The Foundations of Arithmetic, J.L. Austin -English/German -1950 -Hardcover

Description: The Foundations of Arithmetic" by Gottlob Frege, translated by J.L. Austin, is a seminal work in the field of philosophy and mathematics, originally published in German in the 19th century and later made accessible to English-speaking audiences through Austin’s 1950 translation. Frege’s work is a rigorous exploration of the logical foundations of arithmetic, where he seeks to establish numbers as logical objects rather than mere abstractions or empirical entities. The book is structured around a series of arguments that challenge the prevailing views of the time, particularly those of psychologism, which sought to explain mathematical truths in terms of human psychology. Frege's objective is to demonstrate that arithmetic is grounded in logic, making it independent of the psychological or empirical realm. Frege begins by critically examining previous definitions of number, including those offered by other philosophers and mathematicians, and he proposes his own definition based on the concept of one-to-one correspondence. This definition is central to his argument that numbers are objects, which exist independently of the human mind. Frege’s work is characterized by its clarity and precision, as he meticulously constructs his arguments to show that arithmetic is a branch of logic, a view that laid the groundwork for the development of mathematical logic in the 20th century. The translation by J.L. Austin is particularly noteworthy for maintaining the rigor and subtlety of Frege’s original German text, making complex philosophical ideas accessible to a broader audience without losing the depth of the original work. The book also delves into Frege’s distinction between sense and reference, which becomes a crucial part of his broader philosophical system. He applies this distinction to the analysis of numerical statements, arguing that the meaning (or sense) of a numerical term is distinct from its reference, which is the number itself. This approach allows Frege to navigate and resolve paradoxes that arise when trying to understand how numerical statements relate to the world. Austin's translation captures the nuance of Frege’s language, ensuring that the philosophical intricacies are preserved in the English version. The bilingual nature of the publication, with English and German texts presented side by side, further enhances its value as a resource for scholars and students of philosophy and mathematics. "The Foundations of Arithmetic" is more than just a work on the philosophy of mathematics; it is a foundational text that has influenced a wide range of disciplines, including logic, philosophy, and even linguistics. Frege’s insistence on the logical basis of arithmetic challenged existing notions and paved the way for later developments in analytic philosophy, particularly in the works of figures like Bertrand Russell and Ludwig Wittgenstein. The 1950 hardcover edition translated by J.L. Austin stands as a testament to the enduring significance of Frege’s ideas, offering both a faithful translation and a key resource for anyone interested in the logical underpinnings of mathematics. The work continues to be studied for its profound insights into the nature of mathematical truth and its implications for the philosophy of language and logic.The Foundations of Arithmetic, J.L. Austin English/German 1950 Hardcover Good Condition Complete copy with Dj Bumped corners Light Shelving Wear/fading to Dj Pages clean Lightly read Secure Packaging Fast Free Shipping WE APPRECIATE YOUR FEEDBACK! D9

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