The Honest Weasel A Guide for Successful Weaseling

Indispensability arguments are among the strongest arguments in support of mathematical realism. Given the controversial nature of their conclusions, it is not surprising that critics have supplied a number of rejoinders to these arguments. In this paper, I focus on one such rejoinder, Melia’s ‘Weasel Response’. The weasel is someone who accepts that scientific theories imply that there are mathematical objects, but then proceeds to ‘take back’ this commitment. While weaseling seems improper, accounts supplied in the literature have failed to explain why. Drawing on examples of weaseling in more mundane contexts, I develop an account of the presumption against weaseling as grounded in a misalignment between two types of commitments. This is good news to the weasel’s opponents. It reinforces that they were right to question the legitimacy of weaseling. This account is also beneficial to the weasel. Uncovering the source of the presumption against weaseling also serves to draw out the challenge that the weasel must meet to override this presumption—what is required to be an ‘honest weasel’.

What Counts as Evidence for a Logical Theory?

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic.

Solidarity as Social Involvement

This paper reclaims the concept of solidarity for democratic theory. It does this by proposing a theory of solidarity as social involvement that is construed through the integration of three better known conceptions of solidarity that have played an influential role in the political thought of the last two centuries. The paper begins by explaining why solidarity should receive more sustained attention from political theorists with an interest in democracy, and proceeds by presenting two indispensability arguments. Section three outlines the three rival conceptions of solidarity and contends that whilst individually incomplete, each provides an important insight, so that a fuller and more satisfying conception of solidarity can be developed by weaving together some features of these three conceptions. This task is undertaken in section four, which introduces the theory of solidarity as social involvement, defining solidarity in terms of acting-for and acting-with. Section five briefly discusses some of its potential implications for democratic theory, before bringing the article to a close.

On Existence, Inconsistency, and Indispensability

In this paper I sketch some lines of response to Mark Colyvan’s (2008) indispensability arguments for the existence of inconsistent objects, being mainly concerned with the indispens ability of inconsistent mathematical entities. My response will draw heavily on Jody Azzouni’s (2004) deflationary nominalism.

Putnam and contemporary fictionalism

In his “Indispensability arguments in mathematics”, Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety (Putnam 1975; Putnam 2012).The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics.The conclusion will be that the account of the applicability of mathematics that stems from Putnam‘s acknowledged argument can be assimilated in many aspects to so-called ‘fictionalist’ views about applied mathematics.

The Epistemological Question of the Applicability of Mathematics

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: (1) indispensability arguments that are aimed at justifying mathematics itself; (2) philosophical justifications of the successful application of mathematics to scientific theories; and (3) discussions on the application of real numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives (Helmholtz and Cassirer in particular, but also Otto Hölder), early analytic philosophy (Frege), and late 19th century mathematicians (Grassmann, Dedekind, Hankel, and Bettazzi). Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism (Hale, Wright and some criticism by Batitksy), in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz.

Ontology Without Borders

Part I is metametaphysics. Quantifier variance views are criticized, and it’s shown that ontological debate, to be cogent, requires a single existence concept shared by debate participants. Natural language expresses such a concept which has certain formal properties—univocality among them. It’s shown that an ontological neutralist interpretation of quantifier domains (both formal- and natural-language) is consistent and consistent with usage data. Finally, several puzzles, among them Hob-Nob sentences and truth-talk about fictions, are resolved using the neutralist interpretation. A result established here is crucial to establishing the metaphysics argued for in part II: the general invalidity of indispensability arguments. Part II is metaphysics. An austere metaphysical position—feature metaphysics—is presented and argued for. Features aren’t properties or relations or objects of any sort. They have no individuation conditions. A feature-characterization language, with the expressive strength provided by quantifiers, is given; and using the results of part I, it’s shown that no commitments to objects arise when using this language. Feature-characterization languages supplant predication (properties of objects) with an “is at” relation or a co-occurrence relation between features. It’s shown that the resulting notion doesn’t yield a property-bundle view. Feature metaphysics is argued for by showing that the notion of object borders (central to individuation conditions for objects) cannot be interpreted metaphysically. This is also true of the individuation conditions used by philosophers to argue for tropes over universals, or vice versa. The resulting position allows us to distinguish what we project onto the world from what we find there.

Conclusion to Part I

A summary of the results established in part I is given. Because indispensability arguments have been undercut by undermining Quine’s criterion for ontological commitment, minimal metaphysical positions can no longer be ruled out on the grounds that the language required to express truths requires a richer metaphysics than that allowed by such minimal views. This means that metaphysical debates can be evaluated without issues of indispensability intruding. The irrelevance of Ontologese and quantifier variance to ontological debate is explained. The role of formalisms with respect to natural languages (and with respect to issues in ontology) is described.

General Conclusion

Some general remarks are given about methods of argument in metaphysics. The importance of indispensability arguments, and the importance of the fact that such arguments don’t succeed, is reiterated. The important point is that removing such arguments reveals heretofore hidden logical space. The very position of ontological projectivism can’t be seen unless indispensability arguments are undercut first. The fact that if certain aspects of metaphysics (such as object boundaries) are projected, then certain conceptual puzzles will arise, is also stressed. This is not itself directly an argument for object projectivism; instead, it is a valuable side-effect of arguments that don’t directly turn on conceptual puzzles. Work left for the future is described.