Combining Texts

All the ideas for 'Confessions of a Philosopher', 'Lecture on Nominalism' and 'What are Sets and What are they For?'

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


14 ideas

2. Reason / F. Fallacies / 1. Fallacy
The Struthionic Fallacy is that of burying one's head in the sand [Quine]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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]
The empty set is usually derived from Separation, but it also seems to need Infinity [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 / E. Structures of Logic / 6. Relations in Logic
All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Why don't we experience or remember going to sleep at night? [Magee]