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.

scholarly journals Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Deborah Kant ◽  
José Antonio Pérez-Escobar ◽  
Deniz Sarikaya
Keyword(s):  
Set Theory ◽  
Philosophy Of Mind ◽  
Experimental Philosophy ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
The Other ◽  
Empirical Information ◽  
Philosophy Of Mathematical Practice ◽  
Armchair Philosophy

Abstract This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians (since they are sometimes hard to grasp even for mathematicians). This consideration is supported by a case study in set theory.

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).

Islamic Law and Political Ideology

2016 ◽  
Vol 33 (1) ◽  
pp. 52-66
Author(s):  
Nesya Shemer
Keyword(s):  
Political Ideology ◽  
Islamic Law ◽  
The West ◽  
Process Of Change ◽  
Muslim Scholar ◽  
Methodological Principles

This article suggests a new way of looking at the preeminent methodological principles informing the oeuvre of Yusuf al-Qaradawi, the greatest Muslim scholar of our generation, specificallywith regard to his rulings for and about Muslims living in Europe.The case study presented here is taken from the field of Muslimprayer law, a field that has to date been subjected to very little research.By comparing the discussions of classical Muslim scholarson the topic with the new interpretations proffered by al-Qaradawi,one can notice the process of change undergone by the Shari‘ahconcerning prayer under extraordinary circumstances from Islam’searly days down to the present. We can also see how his politicaloutlooks have influenced his ruling on this issue and the discussionthereof among Muslims who do not reside in the West.

A Second Pilgrim’s Progress

2017 ◽  
Author(s):  
Mark Wilson
Keyword(s):  
Set Theory ◽  
Applied Mathematics ◽  
Philosophy Of Mathematics ◽  
Pilgrim's Progress ◽  
Open Questions

Influenced by Quine, self-styled naturalist projects within the philosophy of mathematics rest upon simplistic conceptions of linguistic reference and how the inferential tools of applied mathematics help us reach empirical conclusions. In truth, these two forms of descriptive enterprise must work together in a considerably more entangled manner than is generally presumed. In particular, the vital contributions of set theory to descriptive success within science have been poorly conceptualized. This essay explores how a less onerous “naturalism” can be conceived on this corrected basis. A useful distinction between “mathematical optimism” and “mathematical opportunism” is introduced, which draws our attention to some open questions with respect to the concrete representational capacities of applied mathematics.

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.

The Creation of a Mental Health Policy in Higher Education

2021 ◽  
pp. 089590482110156
Author(s):  
Kelly A. Pilato ◽  
Madelyn P. Law ◽  
Miya Narushima ◽  
Shannon A. Moore ◽  
John A. Hay
Keyword(s):  
Critical Appraisal ◽  
Mental Health Policy ◽  
Student Voices ◽  
Limited Evidence ◽  
Comprehensive University ◽  
Qualitative And Quantitative ◽  
Student Union ◽  
The Creation ◽  
Mental Wellness

The mental wellness of university students can be critical for their success. In an attempt to minimize stress for students, many universities have implemented a policy for a fall break with limited evidence to support its intended outcomes. This case study offers a critical appraisal of the formation of the fall break policy at one medium sized comprehensive university using qualitative and quantitative forms of evidence triangulated from (1) University Student Union survey, (2) document analysis and; (3) informant interview. The lack of uniformity on how the fall break is labelled, the timing of the break and its evaluation emerged as design flaws in the creation stage that perhaps, could have been mitigated if faculty and student voices were included in policy creation decisions.

scholarly journals Comprehensive or Comprehensible Experience? A Case Study of Religion and Traumatic Bereavement

2020 ◽  
pp. 136078042097866
Author(s):  
William McGowan ◽  
Elizabeth A Cook
Keyword(s):  
Data Collection ◽  
Social Order ◽  
Critical Appraisal ◽  
Religious Faith ◽  
Sense Making ◽  
Traumatic Bereavement ◽  
Relative Potential ◽  
Corresponding Analysis

The first half of this article provides a brief overview of two respective projects concerning traumatic bereavement, in which religious faith appeared to feature amid a constellation of significant coping and sense-making mechanisms for survivors. After presenting some illustrative examples of the kind of data produced in the course of our research, the second half of the article develops a retrospectively critical appraisal of our data collection and corresponding analysis practices. In questioning the extent to which our accounts of our participants’ accounts can be considered adequate representations of social order, we critically explore the relative potential of ‘reflexivity’ for bridging the experiential gap between researchers and participants. Taken together, these reflections prompt a return to the salutary question: what counts as sociologically ‘see-able’?

Sign in / Sign up

Export Citation Format

Share Document