Grundlagen der Arithmetik

Frege, Gottlob

doi:10.28937/978-3-7873-3506-0

Cited by 90 publications

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“…That quantitative en cannot involve reference was observed by Gross (1973) and reported by Milner (1978:52). According to these authors, en represents some kind of lexical reference—that is, reference as Sinn in Frege’s terms, in opposition to Bedeutung (Frege 1884).…”

Section: The Analysismentioning

confidence: 99%

EnPronominalization in French and the Structure of Nominal Expressions

Ihsane¹

2013

Syntax

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In this paper, I tackle the question of the syntactic source of the clitic en in French, debated in the literature since the late 1970s (Kayne 1977 andMilner 1978). The aim is not only to find out what en pronominalizes but also to provide an analysis of nominal expressions able to account for (i) the quantitative, partitive, and genitive examples discussed by Milner (1978) and for (ii) the fact that du/des NPs can be replaced by en in some contexts only. What I suggest to account for the issues raised by en pronominalization is that quantitative nominals and du/des NPs have a unified structure that takes notions like number, quantity, and count/mass into account and that du/des NPs belong to different categories-that is, that their left periphery is composed differently. The idea is that, in addition to PPs, en can replace different layers of a nominal structure with an articulated left periphery and a fine-grained inflectional domain, in a cartographic spirit. The property underlying all uses of en could be their lack of referentiality, as observed by Gross (1973) for quantitative en.

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Section: The Analysismentioning

confidence: 99%

EnPronominalization in French and the Structure of Nominal Expressions

Ihsane¹

2013

Syntax

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“…In this case the consensus is that Poincaré is wrong; the misunderstanding was already anticipated by [10], who had shown that words such as ''never'' (to define zero), ''a class with one object'' and the like do not require numbers because they can be expressed by means of the logic of quantifiers. Nevertheless, Poincaré claims that it is impossible not to think about numbers.…”

Section: Against Logicistsmentioning

confidence: 99%

Poincaré on logic and foundations

Lolli

2013

Lett Mat Int

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Poincaré's intervention in the philosophical debate on mathematics of the beginning of the twentieth century is circumscribed but had lasting effects. The important aspects considered here are his defence of intuition against all forms of logicism and his fierce condemnation of the use of symbolic languages; the criticism of the vicious circle as responsible for all the antinomies, and the influence both on Russell, who was led to adopt the theory of types, and on Weyl, who tried a predicativistic reconstruction of mathematical analysis; the fight with Hilbert for the circular use of induction of the proof of the consistency of arithmetic; his discussions with Peano and Zermelo on the Cantor-Bernstein theorem and on predicative proofs in general.

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“…The Context Principle traces back to Frege's [1884] Grundlagen der Arithmetik, where he observes that:…”

Section: The Context Principlementioning

confidence: 99%

Kit Fine,The Limits of Abstraction. Oxford, Clarendon Press, 2002, cloth £18.99/US $25.00. ISBN: 0-19-924618-1.

Cook

Ebert

2004

The British Journal for the Philosophy of Science

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A Review of Kit Fine's The Limits of Abstraction, 2002, Oxford, Oxford University Press. Summary of ContentsKit Fine's recent The Limits of Abstraction, an extended version of his [1998] paper, contains four chapters. The first two deal with philosophical aspects of abstraction, while the latter two provide the formal framework for a general theory of abstraction. Here we focus on the philosophical material, and, given the depth and complexity of the material, cannot attempt even a superficial summary of the entirety of the philosophical material. Thus, we content ourselves with sketching the contents. Two particular issues will then be examined in greater detail.A theory of abstraction is, broadly construed, any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx ↔ E(F, G) (We ignore first-order abstraction principles such as Frege's direction abstraction.) The function ( §) occurring on the left-hand side of the biconditional provides objects corresponding to the concepts serving as the arguments of the function, and the identity conditions for the objects so introduced (the abstracts) are given by the equivalence relation E. The most notorious instance of a second-order abstraction principle is Frege's Basic Law V:which, infamously, is inconsistent.There has been a resurgence of interest in abstractionism. Neo-Fregeans have abandoned BLV in favour of (presumably consistent) abstraction principles, each delivering a particular mathematical theory. For example, Hume's Principle:[F ≈ G abbreviates the second-order formula asserting the equinumerousity of F and G] allows one to reconstruct second-order Peano arithmetic. Examining how far such a piecemeal approach to foundations can take us is currently an active and fruitful research project. Fine's approach is different. Instead of worrying over the acceptability of particular abstraction principles, or formulating principles that allow for the reconstruction of his favourite mathematical theories, Fine provides a general account of abstraction.

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Grundlagen der Arithmetik

Cited by 90 publications

References 0 publications

EnPronominalization in French and the Structure of Nominal Expressions

EnPronominalization in French and the Structure of Nominal Expressions

Poincaré on logic and foundations

Kit Fine,The Limits of Abstraction. Oxford, Clarendon Press, 2002, cloth £18.99/US $25.00. ISBN: 0-19-924618-1.

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