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Showing papers in "Synthese in 1991"


MonographDOI
28 Jun 1991-Synthese
TL;DR: The Semantic Tradition: 1. Kant, analysis, and pure intuition 2. Bolzano and the birth of semantics 3. Geometry, pure intuition and the a priori 4. Frege's semantics as mentioned in this paper.
Abstract: Part I. The Semantic Tradition: 1. Kant, analysis, and pure intuition 2. Bolzano and the birth of semantics 3. Geometry, pure intuition and the a priori 4. Frege's semantics and the a priori in arithmetic 5. Meaning and ontology 6. On denoting 7. Logic in transition 8. A logico-philosophical treatise Part II Vienna, 1925-1935: 9. Schlick before Vienna 10. Philosophers on relativity 1. Carnap before Vienna 12. Scientific idealism and semantic idealism 13. Return of Ludwig Wittgenstein 14. A priori knowledge and the constitution of meaning 15. The road to syntax 16. Syntax and truth 17. Semantic conventionalism and the factuality of meaning 18. The problem of induction: theories 19. The problems of experience: protocols Notes References Index.

395 citations


Journal ArticleDOI
01 Jun 1991-Synthese
TL;DR: In this article, it is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest.
Abstract: It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here.

256 citations


Journal ArticleDOI
01 Feb 1991-Synthese
TL;DR: In this article, a review of the most widely discussed identity conditions for events is presented, with particular attention to the problems commonly associated with them, as well as the difficulties involved in formulating identity conditions.
Abstract: As Donald Davidson has pointed out,1 there are many good reasons for taking events seriously as concrete individuals, i.e., as numerically unique entities which have location in space and time. In the first place, both action theory and explanation seem to call for events qua unrepeatable, spatially located particulars. In excusing an action (a species of event) we frequently describe the action in a number of different ways. My daughter's eating all the brownies in the refrigerator this afternoon is the very same action as my daughter's eating the dessert for tonight's dinner. But she is blameless in that she didn't know that the brownies were the dessert. Similarly in explaining the expansion of a piece of metal, scientists may redescribe it in a number of different ways: in terms of the kind of material it is, in terms of the heat capacity of metal, in terms of molecular bonding and the motion of molecules. All this talk of redescription makes little sense if there are no individuals to be described in the first place. Moreover, as Davidson has shown, an ontology of unrepeatable events has great utility for the purposes of accommodating adverbs in predicate logic, allowing us to validate the intuitive inference from, say, 'Elspeth ate the brownies quickly under the deck at noon' to 'Elspeth ate the brown ies'. In brief, action theory, causation, explanation, and logical theory all seem to call for events which are concrete individuals, as opposed to abstract (timeless) and general (property-like).2 Nevertheless the claim that events are concrete individuals faces a major hurdle. If events are concrete individuals, then it should be possible to provide identity conditions for them;3 for as Quine has cautioned us, "No entity without identity".4 Unfortunately, however, the most widely discussed proposals for such conditions, by Donald Davidson, John Lemmon and Jaegwon Kim, are beset with serious problems. In order to better understand the difficulties involved in formulating identity conditions for events, let us briefly review these three proposals, paying particular attention to the problems commonly associated with them.

