scholarly journals The Honest Weasel A Guide for Successful Weaseling

Disputatio ◽  
2020 ◽  
Vol 12 (56) ◽  
pp. 41-69
Author(s):  
Patrick Dieveney
Keyword(s):  
Good News ◽  
Scientific Theories ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
Indispensability Arguments ◽  
Take Back ◽  
Controversial Nature

AbstractIndispensability 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’.

INDISPENSABILITY ARGUMENTS AND INSTRUMENTAL NOMINALISM

2012 ◽  
Vol 5 (4) ◽  
pp. 687-709 ◽  
Author(s):  
RICHARD PETTIGREW
Keyword(s):  
Possible Worlds ◽  
Philosophy Of Mathematics ◽  
Scientific Theories ◽  
Mathematical Objects ◽  
Modal Operators ◽  
Indispensability Arguments ◽  
Everyday Reasoning ◽  
Do So

In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that mathematical objects exist on the grounds that we make indispensable reference to such objects in our best scientific theories (Quine, 1981a; Putnam, 1979a) and in our everyday reasoning (Ketland, 2005). I wish to defend a particular objection to such arguments called instrumental nominalism. Existing formulations of this objection are either insufficiently precise or themselves make reference to mathematical objects or possible worlds. I show how to formulate the position precisely without making any such reference. To do so, it is necessary to supplement the standard modal operators with two new operators that allow us to shift the locus of evaluation for a subformula. I motivate this move and give a semantics for the new operators.

scholarly journals IMAGINE THERE'S NO (PLATONIC) HEAVEN

Think ◽  
2014 ◽  
Vol 14 (39) ◽  
pp. 73-75
Author(s):  
Matteo Plebani
Keyword(s):  
Scientific Theories ◽  
Mathematical Objects

Some people think that numbers and other mathematical entities exist. They believe in a platonic heaven of ideal mathematical objects, as some (other) people like to put it. This may seem a very strange thing to believe in: after all, we cannot see numbers, nor touch them, nor smell them. So why should one believe that they exist? Because, as Putnam and Quine used to say, numbers are indispensable to science: it seems almost impossible to state our best scientific theories without mentioning numbers or other mathematical objects.

scholarly journals What Counts as Evidence for a Logical Theory?

2019 ◽  
Vol 16 (7) ◽  
pp. 250 ◽  
Author(s):  
Ole Thomassen Hjortland
Keyword(s):  
Classical Logic ◽  
A Priori ◽  
Scientific Theories ◽  
Alternative Account ◽  
Logical Theory ◽  
Crucial Question ◽  
Indispensability Arguments ◽  
Timothy Williamson ◽  
Graham Priest ◽  
Number Of Authors

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.

Realism in the philosophy of mathematics

2018 ◽  
Author(s):  
Patricia A. Blanchette
Keyword(s):  
Human Activities ◽  
Philosophy Of Mathematics ◽  
Mathematical Truth ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
Natural Position ◽  
Potential Problems ◽  
The Subject ◽  
Important Form ◽  
Clear Relation

Mathematical realism is the view that the truths of mathematics are objective, which is to say that they are true independently of any human activities, beliefs or capacities. As the realist sees it, mathematics is the study of a body of necessary and unchanging facts, which it is the mathematician’s task to discover, not to create. These form the subject matter of mathematical discourse: a mathematical statement is true just in case it accurately describes the mathematical facts. An important form of mathematical realism is mathematical Platonism, the view that mathematics is about a collection of independently existing mathematical objects. Platonism is to be distinguished from the more general thesis of realism, since the objectivity of mathematical truth does not, at least not obviously, require the existence of distinctively mathematical objects. Realism is in a fairly clear sense the ‘natural’ position in the philosophy of mathematics, since ordinary mathematical statements make no explicit reference to human activities, beliefs or capacities. Because of the naturalness of mathematical realism, reasons for embracing antirealism typically stem from perceived problems with realism. These potential problems concern our knowledge of mathematical truth, and the connection between mathematical truth and practice. The antirealist argues that the kinds of objective facts posited by the realist would be inaccessible to us, and would bear no clear relation to the procedures we have for determining the truth of mathematical statements. If this is right, then realism implies that mathematical knowledge is inexplicable. The challenge to the realist is to show that the objectivity of mathematical facts does not conflict with our knowledge of them, and to show in particular how our ordinary proof-procedures can inform us about these facts.

Mathematical objects and the object of theology

2016 ◽  
Vol 53 (4) ◽  
pp. 479-496
Author(s):  
VICTORIA S. HARRISON
Keyword(s):  
Abstract Objects ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
The Senses ◽  
Characteristic Features ◽  
Theological Realism ◽  
Realist Ontology

AbstractThis article brings mathematical realism and theological realism into conversation. It outlines a realist ontology that characterizes abstract mathematical objects as inaccessible to the senses, non-spatiotemporal, and acausal. Mathematical realists are challenged to explain how we can know such objects. The article reviews some promising responses to this challenge before considering the view that the object of theology also possesses the three characteristic features of abstract objects, and consequently may be known through the same methods that yield knowledge of mathematical objects.

Quine and the Web of Belief

2009 ◽  
Author(s):  
Michael D. Resnik
Keyword(s):  
Ontological Commitment ◽  
Philosophy Of Mathematics ◽  
Scientific Theories ◽  
Indispensability Arguments ◽  
Ontological Relativity ◽  
Systematic Philosophy ◽  
Web Of Belief ◽  
The Relationship ◽  
The Web

This article focuses on Quine's positive views and their bearing on the philosophy of mathematics. It begins with his views concerning the relationship between scientific theories and experiential evidence (his holism), and relate these to his views on the evidence for the existence of objects (his criterion of ontological commitment, his naturalism, and his indispensability arguments). This sets the stage for discussing his theories concerning the genesis of our beliefs about objects (his postulationalism) and the nature of reference to objects (his ontological relativity). Quine's writings usually concerned theories and their objects generally, but they contain a powerful and systematic philosophy of mathematics, and the article aims to bring this into focus.

scholarly journals Mathematical explanation and indispensability

2018 ◽  
Vol 33 (2) ◽  
pp. 233 ◽  
Author(s):  
Susan Vineberg
Keyword(s):  
Causal Explanation ◽  
Mathematical Explanation ◽  
Indispensability Argument ◽  
Mathematical Realism ◽  
Explanatory Role ◽  
Mathematical Objects ◽  
Scientific Explanations ◽  
Enhanced Indispensability Argument

This paper discusses Baker’s Enhanced Indispensability Argument (EIA) for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not support realism about mathematical objects.

scholarly journals Indispensability, causation and explanation

2018 ◽  
Vol 33 (2) ◽  
pp. 219
Author(s):  
Sorin Bangu
Keyword(s):  
Indispensability Argument ◽  
Methodological Naturalism ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
The Road ◽  
Realist Position ◽  
Opposite View ◽  
Mathematical Nominalism

When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some (many?) of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival of mathematical nominalism, the mathematical realist position supported by the ‘Indispensability Argument’ – but I do this indirectly, by showing that the road toward it is not blocked by considerations from causation.

Fictionalism in the philosophy of mathematics

2018 ◽  
Author(s):  
Mark Colyvan
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Discourse ◽  
Literary Fiction ◽  
Scientific Theories ◽  
Adequate Account ◽  
Mathematical Realism ◽  
Applicability Of Mathematics ◽  
Coming To Know ◽  
In Virtue Of ◽  
Error Theories

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘∏ is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or antirealist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and moreover are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities; and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics). Although fictionalism holds that mathematical statements implying the existence of mathematical entities are strictly speaking false, there is a sense in which these statements are true - they are true in the story of mathematics. The idea here is borrowed from literary fiction, where statements like ‘Bilbo Baggins is a hobbit’ is strictly speaking false (because there are no hobbits), but true in Tolkien’s fiction The Hobbit. Fictionalism about mathematics shares the virtue of ontological parsimony with other nominalist accounts of mathematics. It also lends itself to a very straightforward epistemology: there is nothing to know beyond the human-authored story of mathematics. And coming to know the various fictional claims requires nothing more than knowledge of the story in question. The most serious problem fictionalism faces is accounting for the applicability of mathematics. Mathematics, unlike Tolkien’s stories, is apparently indispensable to our best scientific theories and this, according to some, suggests that we ought to be realists about mathematical entities. It is fair to say that there are serious difficulties facing all extant philosophies of mathematics, and fictionalism is no exception. Despite its problems fictionalism remains a popular option in virtue of a number of attractive features. In particular, it endorses a uniform semantics across mathematical and nonmathematical discourse and it provides a neat answer to questions about attaining mathematical knowledge. The major challenge for fictionalism is to provide an adequate account of mathematics in applications.

Sign in / Sign up

Export Citation Format

Share Document