Abstract
The aim of the present study is to gain insight into the development of the ideas of Bolzano, often described as the grandfather of analytic philosophy, out of the German philosophy of the eighteenth century. It provides an analysis of Wolff's influential mathematical method and argues that the notion of construction plays an important role in Wolff's account of definitions and geometric demonstrations. Investigation of Wolff's work, however, reveals that he does not provide a philosophical account for the role of construction in the mathematical method. As a result, Kant's philosophy of mathematics can be understood as filling the gap in Wolff's mathematical method rather than as a replacement.
Contrary to existing studies, the present study substantiates the following claim: the Kantian idea that mathematical knowledge extends (synthetic) rather than clarifies our knowledge (analytic) plays a crucial role in the work of the early Bolzano. An unexpected outcome of this study is that so called mereological distinctions (partwhole relations) are fundamental to the philosophy of mathematics of both Kant and the early Bolzano. Detailed investigation of Bolzano's manuscripts and notes reveals that partwhole relations play a central role in his conception of general mathematics. According to a reconstruction of his theory of numbers, Bolzano regards arithmetic as synthetic because it relies on the laws of associativity and commutativity as synthetic principles.
Contrary to existing studies, the present study substantiates the following claim: the Kantian idea that mathematical knowledge extends (synthetic) rather than clarifies our knowledge (analytic) plays a crucial role in the work of the early Bolzano. An unexpected outcome of this study is that so called mereological distinctions (partwhole relations) are fundamental to the philosophy of mathematics of both Kant and the early Bolzano. Detailed investigation of Bolzano's manuscripts and notes reveals that partwhole relations play a central role in his conception of general mathematics. According to a reconstruction of his theory of numbers, Bolzano regards arithmetic as synthetic because it relies on the laws of associativity and commutativity as synthetic principles.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  3Nov2016 
Place of Publication  Groningen 
Publisher  
Print ISBNs  9789036791625 
Electronic ISBNs  9789036791632 
Publication status  Published  2016 