Combining Texts

All the ideas for 'Thinking and Experience', 'Philosophical Fragments' and 'What are Sets and What are they For?'

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

22 ideas

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 / 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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
16007 I assume existence, rather than reasoning towards it [Kierkegaard]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
14329 Some dispositional properties (such as mental ones) may have no categorical base [Price,HH]
10. Modality / A. Necessity / 2. Nature of Necessity
16013 Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
9032 Before we can abstract from an instance of violet, we must first recognise it [Price,HH]
9035 If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH]
9034 There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH]
9036 There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH]
9037 Intelligent behaviour, even in animals, has something abstract about it [Price,HH]
18. Thought / A. Modes of Thought / 1. Thought
9033 Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH]
18. Thought / E. Abstraction / 1. Abstract Thought
9030 Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH]
9029 If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9031 The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH]