Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, and offers (...) a pluralistic and open-ended picture of Husserl's phenomenology of mathematics. Her study shows Husserl's phenomenology to be a method capable of both shedding light on and internally criticizing scientific practices and concepts. (shrink)

Principa Practica is a provocative work in which author Arnold Johanson maintains that philosophers since Socrates have been asking the wrong questions, like "What is good?" and "What is right?" The reason for this, according to the author, is that moral philosophers have based their work on a logical framework more suitable to science than to ethics and politics. Striking out in a new direction, the author bases his work on the concept of requirement which he finds not only (...) has a rich logical structure but, if properly formulated, can be used to guide humanity in its struggle to find meaning in life, on one hand, and to find peace, happiness, and order, on the other. The fact that the work has an emphasis on logic may suggest that only those with a technical bent can read this work, but this is not so: much of this work—over two-thirds—is designed to be read by those without a technical background in mathematics and logic. (shrink)

Children's overextensions of spatial language are often taken to reveal spatial biases. However, it is unclear whether extension patterns should be attributed to children's overly general spatial concepts or to a narrower notion of conceptual similarity allowing metaphor‐like extensions. We describe a previously unnoticed extension of spatial expressions and use a novel method to determine its origins. English‐ and Greek‐speaking 4‐ and 5‐year‐olds used containment expressions (e.g., Englishinto, Greekmesa) for events where an object moved into another object but extended such (...) expressions to events where the object moved behind or under another object. The pattern emerged in adult speakers of both languages and also in speakers of 10 additional languages. We conclude that learners do not have an overly general concept of Containment. Nevertheless, children (and adults) perceive similarities across Containment and other types of spatial scenes, even when these similarities are obscured by the conventional forms of the language. (shrink)

Tendo como ponto de referência o pensamento de Henri Bergson e, a partir dele, a relação de identidade entre liberdade e criação, ação livre e ação criadora, este trabalho tem como propósito levantar algumas questões relativas à função do método em relação a uma filosofia que encara a arte, o artista e a atividade artística como exemplos de que o conhecimento acerca do real e do verdadeiro é possível e, justamente em virtude disso, os toma como paradigmas da própria filosofia. (...) Em outros termos, interessa aqui dar alguns passos no sentido da investigação acerca do que quer e o que pode uma filosofia que guarda profundas afinidades com a arte e que, além disso, busca entendê-la em sua essência, compreendê-la em seus princípios e revelar a sua natureza. (shrink)

Resumo: Um dos principais temas postos pela filosofia bergsoniana, no âmbito da subjetividade, é o da distinção entre consciência interior e exterior, entre uma interioridade, um eu interior, profundo, e uma exterioridade, um eu superficial, periférico. Ainda que o lugar seja, em princípio, algo pertinente apenas a um dos dois polos do eu - a saber, aquele relativo à exterioridade, à extensão e ao espaço -, a discussão acerca da natureza própria da interioridade reconfigura a ideia de lugar, no pensamento (...) bergsoniano, pois, na medida em que é duração, também o eu interior se apresenta como uma região muito particular da experiência e da vida. A amplitude e os limites da existência, posta então como efetiva experiência do indivíduo em meio a esses dois lugares extremos, irredutíveis e de naturezas absolutamente distintas, e também, por isso mesmo, a relação entre temporalidade e intencionalidade, é o que pretendemos abordar neste ensaio.: One of the main issues posed by Bergson's philosophy in the field of subjectivity is the distinction between inner and outer consciousness; between an interiority, an inner deep self, and an exteriority, a superficial peripheral self. Even though place is in principle something pertinent only to one of the two poles of the self - namely, that relating to exteriority, extension and space - the discussion about the nature of interiority reconfigures the idea of place in Bergson's thought. This is because insofar as it is duration, the inner self also presents itself as a very particular region of experience and life. In this essay we address the extent and the limits of existence, posited as an effective experience of the individual in the midst of these two extreme, irreducible, and absolutely distinct places. In the same context, we also address the relation between temporality and intentionality. (shrink)

The paper aims to investigate the relationship between knowledge production and coloniality, guided by the question of alterity in the epistemological context of modern subjectivity. Seeking to understand how the relationship between subjectivity and identity (or sameness) occurs, consequently, between objectivity and alterity (or otherness) in modernity, we will seek to critically answer questions essential to philosophical practice in contemporaneity: a) what does the counterpart of the “I” consist of in this philosophy more consecrated among us and for whom the (...) canon is, as such, the ultimate legacy of the legitimate and the true? b) Which can be the possibilities of these “others” coming to relate in a dialogical and positive way to this canonical philosophy? c) Which consequences can be drawn from these responses from the point of view of the constitution of an integrated multiplicity of global and pluriversal knowledges, from which all living beings on planet Earth, and the planet itself, could truly benefit? (shrink)

Em sonsonância com a arte de seu tempo, o esforço de criação, sob a perspectiva bergsoniana, se constitui em meio a uma elaboração material, corporal, relacionada, por sua vez, a uma construção musical. A noção bergsoniana de tempo musical como produção criadora diz respeito, assim, a um meio particular de conhecimento: a intuição. Ela se desdobra, no caso da arte, em obra e, na filosofia, em metafísica.

ABSTRACT This paper seeks to clarify Husserl’s critical remarks about Kant’s view of logic by comparing their respective views of logic. In his Formal and Transcendental Logic Husserl criticizes Kant for not asking transcendental questions about formal logic, but rather ascribing an ‘extraordinary apriority’ to it. He thinks the reason for Kant’s uncritical attitude to logic lies in Kant’s view of logic as directed toward the subjective, instead of being concerned with a ‘“world” of ideal Objects’. Whereas for Kant, general (...) logic is about laws of reasoning. Husserl thinks that formal logic should describe formal structures. Husserl claims that if Kant had had a more comprehensive concept of logic, he would have thought of raising critical questions about how logic is possible. This kind of criticism cannot itself use forms of judgments or syllogisms of logic, nor even the ‘inferential’ [schliessende] method more generally, but should be descriptive in nature. Husserl's transcendental phenomenology is the method for such criticism. The paper argues that this results in reflection, and possibly revision, of the logical principles with respect to the normative goals governing the investigation in question. (shrink)

Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl to (...) a ‘computational’ view of logic. Inspired by Gauss and Grassmann Husserl then undertakes a further investigation of theories of manifolds. When Husserl subsequently renounces psychologism and changes his view of logic, his idea of definiteness also develops. The notion of definiteness is discussed most extensively in the pair of lectures Husserl gave in front of the mathematical society in Göttingen (1901). A detailed analysis of the lectures, together with an elaboration of Husserl’s lectures on logic beginning in 1895, shows that Husserl meant by definiteness what is today called ‘categoricity’. In so doing Husserl was not doing anything particularly original; since Dedekind’s ‘Was sind und sollen die Zahlen’ (1888) the notion was ‘in the air’. It also characterizes Hilbert’s (1900) notion of completeness. In the end, Husserl’s view of definiteness is discussed in light of Gödel’s (1931) incompleteness results. (shrink)

The paper discusses Husserl’s notion of definiteness as presented in his Göttingen Mathematical Society Double Lecture of 1901 as a defense of two, in many cases incompatible, ideals, namely full characterizability of the domain, i.e., categoricity, and its syntactic completeness. These two ideals are manifest already in Husserl’s discussion of pure logic in the Prolegomena: The full characterizability is related to Husserl’s attempt to capture the interconnection of things, whereas syntactic completeness relates to the interconnection of truths. In the Prolegomena (...) Husserl argues that an ideally complete theory gives an independent norm for objectivity for logic and experiential sciences, hence the notion is central to his argument against psychologism. In the Double Lecture the former is captured by non-extendibility, that is, categoricity of the domain, from which, so Husserl assumes, syntactic completeness is thought to follow. In the so-called ‘mathematical manifolds’ the expressions of the theory are equations that are reducible to equations between elements of the theory. With such an equational reduction structure individual elements of the domain are given criteria of identity and hence they are fully determined. (shrink)

The paper examines the roots of Husserlian phenomenology in Weierstrass's approach to analysis. After elaborating on Weierstrass's programme of arithmetization of analysis, the paper examines Husserl's Philosophy of Arithmetic as an attempt to provide foundations to analysis. The Philosophy of Arithmetic consists of two parts; the first discusses authentic arithmetic and the second symbolic arithmetic. Husserl's novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part. In the second part, he founds the (...) symbolic extension of the authentically given arithmetic with stepwise symbolic operations. In the process of doing so, Husserl comes close to defining the modern concept of computability. The paper concludes with a brief comparison between Husserl and Frege. While Frege chose to subject arithmetic to logical analysis, Husserl wants to clarify arithmetic as it is given to us. Both engage in a kind of analysis, but while Frege analyses within Begriffsschrift, Husserl analyses our experiences. The difference in their methods of analysis is what ultimately grows into two separate schools in philosophy in the 20th century. (shrink)

Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. (...) Husserl’s interest in the Memoir is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. Husserl favored a non-metrical approach to geometry; thus the topological nature of Hilbert’s Memoir must have been intriguing to him. The task of phenomenology is to describe the givenness of this logos, hence Husserl needed to develop the notion of eidetic intuition. (shrink)

The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches to mathematical practice and mathematical ontology. First, the paper develops the phenomenological approach based on Husserl's writings to obtain a method for understanding mathematical practice. Then, to put forward a full-fledged ontology of mathematics, the phenomenological approach is complemented with social ontological considerations. The proposed ontological account sees mathematical objects as social constructions in the sense that they are products of culturally shared and historically developed practices. (...) At the same time the view endorses the sense that mathematical reality is given to mathematicians with a sense of independence. As mathematical social constructions are products of highly constrained, intersubjective practices and accord with the phenomenologically clarified experience of mathematicians, positing them is phenomenologically justified. The social ontological approach offers a way to build mathematical ontology out of the practice with no metaphysical magic. (shrink)

This paper presents the metaphysics of the Vietnamese Buddhist Zen monk Thich Nhat Hanh. He interprets the Buddhist principle of interdependent arising in terms of interbeing, the idea that everything depends for its existence on everything else. On his view, everything “inter-is” with everything else, or “to be is to inter-be.” His interpretation is particularly interesting in light of the contemporary debate on fundamentality in western metaphysics. By embracing the idea of interbeing, he opposes the view that there are fundamental (...) entities which do not depend for their existence on anything else. I give an outline of Thich Nhat Hanh’s views, answer an objection, and explain his reasons for adopting his standpoint. My aim is not to offer a full defense of his views, but only to show that the often neglected position of metaphysical coherentism, which Thich Nhat Hanh adopts, deserves further consideration. (shrink)

The paper examines Husserl’s phenomenology and Hilbert’s view of the foundations of mathematics against the backdrop of their lifelong friendship. After a brief account of the complementary nature of their early approaches, the paper focuses on Husserl’s Formale und transzendentale Logik viewed as a response to Hilbert’s “new foundations” developed in the 1920s. While both Husserl and Hilbert share a “mathematics first,” nonrevisionist approach toward mathematics, they disagree about the way in which the access to it should be construed: Hilbert (...) wanted to reach it and show it consistent by his formalism on the basis of sensuous signs, Husserl held that there should be a reduction to elementary judgements about individuals. Husserl’s reduction does not establish the consistency of mathematics but he claims it is important for the considerations of truth. (shrink)

This paper explicates Husserl’s usage of what he calls “radical Besinnung” in Formale und transzendentale Logik. Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical Besinnung and (...) transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological framework within which transcendental phenomenological descriptions are used to criticize historically given goal-directed practices. (shrink)

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...) The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics. (shrink)

This paper discusses Jean van Heijenoort’s (1967) and Jaakko and Merrill B. Hintikka’s (1986, 1997) distinction between logic as auniversal language and logic as a calculus, and its applicability to Edmund Husserl’s phenomenology. Although it is argued that Husserl’s phenomenology shares characteristics with both sides, his view of logic is closer to the model-theoretical, logic-as-calculus view. However, Husserl’s philosophy as transcendental philosophy is closer to the universalist view. This paper suggests that Husserl’s position shows that holding a model-theoretical view of (...) logic does not necessarily imply a calculus view about the relations between language and the world. The situation calls for reflection about the distinction: It will be suggested that the applicability of the van Heijenoort and the Hintikkas distinction either has to be restricted to a particular philosopher’s views about logic, in which case no implications about his or her more general philosophical views should be inferred from it; or the distinction turns into a question of whether our human predicament is inescapable or whether it is possible, presumably by means of model theory, to obtain neutral answers to philosophical questions. Thus the distinction ultimately turns into a question about the correct method for doing philosophy. (shrink)

This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic. It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters (...) into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach to mathematics. The result is a moderately revisionist view that takes the existing mathematical practices seriously, calls for reflection on them, and eventually gives suggestions for revisions if needed. (shrink)

The paper discusses Husserl’s method of historical reflection, radical Besinnung, as defined and used in Formale und transzendentale Logik (1929). Whereas Formal and Transcendental Logic introduces and displays Husserl’s usage of Besinnung in the context of the exact sciences, the paper seeks to develop it as a more general critical method with which to approach any rational goal-directed activity. Husserl defines Besinnung as a method that enables understanding agents and their actions by explicating agents’ typically implicit goals. It leads to (...) the inclusion of historical-teleological activities as part of Husserl’s natural understanding of the world. The transcendental reflection radicalizes Besinnung by clarifying the kinds of evidence sought for in activities and then suggesting revisions to the concepts and principles used. The result is inner critique, which means that the activities are criticized against the norms that arise from reflection on these activities themselves, and not from a comparison with external standards or measures. (shrink)

This essay presents Husserl’s Formal and Transcendental Logic (1929) in three main sections following the layout of the work itself. The first section focuses on Husserl’s introduction where he explains the method and the aim of the essay. The method used in FTL is radical Besinnung and with it an intentional explication of proper sense of formal logic is sought for. The second section is on formal logic. The third section focuses on Husserl’s “transcendental logic,” which is needed to make (...) Husserl’s conception complete, i.e., to understand what makes Besinnung radical, how the proper sense of formal logic has been reached and how all this relates to transcendental constitution of an object in the world. Husserl’s work is connected to his context (in exact sciences) and the relevance of his views for the contemporary approaches is discussed. (shrink)

A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of anaphoric readings of Sobel sequences and reverse Sobel sequences, and proposes an (...) explanation of the original asymmetry on its grounds. This provides an answer to the challenge for Lewis’s theory. (shrink)

ABSTRACT. The paper compares the views of Edmund Husserl (1859-1938) and Charles Sanders Peirce (1839-1914) on mathematics around the turn of the century. The two share a view that mathematics is an independent and theoretical discipline. Both think that it is something unrelated to how we actually think, and hence independent of psychology. For both, mathematics reveals the objective and formal structure of the world, and both think that modern mathematics is a Platonist enterprise. Husserl and Peirce also share a (...) teleological conception of the development of mathematics: both view it to evolve towards a goal. This is where the primary difference between the two can be found: while for Husserl the goal of mathematics is to characterize definite manifolds, for Peirce it is to discover the real potential world as expressed by his conception of continuum. Peirce elaborates the continuum with the notion ‘potential aggregate,’ a totality of the series of uncountable sets (each created by Cantor’s theorem) briefly discussed and compared to Husserl’s notion of definite manifolds. (shrink)

Husserl holds that the theoretical sciences should be value-free, i.e., free from the values of extra-scientific practices and guided only by epistemic values such as coherence and truth. This view does not imply that to Husserl the sciences would be immune to all criticism of interests, goals, and values. On the contrary, the paper argues that Husserlian phenomenology necessarily embodies reflection on the epistemic values guiding the sciences. The argument clarifies Husserl’s position by comparing it with the pluralistic position developed (...) in feminist epistemology, according to which sciences may be guided by several competing sets of epistemic values. Further, the existence of alternative epistemic values suggests that choices among such values are social and historically conditioned. Indeed, this is how Husserl’s mature discussion in The Crisis can be understood: his examination of Galileo’s contribution in physics operates as a criticism of the unquestioned dominance of certain set of inherited epistemic values, including the values of accuracy and universal applicability. Indeed, his The Origin of Geometry endorses another set of epistemic values, most importantly that of ontological heterogeneity. Husserl’s analysis demonstrates that the choice of any set of epistemic values is influenced by historical and social factors. Moreover, Husserl argues that we can only avoid biases due to “spells of the time” by continued reflection – Besinnung, in his terms – on the role of values in science. (shrink)

There has been much theoretical debate on issues of business ethics during the last decades, but there has been little research which could concretise the content of these issues in terms of practical business. Although business life must frequently deal with concepts such as corporate social performance, business ethics and the acceptability of operations, the content and meaning of these concepts has remained flexible. In addition, rapid internationalisation and globalisation have introduced a number of new phenomena related to corporate social (...) performance. An attempt at defining the concepts more precisely and searching for a potential indicator was considered necessary in order to concretise the business environment facing corporations engaged in internationalisation and globalisation. The connection between corporate social performance and stakeholder theory provides a basis for the proposal put forward here that acceptability of operation could be employed as an indicator of corporate social performance. This approach was then applied to developing a model which could be used to assess corporate social performance. (shrink)

This entry aims to explain briefly why Rudolf Carnap is an interesting philosopher, and so especially from the phenomenological point of view. There are two primary reasons for why this should be the case: First, there is a historical connection between the two. Carnap developed many of his philosophical ideas in Freiburg while attempting (in vain) to habilitate with Husserl. This may explain why interesting Husserlian themes can be found especially in Carnap’s early works. Philosophically more exciting is the second (...) reason: the contemporary Carnap research is cultivating a view of him that is more nuanced than the Quinean logical empiricist Carnap. The “new Carnap’s” core ideas compare to Husserl’s views in interesting ways worthy of closer examination. In particular, the two philosophers have in common an open attitude towards the phenomena, which makes them each distinctively undogmatic and pluralist. The two are then compared with respect to what has been called Carnap’s “voluntarism,” intertwined with his method of explication and the principle of tolerance. (shrink)

The paper examines Husserl’s interactions with logicians in the 1930s in order to assess Husserl’s awareness of Gödel’s incompleteness theorems. While there is no mention about the results in Husserl’s known exchanges with Hilbert, Weyl, or Zermelo, the most likely source about them for Husserl is Felix Kaufmann (1895–1949). Husserl’s interactions with Kaufmann show that Husserl may have learned about the results from him, but not necessarily so. Ultimately Husserl’s reading marks on Friedrich Waismann’s Einführung in das mathematische Denken: die (...) Begriffsbildung der modernen Mathematik, 1936, show that he knew about them before his death in 1938. (shrink)

abstract: The first Christian missionaries arrived in Japan in the middle of the sixteenth century. They missionized quite a number of Japanese people but also angered many through their disrespectful behavior and destruction of temples and shrines. Less than 100 years later, Japan closed its borders, persecuted Christians, and banned Christianity in total. The reasons for this drastic step weren't solely political but also theological. Theological arguments concerning theism, eschatology, ethics, and theology of religion are found in official edicts, in (...) "disputes" between Christian missionaries and Buddhist scholars, as well as in theological treatise. One of the reoccurring arguments against Christianity includes the description of the arrogant behavior of the missionaries. According to the documents, they displayed an attitude of knowing everything concerning the world next to the ignorant Buddhists. This exclusivist mindset wasn't compatible with the order of Japan and the three teachings. In the eyes of the authorities, this doctrine secured peace and ensured domestic stability. Especially the Japanese and former Christian Fabian Fucan, as well as the Buddhist monk Suzuki Shōsan, adduce various Buddhist, Confucian, and Daoist teachings against the charge of ignorance. Conversely, Fucan's writing, as well as the edicts, records of religious "disputes," and other treatises, include the accusation that Christianity does not contain any new doctrine advancing the local one. Moreover, it is stated that Christian salvation exclusivism suggests a powerless God, and the missionaries were described as hypocrites and liars, as they did not keep their commandments. (shrink)

The Diamond Sutra is one of the earliest and most treasured of the Perfection of Wisdom Sutras and had a wide influence on the development of Zen Buddhism. There has been, in recent years, great interest in one particular form of sentences that repeatedly occur in the sutra, sentences of the form “A is not A, therefore it is A”. These sentences display what has been called the “logic of not” or the “logic of affirmation-in-negation”. They are of special interest (...) since they do not only encapsulate one of the central insights of Zen Buddhism, that of nonduality, but at the same time seem to go against one of the most orthodox laws of logic in Western philosophy, the law of identity. This paper discusses the interpretation of these “diamond sentences” by the Vietnamese Zen monk Thich Nhat Hanh. I present Thich Nhat Hanh’s interpretation of the diamond sentences in terms of interbeing and go on to argue that and explain how, on his interpretation, the validity of the law of identity is indeed rejected. Finally, I spell out consequences for formulating a “logic of Zen” and for a related debate about the validity of the law of non-contradiction in Zen. (shrink)

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic –Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical (...) inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schröder, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism. (shrink)

The paper discusses Husserl’s criticism of Frege in Philosophy of Arithmetic (1891) and then his later attitude towards logicism as expressed in Logical Investigations (1900-01). In Philosophy of Arithmetic Husserl holds that logicists offer needless and artificial definitions of notions such as equivalence and number. Frege criticized Husserl’s approach in Philosophy of Arithmetic as psychological, thus shifting the focus of the debate away from logicism. However, Frege’s criticism could be seen to lead Husserl to his later transcendental phenomenological concept of (...) correlation and, with it, to a more developed criticism of logicism. In this regard the division of labor between mathematics and philosophy established in Prolegomena to the Logical Investigations (1900) is central. It implies that in Husserl’s view formal methods fail to shed philosophical insight into the essence of mathematics. In his picture the central notions in need of philosophical clarification are, instead of number and quantity, the notions that are central to abstract structural mathematics. Contrary to Frege who can only elucidate the primitive concepts, Husserl engages in detailed description of their constitution. (shrink)

An exciting trend in current analytic philosophy is the emergence of several topics that draw their inspiration partly from the work of Rudolf Carnap, a leading figure in the Vienna Circle. Approaches such as deflationary metaontology, conceptual engineering, logical pluralism, and related views on the normativity of logic are seen to have Carnapian roots; however, these topics are quite foreign to the once-prevalent but rather narrow reading of Carnap that derives from W. V. Quine’s and others’ appraisal of him in (...) the 1950s and 1960s. -/- The case of Carnap raises questions about the potential narrowness of our understanding of the Vienna Circle in general. While the reappraisal of the history of the Vienna Circle has been ongoing since the early 1980s, the more recent developments in analytic philosophy suggest that there might be even more interesting yet previously unnoticed views pertinent to present-day concerns. -/- This Special Issue collects such novel perspectives on the Vienna Circle. The covered topics range from rereadings of the doctrines of the members of the Vienna Circle, such as Rudolf Carnap, Otto Neurath, and Moritz Schlick, but also less well known figures, including its female members or sympathizers. We look for constructive connections between the Vienna Circle and different philosophical traditions as well as new perspectives on various thematic questions, such as the development of contemporary logic and unity of science. (shrink)