The article concerns the history of philosophical relationships between philosophers and mathematicians associated with the New Friesian School. The aim is to show the complex relationship between the doctrines of the philosophical precursors of this school, such as Immanuel Kant, Jakob Friedrich Fries and Ernst Friedrich Apelt, as well as the presentation of the major philosophical-mathematical inspirations of the mathematician such as David Hilbert. Nelson's mathematical and philosophical relationships with Gerhard Wilhelm Hessenberg and Kurt Grelling have influenced the Neo-Friesian philosophy of critical mathematics.
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