Combining Texts

All the ideas for 'Transworld Identity or worldbound Individuals?', 'On Euclidean Geometry' and 'What are Sets and What are they For?'

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18 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]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
16886 The truth of an axiom must be independently recognisable [Frege]
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]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
11984 Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
11980 A possible world is a maximal possible state of affairs [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11982 If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga]
11983 It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga]
11985 If individuals can only exist in one world, then they can never lack any of their properties [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11986 The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga]
11987 Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga]