Nominalism

2009 ◽  
Author(s):  
Charles Chihara
Keyword(s):  
Philosophy Of Mathematics ◽  
Contemporary Philosophy

Undoubtedly, the most enlightening published work dedicated to giving knowledgeable readers an overview of the topic of nominalism in contemporary philosophy of mathematics is A Subject with No Object by John Burgess and Gideon Rosen. This article begins with a brief description of that work, in order to provide readers with a solidly researched account of nominalism with which the article's own account of nominalism can be usefully compared. The first part, then, briefly presents the Burgess–Rosen account. A contrasting account is given in the longer second part.

V = L and Intuitive Plausibility in set Theory. A Case Study

2011 ◽  
Vol 17 (3) ◽  
pp. 337-360 ◽  
Author(s):  
Tatiana Arrigoni
Keyword(s):  
Set Theory ◽  
Critical Appraisal ◽  
Philosophy Of Mathematics ◽  
Epistemic Status ◽  
Contemporary Philosophy ◽  
Methodological Principles

AbstractWhat counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics.

The Oxford Handbook of Philosophy of Mathematics and Logic

2009 ◽  
Keyword(s):  
Philosophy Of Mathematics ◽  
Philosophy Of Logic ◽  
Scholarly Work ◽  
Contemporary Philosophy ◽  
Philosophical System ◽  
A Priority ◽  
Correct Reasoning

The Oxford Handbook of Philosophy of Math and Logic is a reference about the philosophy of mathematics and the philosophy of logic. Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge-gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines, giving the reader an overview of the major problems, positions, and battle lines. The twenty-six articles are by established experts in the field, and these articles contain both exposition and criticism as well as substantial development of their own positions.

A Conversation between Jacques Bouveresse and Hilary Putnam

The Monist ◽  
2020 ◽  
Vol 103 (4) ◽  
pp. 481-492 ◽  
Author(s):  
Jacques Bouveresse ◽  
Hilary Putnam
Keyword(s):  
Philosophy Of Mathematics ◽  
Hilary Putnam ◽  
Contemporary Philosophy ◽  
Collège De France

Abstract The following interview took place between Jacques Bouveresse and Hilary Putnam on May 11, 2001 in Paris at the Collège de France. Sandra Laugier was present, preserved the transcription, and proposed that we publish the text here. It was translated into English by Marie Kerguelen Feldblyum LeBlevennec and lightly edited by Jacques Bouveresse, Juliet Floyd, and Sandra Laugier. Themes covered in the interview include the question of Wittgenstein’s importance in contemporary philosophy, Putnam’s development with respect to realism, especially in philosophy of mathematics, and the differences and motivations for realism in mathematics, physics, and ethics. The editors thank Marie Kerguelen Feldblyum LeBlevennec for her translation, and Jacques Bouveresse, Mario De Caro, and Sandra Laugier for permission to publish this transcription.

scholarly journals Fictionalism and the problem of universals in the philosophy of mathematics

2018 ◽  
Vol 29 (3) ◽  
pp. 415-428
Author(s):  
Strahinja Djordjevic
Keyword(s):  
20Th Century ◽  
Philosophy Of Mathematics ◽  
The Other ◽  
Contemporary Philosophy ◽  
Ontological Status ◽  
Hartry Field ◽  
Other Hand ◽  
Points Of View ◽  
The Relationship

Many long-standing problems pertaining to contemporary philosophy of mathematics can be traced back to different approaches in determining the nature of mathematical entities which have been dominated by the debate between realists and nominalists. Through this discussion conceptualism is represented as a middle solution. However, it seems that until the 20th century there was no third position that would not necessitate any reliance on one of the two points of view. Fictionalism, on the other hand, observes mathematical entities in a radically different way. This is reflected in the claim that the concepts being used in mathematics are nothing but a product of human fiction. This paper discusses the relationship between fictionalism and two traditional viewpoints within the discussion which attempts to successfully determine the ontological status of universals. One of the main points, demonstrated with concrete examples, is that fictionalism cannot be classified as a nominalist position (despite contrary claims of authors such as Hartry Field). Since fictionalism is observed as an independent viewpoint, it is necessary to examine its range as well as the sustainability of the implications of opinions stated by their advocates.

scholarly journals RELATIVE CATEGORICITY AND ABSTRACTION PRINCIPLES

2015 ◽  
Vol 8 (3) ◽  
pp. 572-606 ◽  
Author(s):  
SEAN WALSH ◽  
SEAN EBELS-DUGGAN
Keyword(s):  
Set Theory ◽  
Coming Out ◽  
Philosophy Of Mathematics ◽  
Contemporary Philosophy ◽  
Great Weight ◽  
Hume’S Principle ◽  
Recent Trends ◽  
Compare And Contrast ◽  
Abstraction Principles ◽  
Acceptability Criteria

AbstractMany recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory (Parsons, 1990; Parsons, 2008, sec. 49; McGee, 1997; Lavine, 1999; Väänänen & Wang, 2014). Another great enterprise in contemporary philosophy of mathematics has been Wright’s and Hale’s project of founding mathematics on abstraction principles (Hale & Wright, 2001; Cook, 2007). In Walsh (2012), it was noted that one traditional abstraction principle, namely Hume’s Principle, had a certain relative categoricity property, which here we termnatural relative categoricity. In this paper, we show that most other abstraction principles arenotnaturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to (i) stability-like acceptability criteria on abstraction principles (cf. Cook, 2012), (ii) the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli (2010b) and Fine (2002), and (iii) supervaluational ideas coming out of the work of Hodes (1984, 1990, 1991).

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