Combining Texts

All the ideas for 'On the True Doctrine (Against Christians)', 'What are Sets and What are they For?' and 'There is no a Priori'

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15 ideas

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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
The idea of the a priori is so obscure that it won't explain anything [Devitt]
25. Social Practice / F. Life Issues / 6. Animal Rights
The world was made as much for animals as for man [Celsus]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus]