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All the ideas for 'Lectures on the History of Philosophy', 'Conditionals' and 'works'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

21757

Philosophy is the conceptual essence of the shape of history [Hegel]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

11022

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

11065

The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]

11023

The logical connectives are 'defined' by their introduction rules [Gentzen]

11213

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

10067

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]

10. Modality / B. Possibility / 8. Conditionals / a. Conditionals

13768

Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]

10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional

13770

There are many different conditional mental states, and different conditional speech acts [Edgington]

10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals

13764

Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]

13765

'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]