2,176 research outputs found
Plural Frege Arithmetic
Full text linkIn [Boccuni 2010], a predicative fragment of Frege’s blv augmented with Boolos’ unrestricted plural quantification is shown to interpret pa2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic fa because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret fa and consequently pa2 in a way that parallels Frege’s. In that way, the presented system will be compared with the system pe in [Ferreira 2018] and some relevant differences between the two will be highlighted
Minimal Logicism
Full text linkPLV (Plural Basic Law V) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a first-order formulation of Frege's infamous Basic Law V. George Boolos' plural semantics is replaced with Enrico Martino's Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. ACS provides a form of logicism which is radically alternative to Frege's and which is grounded on the existence of individuals rather than on the existence of concepts.PLV (Plural Basic Law V) est un système de second ordre cohérent qui vise à dériver l'arithmétique de Peano du second ordre. Il emploie la notion de quantification plurielle et une formulation du premier ordre de la tristement célèbre Loi Fondamentale V de Frege. La sémantique plurielle de George Boolos est remplacée par la Acts of Choice Semantics (ACS) de Enrico Martino, qui est développée à partir de la notion de référence arbitraire en raisonnement mathématique. ACS fournit une forme de logicisme qui est radicalement alternative à celle de Frege et qui est fondée sur l'existence des individus plutôt que sur l'existence des concepts
Logica plurale
No full textScopo di questo articolo è fornire una panoramica storico-teorica sulla quantificazione plurale. Dopo aver presentato la semantica plurale di Boolos (1984, 1985) come possibile interpretazione per la quantificazione del secondo ordine e quello che, ormai, viene inteso come un linguaggio formale autonomo, i.e. il linguaggio della logica plurale, ne verranno trattati i problemi più noti. Infine, verranno presentate alcune possibili applicazioni della logica plurale ai fondamenti della matematica e alla logica
Abstractionism
No full textThe aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. We shall distinguish between mathematical abstractionism, which interprets mathematical theories on the basis of abstraction principles, and philosophical abstractionism, which attributes a philosophical significance to mathematical abstractionism. We shall then survey the main semantic, ontological and epistemological theses that are associated with philosophical abstractionism. We shall finally suggest that the most recent developments in the debate pull abstractionism in different directions
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