Gottlob Frege

In the Philosophical Investigations, Wittgenstein famously criticizes Frege's conception of assertion. "Frege's opinion that every assertion contains an assumption", says Wittgenstein, rests on the possibility of parsing every assertoric sentence into two components: one expressing the assumption that is put forward for assertion, the other expressing that it is asserted. But this possibility does not entail that the "assertion consists of two acts, entertaining and asserting" – any more than the possibility of rendering assertions as pairs of questions and affirmative (...) answers entails that they consist of questions. Frege scholars protest that such criticism is inappropriate, not only because Frege doesn't speak about assumptions, but also – and crucially – because Wittgenstein fails to address the logical nature of assertion as reflected in Frege's use of the judgment stroke. They seem to read Wittgenstein's argument in the light of a remark in the Tractatus saying that the judgment stroke is "logically meaningless" because it simply indicates that the author holds the propositions marked with this sign to be true. In this paper, I argue that Wittgenstein's criticism of Frege is not that the latter's conception of judgment and assertion contains a corrupting psychological element. Rather, the criticism is that for Frege judgment and assertion are composed of two separate acts, i.e. an act of referring to a truth value and an act of determining which of the two it is. Through a detailed examination of the 'black-spot analogy' in the Tractatus, I want to show that Wittgenstein presents a serious objection to Frege's conception of judgment and assertion. (shrink)

Le problème de Frege-Geach est un problème qui se pose pour les théories selon lesquelles les jugements normatifs n’ont pas de contenu cognitif, mais expriment plutôt des états mentaux non cognitifs. Dans cet article, je présente le problème de Frege-Geach ; j’examine certaines stratégies existantes pour l’aborder dans sa forme traditionnelle ; et je me demande enfin si un problème de Frege-Geach se pose pour les raisons, et si l’usage des raisons peut mener à une solution. J’esquisse une réponse positive (...) à cette question. (shrink)

This volume does what it says on the tin: it collects Eva Picardi’s (1984-2017) essays on themes in Frege’s philosophy. The first part, ‘Frege in Context: Logic.

Criticizing psychologism about logic in the Foreword of Grundgesetze, Frege examines an answer to the question of how we can justify our acknowledgment of logical axioms as true—the logical laws that cannot be proved from other laws. The answer he entertains states that we cannot reject logical axioms if we do not want to give up our judgment altogether. Suspending his judgment about this answer, Frege points out that it is still compatible with his anti-psychologist conception of logic. There are (...) two issues with this paragraph. First, it is difficult to read this paragraph consistently. Second, it is not clear why Frege brings up this particular view regarding the justification for logical axioms in the middle of his criticism of psychologism. This paper develops a consistent interpretation of this paragraph. The view on the justification for logical axioms, which Frege is dealing with, is neo-Kantian. In the paragraph, Frege is criticizing a psychologistic misunderstanding of the neo-Kantian justification for logical axioms. The way Frege explains away this misunderstanding shows that he takes the neo-Kantian justification for logical axioms to be a non-evidential epistemic warrant if it is an epistemic warrant. It is this notion of non-evidential epistemic warrant that Frege suspends his judgment about. Thus, the paragraph shows that Frege has a reason to have reservations about neo-Kantianism. Furthermore, it turns out that the sole issue between Frege and psychological logicians is whether truth is objective, which provides a different way to explain away a much-discussed tension between Begriffsschrift and Frege's anti-psychologism. (shrink)

The letters that were found after years are the evidence of hard intellectual work that had been conducted under very infavourable conditions. They refer to the time when Wittgenstein was writing "Tractatus" while Frege was working on his articles "Thought" and "Negation". Correspondence between Frege and Wittgenstein prove the common will of communication and mutual understanding. Thus remains the question why those two close and well known to each other thinkers have not realized that willingness.

Die geschichte der macht.--Ewige menschheit und wandel der reiche.--Ahnung der form.--Blick auf das werden.

Moral expressivism suggests that 1) moral sentences lack truth conditions and 2) our purpose in asserting moral sentences is to express non-cognitive attitudes such as desires, approval, or disapproval. Moral expressivism meets a fundamental challenge, known as the Frege-Geach problem. Sentences that express moral judgments can form part of semantically complex sentences. “P” (a moral sentence) contradicts “~P”, and “Q” follows logically, by modus ponens, from (1) “P” and (2) “if P, then Q”. Geach argued that noncognitivists are committed to (...) denying that moral predicates mean the same thing in embedded contexts as they do in unembedded sentences (atomic sentences). If “P” does not mean the same as the antecedent of (2), the argument would be invalid. The problem is that the above-mentioned argument is obviously valid. Blackburn has argued that the complex sentence expresses a ‘higher-order’ attitude toward the attitudes expressed by the smaller sentences which make it up. If we accept the premises of a valid argument but deny its conclusion our attitudes clash in the same way that they do if we both believe that P and ~P. Blackburn's meta-attitudes approach faces several problems. Someone who endorses the premises but denies the conclusion of the valid argument commits himself to a moral inconsistency, not a logical one. In addition, uttering both ‘P’ and ‘~P’ seem to be inconsistent but expressivism cannot explain the inconsistency between these two obviously inconsistent sentences. Blackburn's strategy of inventing a new attitude, such as tolerance, is also unable to solve this problem. Introduction Moral expressivism suggests that 1) moral sentences lack truth conditions (negative claim) and 2) our purpose in asserting moral sentences is to express non-cognitive attitudes such as desires, approval, or disapproval (positive claim). Moral expressivism meets a fundamental challenge known as the Frege-Geach problem (Geach, 1960, 1965). In the following, the Frege-Geach problem and Simon Blackburn’s response to it will be examined. Blackburn has developed several different answers to the Frege-Geach Problem In this article, only the answer which appeals to the higher-order attitudes (Blackburn, 1984) will be examined, and it will be shown that this expressivist recipe can not solve the Frege-Geach problem. The Frege-Geach problem The Frege-Geach problem is the idea that moral predicate functions as a ‘logical’ one so that sentences containing this predicate enter into logical relations with other sentences. Sentences that express moral judgments can form part of semantically complex sentences. “P” (a moral sentence) contradicts “~P”, and “Q” follows logically, by modus ponens, from (1) “P” and (2) “if P, then Q”. Geach argued that noncognitivists are committed to denying that moral predicates mean the same thing in embedded contexts as they do in unembedded sentences (atomic sentences). They cannot explain that the meaning of complex sentences is in terms of the meanings of their parts. They cannot explain why modus ponens arguments are always valid. Arguments of the form of modus ponens, according to expressivism, commit a fallacy of equivocation; because it appears to imply that “P” does have different meanings in premise (1) and in the antecedent of premise (2). “P” is asserted in premise (1) and remains unasserted in premise (2). The utterance of (2) does not seem to express approval or disapproval of “P”. If “P” does not mean the same as the antecedent of (2), the argument would be invalid. The problem is that the abovementioned argument is obviously valid. Geach (Geach, 1960, p. 223) calls this point about assertion the Frege point who was the first logician who made the point in his distinction between the sense and the reference of a sentence. “A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition” (Geach, 1965, p. 449). The higher-order attitudes Blackburn denies that any of his claims entail valid moral arguments are invalid. He employs an account of what we are doing when we use ethical sentences in terms of expressing meta-attitudes about a moral sensibility; The complex sentence expresses a ‘higher-order’ attitude toward the attitudes expressed by the smaller sentences which make it up. There are logical relationships that exist among attitudes as there are among beliefs. If we accept the premises of a valid argument but deny its conclusion, our attitudes clash in the same way they do if we both believe that P and ~P. So we can explain the logical validity of the moral argument via the attitudes one can hold without clash; anyone approving (1) “P” and (2) “if P, then Q” must hold the consequential approval of “Q”. If he does not, his attitudes clash. The inconsistency originates from the clash of attitudes (failing to do something which one has committed oneself to do). Blackburn says that such a clash would involve a “fractured sensibility which cannot itself be an object of approval” because “such a sensibility cannot fulfill the practical purposes for which we evaluate things” (Blackburn, 1984, p. 195). Logical conflict and moral conflict There is a most important problem with this strategy for Blackburn’s expressivism. The clash of attitudes can only show moral conflict and moral conflict does not necessarily lead to logical inconsistency. What needs to be explained in the moral argument is a logical inconsistency. Moreover, as Mark van Roojen (1996, pp. 21-320) has pointed out, higher-order-attitudes logic commits us to believe in logical inconsistency where there is no such inconsistency. He considers the origin of this problem to be the confusion between logical inconsistency and practical inconsistency (van Roojen, 1996, p. 332). The negation problem The other problem for Blackburn’s expressivism was originally raised by Unwin (Nicholas Unwin, 1999, 2001). This problem is known as the ‘negation problem’. As Schroeder points out (Schroeder, 2010, p. 134), the negation problem is the same as the Frege-Geach problem, which has received more attention in recent years than its conditional form, which is presented in the modus ponens argument. The most important semantic property of the negation operator in descriptive sentences is that it makes the negated sentence inconsistent with the main sentence, in the sense that for any sentence ‘P’, ‘P’ is inconsistent with ‘~P’. According to expressivism, “murdering is wrong” (P) is used to express the attitude of disapproval towards the act of murdering. But what is expressed by “murdering is not wrong” (~P)? To utter both ‘P’ and ‘~P’ seems to be inconsistent but expressivism cannot explain the inconsistency between these two obviously inconsistent sentences; because it cannot tell us which state of mind is expressed in the moral sentences like “murdering is not wrong.” To avoid the problem, Blackburn (Blackburn, 1988, p. 189) introduces a new attitude, such as tolerance, and says that “murdering is wrong” expresses disapproval of murdering, and “murdering is not wrong” expresses tolerance of murdering. “Tolerance toward P (T!p) is equivalent to not hooraying ~p, that is, not booing p.” (Blackburn, 1988, p. 189). But there is a real difference between not accepting something and actually accepting its negation (Unwin, 1999, p. 341). Conclusion According to Blackburn, We are expressing our attitudes about a moral sensibility when we use ethical sentences. The question now is whether Blackburn can explain the validity of the inference from the premises of the argument to its conclusion through this strategy. This article has shown that Blackburn’s meta-attitudes approach faces several problems. Someone who endorses the premises but denies the conclusion of the valid argument commits himself to a moral inconsistency, not a logical one. In addition, expressivism has insufficient structure to account for the various ways in which a moral sentence can be negated because it cannot tell us which state of mind is expressed in moral sentences like “murdering is not wrong.” Blackburn’s strategy of inventing a new attitude, such as tolerance, is also unable to solve this problem. (shrink)

Wittgenstein afirma no Tractatus que a teoria das classes é supérflua na Matemática e que isso está relacionado ao fato de que a generalidade exigida pela Matemática não é “acidental” (TLP 6.031). O objetivo deste texto é elucidar essa afirmação chamando a atenção para o que, seguindo Gregory Landini, tomaremos como uma forma de Logicismo compartilhada por Frege e Russell. Esta forma de Logicismo tem dois princípios básicos, a saber: o uso de uma teoria lógica cujas variáveis estruturadas incorporam o (...) que hoje chamamos de teoria dos tipos simples e a análise de atribuições numéricas em termos de afirmações sobre conceitos ou atributos que empregam conceitos de ordem superior exatamente análogos aos chamados quantificadores ‘numericamente definidos’. Argumentamos que é esse arcabouço teórico que Wittgenstein está rejeitando em 6.031 e não apenas o uso da Teoria dos Conjuntos na Matemática. Também é defendido que a noção de classe ainda tem um papel essencial a desempenhar no Tractatus.AbstractWittgenstein claims in the Tractatus that the theory of classes is superfluous in Mathematics and that this is related to the fact that the generality required by Mathematics is not “accidental” (TLP 6.031). My aim in this paper is to elucidate this claim by calling attention to what, following Gregory Landini, I refer to as a form of Logicism shared by Frege and Russell. This form of Logicism has two main tenets, namely:the use of a logical theory whose structured variables embody what we nowadays call the simple theory of types and the analysis of number ascriptions in terms of assertions about concepts or attributes which employ higher-order concepts exactly analogous to so-called ‘numerically definite’ quantifiers. It is argued that it is this shared theoretical framework that Wittgenstein is rejecting in 6.031 and not just the use of Set Theory in Mathematics. It is also argued that the notion of class still has an essential role to play in the Tractatus. (shrink)

Nosso objetivo é responder a uma questão proposta por Richard Heck no artigo “Formal Arithmetic Before Grundgesetze”. Heck indaga a respeito das razões pelas quais Frege levou quase oito anos para honrar suas promessas de concluir seu grandioso projeto de fundamentar a matemática na lógica. Embora Heck tenha fornecido algumas respostas, pensamos que uma discussão filosófica mais adequada ainda pode ser oferecida. Este artigo tentará preencher essa lacuna apresentando o que entendemos ser o problema central enfrentado por Frege em _Die (...) Grundlagen der Arithmetik_: a falta de um critério unificado para fixar o significado das proposições de identidade da matemática. Acreditamos que o filósofo alemão finalmente tenha decidido preencher essa lacuna, fornecendo uma nova interpretação para o conceito de “extensão”, uma que acrescentasse alguns refinamentos importantes a sua concepção anterior. O novo conceito assim construído permitiu a Frege unificar seu tratamento das proposições de identidade, incluindo em seu sistema um critério universal para decidir a verdade de qualquer proposição de identidade apoiado por sua famosa lei básica V. Assim, nossa alegação será que a resistência de Frege e as dúvidas sobre a inclusão do axioma V como uma lei lógica em seu sistema foram a causa primária desse atraso. (shrink)

This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning (...) and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both. (shrink)

Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to Russell concerning both (...) the philosophical materials Frege left behind, as well as information from Frege’s journal revealing his anti-semitic political opinions. Their interaction contains interpretive conjectures and insights on Dummett’s side, and some dark humor on Russell’s. (shrink)

This chapter contains sections titled: Introduction Frege on Function, Concept and Object Sinn (Sense) and Bedeutung (Reference) Identity Statements and Bearerless Names: Russell's View of Names as Associated with Descriptions Names and Communication Russell's Theory of Descriptions Indirect Discourse Conclusion.

Of all philosophers, it is Frege whom Wittgenstein held in greatest esteem. The aim of philosophy, Wittgenstein wrote in the Tractatus, “is the logical clarification of thoughts”, a characterization that might well be taken to be true of Frege's philosophy. The clarity that Wittgenstein saw as an important philosophical virtue is arguably nowhere better illustrated than in Frege's writings, even if one disagrees with the substantive philosophical claims that Frege makes. Peter Geach reports a remark that Wittgenstein made to him (...) when they were discussing Frege's essay “On Concept and Object”. Wittgenstein may have envied Frege's style, but he nevertheless felt it had a strong effect on his own writing. Frege is explicitly cited as an influence on the Tractatus, but although he is rarely mentioned by name in his later writings, his views continued to be a major source of inspiration to the very end of Wittgenstein's life. (shrink)

This chapter deals with the following questions: What does Michael Dummett demand of a “systematic” theory of meaning, and what understanding of Frege's “level of sense” leads him to conclude that, if Wittgenstein is correct in denying that there is such a level, then no systematic theory of meaning is possible? For Dummett, an understanding of the meaning side of language is not “systematic” if it must hold that a sentence is understood only because it has been previously learned as (...) a whole. To reconstruct how Dummett arrives at Frege's level of “sense” as crucial for a systematic understanding of complexity, we can begin with a hypothetical concrete situation and proceed step by step to rule out what is not meant by “meaning” when we speak of it as being systematically developed. (shrink)

This chapter focuses on the linguistic structure to the extent that it can be understood in relation to linguistic activity. In order to arrive at an adequate, non‐formal concept of structure, the author and his colleagues oriented themselves on Frege's thought as the most plausible starting point. Wittgenstein's considerations is then taken into account, without endangering the systematic and comprehensive character of the picture as painted by Frege. The chapter highlights two central statements with which Wittgenstein contradicts Frege. First is (...) his thesis that there is no justification in the philosophy of language for isolating just one “fundamental relation” for the representation of all truth‐relevant contents. Second is the thesis that it is typical of natural languages that one and the same kind of composition of expressions can have various meanings. (shrink)

