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All the ideas for '', 'Interview with Philippa Foot' and 'What are Sets and What are they For?'

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23 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 / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
23438 Full rationality must include morality [Foot]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23437 Practical reason is goodness in choosing actions [Foot]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
23436 It is an odd Humean view to think a reason to act must always involve caring [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
23431 Human defects are just like plant or animal defects [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
23432 Concepts such as function, welfare, flourishing and interests only apply to living things [Foot]
23433 Humans need courage like a plant needs roots [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
23434 There is no fact-value gap in 'owls should see in the dark' [Foot]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
23439 Principles are not ultimate, but arise from the necessities of human life [Foot]
22. Metaethics / B. Value / 2. Values / a. Normativity
23435 If you demonstrate the reason to act, there is no further question of 'why should I?' [Foot]