176 citations


Journal ArticleDOI
01 Dec 1991-Synthese
TL;DR: The problem of logical omniscience in epistemic and doxastic logics has been investigated in this article, where the authors suggest that the divergence between the assumptions of the ideal theory and the facts about the domain of its intended application is described as a problem for epistemic logic.
Abstract: From their beginning, I epistemic and doxastic logics-the logics of knowledge and belief have been modeled on modal logic-the logic of necessity and possibility. Knowledge and belief, in such logics, are analogous to necessity. There is a wide variety of modal logics, but all of the normal ones contain certain distribution or deductive closure principles; for example, if '~-~ ~' is valid, then so is 'ES~-~ []~'. Most versions of epistemic logic are normal in this sense, accepting analogous principles for knowledge and belief. Developers of such logics invariably remark that the principles of deductive closure are unrealistic, since it is obviously false that knowers in general know all of the deductive consequences of anything that they know. The assumption that knowers do, as a matter of logic, have such knowledge-that they are deductively omniscient-is defended as an idealization. Sometimes the divergence between the assumptions of the ideal theory and the facts about the domain of its intended application is described as a problem for epistemic logic-the problem of logical omniscience. My aim in this paper is to try to get clear about just what kind of idealization such normal epistemic and doxastic logics are making, and what the motivation is for idealizing in this way. If there is a problem of logical omniscience, I want to try to see if I can say what the problem is. My broader aim is to try to get clearer about the concepts of knowledge and belief, and about what work we should expect a logic of these concepts to do. I shall begin by contrasting two different ways that the divergence between idealization and reality might be explained, and considering several different kinds of reasons that one might have for idealizing in one or the other of the two ways. Then I shall look at the problem of logical omniscience from the perspective of a certain conception of the nature of belief, the sentence storage model. I have little sympathy with this influential conception of belief; I think the problem of logical omniscience helps to bring out its limitations, and to point the way to a more adequate conception. But the problem of logical omniscience is not solved by giving up the sentence storage model. I shall suggest, 426 ROBERT STALNAKER in conclusion, that it is a symptom of a tension in our ordinary conceptions of knowledge and belief. 2 1. IDEALIZATION …

116 citations


Journal ArticleDOI
01 Aug 1991-Synthese
TL;DR: In this article, four pervasive myths about mathematics are discussed and the acceptance of these myths is related to whether one is located in the front or the back of the hierarchy of nodes.
Abstract: It is explained that, in the sense of the sociologist Erving Goffman, mathematics has a front and a back. Four pervasive myths about mathematics are stated. Acceptance of these myths is related to whether one is located in the front or the back.

90 citations


Journal ArticleDOI
01 Dec 1991-Synthese

64 citations


Journal ArticleDOI
01 Apr 1991-Synthese
TL;DR: In 1923 C. I. Lewis as discussed by the authors wrote to F. J. Woodbridge, editor of The Journal of Philosophy: "I am discouraged by Russell's foolishness in writing the introduction to such nonsense. I fear it will be looked upon as what symbolic logic leads to."
Abstract: In 1923 C. I. Lewis wrote to F. J. Woodbridge, editor of The Journal of Philosophy: Have you looked at Wittgenstein’s new book yet? I am discouraged by Russell’s foolishness in writing the introduction to such nonsense. I fear it will be looked upon as what symbolic logic leads to. If so, it will be the death of the subject. 1

60 citations


Journal ArticleDOI
01 Jul 1991-Synthese
TL;DR: In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences.
Abstract: In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895)

51 citations


Journal ArticleDOI
Steve Gerrard1
01 Apr 1991-Synthese
TL;DR: The calculus conception of Wittgenstein's philosophy of mathematics has long been notorious as mentioned in this paper, but it has not been recognized that Wittdenstein, in fact, had two chief post-Tractatus conceptions of mathematics: the calculus conception and the language game conception.
Abstract: Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period. The goal of my article is to provide a new framework for examining Wittgenstein's philosophies of mathematics and the evolution of his career as a whole. I posit the Hardyian Picture, modelled on the Augustinian Picture, to provide a structure for Wittgenstein's work on the philosophy of mathematics. Wittgenstein's calculus period has not been properly recognized, so I give a detailed account of the tenets of that stage in Wittgenstein's career. Wittgenstein's notorious remarks on contradiction are the test case for my theory of his transition. I show that the bizarreness of those remarks is largely due to the calculus conception, but that Wittgenstein's later language-game account of mathematics keeps the rejection of the Hardyian Picture while correcting the calculus conception's mistakes.

