (shrink)

Parmenides believed that he had found the most reliable way of theorizing about ultimate reality. While natural philosophers conceptualized phenomenal differences to explain cosmic change, Parmenides used the least meaningful but most versatile verb in Ancient Greek to engage in a purely intellectual exploration of reality – one that transcended synchronous and asynchronous differences. In this article I explain how the verb εἰμί was useful to Parmenides in his attempt to overcome natural philosophy. First, I argue that the Eleatic philosopher (...) regarded νοεῖν and εἶναι as equivalent because εἰμί-clauses enabled him to express arguably any conceivable content without providing significant additional meaning. I then show that Parmenides’ concept of being implies the present tense and the imperfective aspect but is grounded in the lexical content of the verb εἰμί, which entails no inherent temporal limits. This explains why ἔστι, ἐόν, and εἶναι could be used to indicate unbounded actuality, regardless of whether these forms represented lexical predicates or auxiliaries for predication. Finally, I maintain that the suitability of εἰμί for talking about all kinds of things without introducing temporal limits allowed Parmenides to avoid what he saw as two mistakes made by natural philosophers: identifying ultimate reality with something that cannot cover the full extent of thought and confusing actuality with present occurrence. (shrink)

What makes a veil of perception? Is it merely would-be objects of perceptual awareness, extraneous to the ‘environmental realities’ of which we judge? Or is it merely the presence of something extraneous along the route from perceptual awareness to awareness that our environment is thus and so? In his Mark Sacks lecture John McDowell seems to suppose something like the first answer. This essay argues for the second, thus that he himself imposes such a veil.

According to what Jonathan Bennett calls the Kant–Frege view of existence, Frege gave solid logical foundations to Kant’s claim that existence is not a real predicate. In this article I will challenge Bennett’s claim by arguing that although Kant and Frege agree on what existence is not, they agree neither on what it is nor on the importance and justification of existential propositions. I identify three main differences: first, whereas for Frege existence is a property of a concept, for Kant (...) it is a relational property pertaining between the concept and intuition of an object. Second, whereas for Frege truth about individuals presupposes their existence, for Kant truth is in many cases independent of the existence of objects. Third, whereas Frege binds logic to existence and removes modalities from logic, for Kant existence is a modal category that is emphatically removed from the domain of logic and set in the core of metaphysics. Due to these differences in Kant’s and Frege’s theories of existence, Frege cannot be seen as giving logical clarity to Kant’s view. (shrink)

The paper gives a historically informed reconstruction of Frege's view of statements of number. The reconstruction supports Frege's claim that a statement can be 'about a concept' although it does not contain a singular term referring to the concept. Hence, Frege's philosophy of number is not subject to the problems Frege sees for singular reference to concepts.

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)

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.

Analytic philosophers apply the term ‘object’ both to concreta and to abstracta of certain kinds. The theory of objects which this implies is shown to rest on a dichotomy between object-entities on the one hand and meaning-entities on the other, and it is suggested that the most adequate account of the latter is provided by Husserl’s theory of noemata. A two-story ontology of objects and meanings (concepts, classes) is defended, and Löwenheim’s work on class-representatives is cited as an indication of (...) how the need for higher types may be obviated, even in mathematical contexts. The paper concludes with a sketch of the taxonomy of the object realm which results from the above. (shrink)

It has been noted before in the history of logic that some of Frege's logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege's Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege's logic. However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, (...) we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege's tenant and lived in the same house as the logician for many years. In der Geschichte der Logik ist häufig bemerkt worden, dass einige der logischen und semantischen Auffassungen Freges in der Stoa antizipiert worden sind. Genannt wurden insbesondere die Parallelen zwischen dem Fregeschen Gedanken und dem stoischen Lekton sowie die Unterscheidung zwischen vollständigen und unvollständigen Lekta, die bei Frege ihre Entsprechung hat. Ein Wirkungszusammenhang ist allerdings nicht behauptet worden. Dazu gab es bislang auch keinen Anlass. Der vorliegende Beitrag versucht erstmalig, einen detaillierten Indizienbeweis für das Bestehen eines solchen Zusammenhangs vorzulegen. Dabei werden weitere charakteristische Übereinstimmungen zwischen Frege und der Stoa aufgewiesen. Als Mittelsmann wird der Altphilologe Rudolf Hirzel vorgestellt. Er wohnte lange Jahre als Mieter zusammen mit Frege im selben Haus und war ein anerkannter Experte der stoischen Philosophie. (shrink)

In this article, I try to shed some new light onGrundgesetze§10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain inGrundgesetzeis restricted to value-ranges, but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the semantics (...) of value-range names. I further argue that despite first appearances truth-value names play a distinguished role as semantic “target names” for “test names” in the criteria of referentiality and do not figure themselves as “test names” regarding referentiality. Accordingly, I show in detail that Frege’s attempt to demonstrate that by virtue of his stipulations “regular” value-range names have indeed been endowed with a unique reference, can plausibly be regarded as a direct application of the context principle. In a subsequent section, I turn to some special issues involved in §10. §10 is closely intertwined with §31 and in my and Richard Heck’s view would have been better positioned between §30 and §31. In a first step, I discuss the piecemeal strategy which Frege applies when he attempts to bestow a unique reference on value-range names in §3, §10–§12. In a second step, I critically analyze his tentative, but predictably unsuccessful proposal to identify all objects whatsoever, including those already clad in the garb of value-ranges, with their unit classes. In conclusion, I present two arguments for my claim that Frege’s identification of the True and the False with their unit classes in §10 is illicit even if both the permutation argument and the identifiability thesis that he states in §10 are regarded as formally sound. The first argument is set out from the point of view of the syntax of his formal language. It suggests though that a reorganization of the exposition of the concept-script would have solved at least one of the problems to which the twin stipulations in §10 give rise. The second argument rests on semantic considerations. If it is sound, it may call into question, if not undermine the legitimacy of the twin stipulations. (shrink)

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...) formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other. (shrink)

Although the notion of logical object plays a key role in Frege's foundational project, it has hardly been analyzed in depth so far. I argue that Marco Ruffino's attempt to fill this gap by establishing a close link between Frege's treatment of expressions of the form ‘the concept F’ and the privileged status Frege assigns to extensions of concepts as logical objects is bound to fail. I argue, in particular, that Frege's principal motive for introducing extensions into his logical theory (...) is not to be able to make in-direct statements about concepts, but rather to define all numbers as logical objects of a fundamental kind in order to ensure that we have the right cognitive access to them qua logical objects via Axiom V. Contrary to what Ruffino claims, reducibility to extensions cannot be the ‘ultimate criterion’ for Frege of what is to be regarded as a logical object. (shrink)

The paper demonstrates that Parmenides’ monism is a logical consequence of his criteria for philosophy, in conjunction with the logical operators he uses, and their holistic connection. Parmenides, I argue, is the first philosopher to set out explicit criteria for philosophy, establishing as criterion not only consistency, but also what I call rational admissibility, the requirement when giving an account of something that the account be based on rational analysis and can withstand rational scrutiny. I give a detailed account of (...) the logical operators Parmenides uses in his argument and of the way in which his notion of being is tailored to fit both them and his criteria for philoso-phy. (shrink)

Why did Frege offer only proper names as examples of presupposition triggers? Some scholars claim that Frege simply did not care about the full range of presuppositional phenomena. This paper argues, in contrast, that he had good reasons for employing an extremely narrow notion of ‘Voraussetzung’. On Frege’s view, many devices that are now construed as presupposition triggers either express several thoughts at once or merely ‘illuminate’ a thought in a particular way. Fregean presuppositions, in contrast, are essentially tied to (...) names. (shrink)

The paper suggests a way of viewing the two Fregean principles of compositionality and contextuality as working together in the enterprise of interpretation. A third Fregean theme, that of elucidation (more precisely, the elucidation of primitive, undefinable terms of logic, mathematics and metamathematics) secures a place for some version of the context principle in Frege's later writings. When thinking about the functioning of elucidations, Frege acknowledges a principle of charitable interpretation. I argue that there is a deep connection between the (...) three themes, and that not only compositionality and contextuality, but also charity is a genuinely Fregean theme. -/- Context. Interpretation. Linguistics. Logic. Meaning. Word. (shrink)

Remarks on the Relations between Neurophysiology and Psychology. In the last decades of Analytical Philosophy, contributions to the so-called mind-body-problem have been suffering by several serious methodological misunderstandings: they have failed, for instance, to distinguish between explanations of particular and strictly general ("necessary") properties and between two important senses of existential statements; and they have overlooked the role conceptual explanations play in the development of science. Changing our methodological premisses, we should be able to put questions like that of the (...) relation between (neuro)physiological and psychological phenomena in a new way - and we should be able to see that such newly understood questions allow answers which evade the pitfalls of both reductionist and holistic positions. The paper tries to illustrate and to defend these contentions by reference to a very elementary example: the rational re-building of our concepts to identify behaviour by which a subject controls the position of his body in space. (shrink)

