The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also (...) central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity. (shrink)

This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting (...) concrete things, and a third sense is linked up with the immediate intuitive experience of multitudes of concrete things. Hilbert's fìnitism is examined with respect to these differences, and it will be shown that there is a tendency to conflate the different senses of number and fìnitude, a tendency which has been a source of problems in the discussion of the foundations of mathematics and in the philosophy of logic and language. (shrink)

This paper deals with Frege’s early critique of formalism in the philosophy of mathematics. Frege opposes meaningful arithmetic, according to which arithmetical formulas express a sense and arithmetical rules are grounded in the reference of the signs, to formal arithmetic, exemplified in particular by J. Thomae, whose “formal standpoint”, according to Frege, is that arithmetic should be understood as a manipulation of meaningless figures. However, Frege’s discussion of Thomae’s analogy between arithmetic and chess shows that Frege does not understand his (...) main point, which is that we must distinguish conceptually between statements about chess figures, and the chess pieces they represent. Indeed, Thomae’s fruitful use of this comparison undermines the ontological conception of arithmetic represented by Frege. The chess pieces do not go proxy for anything, but playing chess is not for that reason just manipulation of physical chess figures. This is also Wittgenstein’s point when he criticizes Frege for not seeing the “justified side of formalism”. Thomae’s formalism can be clarified by using the distinction between sign and symbol. Symbols are never meaningless or empty forms or signs, since they have a role or function in a symbolism, which one may call their meaning. The discussion of the chess analogy shows that Frege fails to see this operative aspect of the symbolism. We can conclude that the “formal standpoint” that Frege criticizes is his fabrication, rather than anything we can attribute to Thomae. (shrink)

Dans cet article, j’essaie de montrer que le dépassement et le rejet du dogmatisme sont un aspect décisif du changement dans la pensée de Wittgenstein qui a eu lieu au début des années 30, quand il commence à mettre en valeur l’autonomie de la grammaire du langage et à parler d’images grammaticales et de jeux de langage en tant qu’objets de comparaison. En examinant certains traits fondamentaux de ce changement, je mettrai en évidence l’impulsion et les idées décisives que Wittgenstein (...) a reçues des nouveaux développements dans les mathématiques et la science naturelle du début du 20e siècle.It will be argued that the overcoming and avoiding of dogmatism is a decisive feature of the change in Wittgenstein’s thinking that takes place in the beginning of the 1930’s when he starts to emphasise the autonomy of the grammar of language and to talk about grammatical pictures and language games as objects of comparison. By examining certain crucial features in this change in Wittgenstein’s thinking, it will be shown that he received decisive impulses and ideas from new developments in mathematics and natural science in the early 20th century. (shrink)

This paper deals with Wittgenstein's statement that our "craving for generality" is a main source of confusion in philosophy. It is argued that difficulties connected with this tendency also affect most attempts to explain or elaborate Wittgenstein's philosophical thinking, since most commentaries elucidate his thinking in general terms, in the notions and classificatory apparatus of some prevalent vocabulary of professional philosophy. It is argued that this craving for generality is closely tied up with another tendency of traditional philosophy, namely the (...) tendency to impose substantive normative claims. The effort to dissociate himself from this tendency is a main feature of the late Wittgenstein's philosophy that has not been sufficiently observed. /// O presente ensaio trata da afirmação de Wittgenstein segundo a qual "a nossa ânsia de generalidade" constitui umafonte principal de confusão em filosofia. O autor procura demonstrar até que ponto dificuldades ligadas a esta tendência tambem afectam a maior parte das tentativas para explicar ou pormenorizar o pensamento filosófico de Wittgenstein, dado que a maiorparte dos comentdrios elucidam o seu pensamento em termos gerais, com as noqoes e aparato classificatorio de certo vocabulário dominante dafilosofia profissional. O artigo mostra assim coma está ânsia da generalidade está intimamente ligada com outra tendencia dafilosofia tradicional, nomeadamente a tendência a impor reivindicações normativas substantivas. O autor considera que o esforço de Wittgenstein para se dissociar desta tendencia é precisamente uma das características principais da sua filosofia tardia que não tern sido suficientemente estudada. (shrink)

This paper is concerned with some of the differences between philosophy and contemporary science, and with the significance of these differences for the question of the nature of philosophy. Differences of particular interest here are ones that tend to be concealed and ignored through the influence of the professionalist attitudes of contemporary science, an influence that manifests itself in the prevailing normative attitude to the vocabularies and linguistic practices of professional philosophy. It is argued that this normative attitude is questionable (...) in the light of a feature that we take to be essential to philosophy: always being open to the question of its own nature and task. (shrink)

Sören Stenlund's work marks a major advance in our understanding of why the philosophy of language has been so dominated over the past few decades by the so-called "creative aspect of language" -- the problem of how we are able to understand sentences that we have never heard before. Stenlund raises some fundamental philosophical objections by demonstrating, for example, how the theory distorts the flexibility and fluidity of word -- and sentence -- meaning. Although words and sentences can (...) have a remarkable number of different, sometimes extraordinarily subtle meanings, Stenlund shows how language-users can readily adapt to entirely novel uses of a word or a sentence. Language and Philosophical Problems presents the results of philosophical investigations into several connected issues of current interest within the philosophies of language, logic, mind, and mathematics. In particular it deals with our tendency to be misled by certain prevailing views and preconceptions of language. (shrink)

ABSTRACT In a recent essay, Sören Stenlund tries to align Wittgenstein’s approach to the foundations and nature of mathematics with the tradition of symbolic mathematics. The characterization of symbolic mathematics made by Stenlund, according to which mathematics is logically separated from its external applications, brings it closer to the formalist position. This raises naturally the question whether Wittgenstein holds a formalist position in philosophy of mathematics. The aim of this paper is to give a negative answer to this (...) question, defending the view that Wittgenstein always thought that there is no logical separation between mathematics and its applications. I will focus on Wittgenstein’s remarks about arithmetic during his middle period, because it is in this period that a formalist reading of his writings is most tempting. I will show how his idea of autonomy of arithmetic is not to be compared with the formalist idea of autonomy, according to which a calculus is “cut off” from its applications. The autonomy of arithmetic, according to Wittgenstein, guarantees its own applicability, thus providing its own raison d’être. RESUMO Em um recente artigo, Sören Stenlund procura alinhar a abordagem de Wittgenstein em relação aos fundamentos e à natureza da matemática com a tradição da matemática simbólica. A caracterização da matemática simbólica feita por Stenlund, de acordo com a qual a matemática é logicamente separada de suas aplicações externas, a aproxima da posição formalista. Isto naturalmente levanta a questão de se Wittgenstein defende uma posição formalista em filosofia da matemática. O objetivo deste artigo é dar uma resposta negativa a esta questão, ao defender que Wittgenstein sempre pensou não haver separação lógica entre a matemática e suas aplicações. Atenção especial será dada às observações de Wittgenstein sobre a aritmética pertencentes ao seu período intermediário, pois é neste período que uma leitura formalista de seus escritos é mais sedutora. Mostrarei como sua ideia de autonomia da aritmética não deve ser comparada à ideia formalista de autonomia, segundo a qual um cálculo é “cortado” de suas aplicações. A autonomia da aritmética, para Wittgenstein, garante ela própria sua aplicabilidade, provendo, assim, sua própria raison d’être. (shrink)

Stig Kanger made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. This is the second of two volumes dedicated to the work of Stig Kanger. The first volume is a complete collection of Kanger's philosophical papers. The present (...) volume contains critical essays on the various aspects of Kanger's work as well as some biographical sketches. Lennart Åqvist, Jan Berg, Brian Chellas, Anatoli Degtyarev, Lars Gustafsson, Sören Halldén, Kaj Børge Hansen, Sven Ove Hansson, Risto Hilpinen, Jaakko Hintikka, Ghita Holmström-Hintikka, Lars Lindahl, Sten Lindström, Ingmar Pörn, Dag Prawitz, Wlodek Rabinowicz, Krister Segerberg, Amartya Sen, Sören Stenlund, Göran Sundholm, and Andrei Voronkov have contributed to this volume. (shrink)

These two complementary works give the reader a unique insight into the breadth and substance of Kierkegaard's thought. One reads like a novel and the other a Platonic dialogue but both concern the nature of love, faith, and happiness. These are the first translations to convey the literary quality and philosophical precision of the originals.

The Cambridge Companion to Philosophical Methodology offers clear and comprehensive coverage of the main methodological debates and approaches within philosophy. The chapters in this volume approach the question of how to do philosophy from a wide range of perspectives, including conceptual analysis, critical theory, deconstruction, experimental philosophy, hermeneutics, Kantianism, methodological naturalism, phenomenology, and pragmatism. They explore general conceptions of philosophy, centred on the question of what the point of philosophising might be; the method of conceptual analysis and its recent naturalistic (...) critics and competitors; perspectives from continental philosophy; and also a variety of methodological views that belong neither to the mainstream of analytic philosophy, nor to continental philosophy as commonly conceived. Together they will enable readers to grasp an unusually wide range of approaches to methodological debates in philosophy. (shrink)

Language and Philosophical Problems investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, Sren Stenlund demonstrates a strategy for tracing out and (...) resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many prima facie different kinds of problems are shown to have common roots, and should thus be dealt and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem. (shrink)

In Either/Or, using the voices of two characters—the aesthetic young man of part one, called simply "A," and the ethical Judge Vilhelm of the second section—Kierkegaard reflects upon the search for a meaningful existence, contemplating subjects as diverse as Mozart, drama, boredom, and, in the famous Seducer's Diary, the cynical seduction and ultimate rejection of a young, beautiful woman. A masterpiece of duality, Either/Or is a brilliant exploration of the conflict between the aesthetic and the ethical - both meditating ironically (...) and seductively upon Epicurean pleasures, and eloquently expounding the noble virtues of a morally upstanding life. For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators. (shrink)

Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by Stig Kanger and (...) a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.-- Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)

The analysis presented in this article reveals an ambiguity and tension in human rights theory concerning the delusional person’s freedom of belief and thought. Firstly, it would appear that the concepts ‘opinion’ and ‘thought’ are defined in human rights discussion in such a way that they do include delusions. Secondly, the internal freedom to hold opinions and thoughts is defined in human rights discussion and international human rights covenants as an absolute human right which should not be restricted in any (...) situation for any reason. These views, if understood literally, imply that a person has an absolute right to hold a delusion. However, this kind of conclusion has not been made in mental health laws, the ethical principles guiding psychiatric care or the practice of psychiatry. Instead, they assume that the use of involuntary antipsychotic medication is justified even thought its purpose is to influence delusions. The ambiguity and tension in human rights theory concerning the freedom of belief and thought challenge us to develop this theory within an interdisciplinary discussion so that people with delusions are taken into account properly. (shrink)

The analysis presented in this article reveals an ambiguity and tension in human rights theory concerning the delusional person’s freedom of belief and thought. Firstly, it would appear that the concepts ‘opinion’ and ‘thought’ are defined in human rights discussion in such a way that they do include delusions. Secondly, the internal freedom to hold opinions and thoughts is defined in human rights discussion and international human rights covenants as an absolute human right which should not be restricted in any (...) situation for any reason. These views, if understood literally, imply that a person has an absolute right to hold a delusion. However, this kind of conclusion has not been made in mental health laws, the ethical principles guiding psychiatric care or the practice of psychiatry. Instead, they assume that the use of involuntary antipsychotic medication is justified even thought its purpose is to influence delusions. The ambiguity and tension in human rights theory concerning the freedom of belief and thought challenge us to develop this theory within an interdisciplinary discussion so that people with delusions are taken into account properly. (shrink)

Deceased organ donation is widely considered as a case of easy rescue―that is, a case in which A may bestow considerable benefits on B while incurring negligent costs herself. Yet, the policy implications of this observation remain unclear. Drawing on Christopher H. Wellman’s samaritan account of political obligations, the paper develops a case for a so-called opt-out system, i.e., a scheme in which people are defaulted into being donors. The proposal’s key idea is that we may arrange people’s options in (...) specific ways for the sake of others. (shrink)

This article clarifies how the freedom of thought as a human right can be understood and promoted as a right of mental health service users, especially people with psychotic disorder, by using Martha Nussbaum’s capabilities approach and Fulford’s and Fulford et al ’s values-based practice. According to Nussbaum, freedom of thought seems to primarily protect the capability to think, believe and feel. This capability can be promoted in the context of mental health services by values-based practice. The article points out (...) that both Nussbaum’s approach and values-based practice recognise that people’s values differ. The idea of involving different actors and service users in mental healthcare is also common in both Nussbaum’s approach and values-based practice. However, there are also differences in that values-based practice relies on a ‘good process’ in decision-making, whereas the capabilities approach is oriented towards a ‘right outcome’. However, since process and outcome are linked with each other, these two approaches do not necessarily conflict despite this difference. The article suggests that absolute rights are possible within the two approaches. It also recognises that the capabilities approach, values-based practice and human rights approach lean on liberal values and thus can be combined at least in liberal societies. (shrink)

This article clarifies how the freedom of thought as a human right can be understood and promoted as a right of mental health service users, especially people with psychotic disorder, by using Martha Nussbaum’s capabilities approach and Fulford’s and Fulford _et al_’s values-based practice. According to Nussbaum, freedom of thought seems to primarily protect the capability to think, believe and feel. This capability can be promoted in the context of mental health services by values-based practice. The article points out that (...) both Nussbaum’s approach and values-based practice recognise that people’s values differ. The idea of involving different actors and service users in mental healthcare is also common in both Nussbaum’s approach and values-based practice. However, there are also differences in that values-based practice relies on a ‘good process’ in decision-making, whereas the capabilities approach is oriented towards a ‘right outcome’. However, since process and outcome are linked with each other, these two approaches do not necessarily conflict despite this difference. The article suggests that absolute rights are possible within the two approaches. It also recognises that the capabilities approach, values-based practice and human rights approach lean on liberal values and thus can be combined at least in liberal societies. (shrink)

Over the course of the twentieth century, nationalistic approaches to the obstacles of racism in the United States have increasingly come to be seen as the more revolutionary of the various forms of anti-racist struggle. This paper explores several historical instances of Black Nationalism and seeks to demonstrate that, despite the many points on which they might diverge, they share in common a tendency to naturalize and embrace the category of race as a basis for political struggle, and that they (...) therefore constitute an ideologically accommodating and hence essentially regressive approach to the questions of race and racism. It is suggested that a critique of the modern category of race and a political practice aimed at its denaturalization will be a necessary aspect of any attempt to overcome racial oppression and inequality. (shrink)

The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...

These two complementary works give the reader a unique insight into the breadth and substance of Kierkegaard's thought. One reads like a novel and the other a Platonic dialogue but both concern the nature of love, faith, and happiness. These are the first translations to convey the literary quality and philosophical precision of the originals.