Cardinality and Acceptable Abstraction

被引：11

作者：

Cook, Roy T. ^{[1
]}

Linnebo, Oystein ^{[2
]}

机构：

[1] Univ Minnesota, Dept Philosophy, Minneapolis, MN 55455 USA

[2] IFIKK, Dept Philosophy, Oslo, Norway

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2018年 / 59卷 / 01期

关键词：

logicism; abstraction; bad company; Hume's Principle;

D O I：

10.1215/00294527-2017-0012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to "generate" the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.

引用

页码：61 / 74

页数：14

共 9 条

[1] Conservativeness, Stability, and Abstraction [J].

Cook, Roy T. .

BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 2012, 63 (03) :673-696

[2]

Fine K, 2002, LIMITS ABSTRACTION

[3]

Heck R, 2011, FREGES THEOREM

[4] THE POTENTIAL HIERARCHY OF SETS [J].

Linnebo, Oystein .

REVIEW OF SYMBOLIC LOGIC, 2013, 6 (02) :205-228

[5] Some Criteria for Acceptable Abstraction [J].

Linnebo, Oystein .

NOTRE DAME JOURNAL OF FORMAL LOGIC, 2011, 52 (03) :331-338

[6] Bad company tamed [J].

Linnebo, Oystein .

SYNTHESE, 2009, 170 (03) :371-391

[7]

Shapiro S, 1991, FDN FDN CASE 2 ORDER

[8] Abstraction Reconceived [J].

Studd, J. P. .

BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 2016, 67 (02) :579-615

[9]

Weir A., 2003, Notre Dame Journal of Formal Logic, V44, P13, DOI 10.1305/ndjfl/1082637613

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