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Switch to: References
Citations of:
On What Possible Worlds Could Not Be
In S. Stich & A. Morton (eds.), Benacerraf and his Critics (1996)
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Jurado: Mario Gómez-Torrente (presidente), Miguel Ángel Fernández Vargas (vocal), Santiago Echeverri Saldarriaga (secretario). [Graduado con Mención Honorífica.]. |
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In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...) |
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I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are widely identified, (...) |
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Modal primitivists hold that some modal truths are primitively true. They thus seem to face a special epistemological problem: how can primitive modal truths be known? The epistemological objection has not been adequately developed in the literature. I undertake to develop the objection, and then to argue that the best formulation of the epistemological objection targets all realists about modality, rather than the primitivist alone. Furthermore, the moves available to reductionists in response to the objection are also available to primitivists. (...) |
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Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...) |
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This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...) |
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Modal contingentists face a dilemma: there are two attractive principles of which they can only accept one. In this paper I show that the most natural way of resolving the dilemma leads to expressive limitations. I then develop an alternative resolution. In addition to overcoming the expressive limitations, the alternative picture allows for an attractive account of arithmetic and for a style of semantic theorizing that can be helpful to contingentists. |
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Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas. |
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This article discusses the argument we cannot have knowledge of abstract entities because they are not part of the causal order. The claim of this article is that the argument fails because of equivocation. Assume that the “causal order” is concerned with contingent facts involving time and space. Even if the existence of abstract entities is not contingent and does not involve time or space it does not follow that no truths about abstract entities are contingent or involve time or (...) |
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In the introduction to his Realism, mathematics and modality, and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge. |
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In this paper, I argue that various disputes in ontology have important ramifications and so are worth taking seriously. I employ a criterion according to which whether a dispute matters depends on how integrated it is with the rest of our theoretical projects. Disputes that arise from previous tensions in our theorizing and have additional implications for other issues matter, while insular disputes do not. I apply this criterion in arguing that certain ontological disputes matter; specifically, the disputes over concrete (...) |
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There is a strong pull to the idea that there is some metaphysically interesting distinction between the fully real, objective, observer‐independent qualities of things as they are in themselves, and the less‐than‐fully‐real, subjective, observer‐dependent qualities of things as they are for us. Call this (putative) distinction the primary/secondary quality distinction. The distinction between primary and secondary qualities is philosophically interesting because it is (a) often quite attractive to draw such a distinction, and (b) incredibly hard to spell it out in (...) |
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There is a strong pull to the idea that there is some metaphysically interesting distinction between the fully real, objective, observer-independent qualities of things as they are in themselves, and the less-than-fully-real, subjective, observer-dependent qualities of things as they are for us. Call this (putative) distinction the primary/secondary quality distinction. The distinction between primary and secondary qualities is philosophically interesting because it is (a) often quite attractive to draw such a distinction, and (b) incredibly hard to spell it out in (...) |
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We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed. |
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The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are shorthand for ‘ordinary (...) |
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I outline a neo-Fregean strategy in the debate on the existence of possible worlds. The criterion of identity and the criterion of application are formulated. Special attention is paid to the fact that speakers do not possess proper names for worlds. A broadly Quinean solution is proposed in response to this difficulty. |
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I start by reconsidering two familiar arguments against modal realism. The argument from epistemology relates to the issue whether we can infer the existence of concrete objects by a priori means. The argument from pragmatics purports to refute the analogy between the indispensability of possible worlds and the indispensability of unobserved entities in physical science and of numbers in mathematics. Then I present two novel objections. One focusses on the obscurity of the notion of isolation required by modal realism. The (...) |
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I develop a technique for specifying truth-conditions. |
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