Combining Texts

All the ideas for 'fragments/reports', 'What are Sets and What are they For?' and 'Truth'

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17 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
10838 To explain a concept, we need its purpose, not just its rules of usage [Dummett]
3. Truth / A. Truth Problems / 1. Truth
10837 It is part of the concept of truth that we aim at making true statements [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
10840 We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
3. Truth / F. Semantic Truth / 2. Semantic Truth
19171 Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [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]
18. Thought / E. Abstraction / 1. Abstract Thought
10839 You can't infer a dog's abstract concepts from its behaviour [Dummett]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]