Abstract:This paper investigates the claim that some truths are fundamentally or really trueand that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense.I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate… Show more
“…However, there is no inconsistency in saying that the concept of naturalness can play an important role in an account of substantivity and conventionality even though there are no reference magnets. See Williams (2010) for a theory of fundamentality that is similar in spirit. 41 Sider (2011: p. 50).…”
In the International System of Units (SI), 'meter' is defined in terms of seconds and the speed of light, and 'second' is defined in terms of properties of cesium 133 atoms. I show that one consequence of these definitions is that: if there is a minimal length (e.g., Planck length), then the chances that 'meter' is completely determinate are only 1 in 21,413,747. Moreover, we have good reason to believe that there is a minimal length. Thus, it is highly probable that 'meter' is indeterminate. If the meter is indeterminate, then any unit in the SI system that is defined in terms of the meter is indeterminate as well. This problem affects most of the familiar derived units in SI. As such, it is highly likely that indeterminacy pervades the SI system. The indeterminacy of the meter is compared and contrasted with emerging literature on indeterminacy in measurement locutions (as in Eran Tal's recent argument that measurement units are vague in certain ways). Moreover, the indeterminacy of the meter has ramifications for the metaphysics of measurement (e.g., problems for widespread assumptions about the nature of conventionality, as in Theodore Sider's Writing the Book of the World) and the semantics of measurement locutions (e.g., undermining the received view that measurement phrases are absolutely precise as in Christopher Kennedy's and Louise McNally's semantics for gradable adjectives). Finally, it is shown how to redefine 'meter' and 'second' to completely avoid the indeterminacy.
“…However, there is no inconsistency in saying that the concept of naturalness can play an important role in an account of substantivity and conventionality even though there are no reference magnets. See Williams (2010) for a theory of fundamentality that is similar in spirit. 41 Sider (2011: p. 50).…”
In the International System of Units (SI), 'meter' is defined in terms of seconds and the speed of light, and 'second' is defined in terms of properties of cesium 133 atoms. I show that one consequence of these definitions is that: if there is a minimal length (e.g., Planck length), then the chances that 'meter' is completely determinate are only 1 in 21,413,747. Moreover, we have good reason to believe that there is a minimal length. Thus, it is highly probable that 'meter' is indeterminate. If the meter is indeterminate, then any unit in the SI system that is defined in terms of the meter is indeterminate as well. This problem affects most of the familiar derived units in SI. As such, it is highly likely that indeterminacy pervades the SI system. The indeterminacy of the meter is compared and contrasted with emerging literature on indeterminacy in measurement locutions (as in Eran Tal's recent argument that measurement units are vague in certain ways). Moreover, the indeterminacy of the meter has ramifications for the metaphysics of measurement (e.g., problems for widespread assumptions about the nature of conventionality, as in Theodore Sider's Writing the Book of the World) and the semantics of measurement locutions (e.g., undermining the received view that measurement phrases are absolutely precise as in Christopher Kennedy's and Louise McNally's semantics for gradable adjectives). Finally, it is shown how to redefine 'meter' and 'second' to completely avoid the indeterminacy.
“…21 For relevant discussion, see (Williams 2010). committed to the number zero, and that all that is required of the world for 'the number of the dinosaurs is zero' to be literally true is that there be no dinosaurs.…”
This paper is an effort to extract some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase-functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases.Although much of the material in this paper is drawn from the book-and from an earlier paper (Rayo 2008)-I hope the present discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications.
NominalismMathematical Nominalism is the view that there are no mathematical objets. A standard problem for nominalists is that it is not obvious that they can explain what the point of a mathematical assertion would be. For it is natural to think that mathematical sentences like 'the number of the dinosaurs is zero' or '1 + 1 = 2' can only be true if mathematical objects exist. But if this is right, the nominalist is committed to the view that such sentences are untrue. And if the sentences are untrue, it not immediately obvious why they would be worth asserting. * For their many helpful comments, I am indebted to Vann McGee, Kevin Richardson, Bernhard Salow and two anonymous referees for Philosophia Mathematica. I would also like to thank audiences at Smith College, the Università Vita-Salute San Raffaele, and MIT's Logic, Langauge, Metaphysics and Mind Reading Group. Most of all, I would like to thank Steve Yablo.
1A nominalist could try to address the problem by suggesting nominalistic paraphrases for mathematical sentences. She might claim, for example, that when one asserts 'the number of the dinosaurs is zero' one is best understood as making the (nominalistically kosher) claim that there are no dinosaurs, and that when one asserts '1 + 1 = 2' one is best understood as making the (nominalistically kosher) claim that any individual and any other individual will, taken together, make two individuals.1 Such a strategy faces two main challenges. The first is to explain why mathematical assertions are to be understood non-standardly. One way for our nominalist to address this challenge is by claiming that mathematical assertions are set forth 'in a spirit of makebelieve' (Yablo 2001). She might argue, in particular, that when one makes a mathematical assertion one is, in effect, claiming that the asserted sentence is true in a fiction, and more specifically a fiction according to which: (a) all non-mathematical matters are as in reality, but (b) mathematical objects exist with their standard properties. This proposal leads to the welcome result that fictionalist assertions of mathematical sentences can convey information about the real world. For instance, one can use a fictionalist assertion of 'the number of the dinosaurs is zero' to convey the information that there are no dinosaurs, since the only way for 'the number of the dinosaurs is zero' to be true in a fiction whereby mat...
“…But though fundamentality applies primarily to representations of reality, this doesn't imply that the subject matter of ontological inquiry is about representations of reality rather than reality itself. As Robbie Williams (, p.107) puts it:For the purposes of metaphysics, we are not just interested in what the true sentences or propositions are: we are interested in the way reality is, in the objects and properties and their arrangements that support the truth of the propositions. Only the propositions which most directly reflect this are fundamentally the case.…”
Section: Fundamentalitymentioning
confidence: 99%
“…(For an overview of Field's changing opinions about its adequacy, see the essays collected in Field (2001).) Compare Williams (2012) who also stresses that the 'translate-and-deflate' methodology described below plays a crucial role in Quine's conception of ontological inquiry. For an alternative reading of Quine, see Soames (2009).…”
In the recent literature on all things metaontological, discussion of a notorious Meinongian doctrine—the thesis that some objects have no kind of being at all—has been conspicuous by its absence. And this is despite the fact that this thesis is the central element of the noneist metaphysics of Richard Routley (1980) and Graham Priest (2005). In this paper, we therefore examine the metaontological foundations of noneism, with a view to seeing exactly how the noneist's approach to ontological inquiry differs from the orthodox Quinean one. We proceed by arguing that the core anti‐Quinean element in noneism has routinely been misidentified: rather than concerning Quine's thesis that to be is to be the value of a variable, the real difference is that the noneist rejects what we identify as Quine's “translate‐and‐deflate” methodology. In rejecting this aspect of Quinean orthodoxy, the noneist is in good company: many of those who think that questions of fundamentality should be the proper focus of ontological inquiry can be read as rejecting it too. Accordingly, we then examine the differences between the noneist's conception of ontology and that offered by the fundamentalist. We argue that these two anti‐Quinean approaches differ in terms of their respective conceptions of the theoretical role associated with the notion of being. And the contrast that emerges between them is, in the end, an explanatory one.
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