Frege: Existence

Between existenz and a hard-rock place, there is the man, trying to not make the same mistakes of the past and recvonciliate himself with himself, even on liberty or prison. Any conclusion is unnecessary, because life goes on.

Gottlob Frege (1848–1925), begründete nicht nur die moderne Logik, sondern auch die Sprachphilosophie. Er erweiterte die funktionale Analyse der Sätze zu einer Systematik des gesamten sprachlichen Bedeutens und Ausdrucks, indem er zwischen den Zeichen selbst, dem Sinn und der Bedeutung der Zeichen unterschied. Dieser Band versammelt Kommentare und Analysen zu den drei klassischen Aufsätzen Funktion und Begriff (1891), Über Sinn und Bedeutung und Über Begriff und Gegenstand (beide 1892). Er verschafft dadurch einen fundierten Überblick sowohl zu den Kernproblemen wie auch (...) den Hintergründen von Freges bis heute kontrovers diskutiertem Ansatz. Dabei wird die enge Verzahntheit zwischen dem logischen Hintergrund und Freges logizistischem Anliegen einerseits und den Vorschlägen zur Deutung einer ganzen Reihe von sprachlichen Erscheinungen erkennbar. Dazu gehören Fragen nach dem Wesen von Begriff und Gegenstand bzw. Prädikaten und Eigennamen als den Grundelementen jeder Aussage überhaupt – aber auch Erläuterungen zu indirekter Rede und fiktionalem Diskurs. Der vorliegende Band bietet dazu informierte Kommentare und Analysen. (shrink)

In this paper, I aim to present the main components of my non-standard interpretation of Frege’s views on existence to the English-speaking public. First, I will outline the standard interpretation and show how to a great but not full extent the standard interpretation can be justified on the basis of Frege’s writings. Second, I show that the main error of the standard interpretation consists in the assimilation of the contents of the ordinary language expressions “exist” and “there is” according to (...) Frege. Third, I evaluate possible sources for this unfounded assimilation. After that, I outline my alternative interpretation that distinguishes in opposition to other non-standard interpretations between a substantive and a deflationary part of Frege’s complete conception of existence in analogy to Frege’s analysis of truth and negation. Fifthly, I justify my interpretation by the reconstruction of a so far overlooked master argument of Frege against the above-mentioned assimilation. In the last section, I introduce and discuss five objections against my interpretation that came to my attention. (shrink)

The paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift ; Peirce’s ‘Algebra of Logic’ ; Peano’s ‘St...

Frege unterscheidet bekanntlich zwischen Gegenständen und Funktionen. Im Falle Letzterer nimmt er eine ganze Hierarchie solcher Funktionen an, von der anzunehmen ist, dass sie ins Unendliche reicht. Für Begriffe, die nur auf eine Stufe anwendbar sind, bleibt deren Einordnung in diese Hierarchie im Wesentlichen folgenlos. Für Begriffe wie den der Existenz, die Entsprechungen auf allen Stufen der Hierarchie besitzen, resultieren aber Konsequenzen etwa in Hinblick auf ihre Ausdrückbarkeit in natürlichen Sprachen: Existenz schlechthin bzw. unabhängig von der Stufe der Entitäten, deren (...) Existenz behauptet werden soll, ist nach Frege nicht ausdrückbar, da es keinen entsprechenden Begriff geben kann, der auf Entitäten unterschiedlicher Stufen anwendbar ist. Damit sind nach Frege auch keine unbeschränkten Existenzquantifikationen über alle Entitäten möglich, wie sie in natürlichen Sprachen möglich zu sein scheinen. In dieser Hinsicht entspricht Freges Konzeption nur schlecht der Existenzquantifikation in natürlichen Sprachen, was zu Ausdrucksproblemen bei der Beschreibung von Freges eigener semantischer Konzeption führt und die Möglichkeit der Formulierung metaphysischer Fragen wie Warum gibt es überhaupt etwas und nicht vielmehr nichts? auszuschließen scheint. (shrink)

In “Kant on Existence, Predication, and the Ontological Argument”, Hintikka argues that the so-called “Kant–Frege view” is wrong, for its supporters erroneously assume that for Kant ‘is’ is ambiguous. In this paper, I will first critically evaluate Hintikka’s arguments against the Kant–Frege view. Then, I will attempt to prove that Kant’s claim that existence is not a real predicate and Frege’s claim that existence is a quantifier are in fact logically interdependent. Finally, I will use the Kant–Frege view in order (...) to reconcile the various claims that Kant makes about existence. (shrink)

This is a review of Dolf Rami's book "Existenz un Anzahl" on Frege's notion of existence.

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)

Freges Konzeption der Existenz zählt zu seinen einflussreichsten und originellsten Beiträgen zur Philosophie. In diesem Buch wird Freges Konzeption neu interpretiert, historisch eingeordnet, mit den wichtigsten verwandten Konzeptionen verglichen und einer detaillierten systematischen Kritik unterzogen.

This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...) and the prospects for a logical grounding of arithmetic in the wake of the paradox. (shrink)

Despite its importance for early analytic philosophy, Gottlob Frege's account of existence statements, according to which they classify concepts, has been thought to succumb to a number of well-worn criticisms. This article does two things. First, it argues that, by remaining faithful to the letter of Frege's claim that concepts are functions, the Fregean account can be saved from many of the standard criticisms. Second, it examines the problem that Frege's account fails to generalize to cases which involve definite descriptions (...) and proper names. To deal with this the proffered analysis deviates from the letter of Frege's views, while remaining within its spirit. It proposes, in opposition to Frege, that expressions which grammatically look like singular terms should not always be read as referring to objects, but are sometimes best analysed as indicating functions. (shrink)

The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute properties to individuals.

I argue that Kant's and Frege's refutations of the ontological argument are more similar than has generally been acknowledged. As I clarify, for both Kant and Frege, to say that something exists is to assert of a concept that it is instantiated. With such an assertion one expresses that there is a particular relation between the instantiating object and a rational subject - a particular mode of presentation for the object in question. By its very nature such a relation cannot (...) be the property of an object and thus cannot be included in the concept of that object. Thus the ontological argument, which takes existence to be a part of the concept of the supreme being, cannot, according to Kant and Frege, succeed. A secondary goal of the paper is to illuminate what I take to be an important affinity between Kant's and Frege's views more generally: that Frege's fundamental distinction between the sense and the referent of a proposition echoes, in an important way, Kant's distinction between concepts and the formal principles for their application to experience. (shrink)

In this paper, the author examines Leibniz inconsistent treatments of the existence predicate in his formulations of the ontological argument and elsewhere. It is shown that, contrary to expectations, Leibniz at times adumbrates insights often attributed to Kant and Frege.

Die Rede von Existenz als Begriff zweiter Stufe ist – zumindest in dieser undif- ferenzierten Kurzform – eine überholte Legende, an deren Bildung neben Kant und Bolzano auch Frege nicht unbeteiligt war; obwohl er sie eigentlich mit sei- ner Begriffsschrift schon überwunden hatte, hat er sie weiter am Leben erhalten.

The paper tries to shed new exegetical light on Frege's "Dialogue with Pünjer on Existence" by showing that Pünjer's position in the dialogue is strongly inspired by Kantian claims about existence. It is argued that Pünjer's wavering between a broadly Meinongian and a broadly Fregean view on existence can be explained by the fact that there are Kantian remarks which seem to speak in favour of each of these views. A suggestion is then made how Kant's claims can be interpreted (...) in such a way that the tension which they seem to entail disappears. (shrink)

One of the characteristic features of contemporary logic is that it incorporates the Frege‐Russell thesis according to which verbs for being are multiply ambiguous. This thesis was not accepted before the nineteenth century. In Aristotle existence could not serve alone as a predicate term. However, it could be a part of the force of the predicate term, depending on the context. For Kant existence could not even be a part of the force of the predicate term. Hence, after Kant, existence (...) was left homeless. It found a home in the algebra of logic in which the operators corresponding to universal and particular judgments were treated as duals, and universal judgments were taken to be relative to some universe of discourse. Because of the duality, existential quantifier expressions came to express existence. The orphaned notion of existence thus found a new home in the existential quantifier. (shrink)

It is a well-known remark of Frege’s that his definition of existence invalidated the ontological argument for the existence of God. That has subsequently often been taken for granted. This paper attempts to investigate, whether rightly so. For this purpose, both Frege’s ontological doctrine and the ontological argument are outlined. Arguments in favour and against both are considered, and reduced to five specific questions. It is argued that whether Frege’s remark was right depends on what the answers to these questions (...) are, and that for the seemingly most plausible ones -- it was not. (shrink)

My wife and I and our three children may stand in various relations: being a family, being a basketball team, and so on. I show that Frege's doctrine of existence, when coupled with this simple point, easily solves the problem of material constitution and blocks the overdetermination argument for eliminativism. It does all this work while providing a plausible and clear reductionistic account of material objects. These seem to be very good reasons for accepting Frege's doctrine of existence.

The fregean conception of existence is presented and defended against puttative objections.

Frege's advances in the development of quantification have rarely been subjected to historical interpretation. While the characterization of existence as a second-order concept awaited the invention of the Begriffsschrift, important philosophical innovations had taken place since Kant's critique of the ontological argument. In particular, Herbart had re-conceptualized the nature of existential judgement and this was recognized and adopted by Brentano. In this light, thepossible influence of Herbart and Brentano (or their schools) upon Frege's work is elaborated and critically considered.