47 citations


Journal ArticleDOI
01 Oct 1991-Synthese
TL;DR: In this article, a critical evaluation of the philosophical presuppositions and implications of two current schools in the sociology of knowledge: the Strong Programme of Bloor and Barnes; and the Constructivism of Latour and Knorr-Cetina is given.
Abstract: This paper gives a critical evaluation of the philosophical presuppositions and implications of two current schools in the sociology of knowledge: the Strong Programme of Bloor and Barnes; and the Constructivism of Latour and Knorr-Cetina. Bloor's arguments for his externalist symmetry thesis (i.e., scientific beliefs must always be explained by social factors) are found to be incoherent or inconclusive. At best, they suggest a Weak Programme of the sociology of science: when theoretical preferences in a scientific community, SC, are first internally explained by appealing to the evidence, e, and the standards or values, V, accepted in SC, then a sociologist may sometimes step in to explain why e and V were accepted in SC. Latour's story about the ‘social construction’ of facts in scientific laboratories is found to be misleading or incredible. The idea that scientific reality is an artifact turns out to have some interesting affinities with classical pragmatism, instrumentalism, phenomenology, and internal realism. However, the constructivist account of theoretical entities in terms of negotiation and social consensus is less plausible than the alternative realist story which explains consensus by the preexistence of mind-independent real entities. The author concludes that critical scientific realism, developed with the concept of truthlikeness, is compatible with the thesis that scientific beliefs or knowledge claims may be relative to various types of cognitive and practical interests. However, the realist denies, with good reasons, the stronger type of relativism which takes reality and truth to be relative to persons, groups, or social interests.

39 citations


Journal ArticleDOI
01 Feb 1991-Synthese
TL;DR: In this paper, the authors suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning might explain the unattractiveness of evidentialism in other cases.
Abstract: Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a natural though unwarranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem.

Book ChapterDOI
01 May 1991-Synthese
TL;DR: Wittgenstein arranged the Tractatus in its final form during the summer of 1918; Part I of the Philosophical Investigations was put into the form in which we now have it during the mid 1940s as discussed by the authors.
Abstract: Wittgenstein arranged the Tractatus in its final form during the summer of 1918; Part I of the Philosophical Investigations was put into the form in which we now have it during the mid 1940s. The Tractatus was published in 1922; the Philosophical Investigations in 1953, two years after Wittgenstein’s death. Because the two books were widely studied and interpreted at a time when the rest of his writing was unavailable, it became common practice to speak of the author of the first book as “Early Wittgenstein”, and the author of the second as the “Late Wittgenstein”. As it gradually became clear that his writing during the intervening years was not only voluminous, but also could not simply be understood as a rejection of one view and the adoption of another, it was natural to speak of the author of this further body of writing, or at least those parts of it which could not be regarded as “Early”, or “Late”, as “Middle Wittgenstein”.

Journal ArticleDOI
01 Dec 1991-Synthese
TL;DR: For instance, the authors argued that self-deception is an intentional achievement, while others object that it cannot be intentional, because that would not be reconcilable with the concept of belief.
Abstract: After all that phiIosophers have written about self-deception in the last quarter of a century, there is little agreement between them about the right way to analyse it, or even about the meanings of the various analyses that have been proposed. Views range between extremes which are, at least verbally, far removed from one another. Some say that self-deception is an intentional achievement, while others object that it cannot be intentional, because that would not be reconcilable with the concept of belief. The difficulty might seem to be circumvented by the postulation of a separate centre of agency within the self-deceiver, but this suggestion has been criticised both for lack of credibility and, more radically, for incoherence. The nature of the terrain may have encouraged extremism. It lay to one side of the main track of post-war philosophy of mind, comparatively untrampled and awaiting development. Those who moved into it often underestimated the complexity of the phenomena and offered a single idea which they promoted without much attention to possible alternatives. If their theories caricatured their rivals, they also caricatured themselves. My contribution to the subject I was not a single explanation for the whole range of the phenomena, but I did develop the idea of the intentional biassing of belief in a form which looked, and may actually have been, exaggerated. This idea would evidently have very little explanatory power if it were not reinforced by the postulation of a rational sub-system, perhaps a separate centre of agency, insulated in some way from the main system which largely controls a person's life. However, my characterisation of sub-systems was too extreme in style, if not in content, and it drew the criticism that such a drastic hypothesis was not really needed in order to explain something so simple and commonplace as self-deception. Mark Johnston argues in a recent article 2 that the theory that selfdeception is produced by sub-systems operating intentionally is incoherent rather than incredible. So, he looks for another explanation and