1. Logik und Philosophie der Mathematik.--2. Logik und Sprachphilosophie.--3. Logik und Semantik.

Este artigo aborda a reação de Frege a Kant e questiona uma influente interpretação, defendida por Jim Conant, de acordo com a qual Frege subscreve os princípios essenciais da filosofia de Kant, nomeadamente a sua conceção antipsicologista avant la lettre da lógica pura. Eu defendo que existem diferenças profundas de ponto de vista entre eles, as quais alimentam o seu bem conhecido desacordo acerca da natureza da aritmética, e que a rejeição de Frege de algumas das premissas fundamentais da epistemologia (...) kantiana levou-o a uma forma bastante distinta de antipsicologismo. No centro da disputa Frege-Kant está um entendimento completamente diferente da objetividade, a qual aos olhos de Frege não pode ser concebida como uma expressão do nosso considerar algo verdadeiro, como resulta do enquadramento de Kant. (shrink)

O artigo começa com uma conversa entre Frege e Wittgenstein. Frege fala primeiro, e apresenta o seu ponto de vista sobre os fundamentos da lógica. Daí, Wittgenstein responde em três momentos: (a) primeiro ele brinca e experimenta com as ideias de Frege para examinar o seu significado, (b) depois ele começa a apresentar as suas próprias ideias sobre a lógica, desafiando o ponto de vista de Frege, (c) e finalmente ele busca um acordo com Frege, deixando um quebra-cabeça para nós: (...) a ideia de uma técnica do pensamento. Daí, é a nossa vez de entrar na conversa, e a nossa participação se desenrola em dois momentos: (a) primeiro nós introduzimos ideias de Turing para articular a noção de um mecanismo de duas alavancas, (b) e depois nós esboçamos um entendimento da técnica do pensamento em termos desse mecanismo. (shrink)

Philosophy undergraduate course completion work published in 2015. This work examines Frege's concept of logical law and its relationship to other normative and descriptive approaches in the history of philosophy, as well as epistemological conceptions of the a priori aspects of mathematical knowledge.

Hybrid expressivists claim to solve the Frege-Geach problem by offloading the explanation of the logico-semantic properties of moral sentences onto beliefs that are components of hybrid states they express. We argue that this strategy is undermined by one of hybrid expressivism’s own commitments: that the truth of the belief-component is neither necessary nor sufficient for the truth of the hybrid state it composes. We articulate a new approach. Instead of explaining head-on what it is for, say, a pair of moral (...) sentences to be inconsistent, expressivists should “sidestep” and explain what it is _to think that_ a pair of moral sentences is inconsistent. To think so is to think they cannot both be true – a modal notion. Since expressivists have given accounts of such modals, we illustrate how sentences like ‘“lying is wrong” and “lying is not wrong” are inconsistent’ express sensible – and rationally compelling – states of mind. (shrink)

Tento článek se zabývá dvěma aritmetickými systémy - konkrétně systémem, který představil R. Dedekind a systémem, který vytvořil G. Frege - a paradoxy, které se zde vyskytují - tedy Burali-Fortiho paradoxem (což je vůbec první fomrulace moderního paradoxu), Cantorovým paradoxem a Russellovým paradoxem. Hlavním cílem je ukázat, co mají tyto paradoxy společného a zdůvodnit, že ačkoli se tyto paradoxy vyskytují v různých systémech, mají společné znaky. Na základě studia uvedených systémů, paradoxů i různých řešení těchto paradoxů, autorka dospívá k tvrzení, (...) že zkoumané paradoxy vznikají na stejném základě, a to na základě problému nehierarchizovanosti.V dodatku tohoto článku navíc čtenář nalezne dva zajímavé historické exkurzy. První z nich předkládá v historicky autentické podobě odvození Burali-Fortiho paradoxu Druhý exkurz je věnován Russellovu paradoxu a představuje jej nejen v podobě, jak jej vyjádřil B. Russell, ale také ve formulaci G. Frega. (shrink)

It is in heavy dispute in the literature whether Frege’s conception of logic is universalism and excludes the possibility of metalogical investigations. In the book, the author argues that there is indeed tension between universalism and non-universalism in it, which finds expression in Grundgesetze. It dismisses the notion of reinterpretation playing a crucial role in the post-Tarskian metalogical investigations as illegitimate; for a language in which a theory, whose subject matter is thoughts rather than formulae per se, is formulated must (...) not be reinterpreted in that fully interpreted formulae express different thoughts once reinterpreted. However, it does not preclude such metalogical investigations that do not make use of the notion: they are not only legitimate, understandable to it but also indispensable to Frege’s logicist project. (shrink)