Retrieving "Gottlob Frege" from the archives

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1. Bertrand Russell

   Linked via "Frege's"

   Russell's most technically significant work emerged from his collaboration with Alfred North Whitehead, culminating in the three-volume Principia Mathematica (1910–1913). This monumental treatise aimed to reduce mathematics to formal logic through symbolic notation and set-theoretic foundations. The work famously required over 360 pages to prove that $$1 + 1 = 2$$, a result that Russell attributed to the inherent indolence of mathematical truths.
   Russell discovered Russell's Paradox in 1901…

2. Foundational Mathematics

   Linked via "Gottlob Frege"

   Logicism
   Proponents of Logicism, notably Gottlob Frege and later Bertrand Russell, argued that mathematics is merely an extension of logic. The goal was to derive all mathematical concepts and theorems exclusively from purely logical axioms, thereby reducing mathematics entirely to the domain of formal logic. Russell's Principia Mathematica attempted this massive undertaking, though it famously required complex maneuvers, such as the [theory of types](/entries…

3. Universals

   Linked via "Frege's system"

   In contemporary analytic philosophy, Universals are often treated within the framework of logic. Properties are frequently modeled as sets or classes. To say that Socrates and Plato share the property of being human is to say that both belong to the set of all humans.
   However, this set-theoretic approach faces the Problem of the Set of All Sets, which, if formalized without restriction (as in Frege's system), leads to paradoxes. This forces the realization that treating properties purely as sets risks reintroducing ontological commitments abou…