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 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)

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)

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)

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)

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)

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)

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)

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)

Philosophy and science employ abstract hypothetical scenarios- thought experiments - to illustrate, defend, and dispute theoretical claims. Since thought experiments furnish no new empirical observations, the method prompts two epistemological questions: whether anything may be learnt from the merely hypothetical, and, if so, how. Various sceptical arguments against the use of thought experiments in philosophy are discussed and criticized. The thesis that thought experiments in science provide a priori knowledge through non-sensory grasping of abstract entities is discussed and rejected. The (...) thesis that thought experimentation consists in manipulations of mental models is examined and found to be of limited epistemological relevance. It is argued that thought experiments are associated with characteristic arguments in a manner similar to ordinary experiments. It is further argued that thought experiments function in the same way as experiments in general: by providing premises for their associated arguments. Like other experiments, a thought experiment is successful when the premises it provides are true. This holds both for philosophical and scientific thought experiments. An argument schema is proposed and shown to be a formal analogue to that associated with ordinary experiments; similar in being subject to epistemological holism; but differing in being modal: in employing statements about possibility and necessity. The evaluation of thought experiments thus depends on how modal statements may be justified. Intuition and conceivability are discussed as sources of modal justification and found problematic. Instead it is suggested that evaluation proceed by accommodation of the statements describing the experiment's hypothetical scenario. The method of accommodation is developed and applied to five influential thought experiments in philosophy: the brain in a vat; Putnam's Twin Earth; Burge's arthritis example; Searle's Chinese Room; and Newcomb's problem. Its application shows some of these to be failed, others to be successful only relative to controversial philosophical doctrines. (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)

The article examines the role of natural kinds in semantic theorizing, which has largely been conducted in isolation from relevant work in science, metaphysics, and philosophy of science. We argue that the Kripke–Putnam account of natural kind terms, despite recent claims to the contrary, depends on a certain metaphysics of natural kinds; that the metaphysics usually assumed—micro-essentialism—is untenable even in a ‘placeholder’ version; and that the currently popular homeostatic property cluster theory of natural kinds is correct only to an extent (...) that fails to vindicate the Kripke–Putnam account. This undermines the metasemantics required for anti-descriptivist semantics. _1_ Introduction _2_ From Semantics to Metaphysics _3_ Metaphysics, Part I: The Demise of Micro-essentialism _3.1_ Original micro-essentialism _3.2_ Placeholder essentialism _4_ Metaphysics, Part II: Homeostatic Property Cluster Theory _5_ Prospects for Natural Kind Term Semantics. (shrink)

Philosophical interest in thought experiments has grown over the last couple of decades. Several positions have emerged, defined largely by their differing responses to a perceived epistemological challenge: how do thought experiments yield justified belief revision, even in science, when they provide no new empirical data? Attitudes towards this supposed explanandum differ. Many philosophers accept that it poses a genuine puzzle and hence seek to provide a substantive explanation. Others reject or deflate the epistemic claims made for thought experiments.In this (...) paper I present a model for many thought experiments in philosophy and science. The model doesn't assume that thought experiments in fact manage to achieve epistemic justifi cation, but it allows us to see how they aspire to do so. It also emphasises both the parallels and the discrepancies between thought experiments and ordinary scientific experiments. (shrink)

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)

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)

Name der Zeitschrift: Jahrgang: 13 Heft: 2 Seiten: 128-146.

Two ways of characterizing natural kinds are currently popular: the Kripke-Putnam appeal to microstructure and Boyd’s appeal to causal homeostasis. I argue that these conceptions are more divergent than is often acknowledged, that they give no credence to essentialism, and that they are both faulty. In their place, I sketch an alternative view of natural kinds, which I call “bare projectibilism”. This conception avoids the appeal to explanation common to microstructuralism and the causal homeostasis view, but is still compatible with (...) scientific realism. (shrink)

Human rights theory generally conceptualizes freedom of thought, conscience, religion, and belief as well as freedom of opinion and expression, as offering absolute protection in what is called the forum internum. At a minimum, this is taken to mean the right to maintain thoughts in one’s own mind, whatever they may be and independently of how others may feel about them. However, if we adopt this stance, it seems to imply that there exists an absolute right to hold psychotic delusions. (...) This article takes the position that this conclusion is ethically problematic from the perspective of psychiatric treatment and the rights of persons with psychosis. The article reflects on this particular challenge and sets forth an understanding of freedom in the forum internum that might apply to situations where for various reasons it is not, necessarily accurate to maintain that persons have an absolute right to their own thoughts. For the purpose of proposing such an understanding, the article engages with current debates within human rights theory and political philosophy and analyzes discussions about psychotic delusions and the way in which involuntary treatment is justified. Based on this analysis, this article in turn conceptualizes freedom in the forum internum as ‘negative liberty’, ‘authenticity’, and ‘capability’. This article suggests that when forum internum is redefined as encompassing a right to certain internal capabilities, the right remains meaningful for persons with psychotic delusions as well. (shrink)

In the last decade, philosophers have offered a number of proposals concerning the logical form of hypothetical cases, or thought experiments, as these are used for purposes of testing philosophical claims. In this paper, I discuss what the desiderata for a formal proposal are. Employing a comparison with general philosophy of science, I suggest that one important desideratum is to highlight recurrent patterns of disagreement surrounding cases. I advocate a proposal in propositional modal logic which, I argue, better meets this (...) desideratum than competing proposals. I also sketch how this proposal may be extended into more fine grained analyses, employing counterfactual conditionals yet avoiding certain problems due to so-called "deviant realizations". (shrink)

Häggqvist and Wikforss argued that in the case of so-called natural kind terms, semantic externalism relies on an untenable metaphysics of kinds: microessentialism. They further claimed that this metaphysics fails, for largely empirical reasons. Focussing on the case of water, Hoefer and Martí European Journal for the Philosophy of Science, 9, rejoin that suitably construed, microessentialism is correct. I argue that their defence of microessentialism fails.