Journal ArticleDOI
Richard Foley1
01 Dec 1991-Synthese
TL;DR: The distinction between evidential and non-evidential reasons for belief is discussed in this paper, where it is argued that pragmatic benefits are in principle relevant to questions of rational belief, but in general these benefits are best won by believing that for which we have adequate evidence.
Abstract: Epistemologists have tended to treat questions about the rationality of our beliefs as if they were fundamentally different from questions about the rationality of our decisions, actions, strategies, and plans. A more promising strategy is to construe the theory of rational belief as a part of a general theory of rationality. In any event, the following will be my strategy. I shall sketch a way of thinking about questions of rationality wherever they arise, whether they be questions concerning the rationality of our decisions, actions, strategies, or whatever. This perfectly general theory of rationality can then be applied to questions of rational belief. But this sketch will be a preliminary to the main matter to be discussed, which concerns the different kinds of reasons we can have to believe something. The most interesting divide is between evidential and non-evidential reasons for belief. The general theory of rationality that I sketch provides a framework within which this distinction can be appreciated and possible conflicts between the two kinds of reasons assessed. In doing so, it reveals a middle ground between 'evidentialists', who insist that there are never good non-evidential reasons for belief, and 'Pascalians', who insist that non-evidential reasons are in no way inferior to evidential ones. The correct position, I shall argue, is between the two: pragmatic benefits are in principle relevant to questions of rational belief, but in general these benefits are best won by believing that for which we have adequate evidence. One way of challenging this position is to cite the important role that simplicity and other theoretical virtues play in our intellectual lives. On the face of it, considerations of simplicity might seem to give us a good pragmatic but not a good evidential reason to believe a hypothesis. But, if so, our evidential and non-evidential reasons for belief threaten to come apart, not just occasionally but regularly. The threat is more apparent than real, however, and the way to see this is to be careful enough about two distinctions. The first is the distinction between evidential reasons and non-evidential reasons for belief, and the second is the distinction between genuine belief and

Journal ArticleDOI
01 Mar 1991-Synthese
TL;DR: In this paper, the authors discuss the virtues of stit against the background of proposals made by these philososphers, including Von Wright, Chisholm, Kenny, and Castaneda.
Abstract: Stit, a sentence form first introduced in Belnap and Perloff (1988), encourages a modal approach to agency. Von Wright, Chisholm, Kenny, and Castaneda have all attempted modal treatments of agency, while Davidson has rejected such treatments. After a brief explanation of the syntax and semantics of stit and a restatement of several of the important claims of the earlier paper, I discuss the virtues of stit against the background of proposals made by these philososphers.

Journal ArticleDOI
01 Oct 1991-Synthese
TL;DR: The relationship between common-sense psychology (CSP) and scientific psychology (SP) is explored in this article, where the authors examine the many differences between the aims, interests, explananda, explanantia, methodology, conceptual frameworks, and relationships to the neurosciences that divide CSP and SP.
Abstract: This paper explores the relationship between common-sense psychology (CSP) and scientific psychology (SP) — which we could call the mind-mind problem. CSP has come under much attack recently, most of which is thought to be unjust or misguided. This paper's first section examines the many differences between the aims, interests, explananda, explanantia, methodology, conceptual frameworks, and relationships to the neurosciences, that divide CSP and SP. Each of the two is valid within its own territory, and there is no competition between them — primarily because CSP is not, and has no interest in being, a ‘scientific theory’. In the second section some implications are drawn. First, neither CSP nor SP has the mind-body problem in its familiar form. Second, CSP, for excellent reasons, is not equipped to handle irrational or non-rational behaviour; there are some grounds for believing that this can and should be the task of SP. Third, ‘philosophical psychology’, or armchair ‘theories’ of action, perception, etc., are doomed to failure. And, fourth, the realm of the psychological is so heterogeneous that no single model for either CSP or SP is likely to succeed.


Journal ArticleDOI
01 Sep 1991-Synthese
TL;DR: The notion of a virtual person is developed, modelled on the concept of virtual machines familiar in computer science, and it is concluded that Searle is correct in holding that no digital machine could understand language, but wrong in Holding that artificial minds are impossible.
Abstract: Considerations of personal identity bear on John Searle's Chinese Room argument, and on the opposed position that a computer itself could really understand a natural language. In this paper I develop the notion of a virtual person, modelled on the concept of virtual machines familiar in computer science. I show how Searle's argument, and J. Maloney's attempt to defend it, fail. I conclude that Searle is correct in holding that no digital machine could understand language, but wrong in holding that artificial minds are impossible: minds and persons are not the same as the machines, biological or electronic, that realize them.



Journal ArticleDOI
01 Oct 1991-Synthese
TL;DR: The construction of scientific phenomena is the main topic of this paper and the view presented here is more adapted to realism than social constructivism.
Abstract: Assuming an essential difference between scientific data and phenomena, this paper argues for the view that we have to understand how empirical findings get transformed into scientific phenomena. The work of scientists is seen as largely consisting in constructing these phenomena which are then utilized in more abstract theories. It is claimed that these matters are of importance for discussions of theory choice and progress in science. A case study is presented as a starting point: paleomagnetism and the use of paleomagnetic data in early discussions of continental drift. Some general features of this study are presented in formalized language. It is suggested that the presentation given is particularly suited for a semantic conception of theories. Even though the construction of scientific phenomena is the main topic of this paper, the view presented here is more adapted to realism than social constructivism.

Journal ArticleDOI
01 Sep 1991-Synthese
TL;DR: This paper argued that the notion of "truthlikeness" is intrinsically language dependent and thus non-objective, and that it cannot supply a basis for an objective account of scientific progress.
Abstract: This paper proposes a solution to David Miller's ‘Minnesotan-Arizonan’ demonstration of the language dependence of truthlikeness (Miller 1974), along with Miller's first-order demonstration of the same (Miller 1978). It is assumed, with Peter Urbach, that the implication of these demonstrations is that the very notion of ‘truthlikeness’ is intrinsically language dependent and thus non-objective. As such, ‘truthlikeness’ cannot supply a basis for an objective account of scientific progress. I argue that, while Miller is correct in arguing that the number of true atomic sentences of a false theory is language dependent, the number of known sentences (under certain straightforward assumptions) is conserved by translation; ‘degree of knowledge’, unlike ‘truthlikeness’, is thus a linguistically invariant notion. It is concluded that the objectivity of scientific progress must be grounded on the fact (noted in Cohen 1980) that knowledge, not mere truth, is the aim of science.

Journal ArticleDOI
01 Nov 1991-Synthese
TL;DR: Propensities as mentioned in this paper describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics, characterized by the fact that their values are determined by the collection of all actual properties.
Abstract: Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.

Book ChapterDOI
01 May 1991-Synthese
TL;DR: In this article, a discussion of the importance of epistemology and the philosophy of language in the resolution of Moore's paradox is presented, and Wittgenstein's assessment of its importance is cited.
Abstract: Wittgenstein “once remarked that the only work of Moore’s that greatly impressed him was his discovery of the peculiar kind of nonsense involved in such a sentence as, e.g., ‘It is raining but I don’t believe it’”.1Present practice is to refer to the difficulties generated by sentences of this form, as well as to sentences of the form “I believe that p but not p”, as “Moore’s paradox”.2 Despite Wittgenstein’s great reputation and regard for the importance of Moore’s “discovery”, little interest has been generated in the topic. And yet, central issues in epistemology and the philosophy of language are involved in the resolution of this paradox. Since this is not generally appreciated, we begin our discussion by establishing what some of those important issues are, thereby crediting Wittgenstein’s assessment of the importance of the paradox. Then, we develop an account of the aberrant nature of Moore’s sentences (hereafter labelled “MS”) that is indebted to Wittgenstein, and which challenges the assumptions that motivate the standard form of discussion of these sentences initiated by Moore.

Journal ArticleDOI
01 Mar 1991-Synthese
TL;DR: In this article, a cognitive-motivational account of intention is proposed to explain both the explanation of action and the rationality of agents, and a holistic conception of intention formation and change is stressed.
Abstract: This paper defends a cognitive-motivational account of intending against recent criticism by J. Garcia, connects intending with a number of other concepts important in the theory of action — including decison, volition, and planning — and explores some principles of intention transfer construed as counterparts of epistemic principles governing closure for belief and justification. Several routes to intention formation are described; the role of intentions in planning is examined; and a holistic conception of intention formation and change is stressed. The proposed conception of intending as embodying at once a cognitive and a motivational commitment to action is thus shown to help in understanding both the explanation of action and the rationality of agents.

Book ChapterDOI
01 Aug 1991-Synthese
TL;DR: The question "Are mathematical ideas invented or discovered?" has been repeatedly posed by philosophers through the ages and will probably be with us forever as mentioned in this paper, and we will not be concerned with the answer.
Abstract: Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever. We will not be concerned with the answer. What matters is that by asking the question, we acknowledge that mathematics has been leading a double life.

Journal ArticleDOI
01 Jan 1991-Synthese
TL;DR: Many criticisms of prototype theory and/or fuzzy-set theory are based on the assumption that category representativeness (or typicality) is identical with fuzzy membership, but several arguments are made against the above identification, the most important being that represent ativeness in prototype theory is exclusively based on element-to-element similarity while fuzzy membership is inherently an element- to-category relationship.
Abstract: Many criticisms of prototype theory and/or fuzzy-set theory are based on the assumption that category representativeness (or typicality) is identical with fuzzy membership. These criticisms also assume that conceptual combination and logical rules (all in the Aristotelian sense) are the appropriate criteria for the adequacy of the above “fuzzy typicality”. The present paper discusses these assumptions following the line of their most explicit and most influential expression by Osheron and Smith (1981). Several arguments are made against the above identification, the most important being that representativeness in prototype theory is exclusively based on element-to-element similarity while fuzzy membership is inherently an element-to-category relationship. Also the above criteria for adequacy are criticized from the viewpoint of both prototype theory and fuzzy-set theory as well as from that of both conceptual and logical combination, and also from that of integration.

Journal ArticleDOI
01 Jul 1991-Synthese
TL;DR: In this article, it was shown that proofs by contradiction were a serious problem in seventeenth-century mathematics and philosophy, and positive mathematical developments emerged from such reflections, such as Cavalieri's and Guldin's mathematical programs of providing a development of parts of geometry free of proof by contradiction.
Abstract: In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism.

Journal ArticleDOI
01 Jul 1991-Synthese
TL;DR: In this article, it is shown that Kant's ought-can principle is incompatible with disjunctive obligation in standard deontic logic, and that none of the conflicting dilemma actions will in fact occur.
Abstract: In moral dilemmas, where circumstances prevent two or more equally justified prima facie ethical requirements from being fulfilled, it is often maintained that, since the agent cannot do both, conjoint obligation is overridden by Kant's principle that ‘ought’ implies ‘can’, but that the agent nevertheless has a disjunctive obligation to perform one of the otherwise obligatory actions or the other. Against this commonly received view, it is demonstrated that although Kant's ought-can principle may avoid logical inconsistency, the principle is incompatible with disjunctive obligation in standard deontic logic, and that it entails paradoxically that none of the conflicting dilemma actions will in fact occur. The principle appears to provide the only plausible safeguard against deontic antinomy, but cannot be admitted because of its collision with considered moral judgments.

Book ChapterDOI
01 May 1991-Synthese
TL;DR: Ludwig Wittgenstein died in 1951. At the time, the ideas he had developed after his return to philosophy in 1928 were known only to a handful of people through his lectures and conversations as discussed by the authors.
Abstract: Ludwig Wittgenstein died in 1951. At the time, the ideas he had developed after his return to philosophy in 1928 were known only to a handful of people through his lectures and conversations and through the typescripts which he had dictated and which were circulating among friends and colleagues. The wider philosophical community was eagerly waiting for Wittgenstein’s ideas to become effectively available.