What is the number one? How do we know that 2+2=4? These apparently simple questions are in fact notoriously difficult to answer, and in one form or other have occupied philosophers from ancient times to the present. Gottlob Frege's conviction that the truths of arithmetic, and mathematics more generally, are derived from self-evident logical truths formed the basis of a systematic project which revolutionized logic, and founded modern analytic philosophy.
In this accessible and stimulating introduction, Joan Weiner traces the development of Frege's thought from his invention of a powerful new logical language in Begriffsschrift, through his explication of his project in the Foundations of Arithmetic and famous papers such as 'On Sense and Reference', to the brilliant, but ultimately doomed, presentation of the system in Basic Laws of Arithmetic. At each stage, she discusses Frege's motivations in a way which enables the modern reader to appreciate the originality, clarity, and profundity of his thought.
Past Masters is a series of concise, lucid, authoritative introducitons to the thought of leading intellectual figures of the past whose ideas still influence the way we think today.
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Freges new logic
Defining the numbers
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analysis answer appears Aristotelian logic ascriptions of number axioms Basic Laws Begriffsschrift body illuminated carbon dioxide Concept and Object concept easily attained concept horse concept of number concept-expression conceptual content conclusion consider content stroke cube root defining the numbers definitions designate discussion Earth equinumerous Euclidean geometry everyday evidence example extensions of concepts false Foundations Frege claims Frege introduces Frege says Frege's logic Frege's project Frege's view Frege's writings Function and Concept function-expressions holds hydrogen identity sign identity statements judgement stroke Julius Caesar knowledge law of identity less-than relation lighter than carbon logical language logical laws logical notation logical notion logically perfect language mammals mathematical induction moon morning star natural language natural number sequence notion of concept notion of function nudibranchs object-expression predicate premiss primitive propositional quantifier regard Sense and Meaning sentence sentential expressions sort square root symbol tion true truth-value truths of arithmetic understand value-range Venus