Showing papers in "Synthese in 2002"
TL;DR: It is suggested that Putnam's, Kripke's and Wiggins' errors stem from adopting an account of the point of scientific classification which implies that relationally-defined kinds are likely to be of little value, an account which is inapplicable to biology.
Abstract: Biologists and philosophers of biology typically regard essentialism about species as incompatible with modern Darwinian theory. Analytic metaphysicians such as Kripke, Putnam and Wiggins, on the other hand, believe that their essentialist theses are applicable to biological kinds. I explore this tension. I show that standard anti-essentialist considerations only show that species do not have intrinsic essential properties. I argue that while Putnam and Kripke do make assumptions that contradict received biological opinion, their model of natural kinds, suitably modified, is partially applicable to biological species. However, Wiggins' thesis that organisms belong essentially to their species is untenable, given modern species concepts. I suggest that Putnam's, Kripke's and Wiggins' errors stem from adopting an account of the point of scientific classification which implies that relationally-defined kinds are likely to be of little value, an account which is inapplicable to biology.
231 citations
TL;DR: It is shown that the state of three-dimensional objects does not supervene on thestate of objects in 3N-dimensional space, and that the only way to guarantee the existence of the appropriate mental states in the wave function ontology has undesirable metaphysical baggage.
Abstract: I argue that the wave function ontology for quantum mechanics is an undesirable ontology. This ontology holds that the fundamental space in which entities evolve is not three-dimensional, but instead 3N-dimensional, where N is the number of particles standardly thought to exist in three-dimensional space. I show that the state of three-dimensional objects does not supervene on the state of objects in 3N-dimensional space. I also show that the only way to guarantee the existence of the appropriate mental states in the wave function ontology has undesirable metaphysical baggage: either mind/body dualism is true, or circumstances which we take to be logically possible turn out to be logically impossible.
81 citations
TL;DR: L'A.
Abstract: L'A. defend l'analyse conditionnelle de la dispositionnalite contre les objections fondees sur les principes stricts de la variation et de la compositionnalite. Examinant les contre-exemples qui cherchent a masquer les dispositions, ainsi que leurs versions contextualisee et modalisee, l'A. demontre l'inconsistance de l'operateur de dissimulation utilises par A. Bird et D. Lewis.
54 citations
TL;DR: A method is described that, by combining Glymour's theory of bootstrapping and Hacking's arguments from microscopy, allows us to test IBE without begging any antirealist issues.
Abstract: Inference to the Best Explanation has become the subject of a lively debate in the philosophy of science. Scientific realists maintain, while scientific antirealists deny, that it is a compelling rule of inference. It seems that any attempt to settle this debate empirically must beg the question against the antirealist. The present paper argues that this impression is misleading. A method is described that, by combining Glymour's theory of bootstrapping and Hacking's arguments from microscopy, allows us to test IBE without begging any antirealist issues.
52 citations
TL;DR: In modern terms Leibniz introduced `Riemannian sums' in order to demonstrate the integrability of continuous functions and with Lebniz's handling of infinitely small and infinite quantities, and with a general theorem regarding hyperboloids.
Abstract: In 1675, Leibniz elaborated his longest mathematical treatise he everwrote, the treatise ``On the arithmetical quadrature of the circle, theellipse, and the hyperbola. A corollary is a trigonometry withouttables''. It was unpublished until 1993, and represents a comprehensive discussion of infinitesimalgeometry. In this treatise, Leibniz laid the rigorous foundation of thetheory of infinitely small and infinite quantities or, in other words,of the theory of quantified indivisibles. In modern terms Leibnizintroduced `Riemannian sums' in order to demonstrate the integrabilityof continuous functions. The article deals with this demonstration,with Leibniz's handling of infinitely small and infinite quantities,and with a general theorem regarding hyperboloids.
51 citations
TL;DR: A naturalistic-cum-formal analysis of therelation between beauty, empirical success, and truth, which supports the findings of James McAllister in his beautifulBeauty and Revolution in Science (1996), by explaining and justifying them.
