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Switch to: References
Citations of:
Nominalism and the contingency of abstract objects
Journal of Philosophy 89 (3):111-135 (1992)
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We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism. |
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Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...) |
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In a lot of domains in metaphysics the tacit assumption has been that whichever metaphysical principles turn out to be true, these will be necessarily true. Let us call necessitarianism about some domain the thesis that the right metaphysics of that domain is necessary. Necessitarianism has flourished. In the philosophy of maths we find it held that if mathematical objects exist, then they do of necessity. Mathematical Platonists affirm the necessary existence of mathematical objects (see for instance Hale and Wright (...) |
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Primitive, unanalysable grounding relations are considered by many to be indispensable constituents of the metaphysician’s toolkit. Yet, as a primitive ontological posit, grounding must earn its keep by explaining features of the world not explained by other tools already at our disposal. Those who defend grounding contend that grounding is required to play two interconnected roles: accounting for widespread intuitions regarding what is ontologically prior to what, and forming the backbone of a theory of metaphysical explanation, in much the same (...) |
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ABSTRACTAccording to Yablo, in uttering sentences that imply the existence of abstract objects, we do not assert their literal content. Instead, we only make a weaker conditional claim that does not have the controversial implication. In this commentary I argue that the conditional claims Yablo suggests we are making are true only if abstract objects exist and, thus, also carry the controversial implication. |
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Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s (...) |
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Platonists and nominalists disagree about whether mathematical objects exist. But they almost uniformly agree about one thing: whatever the status of the existence of mathematical objects, that status is modally necessary. Two notable dissenters from this orthodoxy are Hartry Field, who defends contingent nominalism, and Mark Colyvan, who defends contingent Platonism. The source of their dissent is their view that the indispensability argument provides our justification for believing in the existence, or not, of mathematical objects. This paper considers whether commitment (...) |
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The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) |
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The basic question of ontology is “What exists?”. The basic question of metaontology is: are there objective answers to the basic question of ontology? Here ontological realists say yes, and ontological anti-realists say no. (Compare: The basic question of ethics is “What is right?”. The basic question of metaethics is: are there objective answers to the basic question of ethics? Here moral realists say yes, and moral anti-realists say no.) For example, the ontologist may ask: Do numbers exist? The Platonist (...) |
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The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) |
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In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D. |
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Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics and modality, Blackwell, (...) |
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Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...) |
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This paper concerns Yablo’s theory of asserted content as it is developed in his new book Aboutness. Yablo’s central idea is that in order to specify the asserted content of a sentence, we have to subtract those parts of its full semantic content that concern irrelevant subject matters. The paper argues that it is doubtful whether Yablo’s account successfully deals with its most basic envisaged application: to account for a difference of apparent truth value in cases of ordinary presupposition failure. (...) |
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In Being Realistic About Reasons T. M. Scanlon argues that particular fact about reasons are explained by contingent non-normative facts together with pure normative principles. A question then arises about the modal status of these pure principles. Scanlon maintains that they are necessary in a sense, and suggests that they are ‘metaphysically’ necessary. I argue that the best view for Scanlon to take, given his other commitments, is that these pure normative principles are metaphysically contingent in some cases and necessary (...) |
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Metaphysics is supposed to tell us about the metaphysical nature of our world: under what conditions composition occurs; how objects persist through time; whether properties are universals or tropes. It is near orthodoxy that whichever of these sorts of metaphysical claims is true is necessarily true. This paper looks at the debate between that orthodox view and a recently emerging view that claims like these are contingent, by focusing on the metaphysical debate between monists and pluralists about concrete particulars. This (...) |
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I argue that there are Leibnizian-style cosmological arguments for the existence of God which start from very mild premises which affirm the mere possibility of a principle of sufficient reason. The utilization of such premises gives a great deal of plausibility to such types of argumentation. I spend the majority of the paper defending three major objections to such mild premises viz., a reductio argument from Peter van Inwagen and William Rowe, which proffers and defends the idea that a necessary (...) |
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Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) |
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Metaphysics is supposed to tell us about the metaphysical nature of our world: under what conditions composition occurs; how objects persist through time; whether properties are universals or tropes. It is near orthodoxy that whichever of these sorts of metaphysical claims is true is necessarily true. This paper looks at the debate between that orthodox view and a recently emerging view that claims like these are contingent, by focusing on the metaphysical debate between monists and pluralists about concrete particulars. This (...) |
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One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers. |
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It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence. |
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Mark Balaguer ha elaborado una peculiar variante del platonismo matemático –denominada ‘full-blooded platonism’ o ‘FBP’– para solucionar el problema de Benacerraf sobre la inaccesibilidad de las entidades abstractas. Según FBP, todos los objetos matemáticos consistentemente caracterizables existen, aunque de modo contingente. En este trabajo quisiera mostrar que la plenitud ontológica y la contingencia modal no pueden converger en una teoría de objetos matemáticos filosóficamente respetable. Para esto argumento que FBP no cubre algunos factores elementales de confiabilidad epistémica y que envuelve (...) |
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