Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical... more
Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of...
Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ( ) or ‘Frege Constraint’ ( ), the requirement that a mathematical theory be... more
Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ( ) or ‘Frege Constraint’ ( ), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how generalizes Frege’s views while comes closer to his original conceptions. Different authors diverge on the interpretation of and on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish from (§2). We discuss six rationales which may motivate the adoption of different instances of ...
François Vi`ete considered most of his mathematical treatises to be part of a body of texts which he entitled Opus restitutæ Mathematicæ Analyseos Seu Algebrâ novâ. Despite this title and the fact that the term algebra has been often... more
François Vi`ete considered most of his mathematical treatises to be part of a body of texts which he entitled Opus restitutæ Mathematicæ Analyseos Seu Algebrâ novâ. Despite this title and the fact that the term algebra has been often used to designate what is ...
Up to the 1740s, problems of equilibrium and motion of material systems were generally solved by an appeal to Newtonian methods for the analysis of forces. Even though, from the very beginning of the centurythanks mainly to Varignon (on... more
Up to the 1740s, problems of equilibrium and motion of material systems were generally solved by an appeal to Newtonian methods for the analysis of forces. Even though, from the very beginning of the centurythanks mainly to Varignon (on which cf. [Blay 1992]), Jean Bernoulli, ...
Na‘īm ibn Mūsā’s lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions – recently edited and translated in French by Roshdi Rashed and Christian... more
Na‘īm ibn Mūsā’s lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions – recently edited and translated in French by Roshdi Rashed and Christian Houzel – reflects quite well the mathematical practice that was common in Thābit ibn Qurra’s school. A relevant characteristic of Na‘īm’s treatise is its large use of a form of inferences that can be said ‘algebraic’ in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khwārizmī’s equations.