If logical positivism had any success, it was undoubtedly in rejecting traditional metaphysics as based on an erroneous philosophy of language. The very goal of the metaphysical enterprise itself, namely to say something about „being qua being”, was stigmatized as senseless, considering the fact that being isn't a predicate or property of things, and can therefore not be described. In the eyes of the logical positivists, the fact that being isn't a predicate was clearly shown in modern logic. Indeed G. (...) Frege was one of the first making a consequent effort to eliminate from his system a predicate of existence. Recent study of the matter, in circles familiar to J. Hintikka, focuses its attention to Frege's arguments in his „Dialogue with Pünjer on Existence”, where Frege shows that acceptance of being as a property of things leads to contradictions. In Frege's view, a property cannot be shared by everthing, as it serves to distinguish things one from another. But are there things who are not ? Whereas Frege thus rejects being as a property of things — as a first-order predicate — he accepts it as a property of the concepts by which we grasp them : as a second-order predicate it discriminates instantiated from non-instantiated concepts. Because the focus of interest of this paper is the meaning of „being qua being”, the possible-worlds-getaway is not used, since it leaves existence as such unanalyzed. Whilst examining Frege's argument and the theory in which it is embedded, this paper tries to dig up the presuppositions of Frege's view. First, it is shown that Frege in his interpreted language presupposes flatly the existence of individual objects. In a second move, the epistemological background of this presupposition is scrutinized. In Frege's theory only properties are intelligible, as only senses can be a part of thought. At the other hand, Frege cannot identify objects with clusters of properties, without damaging his whole theory of the straightforward opposition between the complete and saturated objects versus the incomplete properties, a theory which is at the very core of Fregean logic. This leaves us with a kind of misunderstood Kantian notion of a „Ding an Sich”, supposed to be there beyond of reach of our knowledge, but nevertheless having enough determination to be an individual. Finally, an attempt has been made to fill this gap, by pointing out that besides the properties also the existence of objects is part of our knowledge. Metaphysical endeavour purports to take this part of knowledge as its subject. Analysis of conceptual knowledge of the world by means of an interpreted predicate calculus presupposes this knowledge and therefore the study of the subject of traditional metaphysics. (shrink)

The question ''Was 'existence' ever a predicate?" in a way already suggests its own answer, that this is really the wrong question to ask, because 'existence' has always been a predicate. Even those, such as Kant, who supposedly opposed this view, in fact held it. They merely denied that 'existence' is a "normal" first-order predicate. Not only Kant, but also Bolzano, Frege and Russell claimed that it is a second-order predicate. There is substantive disagreement between Kant and Bolzano on the (...) one hand and Frege and Russell on the other over two issues: the former claim that this second-order predicate apphes to no concept analytically and that it can be properly ascribed to a singular concept, whereas the latter deny both of these claims. (shrink)

Die auf G. Frege zurückgehende logische Urteilslehre, die die universalen Aussagen im Sinne existenzfreier und die partikulären im Sinne existenzmitbehauptender Urteile deutet, hat ihren Ursprung in der nicht-mathematischen Logik des 19. Jahrhunderts. Bei J.F. Herbart findet sich die hypothetische Konzeption der Allaussage, die eine bedeutsame, Fregesche Gedankengänge antizipierende Verfeinerung durch Chr. Sigwart erfährt. Die genaue Struktur der partikulären Aussage bleibt vorerst noch im Dunkel. Erst F. Brentano gelingt es, die universalen wie die partikulären Aussagen in ihrer Eigenart herauszustellen. In dieser (...) Entwicklung spielen die Problematik fiktiver Gegenstände und leerer Begriffe, die apriorische Gesetzlichkeit sowie der Einfachheitsbegriff eine zentrale Rolle. (shrink)

Frege argued that 1) in making existence assertions we ascribe (or deny) the second-Level property, 'not being empty', To a first-Level concept. He inferred from this that 2) existence is a second-Level property, The property 'not being empty'. He therefore rejected the ontological proof of the existence of God because, He claimed, It depends on the assumption that existence is a first-Level, And not a second-Level, Property. In this paper it is argued, First, That frege is unsuccessful in his attempt (...) to establish claim 1). Moreover, Claim 2) does not follow from claim 1)--One could accept claim 1) and still maintain that existence is a first-Level property. Thus, Even if the ontological proof does depend on the assumption that existence is a first-Level property, Frege's objection to that proof fails. (shrink)

Language and Ontology: Linguistic Relativism (Sapir-Whorf Hypothesis) vs. Universal Grammar Universal Ontology vs. Ontological Relativity Semiotics and Ontology: Annotated Bibliography of John Deely. First part: 1965-1998 Annotated Bibliography of John Deely. Second part: 1999-2010 The Rediscovery of John Poinsot (John of St. Thomas).