Abstract: In this article I give a naturalistic-cum-formal analysis of therelation between beauty, empirical success, and truth. The analysis is based on the onehand on a hypothetical variant of the so-called `mere-exposure effect' which has been more orless established in experimental psychology regarding exposure-affect relationshipsin general and aesthetic appreciation in particular (Zajonc 1968; Temme 1983; Bornstein 1989;Ye 2000). On the other hand it is based on the formal theory of truthlikeness andtruth approximation as presented in my From Instrumentalism to Constructive Realism (2000).The analysis supports the findings of James McAllister in his beautifulBeauty and Revolution in Science (1996), by explaining and justifying them.First, scientists are essentially right in regarding aesthetic criteria useful for empiricalprogress and even for truth approximation, provided they conceive of them as less hard thanempirical criteria. Second, the aesthetic criteria of the time, the `aesthetic canon', maywell be based on `aesthetic induction' regarding nonempirical features of paradigms of successfultheories which scientists have come to appreciate as beautiful. Third, aestheticcriteria can play a crucial, schismatic role in scientific revolutions. Since they may well be wrong, they may, in the hands of aesthetic conservatives, retard empirical progress and hence truth approximation, but this does not happen in the hands of aesthetically flexible, `revolutionary' scientists.
44 citations
TL;DR: This volume of Synthese is devoted to some general epistemological issues treated from the point of view of a particular program for modelling empirical science known in the literature as “structuralism”.
Abstract: This volume of Synthese is devoted to some general epistemological issues treated from the point of view of a particular program for modelling empirical science known in the literature as “structuralism”. This is not a very adequate label for the program in question, since it may be confused with other approaches in philosophy and the social sciences that have been labelled the same way but have (almost) nothing to do with the present one. It might have been a bit less confusing to call it “metatheoretical, or metascientific, or still methodological structuralism”. But, for the sake of brevity, let us keep the usual denomination here. It is unlikely that a reader of Synthese gets thereby confused. So, structuralism in this sense provides a \"model\" for empirical science. I use the term “model” here in its non-technical, rather ordinary sense; not in the sense of formal semantics. Physicists, chemists, social scientists, etc. often tell us they are devising or advancing a “model” of a particular piece of the experiential world; very likely, they have never heard about Tarski’s model theory, nor about the formal definition of a model; but they think they are using the term “model” in a sensible way and most people who listen to them also seem to think so. In this somewhat uncompromising but useful sense of the term, a “model” is supposed to be a more or less mathematized array of specific concepts and principles intended to represent some essential aspects of a particular piece of empirical reality. Of course, the formally-minded philosopher would probably prefer to speak of a “theory” here; but the good thing about this use of “model” in the scientists’ ordinary language is that it conveys some associated intuitions that are not normally found in the usage of “theory” by scientists and philosophers alike: (a) the “model” is not supposed to cover all aspects of the empirical domain depicted by it, not even all of those considered important for some reason or other; (b) the “model” is not supposed to provide the ultimate truth about the domain in question, whatever this might be; this has as an implication, among other things, that (b′) if you are willing to work with “model” m to examine empirical domain D, this does not preclude that you might also be willing to work with a quite different “model” m′ to examine
44 citations
TL;DR: This paper examines two accounts of (apparently) violated laws, thatthey are merely ceteris paribus laws and that they areifestations of capacities and shows that given a proper understanding of the situation, neither view is optimal because the law is not even apparently violated.
Abstract: It is often claimed that the bulk of the laws of physics –including such venerable laws as Universal Gravitation– are violated in many (or even all) circumstances because they havecounter-instances that result when a system is not isolated fromother systems. Various accounts of how one should interpretthese (apparently) violated laws have been provided. In thispaper, I examine two accounts of (apparently) violated laws, thatthey are merely ceteris paribus laws and that they aremanifestations of capacities. Through an examination of theprimary example that motivated these views, I show that given aproper understanding of the situation, neither view is optimalbecause the law is not even apparently violated. Along the way, Iam able to diagnose what has led to the mistaken belief: I showthat it originates from an element of the standard empiricistconception of laws. I then evaluate the suggestions of how tointerpret violated laws with respect to other examples and findthem wanting there too.
38 citations
TL;DR: It is argued that people usually do have reasons, in the sense of propositions believed, for accepting testimony and these reasons can provide evidence for the testimonial beliefs the authors form.
Abstract: The assumption that we largely lack reasons for accepting testimony has dominated its epistemology. Given the further assumption that whatever reasons we do have are insufficient to justify our testimonial beliefs, many conclude that any account of testimonial knowledge must allow credulity to be justified. In this paper I argue that both of these assumptions are false. Our responses to testimony are guided by our background beliefs as to the testimony as a type, the testimonial situation, the testifier's character and the truth of the proposition testified to. These beliefs provide reasons for our responses. Thus, we usually do have reasons, in the sense of propositions believed, for accepting testimony and these reasons can provide evidence for the testimonial beliefs we form.
35 citations
TL;DR: A diagnosis of what has gone wrong with the indispensability argument is offered, and it is suggested that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.
Abstract: For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue from Mark Colyvan's (1998) attempt to provide a Quinean account of unapplied mathematics as `recreational', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.
28 citations
TL;DR: The token-reflexive version of time is defended against a string of objections from Quentin Smith, which involves a discussion of the ontological and semantic significance of truth conditions, and of the connection betweentruth and reality on the one hand, and that between truth and meaning on the other.
Abstract: There are two extant versions of the new tenseless theory of time: the date versionand the token-reflexive version. I ask whether they are equivalent, and if not, whichof them is to be preferred. I argue that they are not equivalent, that the date version isunsatisfactory, and that the token-reflexive version is correct. I defend the token-reflexive version against a string of objections from Quentin Smith. My defence involves a discussion of the ontological and semantic significance of truth conditions, and of the connection between truth and reality on the one hand, and that between truth and meaning on the other. I argue that Smith's objections to the token-reflexive theory stem from his confusing these two aspects of the notion of truth.
TL;DR: Comparison of the two approaches shows that perennial and severe theoretical obstacles stand in the way of giving an epistemology of the structure of experience, a central requirement for both philosophers’ theories and sheds new light on the reasons for the historically decisive split between the continental and the analytic traditions.
Abstract: Over a period of several decades spanning the origin of the Vienna Circle, Schlick repeatedly attacked Husserl's phenomenological method for its reliance on the ability to intuitively grasp or see essences. Aside from its significance for phenomenolo- gists, the attack illuminates significant and little-explored tensions in the history of analytic philosophy as well. For after coming under the influence of Wittgenstein, Schlick proposed to replace Husserl's account of the epistemology of propositions describing the overall structure of experience with his own account based on the structure of language rather than on the intuition of essences. I discuss both philosophers' accounts of the epistem- ology of propositions describing the structure of experience. For both philosophers, this epistemology was closely related to the general epistemology of logic; nevertheless, neither philosopher had a completely coherent account of it. Comparison of the two approaches shows that perennial and severe theoretical obstacles stand in the way of giving an epistem- ology of the structure of experience, a central requirement for both philosophers' theories. Consideration of these obstacles sheds a new light on the reasons for the historically decis- ive split between the continental and the analytic traditions, as well as on the subsequent development of the analytic tradition away from the structural description of experience. Beginning in the early twentieth century, the idea that our sensory exper- ience of the world has a specific logical structure or form became the basis for a variety of prominent epistemological projects. Most signific- antly for the subsequent development of twentieth-century philosophy, the idea of a connection between the structure of experience and the logical form of knowledge was shared between Husserl's phenomenology and the logical positivism of Schlick and the Vienna circle. But the two schools' agreement on the outlines of the general project of scientific epistemology concealed the wide differences of philosophical attitude and aim between them; and it was precisely on the question of the epistemology and on- tology of the logical form of experience that phenomenology and logical positivism would first publicly diverge, in a dispute between Schlick and Husserl conducted over a long period spanning the origin of the Vienna Circle. In the debate, questions about the logical form of experience in- creasingly became the source of a web of methodological and thematic disagreements concerning the nature of conceptual analysis, the epistem-
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TL;DR: One of the most disputed issues in contemporary philosophy is the following: should the authors admit a vericonditional theory of meaning, which makes room for truth-cond conditions that possibly transcend their ability to know whether they are fulfilled or not, or rather, as the anti-realist suggests, should they replace these conditions by assertability-conditions whose fulfillment, when obtaining, cannot fail to be recognized?
Abstract: One of the most disputed issues in contemporary philosophy is the following: should we admit a vericonditional theory of meaning, which makes room for truth-conditions that possibly transcend our ability to know whether they are fulfilled or not, or rather, as the anti-realist suggests, should we replace these conditions by assertability-conditions whose fulfillment, when obtaining, cannot fail to be recognized? I will not declare myself in this debate, which is notoriously difficult to adjudicate and which tends to look like a dialogue of the deaf on the own confession of some of its protagonists (Wright 1986, 252). For a long time – and one is still in the habit of summing up the matter this way – the controversy has been taken as essentially dealing with the general possibility, for truth, to transcend the recognizability of truth: what the realist would admit, and what the anti-realist, for her part, would deny, is the possibility for a sentence to be true and yet generally not to be likely to be recognized as such. By now however, that demarcation is widely considered inadequate. As Dummett himself eventually recognized in his 1972 postscript to ‘Truth’ (1978, 23– 24), a realist could very well accept the principle of non-transcendence for truth by granting that any truth ought to be recognizable as such, if not by us, at least by some hypothetical being whose intellectual capacities and observing powers would exceed at will those with which we are endowed. As far as she professes a doctrine that significantly differs from realism, the anti-realist is therefore committed to a general definition of the conditions under which, contrary to creatures that could be more or less emancipated from our cognitive or physical limitations, we are ourselves, we human beings are able to recognize the truth of a sentence, that is to recognize the conditions under which a sentence is assertable by us in the first place. In the sequel I shall confine myself to that only question. In other words, I shall not examine whether it might be legitimate or necessary to wholly
TL;DR: It is demonstrated that extensional higher-order resolution is the sole approach that can completely avoid additional extensionality axioms.
Abstract: We investigate several approaches to resolution based automated theoremproving in classical higher-order logic (based on Church's simply typedλ-calculus) and discuss their requirements with respect to Henkincompleteness and full extensionality. In particular we focus on Andrews' higher-order resolution (Andrews 1971), Huet's constrained resolution (Huet1972), higher-order E-resolution, and extensional higher-order resolution(Benzmuller and Kohlhase 1997). With the help of examples we illustratethe parallels and differences of the extensionality treatment of these approachesand demonstrate that extensional higher-order resolution is the sole approach thatcan completely avoid additional extensionality axioms.
TL;DR: L'A.
Abstract: L'A. delimite le cadre general d'une theorie de l'individuation des concepts qui consiste a fixer leurs conditions de possession. A partir d'outils structuralistes, comme la distinction entre observabilite et non-theoreticite, et la notion de reseau theorique, l'A. defend l'integration de plusieurs approches: celle de la regle de correspondance, de l'application des lois chez Kuhn et de l'operationnalisme moderne.
TL;DR: It is shown that Bourbaki's definition of the number 1 runs to some tens of thousands of symbols, but that is a considerable under-estimate, the true number of symbols being that in the title.
Abstract: Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.
TL;DR: This paper provides a common framework for the discussion of both the local and global methods of analysis of Newtonian supertasks, and the areas of disagreement and agreement are made explicit.
Abstract: A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton's laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in a Banach space, to determine the origin of the strange behavior. This paper provides a common framework for the discussion of both the local and global methods of analysis. Using this single framework, the areas of disagreement and agreement are made explicit. Further examples of supertasks are proposed to illuminate various aspects of the discussion.
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TL;DR: It is given a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n.
Abstract: I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals.
TL;DR: It is argued that one influential epistemological response to the so-called `McKinsey paradox' fails to meet the challenge posed by McKinsey but that, if it is set within an externalist epistemology, it may have application to a related paradox that concerns the problem of radical scepticism.
Abstract: A great deal of discussion in the recent literature has been devoted to the so-called `McKinsey' paradox which purports to show that semantic externalism is incompatible with the sort of authoritative knowledge that we take ourselves to have of our own thought contents In this paper I examine one influential epistemological response to this paradox which is due to Crispin Wright and Martin Davies I argue that it fails to meet the challenge posed by McKinsey but that, if it is set within an externalist epistemology, it may have application to a related paradox that concerns the problem of radical scepticism
TL;DR: It is emphasized that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of `` reducibility,'' and some mathematical results proved in this paper.
Abstract: In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility'' This claimrests on some mathematical results proved in this paper
TL;DR: In this paper, it was shown that every physical theory since Newton explains without drawing attention to causes, and that, in other words, physical theories as physical theories aspire to explain under an ideal quite distinct from that of causal explanation.
Abstract: I shall endeavor to show that every physical theory since Newton explains without drawing attention to causes-that, in other words, physical theories as physical theories aspire to explain under an ideal quite distinct from that of causal explanation. If I am right, then even if sometimes the explanations achieved by a physical theory are not in violation of the standard of causal explanation, this is purely an accident. For physical theories, as I will show, do not, as such, aim at accommodating the goals or aspirations of causal explanation. This will serve as the founding insight for a new theory of explanation, which will itself serve as the cornerstone of a new theory of scientific method.
TL;DR: It is argued that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules, and how quite a number of achievements of Pollocks' account can be adequately duplicated within ranking theory.
Abstract: In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology.
TL;DR: Modalmetaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantumstatistics.
Abstract: Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical partition functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics.
TL;DR: An approach to inference to the best explanation integrating a Popperian conception of natural laws together with a modified Hempelian account of explanation and Hacking's law of likelihood provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist, deductivist, and hypothetico-deductivist alternatives.
Abstract: An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important elements of this conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense.
TL;DR: It is argued that both sides of this debate on the nature of Rudolf Carnap's project in his 1928 book The Logical Structure of the World or Aufbau have made errors in their interpretation of Russell.
Abstract: This paper concerns the debate on the nature of Rudolf Carnap'sproject in his 1928 book The Logical Structure of the Worldor Aufbau. Michael Friedman and Alan Richardson haveinitiated much of this debate. They claim that the Aufbauis best understood as a work that is firmly grounded inneo-Kantian philosophy. They have made these claims in oppositionto Quine and Goodman's ``received view'' of the Aufbau. Thereceived view sees the Aufbau as an attempt to carry out indetail Russell's external world program. I argue that both sidesof this debate have made errors in their interpretation ofRussell. These errors have led these interpreters to misunderstandthe connection between Russell's project and Carnap's project.Russell in fact exerted a crucial influence on Carnap in the1920s. This influence is complicated, however, due to the factthat Russell and Carnap disagreed on many philosophical issues. Iconclude that interpretations of the Aufbau that ignoreRussell's influence are incomplete.
TL;DR: It is argued that there exists a tight correlation between the occurrence of these two holistic phenomena, a specific form of underdetermination of terms which occur in the fundamental principles of an empirical theory, and the shaping of the theory's protective belt.
Abstract: The goal of this article is to show that the structuralist approachprovides a powerful framework for the analysis of certain holistic phenomena in empirical theories.We focus on two aspects of holism. The first refers to the involvement of comprehensive complexes of hypothesesin the theoretical treatment of systems regarded in isolation. By contrast, the second refers to thecorrelation between the theoretical descriptions of different systems. It is demonstrated how these two aspectscan be analysed by making use of the structuralist notion of theory-nets, and how they are reflected by a refinedversion of the Ramsey sentence. Furthermore, it is argued that there exists a tight correlation between theoccurrence of these two holistic phenomena, a specific form of underdetermination of terms which occur in thefundamental principles of an empirical theory, and the shaping of the theory's protective belt. After having dealtwith these questions in abstracto, the relevance of these considerations for a better understanding of the dynamicsof empirical theories is demonstrated in a concrete case study. It refers to the role holistic phenomenaplayed in the investigation of the anomalous advance of Mercury's perihelion and in the various attempts to eliminate this anomaly.
TL;DR: It is argued that a closer cooperation between general historians and historians of mathematics might further the integration of the internalist and externalist approaches within the historiography of mathematics.
Abstract: Choosing the history of statistics and operations research as a casestudy, several ways of setting the development of 20th century appliedmathematics into a social context are discussed. It is shown that there isample common ground between these contextualizations and several recent research programs in general contemporary history. It is argued that a closer cooperation between general historians and historians ofmathematics might further the integration of the internalist andexternalist approaches within the historiography of mathematics.
TL;DR: It is argued that in almost all cases, the ``single case'' application of probability can be accounted for otherwise, and ``Propensities'' are needed only intheoretical contexts, and even there applications of probability need only depend on propensities indirectly.
Abstract: The dominant argument for the introduction ofpropensities or chances as an interpretation of probabilitydepends on the difficulty of accounting for single caseprobabilities. We argue that in almost all cases, the``single case'' application of probability can be accountedfor otherwise. ``Propensities'' are needed only intheoretical contexts, and even there applications ofprobability need only depend on propensities indirectly.
TL;DR: How some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics are described and an answer to this question is sketched that uses some ideas of a philosopher to whom Gödel turned in this connection: Edmund Husserl.
Abstract: Godel has argued that we can cultivate the intuition or ‘perception’ of abstractconcepts in mathematics and logic. Godel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Godel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central question that has been raised in the literature on Godel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Godel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward ‘objects’ and the meaning of the term ‘abstract’ in the context of a theory of the intentionality of cognition.
TL;DR: It is suggested, in opposition to both structuralism and explanation, that a causal account of explanation might also sit well with structuralism.
Abstract: This paper is about structuralism as a form of reconstructing theories, associated with the work Sneed, Balzar and Moulines among others, and not about "structuralism" is any of its other manifold senses. The paper is a reflection in that it looks back on some earlier work of my own on the subject of structuralism and explanation, in which I argued that structuralism and my 'instance view' of explanation go well together, with structuralism providing the means to develop the idea of a theoretical instance. Bartelborth has suggested a view that has some similarity with my early ideas, so I reflect on those as well. I suggest, in opposition to both positions, that a causal account of explanation might also sit well with structuralism. This paper will appear in a special edition of Synthese edited by Moulines and devoted to structuralism themes.