Combining Texts

All the ideas for 'Three Varieties of Knowledge', 'Presidential Address of Am. Math. Soc' and 'What are Sets and What are they For?'

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18 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
8868 Objective truth arises from interpersonal communication [Davidson]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
8867 A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
10347 Objectivity is intersubjectivity [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
8866 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
10346 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
8870 Content of thought is established through communication, so knowledge needs other minds [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
8869 The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson]