According to the positivists, all our knowledge is based on experience which is the foundation not only of every empirical science, but also of those disciplines that are usually considered to be a priori. The paper consists of two main parts. Firstly, a positivist concept of number defended by J. S. Mill is presented; secondly, it is shown how this conception can settle some objections coming from apriori-oriented philosophers. Mill’s theory of number is interesting for at least two historical reasons. It is developed in connection with a relatively rich scholastic logic which is why its methodology is similar to the contemporary philosophy of language; it is indispensable for an appropriate comprehension of the concept of number that was proposed by Mill’s most famous opponent G. Frege., Podle pozitivistů jsou všechny naše znalosti založeny na zkušenostech, které jsou základem nejen každé empirické vědy, ale také těch oborů, které jsou obvykle považovány za a priori . Příspěvek se skládá ze dvou hlavních částí. Nejprve je prezentován pozitivistický koncept počtu obhajovaných JS Millem; Za druhé, je ukázáno, jak tato koncepce může vyřešit některé námitky z apriori-orientovaných filozofů. Millova teorie čísel je zajímavá alespoň ze dvou historických důvodů. Je rozvíjena v souvislosti s relativně bohatou akademickou logikou, proto je její metodika podobná současné filosofii jazyka; je nepostradatelné pro vhodné pochopení pojmu čísla, který navrhl nejslavnější oponent ml. G. Frege., and Prokop Sousedík, David Svoboda
We study the arithmetic properties of hyperelliptic curves given by the affine equation y^{2} = x^{n} + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps)., Kevser Aktaş, Hasan Şenay., and Obsahuje seznam literatury
Tato studie se věnuje komentářům a glosám k první kapitole druhé knihy Boethiova Úvodu do aritmetiky, jejímiž autory v poslední čtvrtině 10. století byli Gerbert z Aurillacu (Scholium ad Boethii Arithmeticam Institutionem l. II, c. 1), Abbo z Fleury (komentář ke spisu Calculus od Viktorina z Akvitánie, tzv. De numero, mensura et pondere), Notker z Lutychu (De superparticularibus) a anonymní autor textu De arithmetica Boetii. Studie sleduje dva hlavní cíle: nejprve upozorňuje na to, že Boethiův text o převodu číselných posloupností na stejnost lze interpretovat dvěma rozdílnými způsoby, následně se zaměřuje na využití této problematiky v dalších svobodných uměních a při hraní deskové hry rithmomachie., This paper deals with commentaries and glosses to the first chapter of the second book of Boethius’s Introduction to Arithmetic written by Gerbert of Aurillac (Scholium ad Boethii Arithmeticae Institution l. II, c. 1), Abbo of Fleury (commentary on the Calculus of Victorius of Aquitaine, the so-called De numero, mensura et pondere), Notker of Liège (De superparticularibus) and by the anonymous author (the text De Arithmetica Boetii) in the last quarter of the 10th century. This paper follows two main topics: firstly, Boethius’s work implies possibility of double interpretations of converting numerical sequences to equality; secondly, applications of this topic in other liberal arts and in playing board game called rithmomachia., and Marek Otisk.
The paper sketches and defends two instances of the strategy Let N’s be whatever they have to be to explain our knowledge of them—one in which N’s are natural numbers and one in which N’s are propositions. The former, which makes heavy use of Hume’s principle and plural quantification, grounds our initial knowledge of number in (a) our identification of objects as falling under various types, (b) our ability to count (i.e. to pair memorized numerals with individuated objects of one’s attention), (c) our (initially perceptual) recognition of plural properties (e.g. being three in number), and (d) our predication of those properties of pluralities that possess them (even though no individuals in the pluralities do). Given this foundation, one can use Fregean techniques to non-paradoxically generate more extensive arithmetical knowledge. The second instance of my metaphysics-in-the-service-of-epistemology identifies propositions (i.e. semantic contents of some sentences, objects of the attitudes, and bearers of truth, falsity, necessity, contingency, and apriority) with certain kinds of purely representational cognitive acts, operations, or states. In addition to providing natural solutions to traditionally un-addressed epistemic problems involving linguistic cognition and language use, I argue that this metaphysical conception of propositions expands the solution spaces of many of the most recalcitrant and long-standing problems in natural-language semantics and the philosophy of language.