Combining Texts

All the ideas for 'The Theory of Knowledge', 'works' and 'works'

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11 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7791	The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]

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

23476

Logical constants seem to be entities in propositions, but are actually pure form [Russell]

23477

We use logical notions, so they must be objects - but I don't know what they really are [Russell]

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]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

18273

Logical truths are known by their extreme generality [Russell]

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]

7. Existence / D. Theories of Reality / 8. Facts / d. Negative facts

22315

There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell]

10. Modality / A. Necessity / 2. Nature of Necessity

11002

Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]