Remarks on the Relations between Neurophysiology and Psychology. In the last decades of Analytical Philosophy, contributions to the so-called mind-body-problem have been suffering by several serious methodological misunderstandings: they have failed, for instance, to distinguish between explanations of particular and strictly general properties and between two important senses of existential statements; and they have overlooked the role conceptual explanations play in the development of science. Changing our methodological premisses, we should be able to put questions like that of the relation (...) between physiological and psychological phenomena in a new way - and we should be able to see that such newly understood questions allow answers which evade the pitfalls of both reductionist and holistic positions. The paper tries to illustrate and to defend these contentions by reference to a very elementary example: the rational re-building of our concepts to identify behaviour by which a subject controls the position of his body in space. (shrink)

In this paper I discuss Frege's distinction between objects and concepts and suggest a solution of Frege's paradox of the concept horse. The expression ''the concept horse'' is not eliminated and the concept is not identified with its extension, but the concept is identified with the sense of the corresponding predicate. This solution fits better into a fregean ontology and philosophy of language than alternative solutions and allows for a general answer to the question why Frege's system is infected with (...) Russell's paradox. Russell's paradox is caused by the reification of a concept. Certain problems of modern set theory seem to have a similar cause.Eine weithin sichtbare Warnungstafel muss aufgerichtet. (shrink)

David Chalmers’ two-dimensionalism is an ambitious philosophical program that aims to “ground” or “construct” Fregean meanings and restore “the golden triangle” of apriority, necessity, and meaning that Kripke seemingly broke. This paper aims to examine critically what Chalmers’ theory can in reality achieve. It is argued that the theory faces severe challenges. There are some gaps in the overall arguments, and the reasoning is in some places somewhat circular. Chalmers’ theory is effectively founded on certain strong philosophical assumptions. It is (...) concluded that it is unclear whether the theory can deliver all it promises. (shrink)

This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature (...) of logical types in the context of Constructive Type Theory allows elucidation of the role of the previously introduced notions. Finally, the connection to the analysis of abstraction in computer science is drawn, and the methodological contribution provided by the notion of information is considered, showing its conceptual and technical relevance. Future research shall focus on the notion of information in distributed systems, analysing the paradigm of information hiding in dependent type theories. (shrink)

After describing the philosophical background of Kerry’s work, an account is given of the way Kerry proposed to supplement Bolzano’s conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege’s work and Kerry’s views were then attacked by Frege.The following two issues were central to this controversy: the relation between the content of a concept and the object of a concept; the logical roles of the definite article.Not only did Frege in (...) 1892 offer an unconvincing solution to Kerry’s puzzle concerning “the concept horse” but he also overlooked the many criticisms levelled by Kerry against the notion of an extension on which his own definition of number was based. (shrink)

After describing the philosophical background of Kerry's work, an account is given of the way Kerry proposed to supplement Bolzano's conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege's work and Kerry's views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article. Not only (...) did Frege in 1892 offer an unconvincing solution to Kerry's puzzle concerning 'the concept horse' but he also overlooked the many criticisms levelled by Kerry against the notion of an (indefinite) extension on which his own definition of number was based. (shrink)

Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory (...) and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic. (shrink)

In this essay I will consider two theses that are associated with Frege,and will investigate the extent to which Frege really believed them.Much of what I have to say will come as no surprise to scholars of thehistorical Frege. But Frege is not only a historical figure; he alsooccupies a site on the philosophical landscape that has allowed hisdoctrines to seep into the subconscious water table. And scholars in a widevariety of different scholarly establishments then sip from thesedoctrines. I believe (...) that some Frege-interested philosophers at various ofthese establishments might find my conclusions surprising.Some of these philosophical establishments have arisen from an educationalmilieu in which Frege is associated with some specific doctrine at theexpense of not even being aware of other milieux where other specificdoctrines are given sole prominence. The two theses which I will discussillustrate this point. Each of them is called Frege''s Principle, but byphilosophers from different milieux. By calling them milieux I do not want to convey the idea that they are each located at some specificsocio-politico-geographico-temporal location. Rather, it is a matter oftheir each being located at different places on the intellectuallandscape. For this reason one might (and I sometimes will) call them(interpretative) traditions. (shrink)

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...) entities. (shrink)

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

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

The author defends the view that the notion of concept, if used in the logical tradition, should be explicated procedurally . He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.

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