Combining Texts

All the ideas for 'fragments/reports', 'Vagueness' and 'works'

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9 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Logical connectives have the highest precision, yet are infected by the vagueness of true and false [Russell, by Williamson]
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Since natural language is not precise it cannot be in the province of logic [Russell, by Keefe/Smith]
Vagueness is only a characteristic of representations, such as language [Russell]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]