Combining Texts

All the ideas for 'Three Varieties of Knowledge', 'Letters to Wolff' and 'Elements of Set Theory'

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16 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Objective truth arises from interpersonal communication [Davidson]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
9. Objects / D. Essence of Objects / 9. Essence and Properties
The properties of a thing flow from its essence [Leibniz]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
Objectivity is intersubjectivity [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett]
19. Language / F. Communication / 4. Private Language
Content of thought is established through communication, so knowledge needs other minds [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson]