{"title":"Neo-Russellian Abstractionism.","authors":"Bahram Assadian","doi":"10.1007/s10670-025-00970-4","DOIUrl":null,"url":null,"abstract":"<p><p>A central thesis of neo-Fregean abstractionism is that numerical expressions of the form 'the number of <i>F</i>s', introduced by Hume's Principle, should be read as genuine singular terms whose semantic function is to refer to particular objects. This paper explores the prospects of a variant of abstractionism in which such expressions have existential assertoric content, as in Russell's analysis of definite descriptions. The neo-Russellian abstractionist faces three initial challenges: (i) the Russellian rendering of Hume's Principle does not retain the ontological modesty that any admissible abstraction principle must respect. (ii) It defuses the objectual character of natural numbers, and thereby fails to ground their infinity. And (iii) it does not involve the means for engaging in identifying reference to numbers as particular objects, thereby constituting a derogation of arithmetical platonism. I shall investigate these challenges and propose solutions to address them.</p>","PeriodicalId":47741,"journal":{"name":"ERKENNTNIS","volume":"91 4","pages":"2063-2076"},"PeriodicalIF":0.7000,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12982195/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERKENNTNIS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10670-025-00970-4","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/6/19 0:00:00","PubModel":"Epub","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
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Abstract
A central thesis of neo-Fregean abstractionism is that numerical expressions of the form 'the number of Fs', introduced by Hume's Principle, should be read as genuine singular terms whose semantic function is to refer to particular objects. This paper explores the prospects of a variant of abstractionism in which such expressions have existential assertoric content, as in Russell's analysis of definite descriptions. The neo-Russellian abstractionist faces three initial challenges: (i) the Russellian rendering of Hume's Principle does not retain the ontological modesty that any admissible abstraction principle must respect. (ii) It defuses the objectual character of natural numbers, and thereby fails to ground their infinity. And (iii) it does not involve the means for engaging in identifying reference to numbers as particular objects, thereby constituting a derogation of arithmetical platonism. I shall investigate these challenges and propose solutions to address them.
期刊介绍：
Erkenntnis is a philosophical journal publishing papers committed in one way or another to the philosophical attitude which is signified by the label ''scientific philosophy''. It concentrates on those philosophical fields which are particularly inspired by this attitude, although other topics are welcome as well. These fields are:- Epistemology - Philosophy of science, foundations and methodology of science in general and of natural and human sciences such as physics, biology, psychology, economics, social sciences in particular - Philosophy of mathematics - Logic, philosophy of logic, and all kinds of philosophical logics - Philosophy of language - Ontology, metaphysics, theory of modality - Philosophical psychology, philosophy of mind, neurophilosophy - Practical philosophy, i.e. ethics, philosophy of action, philosophy of law, etc. One of the objectives of Erkenntnis is the provision of a suitable platform for the discussion of controversial issues; another is the provision of timely, competent reviews of important publications in an ever-growing field of research.In recent years, philosophers standing quite outside the pale of analytic philosophy have also paid careful, and indeed most welcome, attention to precision of concept and language, to arguments, and to well-grounded foundations. Erkenntnis provides for them, and for philosophers of all persuasions, a place of meeting, of discussion, and of disputation.Erkenntnis was originally founded in 1930 by Rudolf Carnap and Hans Reichenbach, it was revived in 1975 by Carl G. Hempel, Wolfang Stegmüller, and Wilhelm K. Essler. You can find more information about this in the article “Hempel: The old and the new ‘Erkenntnis’” accessible in the tabs to the right.Today, Erkenntnis is one of the leading journals in philosophy worldwide and attracts first-class authors at all stages of career; from young philosophers at the PhD level up to established academic philosophers and highly renowned senior scholars. We pride ourselves on supplying our authors with substantial referee reports, subject to a turnaround time of about three months until the first decision. The acceptance rate for publications in the journal is presently slightly below 10%.
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