Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'What are Sets and What are they For?' and 'Ontological Dependence'

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31 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
14255 We understand things through their dependency relations [Fine,K]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
14250 Metaphysics deals with the existence of things and with the nature of things [Fine,K]
2. Reason / D. Definition / 4. Real Definition
14259 Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
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 / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
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 / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
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 / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
14253 An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14251 A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K]
14254 Dependency is the real counterpart of one term defining another [Fine,K]
14257 An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
14261 There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
14252 We should understand identity in terms of the propositions it renders true [Fine,K]
9. Objects / D. Essence of Objects / 2. Types of Essence
14256 How do we distinguish basic from derived esssences? [Fine,K]
14258 Maybe some things have essential relationships as well as essential properties [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
14260 An object only essentially has a property if that property follows from every definition of the object [Fine,K]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]