Combining Texts

All the ideas for 'The Basing Relation', 'The Philosophy of the Inductive Sciences' and 'On boundary numbers and domains of sets'

expand these ideas     |    start again     |     specify just one area for these texts

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6 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17832

Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

13028

Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]

5. Theory of Logic / L. Paradox / 3. Antinomies

17626

The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]

11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs

19696

There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]

19697

The basing relation of a reason to a belief should both support and explain the belief [Neta]

14. Science / D. Explanation / 2. Types of Explanation / d. Consilience

20643

Consilience is a common groundwork of explanation [Whewell]