Combining Texts

All the ideas for 'Thought and Talk', '06: Book of Joshua' and 'What are Sets and What are they For?'

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19 ideas

3. Truth / A. Truth Problems / 1. Truth
A sentence is held true because of a combination of meaning and belief [Davidson]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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
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
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
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Having a belief involves the possibility of being mistaken [Davidson]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
The concept of belief can only derive from relationship to a speech community [Davidson]
18. Thought / A. Modes of Thought / 1. Thought
Thought depends on speech [Davidson]
18. Thought / A. Modes of Thought / 8. Human Thought
A creature doesn't think unless it interprets another's speech [Davidson]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
Concepts are only possible in a language community [Davidson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
An understood sentence can be used for almost anything; it isn't language if it has only one use [Davidson]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
The pattern of sentences held true gives sentences their meaning [Davidson]
27. Natural Reality / E. Cosmology / 1. Cosmology
Joshua said, Sun, stand thou still [Anon (Josh)]